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Best Way To Teach Oneself Math?
An anonymous reader writes "In high school I failed two out of three years of math classes and eventually dropped out of school completely. I earned my general equivalency diploma as soon as was legally possible and from there went on to college and beyond. That was many years ago and my most basic algebra, trigonometry, and geometry skills are slipping away at an alarming rate. I'm looking for a self-guided course covering the equivalent of 4 years of high school mathematics including calculus. My math skills are holding me back. How can I turn this around?"
There are plenty of self study guides that one can purchase.
Another option, if it fits into a persons schedule, would be to take classes through a community college. Costs are lower, classes are generally smaller than a university and schedules are often flexible for working adults.
Another thought I had is home schooling materials. I've never personally been involved in homeschooling, but as I understand it these kids can earn a highschool diploma at home. So why couldn't someone put themselves through such a program just to learn the information? I'm sure there are lots of resources out there for this, a quick google turned up this one.
It's hard to believe that's how Micronians are made. Why don't we see it right now by having you both kiss one another?
... the Bible. It contains more math than you can shake a stick at and it's pretty entertaining too!
Why not just stop by your local college bookstore? Just pick up a math text book, go through it, do the problems, check your answers, etc etc. Millions of students have used them. Probably will work out for you.
learning to use a mathematics package like Mathematica or MATLAB. I'd go with the former to begin with. I just got a book that solved some basic scientific questions regarding making models of physiological processes and tried to replicate those in Mathematica. In the process of learning the syntax for Mathematica, you're forced to learn calculus, which I used Google search for in order to understand the problem completely. The result was very satisfactory because the computer did the number crunching, I could concentrate on the conceptual understanding in calculus rather than spending time doing calculations by hand.
Essentia non sunt multiplicanda praeter necessitatem.
The way I kept my math skills fresh was to invent new problems to solve. Also I would derive every new formula instead of just memorizing it. Some random examples off the top of my head:
Derive newton's method.
Find the formula for the circle that passes through any three arbitrary points
Derive all the trigonometric identity functions
I don't have a great answer for your question. However, for me the key to learning math was to stop being intimidated by it. I don't think they do a great job of teaching it in school where they take a very linear approach. They tell you about a concept (e.g. integration) and show you how to do it in certain situations, etc. If someone from the beginning had told me how to visualize what integration was, I think I would have gotten it immediately. Instead I was worried about writing down every little thing the teacher said. Having now gone through six years or so of advanced math, it's somewhat difficult for me to completely empathize, but I guess I would start with the basics. Wolfram, wikipedia, whatever are all fine resources for math. Start reading the simple stuff and if it's confusing, don't be afraid to move backwards and get even simpler. We all forget that stuff now and then.
http://ocw.mit.edu/
Does it go on forever?
if you're good with trig and algebra, you can pick up the calculus ap and bc books from barnes and nobles and catch up probably in a matter of 2-3 weeks depending on how much time you put into it. these books show you more than just how to do the questions but also the applications in some abstract ways which'll help you quite a bit
You lack of math skills are holding you back from what? I have a degree in math, and I never use math. Ever. Unless you're going to teach math, I can't imagine how your lack of math could be holding you back. What is it that you want to do?
How about starting off with some fun training to keep your mind flexible. Something you can do a few minutes a day.
http://brainage.com/
Get a math textbook. [Hungerford's 'Contemporary Pre-Calculus' worked for me. For Calculus, Larson's 'Calculus' is keen.]
:My $0.02.:
Set aside 30 minutes a night.
Work the problems out with pen and paper.
Where necessary, remember formulas however best suits you.
Avoid technological fixes.
Perhaps life really is full of possibilities.
The first poster has it right. It's difficult to maintain the motivation to learn math unless you are in a formal program with deadline. Most community colleges have sections of math for people who made it through high school with inadequate preparation. Begin with these.
In some ways mathematics is a frame of mind you need to train your mind to think mathematically.
In Australia the last 3 years of high school are years 10,11 and 12. Pick up the equivalent of a year 10 maths/exercise book. There will bechapters explaining some stuff and then it will have lots of exercises to exercise your mind. Answers will be in the back.
At year 11 and 12 level you are looking at what we call "Mathematics II". The yr 10 book will have given you the basics of differentials and Integrals, the 11 and 12 stuff will then go into how you can use them.
After that you need to pick what field you are looking at. Control systems, bridge design, chemical reactions, and pick up the book that covers the mathematics for that. This will be fairly advanced stuff normally taught at university level. I did Engineering which uses calculus quite heavily.
So basically, RTFM.
Australian running a company that does C# / C++ / Java / SQL / Python / Mathematica
By Michael Spivak.
Lock yourself in a library and do every exercise. Make sure you have access to a university prof to help you when you get stumped, especially with the first few chapters while you're still getting the hang of doing proofs.
If you don't like Spivak's style, Walter Rudin's Principles of Mathematical Analysis is quite nice.
Note you can get your arithmetic rules from Spivak's book, so you don't have to relearn those first; you just have to read very carefully.
You study Maths (the full name for the science is Mathematics)
one highly rated on amazon.com and simply start doing problems. This is what I did before entering college again. I never failed math, but I did the minimum in highschool and that was bad later on.
There are no two ways around it. You can learn or pretend you learned the material, but if you never have to apply it (doing problems) you'll never know. Community College courses like some suggested I offer hesitantly - I never liked classes as I have to keep to their schedule - in going there, etcetera. I learn faster than their pace, but some don't. Also a different perspective (that of the teacher and fellow students) may help you and a teacher may guide you to the correct higher maths you need for your job/career.
I would suggest doing the odd or even half of the problems in your notebook and keep trudging on. If you think you know a section, there is no need to be anal about it and write down the problems, but do them mentally and check if you have the correct answers. At least that is how I did it. I actually like math now that I'm not tethered to a boring class and for it's own sake.
Also, fundamentals are most important. If you don't know your pre-calc, you aren't going to do well with calculus. Get your calc book after you went through your pre-calc. Don't trust people who offer easy solutions - study after study has shown you get in what you get out. Even if you learn fast (or think you learn fast), you can forget fast without ever applying what you learned.
If you do consider a community college, check out the reputation of the professors you are selecting at ratemyprofessors.com, there is no need to stumble upon a nightmare teacher. Adult students have enough things to worry about without adding another obstacle to their path.
There's probably a community college in your area that teaches courses in all of the above and beyond. The fees are low (my local community college charges $20 per class credit) and there's usually no requirement that you formally enroll, declare a major, etc. The advantage is that you have an instructor who can answer your questions, plus who assigns you homework. In my experience, the only reliable way to learn math is to do it, and it's too easy to get lazy with self-directed study.
Breakfast served all day!
Clearly that's not sarcasm there. Couldn't be. No way.
What is is all that is. Isn't that obvious?
When growing up, I was forced to do pages of simple math problems - just simple addition, subtraction, multiplication, and division. Imagine sheets of paper with 20 rows and 3 columns filled with questions. I would then get timed to see how quickly I could complete these questions. This was done time and time again until I didn't have to think in order to solve such problems. I benefit from this even today..
The thing is, when you're learning math you want to focus your efforts on the subject at hand - not the other simple math that accompanies it. For example, when a prof is going over a question on the board you don't want to waste time with the simple stuff. It takes away from what you should really be learning.
So I guess my suggestion is this - make sure you know the basic stuff really well. You will always have to use it and without it you will always be at a disadvantage.
Willy
Math by itself is not useful unless you just like adding numbers. It's only by actually having an applied purpose that you'll need it (physics, economics, chemistry).
Any sort of advanced math is very easy in which to develop bad habits. Advanced math "build", unlike other subjects in those same grades. If you didn't "get" Death of a Salesman, you still have a shot at understanding Moby Dick. However, if you did not "get" fractions or percentages, then you really can't go a lot further.
If your math skills (or, rather, lack thereof) are holding you back, think of the tutor as an investment.
On a side note, you would be surprised at the proof of "bad math skills" that can be seen in the corporate world. People rarely / never stop to do a reality check. "Can it be that 105% of the people required to take the training have taken it?" Ugh.
You lost your girlfriend to a black guy in high school, right?
Time to get over it or you'll never find another one.
LK
"Hi. This is my friend, Jack Shit, and you don't know him." - Lord Kano
Two books which helped me (years ago) were Asimov's Realm of Numbers and Asimov's Realm of Algebra. Unfortunately, a quick search at Google shows the hard cover edition of Realm of Algebra is outrageously expensive. I had the paperback editions of each, and they were terrific. A huge help.
Asimov wrote a whole lot of non-fiction books on math and science. His books demystify otherwise hard to approach subject matter. Highly recommended.
I was consistently at the bottom of my class in high school math. I had to lie cheat and steal to get into community college. I eventually made it through a BA, and now a few years later I find myself in a full-time MBA program where math proficiency is a foregone assumption. I told myself before I started my MBA that a couple of "...for Dummies" books and some online courses would get me caught up with the pack. I was wrong. It has taken a herculean effort through private sessions with professors and other students to keep me from failing out of Accounting and Statistics. As great as online courses and the like are, there is no substitute for a good teacher. You will be amazed by how much more effective a tutor is than taking a self-directed online tutorial. If you are the kind of person who is bad at math, you'll probably always be bad at math, but you do have to learn how to get by when necessary. Get yourself a private tutor, suck up the cost, and see the results for yourself.
I had a lot of trouble with maths in high school and college. I find it difficult to learn by rote and my experience with math education has been nothing but. Get the book "Mathematics from the Birth of Numbers". This helped me to actually understand what I was doing rather than following a 'recipe' that someone said should work.
Try any book by Haese and Harris http://www.haeseandharris.com/home.asp They do all of the textbooks for south australian mathematics, very clear, very well laid out. just be carful, I think american highschool year 10 maths is closer to australian year 9.
Kids! Bringing about Armageddon can be dangerous. Do not attempt it in your home!
12 years ago I got an 800 on my math SATS and got A's in every math class I took in high school and college. These days, I struggle with the simplest day to day mathematical problems. I imagine it's just a matter of practice, but it's alarming nevertheless.
we have used www.chalkdust.com for home school math for years - highly recommened. I listen in once in a while - great instructor, you can always rewind, comes with ask-the-teacher service
As a math teacher, I'd say you're better off getting help from someone competent than going it alone.
That being said, and the understanding that you don't want to pour in the money required to get a good teacher (craigslist looking for a math tutor is a place to start. If you start off with one and it doesn't feel like a good emotional fit, then get a different one. A good tutor will try to get a solid grasp of where you are now, and then start taking steps to get you moving forward from where you are. A great tutor will help you when you're stuck, but also give you specific resources that you can use to work on exactly what you need to be working on right now in your time away from the tutor), here's my advice.
First off, understand what exactly it is you are trying to do. You are trying to build abstract thought paths in your brain. This is hard to do. Many of the math problems you were presented with in high school were an attempt to get you to make the leap from specific application of concepts in lots of different ways to the abstract concept itself. In algebra, you do tons of factoring and other ways of solving the quadratic equation. The point of all those problems was that you would, through many problems approaching the concepts from different angles, fundamentally understand what parabolas are all about. Accurate quadratic thinking is much much harder than linear thinking. When you see a line, you know it's a line, but when you see a curve, it might be quadratic, cubic, exponential, logarithmic, or any of a host of variations.
So, do a bunch of problems to build your skills and gain fluency with the concepts. Then try to figure out exactly what it is that's really going on. There's often some really obvious reason that something works the way it does, if you can find it. For instance, the whole FOIL method for multiplying binomials like this: (x+3)(x+2). If you draw a rectangle, and put the x+2 on top and the x+3 going down the side, and break the rectangle into an x part and a 2 part vertically, and an x part and a 3 part going horizontally, then you'll get 4 rectangles that all add up to make the original rectangle. Their areas are x^2, 2x for the first row and 3x, 6 for the second row. Those are, respectively, the First, Outer, Inner, and Last products of the FOIL method. If you draw the picture, it's really obvious, and you'll wonder why you struggled with it for so long (if you did). A good tutor can help make it all easy for you by showing you the really obvious reasons why things work the way they do.
Good luck
an "anonymous" reader asks for tips on spelling and grammar.
That's the key question. What tasks are you doing regularly that your past failures to learn high school math are stopping your from?
I use some form or another of "math" regularly, but I'll tell you one thing: most of high-school math isn't very useful for me. I've never needed calculus, and barely ever needed geometry. Algebra is ocassionally useful, but the very basic bits of it are good enough (I remember that there is such a thing as the quadratic equation and factorization of polynomials, but I've never really needed to use them).
On the other hand, graph theory, mathematical logic, lambda calculus, probability and statistics have been very useful, and I suspect abstract algebra would also be so if I understood it. But guess what? None of those are regularly taught in high school. (Hell, mathematical logic isn't even regularly taught in university math departments.)
Don't just assume you need high school math. Make some effort to figure out what kind of math would be useful, and go with that. If you're into programming, you may want to try a discrete mathematics textbook.
Are you adequate?
http://jumpmath.org/about/myth-of-ability
John Mighton, a math PhD and award winning playwright, founded a math tutoring program called Jump Math. It has been very successful with all kinds of student. In particular, it has worked for adult learners in jail. "The Myth of Ability" gives the basic philosophy of the program. Once you have read it, you will have the clues you need to direct your own math learning program.
Almost all the things we think about as intelligence are a result of pattern recognition. We really don't work by logic. Master level chess players, for instance, don't work out positions by logic. They can't work out moves much farther ahead than non-experts. What makes them experts is that they have studied thousands of games and they recognize situations when they see them. The way they got to be experts was by 'deliberate practice'. That's how you are going to learn math. http://www.nytimes.com/2006/05/07/magazine/07wwln_freak.html?_r=1&n=Top%2FFeatures%2FMagazine%2FColumns%2FFreakonomics&oref=slogin
Once you understand the underlying principles of how we learn and once you understand that the effort required will almost certainly lead to success, you will be much more likely to put forth the effort required.
Buy a good calculus book, and read it. Work through all the proofs and derivations. Stay on each section until you understand it.
It helps a lot if you have a reason to use it.
If you don't have the discipline to do this, take a class.
(Well, it's always worked for me....)
I recommend that you take a pencil and paper to a bookstore that has a large math selection and a large selection of Schaum's Outlines series. Then review several of the math Outlines and pick one that you think you can do. Then start doing it right there, starting with chapter 1. Solve, on paper, every problem (including the ones they solve for you). If you can finish chapter 1, buy the book and continue to solve every problem *on paper*.
http://www.x2ii.info/
The harder the math is, and the harder it is for you, the more problems you need to work. Obviously the "understanding" part is necessary, too, but sometimes understanding comes in dribs and drabs, and often it only comes after much experience. After working many problems, you suddenly see the pattern (Aha!) that the teacher or textbook was trying to explain to you. Educators sometimes assume that if you don't get it immediately, the only remedy is to try a different teaching method (tactile learning, culturally appropriate stories, and whatever else they can come up with.) That's simply wrong -- don't get discourage if you don't immediately understand something without any practice. You should use whatever means of learning and understanding works best for you, but it just takes a while for some things to sink in. (Different things present difficulties for different people.) Sometimes too many ways of explaining something are just confusing and overwhelming -- sometimes you just have to work through problems over and over again until it finally clicks.
Plus, understanding does not guarantee facility with solving problems, and facility with solving problems is a very large advantage when it comes to the rest of your education. Consider the significance of calculus to learning college physics: If you're slick with calculus problems, you spend most of your time thinking about physics, and you actually get a deeper understanding of calculus in the process. If you have a hard time solving calculus problems, then you don't have any time to learn much about physics, because you spend all your time struggling with the calculus. I'm sure the same thing applies to economics. "Understanding" of calculus concepts won't save you if you have to spend eight hours struggling to solve the math problems in your econ homework, while your classmates knock out the math in two hours, spend two hours discussing the concepts with each other, and then spend four hours drinking and chasing women. You work twice as much, and they're still ahead. (Plus they have more fun and are fresh and energetic the next day.)
So, work problems. Working problems helps you understand things in the first place, helps cement your understanding, and helps you get faster and more confident in your work, which enables you to work and learn more efficiently.
As someone who has had to ramp up his math skills recently, I admire what you're doing and wanted to share my experience. The main thing that struck me is that you're looking to do an entire high-school equivalent math program, which to me seems like a daunting and boring approach.
Instead of looking for a curriculum, it sounds easier to find some relevant problems and work backwards. You mentioned that your lack of math is holding you back. Why not identify some specific cases of this, and learn enough math to overcome whatever issue made you feel this way? Doing this enough times will give you a solid background in math, I think.
In my own case, the reason I had to ramp up on math is that I was taking a pretty hardcore machine learning class during my masters. The course assumed a much deeper knowledge of linear algebra than I had. I literally had to do hours of research to understand many slides from the lectures which were really intended to be background and proofs, not the meat of the course. You can imagine that by the time the course ended (I got an A- which was a big deal for this class) I had a much stronger foundation in linear algebra and other math concepts than I did initially - even though I didn't set out to learn that stuff. Call it just-in-time learning. Now I am studying for the CFA (Level 1) and it also has some math, although nothing too hardcore. Still, the first volume contains a quantitative methods section which talks about statistics and the like. So again, even though my goal is to learn Finance, not math, I ended up refreshing a bit of math in the process.
Maybe this "just in time" learning isn't for everyone but it seems good to me in that it forces you to learn math that's the most relevant to your life, and it in a sense forces you to make sure you've learned it well, given that you'll be applying it immediately.
Also, MIT has some online courses that you should check out. I know you talked about highschool level stuff but why not be even more ambitious? For example, there's a series of video lectures with dr. Gilbert Strange about Linear Algebra. I don't think the course requires too much other background (and again, if he talks about a concept that you don't know, this is a great opportunity for additional just-in-time learning).
The main thing I am trying to say is that you should set a goal for yourself that's narrower than "learning everything". Define a concrete problem and solve it. For example, your problem could be as simple as watching all of the lectures mentioned above, or reading some calculus text. Instead of spending years learning everything everyone tells you that you need to know before you can do calc, just do the reading and then branch out into understanding pre-requisites as you encounter them in the text. I think this is a much more structured and motivating way to do it.
Good luck!
http://ed.markovich.googlepages.com
Math was one of my worst subjects.. and really this all came down to boredom and lack of motivation. If you're serious about learning what you missed the first time around, find a community college offering high school upgrading courses. These are generally equivalent to the highest level of high school math, but they won't make any assumptions beyond simple arithmetic, so don't worry about what you think you missed.
(I did this and, quite accidentally, discovered it was actually enjoyable. I'll be graduating this year with a BSc in mathematics).
Okay, so it's more of a kids book, but I recommend The I Hate Mathematics! Book by Marylin Burns, and also Math for Smarty Pants by the same author. Martin Gardiner's recreational math books are also quite excellent. The best way to teach yourself math is to actually get interested in it, which the average textbook will not help you with.
Fair warning: I'm now getting a PhD in applied math.
One thing to consider is going to a local college and taking a pre-calculus class. Ratemyprofessors.com and sites like that can tell you if the professor is good or not. You can get a whole semester at a good state school for less than $1000 often. Plus you get college credit, and pre-calc is usually a prerequisite for the Computer Science courses (I had high Math SATs so I didn't need it, I went straight to Calculus). As far as the pre-calc books out there, I liked Barron's precalc book myself. I wanted to brush up on it since I never really did relatively well in trigonometry, and I only had a vague recollection of what the quadratic equation was etc.
That's how I taught myself math as a kid. Start with the last chapter. If you don't know it, go back a chapter. Once you've seen the later chapters, you'll know how the earlier stuff applies, so you'll learn it much, much faster.
Possibly the most important point is to truly understand the concepts. Mathematics in some sense are self-evident - 2+2 will always equal 4, and the derivative of 2x (with respect to x) will always be 2. More complex ideas in math are equally self-evident, but are much harder to understand. As a result, a lot of math classes focus on memorization without understanding the ideas.
Buy a textbook and do the problems. But also be sure to read what the textbook is trying to say - why does the math work the way it does? For some people visualization helps. For others, verbally analyzing the logic is easier. However you go about it, don't try cramming formulas or theorems without understanding them. Memorization is hard, yet learning is more difficult - and more rewarding. Best of luck.
You can lead a horse to water, but you can't make it dissolve.
In order to learn it on your own, you want to enhance your curiousity at any chance you get. If you get the feeling that you're forcing yourself through it, you might not continue. To maximize curiousity, i suggest you find several math books. Each day, you set aside some time to do something, anything, without a preconception of what it will be (unless there's something you're really keen on doing). When you sit down, you bring out your 3 or 4 books and you flip through until you see something interesting and work on that.
Sometimes you'll find something that requires previous concepts that you don't yet have. This is fine, because now you can go look up those concepts with a sense of purpose. This will help you to your larger goal of the more interesting thing that you flipped to in the book. I did this when i picked up a book on fractals...lots of bright pictures, it seemed interesting. In there, they talked about integrals, which i hadn't learned yet, so i set out to find out what those were.
As for practical tips when you're learning one particular concept, reading textbooks is sorta like reading manpages in unix. it takes a certain mindset, and you usually want to pick out the relevant pieces from the page the first time around and then go back for specifics later. Textbooks are usually written very precisely and they sometimes have a lot of formal jargon or formulae that aren't useful the first time you read it, but can be helpful when you go back to get more details. So read it with that in mind. The first time through, don't expect to understand everything there. Just skip past the parts that are too hard and continue on, trying to get the general idea.
Next, do some of the easiest questions at the end of that section or chapter. Sometimes those questions may seem too easy, like you can just look at them and you think you know how to do it already. I suggest doing some anyway rather than skipping them. There's a difference between knowing the concept enough to recognize it in the questions, and actually knowing it well enough to do the questions quickly and correctly. Doing more questions is always good practice even when they seem easy at first glance.
When you've done several of the easy questions, you start to get more of an intuitive feel for the concept. Go on to the medium questions, and now you'll probably better understand the parts of the text that were difficult to understand on the first time you read the section. I suggest that you try hard to really understand the concepts in one chapter before you go onto the next one. If you have a solid grounding in the beginning, then the later stuff will be much easier and it'll be easier to get that intuitive understanding that lets you see the direction to the answer right from the start.
If you have several textbooks to choose from each time, then as you work your way through bits of each of them, you'll start to see the connections between different areas of math. This is something that most people don't get in their normal classes because they tend to focus too closely on one topic. If you wander through several topics following your curiousity, i think you'll get a better broad understanding of the connections, and it'll help you personally keep your motivation up so that you can continue to do it. remember to have fun with it. if it turns into a chore, then you'll stop doing it before you reach your goals.
have fun!
"The value of a man resides in what he gives,
and not in what he is capable of receiving."
--Albert Einstein
I've found that the best ways to motivate myself to learn something, and actually retain what I've learned, is to have a use for the information, and to teach it to others.
Assuming you know a computer language, writing a computer program is a great way to do both of these things, since programming can be looked at as teaching the computer how to solve problems.
Start writing a program that is likely to involve the kind of math you want to learn, and since the development of your app will be dead in the water until you learn and successfully apply the math, you will have a great motivator for learning it and getting it right. Just get your hands on an applied math (applied algebra, applied calculus, etc.) book and look at the kinds of problems it has in it, then write programs to solve those kinds of problems. I would pick the books up at a used book store or thrift shop, since there's no need to spend big bucks on the latest shiny new edition from Amazon or a college bookstore.
My truck is like a series of tubes.
If you fit into my category and have a tough time improving math skills by yourself from a textbook, I would highly suggest a part time college or university course (i.e. outside work hours). Make it a credit course so you will have a goal (of passing). Certificate courses are usually based only on attendance on not useful if you need to be goal-oriented like most people. Pick a time in your life when you can devote the time to it. Don't try picking it up when many other things are on the go because more than likely you'll drop the ball. This might require some scheduling and planning before making the commitment. If you don't go with a school course or tutoring, it would be good to find a group of like-minded people who want to improve themselves because two (or more) heads is always better than one. Going through the process with other people also bolsters a sense of accountability and responsibility. I suggest not trying it on your own unless you have a very high level of commitment to such things.
your have a terribly low IQ...
Take an evening class at your local community college. Most of them teach highschool-level mathematics.
And our good friends at MIT - http://ocw.mit.edu/OcwWeb/web/courses/courses/index.htm#Mathematics
Put yourself in life-threating situations that make you rely on math skills to get out. For example, the car keeps speeding up until you enter the proper roots of the polynomial equation into the dashboard computer. OnStar math class if you like.
I've found a number of helpful math lessons on youtube recently. Some are actually pretty good. Just search for algebra or whatever you're looking to learn. Last week I got refreshed on statistics.
Obviously there's a signal-to-noise ratio problem, just skip over the noise.
O lord, bless this thy holy hand grenade, that with it thou mayest blow thine enemies to tiny bits, in thy mercy.
Vlad, is that you?
Its kind of difficult to give advice if you can't tell us why your lack of math skills is holding you back? Math is best learned in context, which is not at all how it is taught (or not) in America.
Democrats and Republicans are like AIDS and Cancer, I want neither!
As someone who was homeschooled for a while and actually have better maths skills as a result, I can personally recommend Saxon Math as being a great curriculum. Not only are they the best math coursebooks around, but they are also written with adults in mind. The amount of forsight and diligence that these authors have put into the materials make them great for children and adults.
Disclaimer: I'm not related in any way to the publishers other than the fact that for a period on my life my mother would hand me one of their books every year.
somewhere, on a Big Red Sign:
if(color==blue){speed--;}
I'm a math teacher and /. troll. I have found that to have success in math, you must: Take your time. If you are in a rush you are almost guaranteed to screw up. Next, repeat each problem over and over. There is a reason that the textbooks give you so many problems to work out. Never try to take a shortcut when good 'ol paper and pencil work is handy. ***Most important!! Unless absolutely required for problem solving, DO NOT USE the Demon Machine, uhhh..., calculator.*** Finally, if you go into a study session with negative emotional energy, YOU NOW HAVE TWO PROBLEMS. You will rarely solve the math work while you carry this second problem. Disengage from the emotional part and you will be amazed at how your inside-your-head work will improve!
CW
Get the book "What Is Mathematics?" by Courant.
It's a from-the-basics survey of modern understanding of math, and an excellent reference for all levels.
Here's a Wikipedia booksearch link.
For Self Teaching- don't do it. Your main problem is finding out what learning mechanism works best for you and then finding a compatible mentor. Don't go to a local college and merely buy the textbooks there, you will get through the first chapter then realize you wasted $100 on a book you have no idea how to read.
Also, you need to decide how far in math you need to go. For calculus not all books are created equal. Find a simple book that has easy to understand examples but does not go too far. Make sure it has a few chapters on limits only- you need to know these to know calculus. On the other hand, you likely do not need to know how to check if an integral is converging or diverging, knowing how to do Taylor series, Laplace Transform, Invariant coordinate systems, etc. The book you select should have basic differential and integral calculus but nothing too advanced. Take baby steps. If you can work your way (with someone) through these things you will have a better chance to succeed and know what types of math you need to specialize in and how much.
Also, tell us what types of problems you are running in to or else we can't pin down a specific way to help you. What types of applications are you doing and what do you need to find out? You may only need differential and some basic integral calculus do to the work you need.
That's my advice for self-teaching, but I would suggest going to a community college or finding a mentor who will (maybe for a small fee) teach you the math.
Finally, if you do not understand the math you will not be able to use it in your job. Make sure you don't waste your time going down the wrong path. It's essential to have someone to ask and review your work so that you find out you are not doing things backwards and upside-down.
Learning math is similar to learning a language, although the constructs are vastly different between the two. It doesn't happen through osmosis and it's hard to get a good understanding of the "pronounciation" unless you have someone you can go to. Again, seriously consider taking some precalculus classes at a Community College then going on to calc. Without the foundation for the more advanced stuff you will get nowhere. De toute façon, on chance!
Everyone will tell you it is unreliable and whatnot, but compared to some of the lecturers I had... I could swear the guy who was teaching us ordinary differential equations must have been smoking something which wasn't quite pure...
http://www.saxonpub.com/ .
they've changed their URL, but it redirects pronto, and the new one isn't rememberable. .
Diff between these and the normal ones?
One concept, one lesson.
Big concept? broken into several components, and distributed over several lessons.
Syncopated plan: one gets the chance to get a knowing into long-term-memory/function before one hits the next lesson that relies on it.
having tried many, and lost my math in some brain-damage I got in my teens, this is THE required one.
Find the book you need,
by doing a placement-test,
then get the ISB# for that recommended book,
then find a second-hand copy on http://www.abebooks.com/ for cheap.
Try also my gallery: http://photo.net/photos/AntrygRevo
for 15 bucks an hour, just hire a local high school student to teach you.
Don't just repeat the same things that didn't work for you in high school. If you had a hard time with textbooks and assigned problems in high school, you'll probably still find it frustrating today.
I'd suggest that you find yourself a project that you will be really interested in that requires math skills a bit beyond your abilities. Learn the skills that you need to accomplish this project, and then pick something else that will stretch you further. Use textbooks and online references to accomplish these tasks -- not as the tasks themselves.
If you're a programmer you probably won't have much difficulty coming up with projects to stretch your skills. Computer graphics, machine learning or science applications (among others) offer plenty of opportunities to use advanced mathematics.
If you can't come up with a project that you'd like to work on then you might ask yourself if you really need (or perhaps want?) to better your math skills.
Good luck!
I've taught a number of community college classes out of Michael Sullivan's "Algebra & Trigonometry" and overall I'm pretty pleased with it. Currently on edition 7+ (so well edited & typo-free), contains all the basic stuff you mention (algebra, trigonometry, analytic geometry), pretty comprehensive.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
If you follow my suggestions, please look at the books on Amazon or in the bookstore. I'd hate to recommend something that discourages you. I prefer terse books of a few hundred pages as opposed to glossy, 1500 page tomes that explain simple topics in 15 pages.
"What Is Mathematics? An Elementary Approach to Ideas and Methods," by Courant is a good but terse introduction.
"Mathematics: From the Birth of Numbers," by Gullberg is a really fun book that explains all facets of mathematics. It's not as rigorous as a college text. It's on books.google.com too.
A good intro to Calculus that I often recommend is "Calculus Made Easy," by Thompson and Gardner. It's not a mass produced "How to Ace Calculus without trying" type book, rather a very nice and easy to understand primer for those who know algebra and trig. I wish I had the time to work through this book every so often, as I rarely do any calculus professionally and get rusty.
I'm not sure if you have a programming background, but working though a textbook on Discrete Mathematics will probably hone your logical thinking and allow you to practice algebra with exercises that are relevant to programming and Computer Science. Excellent book, but not for beginners, is "Foundations of Computer Science," by Aho and Ullman.
There are also free and commercial "workbooks" for packages like Mathematica and Maple that will allow you to visualize math problems and solve them. This is especially useful in Calculus.
Whichever route you choose, you have to actually do the problems and work them out to learn. And then the things that you do learn are soon forgotten if you don't practice them. I still think that even if you forget it, it's beneficial to learn it for the sake that a similar problem may come along in the future, and even though you can't remember the specific identity or formula, you know that one exists and can be used to solve the task at hand. That's knowing math good enough to be anything other than a mathematician, as far as I'm concerned.
Good luck!
I would agree. I tutored a number of students in high school, and one of the things that really made a difference was the feedback that you can get from a tutor while working through problems. It makes a huge difference if you know that you are on the right track. The tutor doesn't necessarily have to do it for you, or even teach you, but if s/he says, "Yes, continue, you are on the right track even though it looks like you're heading down a dead end," that is something that textbooks will never be able to replace.
404555974007725459910684486621289147856453481154 in hex is "You sank my Battleship?"
[GPG key in journal]
Student with glasses also quite smarter than average....
I suggest you read Slashdot
Buy the same textbooks that the students at those universities use. For the pre-calculus mathematics, UC-Berkeley would be your best bet. MIT caters to only students who have already taken calculus in high school.
My best advice is to try a two-track approach: non-discrete mathematics and discrete mathematics. Traditionally high schools teach only non-discrete mathematics: e.g., trigonometry and calculus. Since you are studying the material on your own, you could improve upon the standard curriculum. Read a good book on discrete mathematics first. It will build your intuition of mathematics. Then, study the standard topics in non-discrete mathematics.
Discrete mathematics and non-discrete mathematics are quite different, but the reasoning in discrete mathematics will hone your skill in handling mathematical proofs, which are central to both branches of mathematics.
For a real challenge, after you finish your studies, try to determine whether P = NP.
One of the most innovative, and arguably, bizarre, math books to be written is Who is Fourier? A Mathematical Aventure. It's a wonderfully easy approach and fun approach to quite a lot of math (some of which is high level.) By no means is it an academic study, but it's a strong enough introduction that you'll feel more comfortable with math.
Having said that, it's not for you if you don't like cutesy. Parts of it are essentially Hello Kitty does math.
On the other hand, quite a lot of people in this world would likely get off on that.
If you learn better from watching/listening to someone than just from a book, you might like Mathcasts. Free online videos discussing typical math topics ranging from grade 4 through college.
Come play free flash games on Kongregate!
I don't have any recommendation for the algebra and trigonometry books, but the classic self-teaching text for calculus is Calculus Made Easy, by Silvanus P. Thompson.
-jcr
The only title of honor that a tyrant can grant is "Enemy of the State."
Go to law school!
;-)
That way, you can afford to hire an accountant...
In all seriousness, I was a geek in high school and did well in every subject except math. I aced AP Computer Science and, yes, received full credit. I aced Geometry without any real effort - it made sense to me, and I could apply it to a real object. But when it came to algebra or any form of math I could not immediately apply to something that mattered to me I simply could not get my head around it. I just didn't care unless I could actually use it.
I realized this was a weakness of mine, and shifted away from computer work to other areas. If math is your weakness, but you have strengths in other areas, you may want to consider doing the same. I'm sure I could be good at math if I really put my mind to it, but I just don't find it enjoyable - why kill myself when I can make a living at something I enjoy more?
I am from the opposite end of things, someone who did math competitions from elementary through undergrad and who misses having them in graduate school. That said, The Art of Problem Solving books might work for you. They are intended to help students prepare for middle and high school math competitions, have solution manuals, and are $73 for both books and their solution manuals. There is also a new strictly algebra book available. My main reason for recommending this is that the whole point of most math competitions and these books is to teach you problem solving techniques, you will learn algebra, geometry, trig, etc, but also learn more of how to apply them to more interesting/applicable problems. http://www.artofproblemsolving.com/
- Basic Match
- Algebra I
- Algebra II
- Geometry
These courses are going for about $80 each. The advantage of courses on DVD is you can set go over the material at your pace based on your own schedule, and repeat sections of lectures (or entire lectures) as necessary. Disadvantage is of course there is no instructor to answer specific questions you may have. If you learn better through personal interaction, taking courses at a local community college as suggested may be a better option.I'm the same story - skipped out on most math in High School by programming (Basic and Fortran so I guess I'm old now). Got obsessed a few years back and started learning some advanced stuff - matrix algebra, calculus. Got the concepts but without the basics it was too frustrating so I decided to relive 10th grade - except now I get the chicks.
Algebra Demystified/McGraw-Hill - The whole series has been working for me. Each solution is spelled out step by step. I've been doing them in a notebook so I can go back and do them again for review. The Trig book was great and I'm moving through Calculus. You've got to put in the time but once the terror subsides you get in a rhythm.
Physics is like sex: sure, it may give some practical results, but that's not why we do it.
Is to sit down with a math book, and work the problems. The more you do, the better you are. Sorry man. There is no other way. Speaking from experience.
I'm taking a stat course for a doctoral program, and part of the course is an online tutorial called ALEKS. I get more out of doing the work in ALEKS than doing just regular problems out of a book because on the tough stuff the program can tell me that I've gotten it wrong and give me another chance. There's also a lot of explanation and easy access to formulas relevant to the problem at hand.
The ed psych department I'm taking this class in has an institutional license, but you can apparently buy a personal subscription to ALEKS without having any affiliation with a school or university. Looks like they've got a thorough set of offerings from elementary to pre-calc and statistics. Also looks like there's a free trial so you can try it out.
I'm not crazy about the implementation - Java plugin that's got a somewhat clunky UI. All the same, I'd recommend trying it.
I just finished taking the GMAT test. the quantitative (math) section covers almost all of the math you are looking to learn. A good book (like the official guide to the gmat) has problems arranged in order of difficulty and explains all of the answers in a step by step process.
GMAT math covers basic athrimetic, geometry, algebra, combinatorics, probability, word problems and data sufficiency. I haven't done long division
by hand in probably 15 years so I found the steps to be quite helpful.
One plus of using the gmat math as a stepping stone is that if you ever want to take the test yourself then you will be pretty well prepared for it.
Another plus is that there is a ton of free material out there for gmat math preparation - study guides, practice tests, quizzes, etc. that can all be downloaded for free.
Perhaps the best place to start for a thorough understanding of Math is the Lakoff and Nunez "Where Mathematics Come From: ..."
http://www.amazon.com/Where-Mathematics-Comes-Embodied-Brings/dp/0465037704
Cheers!!
Joseph Bacanskas [|] --- I use Smalltalk. My amp goes to eleven.
If you are going to teach yourself, I highly recommend firstly finding out how you learn. Knowing that you learn better by reading, or by hearing, or by drawing, modelling or however can save you a lot of time later on. A quick google search shows a few sites. As with all internet quizzes, never rely on one, but do a few. My girlfriend recently went back to Uni and after determining her learning sytle is doing much better now.
That said, I do maths at Uni and still occasionally forget some of the specifics about the basics. For that reason, I still have all of my high-school text books and even a few second-third-forth hand. One of them is particually good at one thing, another is concise at another. So, my suggestion is to go to second hand book stores and garage sales and pick up a couple of these. Few people want these after school and if the textbook was fazed out, they wouldn't of been able to sell it. As a result, you can often pick these up for $5-$10, especially if you aren't worried about it being brand new.
I learned most of the math concepts _before_ the school lessons.
My father gave me his old scientific calculator when I was 12 or so. That was 80's, and I had no computer yet, so a scientific calculator was the most exciting "gadget" a boy could put your hands on, then I started to learn how to use that machine, asking him about every function of each of its buttons. For each function I asked, he introduced me some basic concepts, and properties, and then I passed days experimenting and exploring that, before coming back with new questions, about new functions. And this was the way I learned trigonometry, logarithms, statistics, base conversions...
Sometimes, his explanations about something was somewhat boring (i.e. I was not prepared to handle that), and I naturally jumped to question about another "button"... so I defined the "sequence" of my learning, based on my curiosity, or interest, at that moment. In a short time, I learned almost all of its functions. Its important to say that he _never_ tried to "force" some sequence.
Looking back, I think it is the best way to learn math. Pick one topic at a time, ask someone to introduce some basic principles and properties, but without formalism, and enjoy, play with the numbers, plot graphs, explore, imagine what kind of practical problems you can resolve with that new knowledge. After you do that, the concepts will be naturally incortporated into your mind, and the formalism will be easily learned, when taught.
Good luck!
The essence of understanding math is being able to use it to solve problems. Math problems are like chess problems: they both have a start state and an end state and a solution consists of a sequence of legal moves. Routine problems are easy, like mate-in-1 or a simple application of a single mathematical rule. Non-routine problems require you to think a few moves ahead, but if you can't do that, you don't really understand the moves/material.
It's important to become proficient at non-routine applications of basic material before moving on to more advanced material like calculus. As the author of The Calculus Trap writes: Rather than learning more and more tools, students are better off learning how to take tools they have and apply them to complex problems.
To this end, I recommend The Art of Problem Solving Volume 1: the basics & The Art of Problem Solving Volume 2: and beyond. They are the best math textbooks I have ever seen. The intuitive explanations really sink in, so no memorization is required. But the key is that each section is followed by a bunch of non-routine problems from middle-school and high-school math contests like MATHCOUNTS and AMC. These are a fun way to make the material second nature, and besides, it's pretty motivating to know that a bunch of middle- or high-school kids solved the problem you're struggling with. (I want a shirt that says I'm as good as a middle schooler on the front, and on the back says MATHCOUNTS.)
After studying the first few chapters of Volume 1, you will be able to solve problems such as these:
- The formula N = 8 * 10^8 * x-3/2 gives, for a certain group, the number of individuals whose income exceeds x dollars. What is the smallest possible value of the lowest income of the wealthiest 800 individuals? (AHSME 1960)
- Find Sqrt[53 - 8 Sqrt[15]]. (MATHCOUNTS 1990)
- If for three distinct positive numbers x, y, and z: y/(x-z) = (x+y)/z = x/y,
then find the numerical value of x/y. (AHSME 1992)
- For each of n = 84 and n = 88, find the smallest integer multiple of n whose base 10 representation consists entirely of 6's and 7's. (USAMTS 1)
There can be a surprising amount of depth to these "middle-school math" problems. The concepts they cover are the fundamental building blocks upon which calculus is built.This post is based in part upon similar posts of mine at Reddit and MathNotations.
Having taken many years of math classes in high school and college, I have to agree that I've found that for the most part every class boils down to a few simple concepts. For example, with calculus there's a lot of theory behind integration and differentiation and how they were originally derived, but really all you need to know is a few simple concepts like area under the curve, how to integrate/differentiate some basic cases, and how it works with a real world example (e.g. how acceleration, velocity, and position relate).
My advice is to learn and understand the core concepts that cover 99% of what you would ever need. Ask someone who's taken those classes to boil it down to the essentials. Forget about all but the basic theory (at least for now). So I'd definitely second the advice about visualizing what's going on first, and not getting caught up in the details. In the case of calculus, you're adding up area of rectangles under the curve (once you understand that you're practically halfway there). And definitely don't get discouraged; there's hardly anything in the world that is so complicated a regular person couldn't understand at least the basics, if you can find a good summary (or teacher), IMO.
The sending of this message pretty much inconveniences everyone involved.
I used to tutor Juniors, Seniors and Grad Students in Math and Physics. ALL learning is self-learning. No one "teaches" you; YOU do the learning. Remember to practice, and I suggest spending a lot of time doing word problems, since they are the reality of math.
OK, Arithmetic: "The Trachtenberg Speed System of Basic Mathematics" by Ann Cutler and Rudolph McShane. This will teach you to do Addition, Subtraction, Multiplication, Division and Square Roots, much of it in your head. Learn to use an Abacus/Soroban. It helps to bring arithmetic into focus. there are a couple of computer-based practice utilities on the net to help you memorize the rules and gain quickness in TSS.
Algebra: "Programmed Reviews of Mathematics" by Flexer and Flexer. Six small books with a good introduction to the basics of many Math concepts.
"Algebra", "Functions and Relations", and "Trigonometry and Analytic Geometry": "Pre-calculus Mathematics" Vols I, II, III by Vernon Howe.
Calculus: "Quick Calculus" (Wiley Self-Study Guide) by Kleppner and Ramsey, and also "Calculator Calculus" by McCarty.
Most of these books are older and you will need to look for them. Most of them are "programmed instruction books", which is not a popular Thing to publish these days. Programmed Instruction was developed by B. F. Skinner and Norman Crowder and has been used to teach almost any subject imaginable. The information is presented in "frames" with questions and answers, on the principle that people learn faster in short, successful segments than they do with larger difficult presentations. Programmed Instruction seems to have fallen out of favor about the time that B. F. Skinner was castigated and demonized for his rigid behavioral views. I have never known anyone to NOT learn from good programmed instruction, if they could read the material and understand it. You might want to check with your physician to make sure you don't have an issue like dyscalcula (similar to dyslexia) or some other learning disorder that needs to be overcome first. If so, that could explain much of your frustration and can be handled.
Good programmed instruction takes a long time to develop and test. Each frame should lead to 96%+ success for people taking the course. Many older books simply broke up their information in short segments and asked a question without actually testing the goal and result. I am least satisfied with the Wiley Self-Study guides, but they are usually adequate for learning.
Good luck!
"The mind works quicker than you think!"
Get some high school or college textbooks. (Algebra/Precalculus, Calculus, Geometry, whatever you want to learn)
Get the solutions manual for each book.
Work through the textbook. I really mean work, so write down and think through all of the examples in each chapter. Then, do 'enough' problems at the end of the chapter. Check your answers with the answers in the solutions manual. If you didn't get it right, do it again. If you still didn't get it right, then read through the solution provided. If you STILL can't get it, ask someone, possibly on a forum online or in person.
It worked for me--6 years ago I was a B- high school math student and now I'm taking graduate level math courses.
Allow me to put in a serious, but negative, reply. Math is a game for the young. Mathematicians trying to prove things talk about the fact that no-one who hasn't gotten a major result before the age of 30 ever gets tenure, and really 25 is the age limit for showing real talent. In my experience (college teaching, science, outside of mathematics) no-one who didn't get calculus as a teenager every really gets it. (There are inevitably exceptions out there, some of whom will flame me.) Cope with the fact that you'll never be really good, and learn what you need. Sorry.
Just use the new math! This used to be so easy that only a child could do it.
Ask yourself frankly, was I just slacking, or did I not get it?
... what do I do about this?
If you were just slacking the first time around, most of the posts in this forum are applicable. Take classes, get texts, etc. Just set reachable goals and keeping whacking away at them. Classes will keep you on track.
If you genuinely had trouble with it, the first or second book in your scheduled reading might actually be in cognitive science, pedagogy and so forth. Various fads have swept the nation in math education. Ignore the fads and you'll find most of the basics are the same. Anyway, young kids have a learning advantage in many ways, but adults can understand how to learn something, which can make all the difference. Just for example, part of maturation is better skills at handling frustration. When you hit sticking points, you will have the ability to say: why am I confused? What part of this problem is hard and what part is easy? OK
My motto: "A cat is no trade for integrity."
"Recognise your wakness and go back and make sure you understand whatever is being assumed at the level you are having diffculty with and again, do those exercises."
:]
Oh I will.
Now a suggestion for the OP. I recommend children's math software. Why? Well the better ones are adaptive to your speed and degree of learning.* Two and more important than people think. It's nonjudgemental. The biggest turnoff for someone in a situation and doesn't really want people to know (like reading).
*Starting at 2 plus 2? Nothing to be ashamed of. Some will take you as far as algebra and at that point you no longer need training wheels.
Bob the Janitor don't need no fancy computin' machine, but he showed up at the mangement-mandated training courses anyhow.
:p
There's yer extra 5%, bub.
These are the books that Richard P Feynman used to teach himself math.
Algebra for The Practical Man.
Geometry for The Practical Man.
Trigonometry for The Practical Man.
and Calculus for The Practical Man.
They're old self study guides and they're the best I've seen. I've seed the Idiots and Dummys guides, they're horrible. The Practical Man series really explain how it all works, not just memorizing formulas. I found them on Amazon.
The OP's concern is a little bit of a challenge not knowing what the actual objective is. Most of the direct skills learned in school aren't that useful applied directly in life. However, it does form an important base for many items of curiosity that one hopefully encounters later on.
If your goal is just to master things that escaped you before, first figure out why this will benefit you, and what your incentive is to master things for the intellectual value alone.
It's great to learn new things (or master old things), but I have always needed a practical application for the information in order to keep moving with it.
In theory, learning math independently (as opposed to taking courses or hiring a tutor) basically boils down to (1) obtaining some good, relevant books, and (2) actually doing enough problems in said books to learn the material.
With that said, the quality of available books varies widely. Some are much better suited to independent study than others. Some books simply focus on showing you suitable algorithms that will equip you well enough to "solve" routine problems, while others focus more on providing a theoretical basis for the material and making sure that you actually understand what's going on. Books of the latter sort are typically more work, but with a higher payoff.
Here are my specific book recommendations for learning high school mathematics and Calculus. The bias is toward being thorough, covering all the theoretical foundations, and assuming that you are willing to do a lot of hard work (though with very high payoff!). If your bias is toward just memorizing a few key formulas or getting off easy, this is not the right list.
How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) by George Polya
How to Read and Do Proofs: An Introduction to Mathematical Thought Processes by Daniel Solow
Mathematics 6 by Enn R. Nurk and Aksel E. Telgmaa translated and adapted by Will Harte
Algebra by I.M. Gelfand, Alexander Shen
The Method of Coordinates by I.M. Gelfand, E.G. Glagoleva, A.A. Kirilov
Functions and Graphs by I. M. Gelfand, E. G. Glagoleva, A. A. Kirillov
Trigonometry by I.M. Gelfand, Mark Saul
Basic Mathematics by Serge Lang
Kiselev's Geometry / Book I. Planimetry by A. P. Kiselev (Author), Adapted from Russian by Alexander Givental (Editor)
Euclidean Geometry: A first course by Mark Solomonovich
Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra by Tom M. Apostol
Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications by Tom M. Apostol
All you need is passion, interest and love for it. It is much easier to learn than any other subject, no need to memorize anything, just try to understand it and develop your logical thought; everything else comes naturally.
I always loved mathermatics, although I did not become a mathematician, but a theoretical physicist. Believe me, mathematics is easier to learn than physics.
Your point is noted but as a teacher you know that everyone learns differently. Some people even have certain learning disorders. Courser to finer aka progressive disclosure doesn't imply only one way of here to there.
"To quote Prof. Patrick Winston of AI fame"
Well AI is also famous for it's failures as well so you'll excuse me if I don't fall for the appeal to authority.
"For the basic mathematics that the original post is inquiring about, the concepts are reasonably simple and straightforward. What they require, however, is what often appears to be mind-numbing repetition."
There are different ways of saying color.
You are to be commended for your desire to keep your mathematical and analytical skills in good working order. The world needs more people with your attitude.
One way of starting to learn something is to be motivated by its potential to help you or give you new insights into today's world. While I always liked math, it wasn't until I found some good, practical applications that I decided to build a career around it.
What turned the corner to me was the field of Operations Research, which applies mathematics and computing to real-world decision problems. Problems like work scheduling, vehicle routing, staff planning, production and inventory management, queueing, quality control, and general optimization. The basic approach is to identify the underlying problem, build a decision model, solve the mathematical model, and implement the results. Check into such classic models as linear programming, the transportation problem, integer programming, network flows, queueing theory, and Monte Carlo simulation.
Others can explain this better, and a good place to start is:
- http://www.scienceofbetter.org/
which describes Operations Research (O.R.) as "the science of better" and defines it as "The discipline of applying advanced analytical methods to help make better decisions." That site has lots of examples and links to more information. Other good sites are:In O.R., mathematics underlies everything, but is always applied to a wide variety of real problems. Without the applications, the field would simply be applied mathematics or statistics. By combining the two, the problems become not only interesting, but relevant and, sometimes, quite profitable.
Good luck in your quest, and thanks for asking...I don't think you'll find all of the high school math in one book, but I do know of a great book that I taught myself Trig with because my school won't let me take it. It's "Trigonomerty: An Analytic Approach. By Drooyan/Hadel. Amazingly awesome book that not only teaches you the circular functions and other stuff people associate with Trig, but it does a damn good job of showing you how everything works, and why. The first chapter is about the unit circle in case that helps clear up what I'm trying to get across. :)
:)
I'll admit it isn't the most visually appealing book or the easiest thing to read, but if you spend a few hours really working to understand the contents of a chapter, it's totally worth it, because in the end you'll have a very very deep understanding.
Also, the Blitzer: Precalculus book is very good. Great if you need to refresh your algebra skills. It also has a great Trig section.
For calculus, I would suggest, "The Complete Idiots Guide to: Calculus" (to get started), it was surprisingly good. And most of all, Calculus: An Intuitive and Physical Approach. That last book is practically my bible.
Anyways, good luck, you learn your math, and I'll struggle to get my stupid high school to let me take an interesting math class I won't be bored in.
If con is the opposite of pro. Then isn't congress the opposite of progress?
I know you're looking for ways to teach yourself math, but I'm surprised no one suggested auditing classes at your nearest public university. Many will let you sit in on the class(es) at no cost (or very low cost). You're not required to complete the assignments or tests. Of course, you don't get any official credit for the course either.
N = 8 * 10^8 * x-3/2
doesn't seem right. That's
N = 800000000*x - 1.5
and N increases with x, which is inconsistent with the problem statement.
Instead of numbers, imagine something you really like, such as cake. If you have twenty cupcakes, and your roommates mooch a third of them, how many are left to stuff in their socks? And always remember that Pi = 3.141592654 cakes, proving that it can in fact be squared in the proper pan, but brownies are better.
But seriously, I was a C student in high school algebra, dropped out for 5 years, got my GED just 'cuz, THEN upgraded through Adult Basic Education at the city's technical college for a year and got Honour Roll. My grade 12 math average is now 95%+. Since then I've kicked ass at tertiary education and have a good career track that will afford me time and money to gradually finish my Bachelor's degree. Sometimes as teenagers we don't care or aren't ready to learn. I worked for those 5 years before starting college.
My real advice: find a good teacher. No substitute for it. (Pun !-in-10-did.)
I was someone who was once considered to be exceptional in math. Unfortunately, I made the mistake of stopping at calculus.
To regain my mastery of mathematics, I decided to take a single math problem very seriously. I figured that I would try to
understand the solution by grounding all ideas down to postulates.
I figured that this was a great way to learn mathematics anew and really get advanced. I soon learned that there were wonderful
math resources on the web. Wikipedia is really great. There's also MathWorld.com.,
PlanetMath, MathForum.org, and
Cut-The-Knot.org.
Being pretty ambitious, I chose Fermat's Last Theorem and Andrew Wiles's solution as my jump off point. I started this adventure
in 2004. Since then, because the problem is so tough, I started blogging through the different threads of the problem and I find
myself recreating the history of mathematics from the perspective of number theory.
I am not sure that this approach would work for everyone but if you are a solid problem solver, it can really make advanced
mathematics more fun. If you are interested to see what I came up with, you can check out my blog a My math blog.
I also started a general math blog.
Best of luck in learning mathematics.
-Larry
I was in your position a few years ago, now I have a degree in mathematics. The first thing you should realize is your not bad at math, you just had bad teachers. Your best bet is to completely rebuild your foundational knowledge. You can do this by taking, self paced / no calculator permitted, remedial classes (i.e. 5th or 6th grade math) at a local community college and then work your way up to wherever you'd like to stop. It's a lot of work in the beginning, and you will feel embarrassed taking remedial classes, but in the end it pays off. For me it was a 4.0 GPA and a well tuned analytical mind.
Also... Once you ace college algebra, go buy a book called "Mathematics: From the Birth of Numbers" by Jan Gullberg.
I know that calculators killed me. I used to be able to do all kinds of math in my head but found I was losing it. Now, I only use a calculator if I really need to. I try and do more in my head or on paper. Seeing it is different than punching buttons on a calc. Now, I'm finally able to again add up the entire shopping cart of goods so I know what to pay at check out. Division and multiplication are again a snap. Trig still requires the rule or calc but I try and use my ole slide rule again because it forces you to do more in your head. I also find that when somebody else uses a calculator and makes a mistake that I see it almost immediately while they trust the number on the display. Calculators ruined math for me but, by not using them much, it does come back.
Banjo - The more I know about Windoze, the more I love *nix
This may sound flippant , but it is not intended that way. Maybe math is not your forte. ... ?
Maybe you need to change your career path. Can you write? How do you do at selling something.
Could you be an accountant, electrician, nurse, potter
There are many people working at jobs that require little math , having a good time and making good money.
I spent two years as a physics/math major before realizing the accounting was fun, and became a CPA.
. . . is a great book. I recently picked it up to review a few things, and I ended up reading it cover to cover. It is short, covers the essentials, and has good exercises.
That reminds me. How many remember this book?
In addition to the monolithic Physics and Chemistry Handbook, CRC makes a more compact handbook for Mathematics; it provides a thumbnail sketch for most math topics, useful as a reminder for what you learned long ago.
Another key: keep your textbooks. The piddling $5 or so apiece you get when selling them back to the college bookstore is, in the long run, worth considerably less than a handy reminder for what you learned way back when. For textbooks you sold back, check Amazon.com for previous editions. Until you get to graduate level math, damn little progress has been made in the nature of the course. Most university professors are willing to recommend good textbooks if you stop by during their office hours, even if you're not in a class. If you look motivated and desperate, it's not unheard of for them to dump extra copies of prior editions onto you.
Check your area for major library or college booksales; there's often a textbooks area. While I mostly focused on getting O'Reilly press titles for my computer needs, I've also found cheap introductory course materials for Group Theory, Spanish, and Trigonometry.
If you're a practical type, see if you can find a good collegiate Physics textbook. (Halliday and Resnick in any edition is the classic.) Physics makes heavy use of Algebra, Geometry, Calculus, and some Trig, too; plus, there's the occasional fun problem involving things that go "POW!"
//Information does not want to be free; it wants to breed.
When you get to the calculus level, check out "How To Ace Calculus". It has a lame sounding name, but is a fantastic book that keeps everything in the real world vocabulary. Now, I did use this book alongside a course in real life, but I am a very independent learner and would have gotten at best a C otherwise.
:-)
P.S. One of my favorite parts is how the authors will say stuff like "your teacher really means this, but the other way makes them sound more important"
The only way you are going to learn math is if you're not completely bored while learning it.
I think the best way to practice math is to find fun ways to exercise the analytical side of your brain.
When I was young I grew up playing starcraft. Math was never a problem for me.
Playing games like starcraft is probably not the best way for most people,
but I'm sure there are good interactive learning tools that won't get you bored..
I'm suprised no one mentioned Wikibooks yet.
http://en.wikibooks.org/wiki/Category:Beginning_Mathematics
Wikibooks is by the same group that runs Wikipedia; this site is designed for just this type of thing.
but interestingly it turns out you can fit thousands and thousands of pins into one angel. Which is nice.
It really depends on what level you're at, and what you're aiming for, but I will say one thing however, if you are into programming do not separate the two - they can be done together to great effect.
Obviously this is only really for someone who can program, as that's the only viewpoint I have. Whilst I was young and had only just begun algebra I got into raytracing and similar computer graphics issues, and after a short time of reading what you will discover is that maths and computers graphics are integrally linked on so many levels.
To warm up, begin by programming the equivalent to a graphical calculator for 2D graphs - something that'll plot x^2 + y^2
Even the simplest 3D raytracer still means you have to learn and fully understand ray-sphere intersection (basically, whether or not a line intersects a sphere, and if so where) and that requires a respectable amount of math. By the end of it you may end up with something as simple looking as this but to see your math serve a purpose and come to life is really something.
By programming the math it actually forces you to understand what you're doing intimately, and whilst it can't necessarily replace the pen and paper in teaching it is certainly more interactive and more fun, and you'll never forget it =]
Wouldn't a circle of infinite radius work?
Where are we going and why are we in a handbasket?
As someone who has taught math at the level you are asking about, I thought I'd add my 2 cents. The tutor idea previously mentioned is a good one.
Taking classes at a local community college is a good one.
But, I can also commend Saxon Math products to you. They are designed for homeschoolers, so if you are disciplined, they can be a good fit for someone looking to relearn math. They key is doing the homework. Math takes practice, and that is what Saxon is particularly good at, spreading the practice out. So, if you learn about a concept today and have a 30 problem set for homework today, you will maybe only have 6-10 problems on what you just learned. Tomorrow's lesson, you will still have problems from today. Next week, you will still have problems from today's lesson. Fewer and fewer as time goes on, but it's comprehensive. If you are disciplined to do the work, Saxon is an excellent curriculum.
You can also pick up Saxon materials used on Amazon at a steep discount, but carefully watch ISBN numbers and editions. It does no good to get solutions to a different version's problem sets. There is no particular reason I can discern to use the latest version.
I found these websites dedicated to a free learning experience!
The first website is from a group of authors who have
been involved in the math textbook publishing business
for quite some time and feel the need to give back to
the community and offer their books/CDs for free:
http://www.totallyfreemath.com/math.html
The second website is from a professional math tutor with over
23 years of experience. He has quite a bit of videos covering
algebra and geometry:
http://www.videomathtutor.com/
The trouble with text books is that they don't have the right emphasis. Stick to visual aids and use text books for exercises and proofs.
This may sound stupid, but I'd suggest you start by simply calculating and estimating stuff in your head to a precision of two or three significant digits. Nothing fancy, just summing up your purchases in the grocery, estimating the monthly interest on a mortgage, estimating the size of a room etc. Make up the questions or pick ideas from the environments and situations you encounter. Make a point of doing two of these exercises a day, e.g. during your daily commute.
Over time (couple of years probably) this will give you a basic feel for numbers and also the ability to double-check answers. This is a fundamental skill that will make it much easier to pick up the geometry and calculus skills you are interested in.
--Bud
Maybe. What exactly is this "circle of infinite radius"?
Hello. What you need is to demystify the math. There's a great book that does it. I am sorry for being so plain "advertising", but here: http://www.amazon.com/Demathtifying-Demystifying-Mathematics-Ilan-Samson/dp/1858532175/ref=sr_1_1/102-2691669-6697718?ie=UTF8&s=books&qid=1192428885&sr=8-1 It is like advertising to live a healthy life. The only reason it is not being sold so well is because this book is not the main business of the author, so he doesn't invest his talents into its marketing. Just take a look at the reviews, and then get it :).
This book is explaining all you have mentioned.
According to this book the reasons for not understanding math during the high school are:
teacher incompetence in math and teaching, difficult for a child and non unified naming convention, not enough time invested, etc.
The author is a physicist by education, and his son is a living proof he knows what he's writing about.
Good luck!
Yes. Asimov is god-like in his ability to make complex material comprehensible to use mere mortals.
I've got about a dozen collections of his essays that he wrote for Magazine of Fantasy and Science Fiction, and they're amazing. Also, he did massive guides to the Bible and Shakespeare, if you're in to lit. They are both really, really good; the one on the Bible's not anti-religious, but at the same time it doesn't put up with any bullshit. It posits alternative explanations for why certain outrageous things are described in the way that they are, and in many cases helps the Bible's case in this way, but also accepts some miraculous occurrences or simply doesn't comment on them at all when doing so wouldn't help the reader. Good non-offensive, down-the-middle orthodox secular view of the Bible, though a bit dated (from the 70s).
In my experience, his non-fic is better than his fiction, which ranges from "crappy" to "mediocre" and all points in between, IMO. His guides to Gilbert and Sullivan and to Swift are next on my to-buy list, but now that I've seen a recommendation for his math books I may bump those up closer to the top.
Point is, you can never have too much Asimov non-fiction. Just wait to buy yours until I've got all of mine, so the prices don't go up. Heh.
Saxon is probably the best way to learn maths and keep it in your head. The daily repetition really helps to reinforce it. The best solution of them all, IMO.
Try learning 3D graphics and game programming. You'll need a lot of math, starting from simple geometry (finding line intersections, interpolating values) to high-school physics (f=ma for simple and fun particle systems, spring equations) to university-level math (linear algebra, planar projections, intersection of 3D polyhedra, rotational mechanics, iterative solvers, differential equations, fluid flow, motion along curves, constraint modeling, etc). If you develop a strong foundation in 3D programming, you then have the ability to easily write programs to visualize other mathematical concepts you want to learn, which is valuable - not to mention fun.
You might want to look at some introductory 3d graphics programming books, like "Linux 3D Graphics Programming".
This is a nice book that takes you through step-by-step so that you can work at your own pace. I found it really helpful when starting a university course and realising that my school maths course had been very old fashioned and didn't contain all the concepts I needed. The first term I was drowning in concepts that everyone else knew and ended up with a low 20s test score. I was recommended this book (there are more in the series now!) and worked my way through it. Second term I scored in the high 80s.
Good luck.
----------------------------------- My Other Sig Is Hilarious -----------------------------------
ok. Your gonna need a tutor or teacher to correct your work.
::))
But here is my two cents. ( Umm BA Math Analisys )
I did these things:
1. Work out EVERY PROPBLEM. ( No royal road, just practice )...
Do the examples, the simple problems, the good problems, and tackle the tough problems.
( and you will notice your correcting other mistakes...like the teachers
I had large binders full of paper left from courses. ( and you know that thing...Show Your Work, start with showing everything, and you'll soon get to the point where you can do an increadible amount in your head...I fixed my addtion problems and my multiplication problems that plagued me from elementry school, and actually started liking trigonometery )( too bad my spelling still needs work. )
2. Mark your work up in RED INK for mistakes, BLUE INK for the corrections, missing formulas, etc.
You also start to learn tricks that allow you to check your work faster.
3. Set aside 3-3 hours sessions a week. Mine were Teu, Thu, Sat or Sun,
and READ Ahead, review, and look over your past work.
( This has a basis in psychology, called prograde/retrograde interference )
Since I have also tutored math, I have several sucess stories. All this because I failed Trig. 2nd time, I got more As then Bs, and Aced the class. Got As from then on until my degree was done.
I saw several people here recommending tutoring, college courses, and college text books. I don't recommend any of these to begin, although they are good if you want to continue.
What I recommend here is the "low-brow" way. The easy, the "dirty" way that purists and snobs will turn up their nose at. This is equivalent to the advice of those people who give children comic books to encourage them to read. The method works, right? This will work for you too, and you'll enjoy it as much as comic books.
The key, essential text, is a book written a long time ago, called "Mathematics for the Million". It is still in print, and is excellent. It takes you from early chapters on counting from one to five, and works up through simple geometry through to algebra, logarithms, trigonometry, spherical trigonometry, calculus, and ends off with combinators and linear algebra. It is written in a great style, easy to read, but packed with information. It has lots of interesting stories and applications of the math, but not any fluff. This is the key text. It is 800 pages long, and worth every page. The price is astoundingly cheap. A chap on a desert island could rebuild much of civilization if he had this book with him. If I was on a desert island, this book would come second on my list, right after the Bible. With each chapter, it puts the mathematical developement in historical context, showing how real people developed the math out of the math that went before it, which will be fresh in your mind from the chapters you already read.
After that, you may want to work through these books: "Algebra The Easy Way", "Trigonometry The Easy Way", and "Calculus The Easy Way". In the "Easy Way" series of books, each concept is introduced in the context of a story and a practical application, as a group of people "discover" these fields of mathematics for themselves, to solve their problems. It is set in a fantasy setting with kings, queens, dragons, etc.
Finally, for inspiration, and "fun", I recommend all of the mathematics books by Martin Gardner, Ian Stewart, and A.K. Dewdney. All three of these men ran a very successful mathematical amusements and puzzles column in Scientific American. Their books are compilations of their columns. They make math interesting, showing interesting relationships between the different bits of math that we are told are "important". And they show interesting applications, puzzles, and pictures resulting from the mathematics. One Martin Gardner column that really stuck with me was the one on the "super ellipse". It has the interesting property that it looks like it should tip over, but it actually keeps itself balanced, and resists being tipped over.
As an earlier commenter said, you can't just read about math. You have to do it. You have to practice. If you are willing to practice though, the books I listed above will get you where you want to be, with a minimum of head-scratching.
Good Luck!
It isn't true unless it makes you laugh, but you don't understand it until it makes you weep.
Bottom of the math class? Could barely get into a community college? Failed by a book written "...for Dummies"?
Thank you, you've gone a long way towards explaining what kind of people get MBA's.
Like the author, I dropped out of HS at age 15 and got my GED right when I turned 16. I eventually went to university and earned a BS in Computer Science, and now have a job as a Software Engineer in the Video Game Industry. The time frame from GED to University was about a decade and when I started classes my math skills where dull to say the least.
The best advice I think has already been given. Go to a community college and retake College Algebra, Trig, and how ever many calculus courses they offer. A probabilities course wouldn't hurt either. If you are getting into Software I would strongly recommend a Linear Algebra course as well.
In the end it will cost about a grand or so and take about a year, but at the end you'll have most of the math knowledge you need in non-academic settings. If you are a self disciplined kinda person then just buy the text books and go through them completely. But the structure of a class will help.
Now I've seen Everything
If your math skills are faltering due to disuse... why even bother? Obviously you don't need them. Learn something useful, or at least something that'll make you interesting to talk to. Or learn some math that you never knew- did you know any discrete math?
Being able to do something that a) you don't need to do, b) nobody cares you can do, and c) even if you did need to do it once, you could use a machine to do it- is not going to make you much better of a person.
The University of Illinois offers a mathematics sequence, beginning at pre-calc, which uses Mathematica. It's basically directed self-study. You work w/ Mathematica notebooks, there is no text. http://www.netmath.uiuc.edu/ Also you might read-up on foundational mathematics - e.g. these topics http://sakharov.net/foundation.html
...I failed two out of three years of math classes...
What part of high school math did you not understand at the time? Addition with carry or drawing circles?
I would suggest to you that there is no hope for you.
If you failed because you were sick or similar, and you are now OK, you should be able to cover the high school curriculum with a weekend course.
MIT uses "Calculus with Analytic Geometry, by Simmons" for their freshman class 18.01 for students with no calculus in highschool; Read it!
don't cut it off www.mgmbill.org
You don't really need to know math, except for the very basic operations (+ - * /), to be a very good programmer. I'm very bad on math and I don't know almost anything except for the basic + - * / operations. I don't really need it to be a programmer.
To be a good programmer you just need good logic skills and logic is NOT equal to math.
Math may also based on good logic skills but it's not the same - it's a different kind of logic.
While you can use math to solve a logic problem it's still just ONE WAY to solve it and you can still solve it without math. For some logic problem it's easier to use math but for some other it's easier to use other kind of logic based skill.
Lancelot Hogben's "Mathematics for the Million" did it for me.
I am sure you can find this on the net. It has all the books for 4 years of college.
"Fix it"
It's great that there are so many solutions being offered, but the real red flag is that you failed two of three years of high school mathematics.
I'm going to try my best not to call you a dumbass, but I will say that I think there's more of a symptom here that needs to be explored before you seek solutions. Why'd you fail? School system sucked? (Why'd other people pass where you didn't?) If you really think it was the school, why not try to fund your pursuit the "American Way"(r) and file a law suit? (Hell, if you're successful, you might make the news and a big change in the educational system giving further incentive for the system to pay teachers more and administrators less.)
Were there other causes that might presently remain to inhibit your goals? If you know the cause of failure, do you think the cause still exists? If so, can you address the cause now? If not, it'd be a wasted effort.
Is it "too late" for you to learn this stuff? That's a very real possibility too. My point is that during those sensitive years of youth, we should be learning how to learn. If you haven't set up those crucial neural pathways in time, you may never be fully capable of new types of thought. Learning a skill that requires a new type of thought process at an older age is a MUCH more difficult task than anyone may realize. (I think this assertion should go a LONG way to explain the failure of so many "Cert Chaser" careers. Sure you may learn to pass some tests, but to actually LEARN a skill is another matter... it's hard to fake your way through a math test without actually knowing the skill. But anything that leans on memorization of data can routinely be captured long enough to pass a test and then forget it.) And mathematics is so diametrically opposed to other forms of thought that it's stretching my mind just considering how different the types of thought involved are.
I guess what I'm saying is what I placed in the subject line: Determine the cause before you even think about addressing a solution. It would be a logical and mathematically sound approach.
I would recommend sleeping with the teacher, that is always the best way to get ahead in school.
I hold very few opinions. I hold information based on observation and fact. If you wish to disagree, please use facts.
Know yourself, and how you learn. People either tend to be visual, auditory or kinesthetic learners. Figure out which you are and make sure that you are getting that kind of information. All people benefit from all styles, but you will have one that you learn better form than the others, and you should make sure to make use of that. So if you are an auditory learner, don't just read a book. You need to go to a lecture as the hearing is an important part for you to learn.
Don't shy away from calculators, embrace them. I know too many people who try and learn higher level math (and too many teachers) who don't want to use calculators because they don't want to rely on them. Ok, there's something to that, but because of the immense amount of calculation involved, you will really cripple your learning without one. You need a calculator to quickly take care of the simple stuff so you can use that to solve more advanced problems. Also, programming a calculator to do something is a good way to learn it. In general, if you understand a concept well enough to write a program for it, you've got a fairly solid understanding of it. Don't just put everything in the calculator to get the final answer, but do use it to simplify things you already understand. For example if you can do division, there's no reason to do long division every time you need an answer, just let the calculator handle it and work on the problem.
Make sure to get applications for the math explained to you. At the level you are talking about, I think essentially everything has a real world application. Make sure this is taught to you. It can really help your understanding to get some real world examples. I always had a really hard time with imaginary numbers in high school because I couldn't understand them (or why you'd need them if they were imaginary). Wasn't till many years later I learned what they actually are, and that they aren't imaginary at all.
Now, all that said, you need to ask yourself why it is you think math is holding you back. What is it that a higher level of math understanding is preventing? I ask this for two reasons:
1) You need to focus on what to learn. Many people think there's a certain, immutable, order you need to learn math in, or that you must know certain fields for no good reason. That's not the case. While math builds on more basic concepts, you do reach a point where you can learn only certain parts. If you are talking about math related to programming, then calc really isn't so useful, that's more linear algebra. Figure out what you need to focus your studies on. Not saying you can't learn more for fun, however if the point is to improve in something you need, make sure you learn the right things.
2) In most fields you need way less math than you think. I took through calc 2 in university and I use basically nothing past what I learned in 6th grade (algebra) in my life. There just isn't a lot in the world that requires more than basic math. If you aren't in a field that does, or don't want to move in to one of those fields, I don't know you'll find it that useful. My math skills have dropped way off through disuse. To the extent I use higher math at all it is usually solving a problem just for fun, one I could easily look up a solution to.
Please don't misunderstand, I'm not trying to discourage you from learning, I just want you to consider why so it is as successful as possible. I'd hate for you to struggle through learning new math, only to find that it does you no good at all.
Because one thing to remember is that it really isn't going to be any easier. If you take the advice of others and get a good teacher, that'll help a lot, there are plenty of lousy highschool math teachers, however you probably just don't have much of an affinity for math. Like most things, there are just some people that get it, some that don't, and a whole range in between. Unless your failure the first time was related to drugs, teenage rebellion, inattention, or something like that you'll probably still find it hard. Nothing wrong with that, I just don't want to see you getting frustrated for no reason.
My answer: math is boring, make it fun ! I was uninterested in mathematics until I discovered Martin Gardner's articles. At this moment, I became the major in my class. I recommend you any of his books. Once you'll understand that you can have fun, you'll concentrate on the domain your are more interested, since math is a very large domain.
Paul's Online Math Notes
http://tutorial.math.lamar.edu
It drops connections you don't need and grows new ones... So, use it or lose it. You'll now be much better at something else entirely.
Deleted
There are some very interesting replies here. Two I'd like to repeat because I find them particulary true:
1.) Don't be intimidated.
2.) Stay curious. Find ways to get curious about certain fields of math.
These are from different posts, but I think they go good together.
The truth is, math is a mess. It's a historically grown mumbo-jumbo of countless variations in notation. The problem is that with programming languages - no matter how crazy they may be - they allways come with a reference manual to explain their syntax. In fact, that is the main element by which we judge the viability of a PL. With math on the other hand academia kind of expects us to understand what the Professor is writing on the blackboard without even addressing the issue of a solid reference in which I can look up the meaning of the sum-symbol or what a limes means and how it looks like. It's like music-notation. Somewhere back in the day - often a few hundred years ago - someone came up with a certain notation and since then that's the rule of thumb by which everybody sticks to sorta-kinda 50% of the time. If he feels like it. These notations are mostly literally bolted on to terms and expressions in the most chaotic and hideous way one can imagine. It's like trying to understand a Perl obfuscation contest without the manual.
This is IMHO the single biggest problem in grasping math. Especially for Computer Geeks who are used to strict syntax constraints.
I' currently studying the first semester of BS-CompSci and am glad for having finished my German GED just this summer, with all the accelerated math (barely made it with a D+ due to the time-constrained tests) still in my head. I can just about keep up with the lectures. We allready have quite a few students bickering about the lack of a symbol and notation reference.
Bottom line:
Math is a mess. It is a non-trivial science and takes work to understand, but it's a mess none-the-less. If one keeps that in mind without using it as a cheap excuse not to fully work out and understand the details then learning math is much less frustrating. That's how I feel about it anyway.
We suffer more in our imagination than in reality. - Seneca
As others have said here, to 'get' mathematics requires repetition until you've got a particular concept down pat. The Kumon program breaks math down into small pieces, and drills the hell out of each piece with take-home worksheets. It's basically a Japanese cram school, marketed world-wide. Their web site says they now cost around US$80 - $110/month, depending on the math level you're working on. Don't let the little kids on the home page throw you, they offer big kids math (trig, various calculus), too.
When my wife went back to school in '92, she too was suffering from a number of gaps in her previous math education, and used Kumon to fill in those gaps prior to taking a college statistics course.
Luke, help me take this mask off
I was lousy at Maths at school. But I wanted to study physics. Started reading some physics stuff after I left school and realised I needed some mathematics to understand it. So I started reading the advanced mathematics school books. I had a lot of motivation. Also because I had a reason, and I was studying at a higher level it was all new with a different viewpoint. I took notes. I had to force myself to get very particular about deriving things, memorising important rules etc. This was to get out my imprecise way of looking at problems. I was starting to actually get quite good at it.
I decided to go back to school via what we call TAFE here (Technical And Further Education). I redid my end of school exams going up 2 levels of difficulty in one year for a two year course. I got good passes allowing me to easily get into a number of good universities. Trouble was I liked mathematics so much by this stage it was even more interesting than the physics. Eventually ended with a degree in mathematics and a love of problem solving.
The lesson of the story is a high level of commitment. Motivation. Belief that you can do this. Love of the subject (which comes easier than you would believe). Any additional high level stuff you can come across is good too. I'm sure there are many paths one can take. There are many books that are excellent e.g. Courant's "What is mathematics?", Martin Gardner's stuff to get your head in the right space.
To the original poster: Best of luck.
Bitter and proud of it.
For anyone seeking to master mathematics this is the one way I have found to start.
Google: On the study and difficulties of mathematics by Augustus De Morgan... you can download it for free from google!
after reading that title I suggest reading De Morgan's Trigonometry and double algebra title also available for free from google
Followed with elements of algebra also by Augustus De Morgan
followed with elements of trigonometry by De Morgan
I would also supplement this study with project MATHEMATICS! by Tom apostol
Then work through Tom Apostol's Calculus ( M.I.T. uses this text for their theory calculus courses) you can find this ebook
floating around on most bit torrent sites.
I would also suggest you have a look at Dover Publications, they have great reprints of math classics including some by De Morgon.
Truly, once you get the basics firmly in your head, the more advanced topics come much more readily.
I hope this short list can help others as much as it has help me in the self-study of mathematics.
I wouldn't recommend self study through books, as you have nothing pushing you to do the work, such as assignements. The Open University does a very good maths course (MU120 I think). Your only problem will be doing the exams if you're not in the UK, but the course teaches you up to University level.
Course details are: http://www3.open.ac.uk/courses/bin/p12.dll?C01MU120
It will cost you around $600 if you can afford that, but is far more effective in my view. You get a tutor and set texts all online, plus messageboards for the other students and tutorials if you are in the right country.
You don't need math to think spatially. You need math to explain it to others though.
Other posters have suggested that there is probably some hole, or holes, from way back when that caused problems later on, and they are probably right. A tutor would certainly help, but if this is not feasible, I suggest that you start off by going on a hole-discovery quest.
Try this technique:
Find an interesting but non-trivial problem.
Now assess yourself:
Do the problem, giving yourself a commentary as if you were explaining it to your high school self. Take notice of any spot where you stumble or hesitate. This will point you to either a hole in your understanding, or a lack of skill that is holding you back. Don't worry about whether you 'should' know this or not; you are searching for something that you think you understand, but haven't mastered properly.
It might be that you don't recognise factors of numbers larger than 20 (more common than you might think), or perhaps there are aspects of fractions or ratios that you haven't quite mastered (lots of students are caught out here, and it makes everything else so much harder). Other "gotchas" include limits, complex numbers and calculus. It might be that your middle school teachers emphasised concepts but not mathematical language, without which thinking mathematically can be quite difficult.
Whatever, once you have found a hole, work at getting absolute mastery over this area.
Repeat. Have fun.
In most times, most places, by most people, liars are considered contemptible. - Ursula Le Guin
If you learn the same way I do, for each topic get a concret and complex real world problem, get the teaching matierials (books, websites) and start trying to solve your problem. Let the questions you'll start having be answered by the book then website then discussion forum. When done read the chapter/book again in full. Solve some more abstract problems (excersises probably included in the book) of the same kind. Rinse, repeat. It really helps if you are able to program as you'll be able to come up with real word problems to math concepts easiely.
___
No power in the 'verse can stop me
Personally, I'm pretty strong at math, but have had problems dealing with the whole school environment, so I've only completed some calculus, and parts of some other higher math courses. It wasn't that they were *hard*, it was more that the whole learning method was *boring*.
In any case, I've recently felt the need to refresh and extend my higher math skills. In a similar quest for the same time of course as the original poster, I came across "Engineering Mathematics" by Stroud. This book starts with the basic mathematical rules (how to add and subtract, etc), and covers a lot of territory, including calculus (and of course trig and algebra along the way). It works great for me, as it explains the concepts concisely without wasting a lot of time on each step along the way. This isn't the book for someone who needs a lot of verbosity for each step, but it definately is good for those with some mathematical aptitude.
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The best learning experience I had was to work at a college tutoring center: students patiently wait their turn to ask you to explain and demonstrate simple mathematical concepts.
On the surface you are explaining and demonstrating to them, really you are explaining and demonstrating to yourself. If you get it wrong, "no sweat", they go on to another tutor, and you get some time to reflect on the issue as well another crack at understanding the concept the next time a student asks you the same question. Since there are other tutors in the room, you can ask one of them if it really stumps you.
Benefits:
Non-linear:
-- questions are asked out of order
-- common misconceptions are asked about most often. (And if they're common, chances are that you share them. Also, less time spent on the easy stuff you already know).
-- social. You realize math is not a solitary chore or penance. Math is a language to communicate about ideas and reality: you're practicing communicating with Math. (Would you rather learn French by speaking with people in a coffee shop in Paris, or alone in a basement with headphones on repeating phrases mindlessly?)
--gets you on the right side of any dominant/submissive, worthy/unworthy, smart/dumb subtext in the teacher-student relationship that you might be sensitive to: when you're the teacher the student looks up to you. When you help them chart a course to understanding, they are impressed with you. After enough students, some of their positive impression of you "rubs off" and you start feeling confident and positive about yourself, which in turn helps you learn math better because you start losing your victim self-image with respect to math.
The phrase "those who can *do*, those who can't *teach*" is usually interpreted derisively. But one of the best ways to learn to "do" is to teach. Rather, the phrase should be interpreted as a successful recipe for learning.
Incidentally, if you haven't already taken a course in the subject, e.g., Algebra, Trig, Calculus, I do recommend that you take one from the best teacher that you can find in order to get a one-time perspective on the subject and hear how someone else teaches it. Tutor/teach the subject either concurrently, or after the course, to actually learn the material (like all the graduate students do).
Regards,
-- "Forgotten Password" Phil
Parent post is right. Doing problems is very important, even if you find them easy. Nothing helps you learn math like doing the problems, even the easy ones.
As a professional physicist/statitician I can tell you that almost all math problems are easy, if you know how to do them. However knowing how to do them requires you to do them, perhaps several times repeatedly.
I recommend QAX - Questions - Answers - Solutions from Triple G technologies http://www.qax.com.au/
I'm not saying this is necessarily the case, but perhaps it's possible that using IIS indicates a certain type of web management that is less conducive to standards-based web design?
Just a thought.
You are welcome on my lawn.
It depends on your learning style. If you are more self reliant: get a good text book. Many have been suggested already. Otherwise, get some interactive course with a teacher. In any case, I found the books of G. Polya very helpful. I strongly recommend his "How to Solve It" For example: http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X/ref=pd_bbs_sr_1/104-6874125-7411138?ie=UTF8&s=books&qid=1192445065&sr=8-1
Start with Boolean algebra. If not useful in daily life, it will at least help you to understand the 10 jokes made on /.
Do you love and enjoy maths? If not, and you need to know maths, then I suggest enrolling to Open University or other course. Another way is to hire a personal tutor to come at your home every weekend or so and teach you.
If you enjoy maths then you can try with a book. You can also go to Wikiversity.
If you know some computer programming, then you can try writing software using maths. Try developing a small graphical application showing a circle and then attempt to create coloured slices in it by using trigonometry, eg like this. Actually programming is full of mathematics and logic, if you know how to look at it.
Check out the Schaum's Outline series. Math, Algebra, Physics, even Java & C++.
I find this site fairly useful:
http://mathworld.wolfram.com/
This is what city colleges are for, just refresh yourself on the math you did take. Like pick up a trig textbook (either at the city college library, since they also do those low level courses, or buy a cheap used one) and do a handful of problems for each chapter. Once you've done this part, sign up for calc I and beyond. Picking times that work for you, some classes can be held online at the swankier city colleges. But night school works just as well for must of us working stiffs.
“Common sense is not so common.” — Voltaire
I agree, the "Easy way" series are quite good, probably the best "teach yourself" math books I've seen. A Textbook I've used recently is Thomas' Calculus which while dry is much better than most out there.
Bork Bork Bork!!
Sure, deriving the radius is easy for colinear points - now what are the co-ordinates of the center?
That is *exactly* what got me interested in math, I couldn't agree more. I took advanced math in high school just for the sole purpose of learning complex numbers, when I came across fractals. I've no idea of how many hours were spent in reading about the math online and writing programs in C to render them using everything from SVGALib to ray-tracing to my little TI-83 graphics calculator. (hehe, they took a while to render, that last one)
excellent comment. find something interesting and work at it. when you do hit a stumbling block you go back with purpose to learn something new.
Yes, math can be fun. =]
Step 1: Figure out what you want to know and why you want to know it.
You are probably living a rich, full life without knowing advanced group theory. So you are probably thinking about learning math for a specific reason, either for professional advancement or curiosity. If you are going to be successful, figure out what it is you really want to know or what it is that piques your curiosity. Are you frustrated because you want to save for retirement but don't know how to handle investment returns? Do you just want to not be embarrassed when you have to do simple addition and subtraction in front of your peers? Are there specific problems that crop up at work?
Once you've identified these issues, then refer to the advice from the other posts and put together a game plan.
The key is to pursue the things you're interested in. The approach is the same as, for example, you want to know more about cars. Finding out about auto mechanics is much easier and more interesting when your car is broken and you've got a specific problem to solve. Or if you have friends who are grease monkeys and you want to be able to talk to them on their own level.
Pick some problems in the books or classwork, but also just pick little problems that crop up in your life and try to work them out while you're on the bus, waiting in line, at the gym, whatever. And be sure to talk to other people who know more. Don't be embarrassed. If you don't meet someone in your class, join in online forums. Trust me, people who enjoy math really enjoy talking to other people about math. Like learning a foreign language, you can't learn it by reading a book. You have to do it and you are most efficient when you engage other people in your learning process.
I base this advice on experience: I stopped taking mathematics courses in my sophomore year in high school because I found it boring. (Unfortunately, the way high school math is typically taught, it usually is boring). Later, because there were things I was interested in, I took it up again in college and went on to earn a BA in mathematics, probably one of the best choices (both for my intellectual enrichment and my professional life) I've ever made in my life. I kept my focus by finding things that made me curious and following up on them and have never looked back.
-- My choice of computing platform is a symbol of my individuality and belief in personal freedom.
IAAMN (I am a math nerd), but when I was in junior high I found the book "Algebra The Easy Way" by Douglas Downing to be a remarkably readable and enjoyable introduction to the subject. I still recommend it to people who are struggling with the subject using textbooks. Definitely start here, even if you go another route.
The same publisher is responsible for "Geometry The Easy Way", "Trigonometry The Easy Way", and so forth, although not all are by the same author.
I just wanted to say that this I reckon that this is one of the best answered "Ask Slashdot" questions in ages. It could have descended into a "don't drop out in the first place..." argument but instead it appears that many people here have either been there and done that, or have a "There but for the grace of God go I..." mentality. Great work guys.
I've used MyMathLab a couple of years ago for help with algebra and found it really helpful. Has anyone else had experience with it?
SAT prep books are great for reviewing basic math concepts, especially ratio and percentage problems, which come up in everyday life. (The kind of algebra that can help you spend money wisely.) The SAT will also give you an idea of what is considered fluency with math at the high school level.
Better yet, stop by your local used book store and get last year's edition. Math doesn't change that fast. You can spend $150 for this year's edition, or get the same material for 90% off used. The only reason to buy a new math textbook is if you have to work the specific exercises assigned by a professor. I taught myself basic-to-advanced calculus using three different textbooks purchased for less than $10 together.
One thing that is worth investing in as a self-learner is a Schaum's book with the worked examples. For $40 or less, especially if you find one used, you can have 1000's of practice problems with detailed answers. It's about the closest thing to having a real live teacher walk you through the tough stuff.
yp.
I too am forgetting my advanced math skills, concepts that I used to regularly dream about are slipping away. Differential equations, calculus of variations, I just don't use these things any more and I doubt that I ever will ... well, never say never. This is a fun read to get the mathematical juices flowing again. It's written in the form of a novel and while not great literature is fun to read and covers a lot of ground.
Salut,
Jacques
MIT OCW
Dedicated Cthulhu Cultist since 4523 BC.
Start with Euclid's books and progress organically from there. And always be prepared to research words, like 'induction' (used in maths but has serious philosophical problems). And pick up plenty of 'popular' maths book: they give depth and dimension to dry old equations.
If you just go to a library and get a collection of books, or pay for a course, you will learn to solve equations and yet understand very little. It would certainly be enough for employment purposes, but not for enjoyment and creativity that might actually be finacially much more rewarding.
I managed to get my bachelors in math, but I was a struggler, not a natural. At first, I did absolutely awful in college - although I did very well in high school. I managed to do better in college, by improving my study skills.
1) Make use of other people. Unlike many other subjects, with math it can really help to have something explained by a live person. Make use of teachers, tutors, and fellow students.
2) Don't fall behind. Unlike many other subjects, cramming seldomly works with math. You can get hung-up on some concept and not be able to go any further. In math, you are always building on what you have already learned.
3) If one source doesn't work, use another, and another. If you read on books explaination, and it doesn't make sense for you, get another book and read that explaination. Read a few explainations.
4) Of course, do as many problems as you can.
5) If you having trouble, do your best to isolate exactly where the problem. That way you can explain to somebody else much better. Also, the process of isolating the difficulty will lead to the solution.
6) Sometimes it helps to know the history of certain areas of math.
I had the same problem until I had to take a class for my education degree in teaching basic arithmetic. In one semester, I discovered that I had missed a lot of learning of the basics. (I don't blame anyone; I just didn't get it the first time through.) After learning this, my learning accelerated at a furious rate, such that in graduate school I had a perfect score in two semesters of statistics. See if you can find a similar course. Good luck!
An Elementary Approach to Ideas and Methods by Richard Courant, Herbert Robbins, and Ian Stewart http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192
I've been wanting to go back and use the books I bought in college, but all the interesting problems are even and have no answer in the back of the book. I always thought this was frustrating as it wasn't as though one could just write the answer and get credit without showing work. Is there any place online were one can get the complete answers to old college math books (possibly outdated editions)? I guess I could check the publishers' sites when I get home tonight, but I was wondering if there was a common source for this information.
I find myself often times walking down the street and thinking "If someone threw a penny off of that roof, how hard would it hit me on the head?" and other such silly questions. When Slashdot posts about solar panels approaching X% efficiency, I wonder "So how long will it take to pay themselves off?" These are questions I find interesting, so I solve the equations and come-up with the answer. It keeps me proficient in a few subjects I don't otherwise use, but I know are useful and can even be fun.
I failed miserably at math in high school; in fact, I hated it. Only later in life (in my 20's) did I discover I had a learning disability (ADHD) which explained a *lot* of things in my life. Back in those days (1970s) they didn't have a term for it - they just thought you were inattentive. I feel cheated, and I partly blame my boring teachers for this failure (I really tried). It was the advanced math (pre-algebra, etc) where I began to get lost.
;-)
In any case, for most people, self-learning is probably fine, but I've longed to get back into learning advanced math; only I can't seem to find a resource that will help someone in my situation 'get it.' I learn visually, so if I can see and interact, I'll learn better - but if I have a plain, non-interesting teacher, forget it.
Surely there must be someone reading this that can relate.
The irony here is that I'm a UNIX sysadmin, and I'm pretty good. But it's taken a lot of hard work (and some mistakes) for me to learn these things over the years. Usually it takes me 2 or 3 or more times more effort to get information into my brain - once it's there, I'm golden.
Go figure!
Many people are scared of math. If your failure in math really proved to be so devastatig for you, I guess you really qualify for this. Find yourself a fun tutor that you can relax with and try to work with him.
I also had a lot of problems with math. however i was really good at sports. The difference between the two was that I would do the homework for math and think that I was ready for the test, and maybe memorize some stuff. While in sports I would go practice the play over and over again until it was second nature. What I started doing was coping over and over my homework until I memorized the question and the solution ( and not just copy for copying sake but really know what you are doing). The teacher has only so many questions within the chapters to ask so the questions on the test will be very similar to the questions on the homeowork. -QAK
So, here's to studying mathematics:
* My bookmarks on mathematics [~600?]
* Wikipedia mathematics portal-- recursively read through these, do a depth-five and you should be good to go.
* Synopsis of elementary results in pure and applied mathematics (G. S. Carr)-- lists 1200 theorems in mathematics, re: Ramanujan. Highly recommended.
And some math discussion forums:
* Mathematics help
* Another one
* More
* Even more
Also use irc.freenode.net #math and #not-math, as well as efnet.
Try the Teaching Company. They offer high-school level math. I have thoroughly enjoyed the many classes I have purchased from them.
--- There are two kinds of people, those who accept dogmas and know it, and those who accept dogmas and don't know it
Your mindset is very important here, so by all means get the book Overcoming Math Anxiety by Sheila Tobias. She too had difficulty with math and dropped it, and later on, picked it up again, just as you wish to do now. She runs a university math clinic for people who have had problems similar to your's, and her insights might be very useful. (There also might be such a clinic at your local university).
Author : John Bird -
;)
;) availible
Titel : Basic Engineering Mathematics
4edt.
- starts low, but increases
- good and detailed examples
- online availible
Navy Courseware
- good examples
- from basic to advanced
- online
for german and german speaking readers
Author : Lothar Papula
Titel : Mathematik für Ingenieure und Naturwissenschaftler 1,2,3
- detailed solutions
- determined for people who want to apply mathematics rather than study mathematics
Either that or you need to find yourself a real-world math problem, something that interests you, and force yourself to find the answer.
I don't use math much in my daily grind, but I force myself to come up with problems so I can exercise my skills. There is math everywhere, so if you get in the habit of trying to find problems to solve, it's easy to stay in practice. Calculus, especially, is easy because it has so many applications...Any question that starts with "How much?" or "How fast?" is probably calc friendly. I keep my geometry skills sharp by figuring out the height of buildings by the length of the shadow they cast.
I don't consider myself to be much of a math person...I certainly never had the flair for it that everyone else seemed to. But diligence will take you farther than inborn ability, and the fact that I'm obsessed with real-world applications pushed my skills a lot farther than people who never really understood the why even though they did better than me on paper.
ad logicam Claiming a proposition is false because it was presented as the conclusion of a fallacious argument.
I remember thinking "when will I ever need this" through algebra and trig during high school... More often than I thought.
:) Calculate its height.
Here are two real-world questions I've had to solve with math over the past few years. I'd start by learning to answer them, and then identify other problems to solve! Yes, there are a lot of people who agree with me, but I didn't see too many examples.
1) In a previous life I co-founded a wireless ISP. I'd often need to calculate how tall a tower was, how high up on the tower an antenna was, and where the signal from said antenna would reach the ground. So, find a cellular or some other tower and figure out how tall it is. Then, find an antenna array on the tower (sometimes at the top, sometimes not). If you can't tell, just pick something obvious and assume it's an antenna.
Now, assume that the antenna has a 30 degree vertical beamwidth. At what distance would the "beam" reach the ground. This calculates what I call the "umbrella effect", or in other words, the area where you are actually too CLOSE to a tower to be within it's coverage area.
(Most carriers will angle their sectors downwards as to not waste beamwidth going up into the atmosphere and maximize coverage, but for the purposes of calculation assume that the center of the "beam" is perfectly horizontal.)
2) Find a swimming pool and figure out it's depth. Then, figure out how much water is in it. Calculate how much water would need to be added to increase the water level by one foot.
I know the above doesn't really tell you how to learn, but hopefully having some interesting real life questions to answer might help. Of course, you might not find the above problems remotely interesting. If that's the case, I apologize for wasting time and bits!
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First: Many calculators being marketed to high school students come with a CD of practice problems. Different models teach different arithmetic methods of handling identical problems, depending on the particular strengths of the model. Some models have a "natural expression" feature, others allow easy modification of multi-line processes, and I'm pretty sure there are still some RPN calculators available at low cost.
So buying two or three calculators that have different feature sets and comparing how each handles the same general problem would be one way of sharpening the old skills. Take some notes and blog about your findings, and you might make some new friends, too. These calculators range in price from about 10USD to 40USD, so getting a trio or foursome would cost less than the new price of a set of Algebra 101, Discrete Math 101, and Statistics 101 textbooks.
Second: In the US, there are several CDs available for about 10USD each that provide preparatory exercises for the math section of the SAT exams. Working through one of these would assure that you have covered all the basics.
Third: But in my personal experience, I found that the best practice is to reserve a foot of personal library shelf space for math books, and fill that with the textbooks, "Blah Made Simple" booklets, and so forth that cover the various subjects and that I am familiar with. When I encounter a kind of problem that I haven't had to deal with for a while, I can almost always locate it quickly in these books and review how to do the work. For instance, it has been more than thirty years since I last had to use matrix algebra, and I don't remember the first thing about it. But if on Tuesday I find I run into some matrix problems, I'm confident that by Thursday I'll have completed a review of the subject and I'll be on my way to the answer on Friday.
In short, don't bother attempting to remember how to do something you aren't going to need to do very often. Instead, find a way to assure that you can quickly look up and review the process when you need to do so. A personal library is an extension of the mind.
But which one is which?
Take a look at http://ocw.mit.edu/OcwWeb/web/home/home/index.htm
i don't know what level you're at, so this may not be the best suggestion. i learned maths by reading mary boas 'mathematics in the physical sciences'. it is in my opinion a pedagogically excellent book, though nowhere near as thorough as more specialist literature. if you do work your way through it, you'll know most of the maths you need for any of the other sciences up to masters level (though statistics is pretty weak and fourier analysis could also be longer).
just a suggestion, i imagine other books are just as good. i would recommend staying away from arfken however, until you've got a good basic grounding. and whatever you do, don't read any pure maths books for mathematicians until you understand the subject. in my experience, maths books for mathematicians seem to be about condensing and archiving knowledge, not about making knowledge accessible.
I don't believe so - I've heard of lines being considered as "infinite circles" before, but for each point on a line to be part of a circle, they would all have to be equidistant from the center, since that's the definition of a circle. Intuitively (meaning without doing any proofs), it seems to me that no matter how far you move the center away from the colinear points, they will never be exactly the same distance from the center.
"Slow down, Cowboy! It has been 3 years, 7 months and 26 days since you last successfully posted a comment."
I wrote a little program that presents me with random addition, subtraction, multiplication, and division problems (usually not going beyond three digits) for me to attempt to solve in my head. It tells me if I am right or wrong, and gives me a running score.
I don't practice trig, algebra, or calculus though. Why? Because I don't use it at work (or anywhere, for that matter). Perhaps if I was developing the Half-Life 3 engine or something I would need it, but for the business applications stuff I am doing, that is complete overkill.
I have been under the impression that this is the norm; most jobs (even software development jobs) don't require advanced math. There are some that do, of course, but they are the exception and not the rule.
Does anyone disagree?
The best short book I know of on the subject is Kaj Nielsen's "Math for Practical Use". It's out of print, but it's brief, clear, and contains just enough to get the point across. (Additional books for drills can be helpful if you want to be fast--and honestly, if you're too slow, you may as well not have the skill at all.)
At the other extreme, the VNR Concise Encyclopedia of Mathematics contains most math you'd want to know.
Finally, doing math is a skill, and it's cumulative. Practice. You may need to practice your algebra in order to do trigonometry. You may need to practice your fractions to do algebra. You may need to practice your arithmetic tables in order to do fractions.
I'm sure that at least part of the reason students find math[s] difficult is that much of the time it seems dull and irrelevant. It might be worth looking at some books by popularisers of recreational math[s], who relate it to real life (or at least to interesting anecdotes) in fun ways. You'll still end up having to do classes or read real textbooks, but if you've learned to see some of the possible fun in it, and learned the puzzle-solving "aha!" satisfaction that mathematicians get, then I think you're likely to get on better with the grind work. Authors to look out for include Martin Gardner (especially his earlier maths stuff -- his humanities essays probably won't be any direct help), Ian Stewart and John Allen Paulos -- I'm sure others can add to that list.
Quidnam Latine loqui modo coepi?
Having taken a few of those MIT courses, I don't think that failing 3 years of HS math qualifies as good preparation. Better try elsewhere. Seriously.
Anonymous Coward.
I feel your pain. I had a bit of a "math block" until I encountered computers
in high school due to an abusive teacher at the elementary school level.
I avoided math for many years due to that. But I later realized that when I
got into computers I was using it all of the time but it was just not couched
as "you're working on math problems!"
That being said, the recommendations to do math problems that fit into your
real life situation is not a bad idea - for instance I do a lot of bike riding/
cycling.
And if I know my destination is 20 miles away and I'm going 17 miles an hour
I can mentally calculate how long it will approximately take me to get to the
destination I have in mind or if I adjust my speed to modify it.
Or if you're doing the laundry and you can calculate the approximate washing/
drying time for given pieces of clothing or mentally adding your grocery
purchases before heading to the cash register etc.
Books also help. My mom had a book in her old bookshelf called "the last
math book you'll ever need" that's worth a look see - she had some of the
same problems with math in general and that helped her out.
When I was a teenager, my family was in a illegal business. Not having responsible adults around me, I ended up in this illegal business, dropped out of high school in the 9th grade, and landed in Federal Prison 1 week after my 21st birthday. I spent the next 5 years there. While I was there, I decided to use that time to change my life. So, I applied for the Pell Grant, but the republicans changed the law in 1994 so that prisoners can't get the Pell Grant. I did not let that stop me. I did have the inter-library loan system. So, I could get almost any book I wanted. I got textbooks, and started on page one, and taught myself Algebra, Calculus and Statistics. My "secret" is that I took notes, page by page, as I went. The act of taking notes increases your retention dramatically. It's like "writing into your brain". Also, I had friend named Renee Texadore, who was a Mathematics professor in Cuba. He had been in Federal Prison since the Mariel Boat Lift in 1980. He could not obtain citizenship, and Cuba would not take them back. They are still in Federal Prison indefinately. Anyway, he kept challenging me and pushing me. Between taking notes and Mr. Texadore, I became good at Mathematics. But Mathematics is like working out for your brain. There is no substitution for working Mathematics problems out. The more you do, the easier it is. At first, it seems like your getting nowhere, just like working out, but over several months and years, you'll be surprised. The most valuable skill I learned while on "vacation" was HOW to learn something. I use this method still today. I can go through a 500 page technical book on programming languages in about 25 hours. I can learn new material at the rate of 20 pages per hour. I hope this story will help you and reverse some of my bad karma :) Good luck.
Floating point schmoating point. If I need more significant figures, I gets out my trusty ol' magnifying glass and look at my slide rule - which I made myself - through it.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
I know how to teach women math. Subtract the dress divide the legs and multiple.
Why do you want to improve your math skills?
If you're just wanting to keep your current skills from slipping, that nice, in a few years you're going to have to go back and repeat what you've done. But if you come up with something you want to use them for, personal project or hobby, learning and using them is the best way to go.
I had the same trouble in high school. I was fine through junior high until the 10th grade, where they started introducing "new math". Essentially, one of those really annoying post-modern theorists took control of the administration in my province and introduced a curriculum where people were supposed to learn through analysis and creativity, rather than through a teleological approach. So the math books all had questions, with no advice, and Buddhist-esque thought problems like, "Analyze the simplification. What do you notice about it that is curious?" There was no process. While this approach is great for pure mathematics at the graduate school level and extremely useful for generating pupils with mathematical minds (e.g. not pupils who use their other strengths and then wrap math around them -- e.g. using verbal reasoning to understand math, rather than math to understand math), it was terrible for the majority of students in my province who, like me, barely graduated. I went from an A in junior high in math to a D in my last year. Now, in university, about to graduate with an arts degree, I am returning to math and starting at the basics, with math books written in the 1950s. I just went right to my library and pulled out whatever math book I could find that included basic math. I suggest you do the same. You don't need a tutor! You also don't need any new creative existentialist, post-modern approach to learning math. Just get a book from the 1950s, written in the years of the military industrial complex, where every American was trying to become an astronaut, and read it. Practise some equations. That's all there is to it. DIY and good luck!
Err, I mean, MIH.
but seriously, http://www.3dbuzz.com/ has very high quality video math tutorials, it's definately worth a look.
I think a lot of the replies are missing the point in telling the author to attend a education course>
heres a hint: his title is asking for a teach yourself method! ¦)
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Some of the posters suggested avoiding technology but I disagree. Two of my kids are home schooled, and even though my wife and I are both math majors we use a web site for our kids. It's essentially a K-12 math education via instruction and testing. Lots of practice exercises, complete information on what you know and what you don't, and easy increments of subjects to make it easy to pick up for a few minutes and make progress. It's for fee. (I have no affiliation except a happy user). http://www.aleks.com/
Mathematics for the Non-Mathematician is a good book for liberal-arts types. Written be Morris Kline, professor emeritus at NYU; it's a great book that takes one through the development of the mathematical world via a cultural and historical context. I find the extra information helps me retain the knowledge. Along with knowing why and what you want to know, being aware of how you learn things and honest about it will go a long way. Math is really awesome, and it's a shame that it is taught so mechanically in elementary school. Cheers.
Really, you wont get it. For me, it drew my fascination for numbers when i was at 3rd or 4th grade.
I picked up Clif's notes (the black/yellow cheat books) on a couple math subjects (Calculus). They aren't useful for learning, but they were actually quite helpful for refreshing things that I once knew, but forgot.
I tutored mathematics for several years and noticed a few things about people that struggled in mathematics (as I did, until one day it all "clicked").
Math is highly layered. You need to grasp the lower levels before the higher ones are attainable. You may actually have a mathematical mind, but earlier one may have misunderstood a concept that hinders later understanding. For example, without a clear understanding of the number line, concepts such as points and lines are more difficult to grasp. Without points and lines, trying to grasp quadratics is tough. Spend a couple weeks on the absolute basics first (real numbers, integers, multiplication, fractions) even if you think it's way too simple. You may be surprised to find that you have a misconception somewhere.
People learn in different ways. Some people are better able to grasp trigonometry concepts using the _unit circle_ method. Others learn better by graphing points on the number line. For this reason, try to get several books on a subject and study each. Many times one will reinforce or clarify a concept in another just on the basis of how the concept is presented.
Do the time. Even if you believe you have grasped a concept, keep on doing the lessons until you can visualize the solution in your mind. This means lots of practice exercises. Keep on doing them until they're boring and second-nature.
...and I hardly remember how to do any of it now that I've been out of college and in the workforce for 10 years. As an IT manager, I need to use nothing more than an Excel spreadsheet for all the math I deal with on a daily basis. Once upon a time, I used to be able to solve complex systems of third-order differential equations and could show you all the math necessary to describe a multistage rocket taking off from Earth all the way to placing its payload satellite into a particular orbit around Mars. But I barely remember any of that stuff since it's completely irrelevant to my livelihood and career. If you don't use it, you'll lose it for certain.
Ah, a topic of discontent.
You know I can remember thinking about mathematics and the legends behind the basic foundations in analysis, calculas and the like. (i.e. Euler and Newton and Kepler et al.)
I thought WOW I must be stupid, these guys just picked up Mathematics no problemo......
Well....not quite. I mean, make no doubt, Newton, Kepler and Euler all where very adept at Mathematics.
But, they also worked VERY....VERY very VERY hard at it.
Can you imagine the PAIN and SUFFERING, Kepler had to go through in building even the most basic elementals of planetary motion by doing the same calculation sometimes 100 times to prevent error?
Even then, he got the calculations wrong for the orbit of Mars and missed the eccentricity factor that would have been a shoe in while he was testing different shapes of orbits for Mars: namely an ellipse.
It would take Kepler WEEKS to perform these calculations, which now I can do in a fraction of a second on my laptop.
The labor required in those days to do mathematics was intense, and highly error prone.
Newton would lock himself away for DAYS barely eating anything performing every possible experiment, and when not satisfied with just experimentation, he wanted quantitative results from the experiment as well.
Has anyone, I mean anyone here gone for days barely eating anything working non stop on a mathematics problem for 18 hours at a time?
You know the "greats" in Mathematics worked at it with super human resolve and zeal, only if you would care to read about this HISTORY of mathematics you would find it as so.
Expect to put in at LEAST as much effort if you want to really join their ranks.
I would like to point out that with tools like: http://www.gnu.org/software/octave/ you can bypass the pain and labor of mathematics and get to the core of the matter MUCH faster than Kepler or Newton ever could. So you could literally "cheat" out of the labor these guys had to put in, and put the machine to work doing the calculations to develop methods of computation much quicker to solve problems.
So, although no doubt, these men became literal geniuses, if you look at their lives and what governed their passions with regards to numerical studies, they put in huge amounts of time to the problems they wanted answers to. They earned the right to be called geniuses, it certainly wasn't given to them at birth.
Keep this in mind the next time you are stumped on any sort of mathematics problem. Also keep in mind that like the "greats" you have to be stick with it, and never give up!
-Hack
Got Geometrodynamics? Awe, too hard to figure out? Too bad.
...one math problem at a time.
It was extremely difficult for me but after tackling more than the average number of problems it finally started sinking in.
Just my 2 cents
Hedghog
start with something easy like http://www.mikesmath.com/tribune.htm
There are many messages in this thread that tell you to take classes, pick up study guides, use entertaining internet approaches to learning math, and so forth. None of them are particularly wrong.
But there is another side to this. For math, the way to learn it, to really learn it, is enormous amounts of hard work. If you remember math books, they have problem sets in them. The way to learn the math is to study a bit, and do all the problems. Perhaps twice, if it takes that. Learning math is really about practicing the solving of equations and so forth. While the other things will help you understand what it is you're trying to do, if you don't really focus yourself on the solving of many equations.... again and again and again.... you won't learn math. Except for perhaps the simplest of stuff.
I learned this the hard way. I have an IQ of 128ish. I.e., "very smart but not a genius". Going through school, I grew accustomed to listening to lectures, scribbling notes, and getting a B or an A if I was lucky, but otherwise working very little. And then I hit Calculus. The "working very little" strategy failed to work here. This was the first time I ever had to do a class twice. Ouch. It's not the "studying" here that counts, but the running through problem after problem after problem until you really and truly understand.
C//
Sweet, good luck! Math is fascinating. I think an essential component of teaching yourself math will be to find people who will help. A book can't help you when you're confused, and it's just not possible to write a book that will be clear to everyone all the time. So I think you'll need to find people who will answer questions when they come up. Don't start by hiring a tutor. Lots of people will give free advice (which is what you're getting here.) Go to parties where there are math, physics, and engineering graduate students. Some will talk about math for fun. Listen interestedly. Let on that you're trying to teach yourself math, and some of them will get excited. Ask questions about what you're reading in the books and resources other people have recommended. I bet you'll find a few people who will enjoy helping you work through things, and who communicate well to you. Now if you're willing to pay, you might be able to get someone who has shown themselves to be capable to help you further. They're grad students, so some of them could likely use the money. Say that you're learning well from them, and you'd like to learn faster, but that you respect that their time is valuable. If they could meet with you weekly for an hour and a half, you could pay them (I'm not sure what a reasonable rate would be). If you don't want to pay, or if you find that you can get enough free help without frustrating these people, that's great!
This struck a chord with me. I'm reading Pearl's book on Causality and I've got stuck on the graphoid axioms at the bottom of page 11. I found an hour to work on it on Saturday morning and covered three sheets of paper with notes. I'm not even a single line further forward. I constructed a simple example to help me become comfortable with the notation (X _||_ Y | Z) and the idea of X and Y being conditionally independent given Z and worked through my example.
I'm a mathematician. So I'm used to getting stuck and I know what to do. I stop and make up my own examples. I keep making up my own examples and playing with the ideas until they are clear to me. This is like stock piling ammunition close to my artillery. When I'm ready I will launch a new assault on the tricky passage.
Reading a mathematics book is more like playing a video game than reading a novel. It is interactive, except that the book itself is passive, you have to supply the interaction yourself. Some posters are suggesting hiring a tutor. I think that is right. Otherwise it will take you too much time to work out how to get to the next level and the game will be unplayable.
This guy started a few years ago selling his hoome brewed tutors as a bunch of mpgs ona couple CDs now there is a whole line of DVDs. They are awsome. Best $120 I ever spent. http://www.mathtutordvd.com/
I object to power without constructive purpose. --Spock
I think it depends on what you want to do- if you're writing software for business or doing web design, math beyond division probably isn't necessary. If you're in games or manufacturing, you'll need at least trig. If you're making something that flies or designing simulations, you'll need calculus.
Of course, any programming relies a lot on algorithms and discrete mathematics, but trig and calculus aren't needed for most of that.
You are reading a copy of my copyrighted post.
You're a sharp individual. I liked reading that story.
I think the original poster should take a quick look at their learning style (Global Learner or Sequential Learner), which may have been part of the problem from the very beginning:
http://www.jcu.edu.au/studying/services/studyskills/learningst/sequential.html
As simple as that.
He'd quiz me on arithmetic problems when I was 5-8 years old. When its fun, it seems easy. the opposite is when you think something is hard, then it becomes hard.
I used Saxon in middle school which included teaching myself algebra 1 in 8th grade. This was 10 years ago so I don't remember how good the course was, but it worked for me. I now have a math and computer science degree.
I know this post will be lost in the shuffle, but I want to thank you all for taking the time to reply to this topic. You have given me a ton of practical advice, and more importantly, hope.
Perhaps I should have replied earlier to this topic to give a little more background on my situation, some details were omitted by myself or Slashdot editors. But I'm actually glad I didn't get too specific because of the breadth of answers I have received. Many others will benefit from them, so I thank you for your indulgence.
Some of you wanted to know more background, well here it is for the interested.
I moved around a lot as a child, five different school systems up to junior high. Mismatched curriculum was always a problem, each school I'd start at was more advanced than the last, but my real problems didn't begin until I stopped moving. I went to a very reputable New York high school in the mid-80s. In my latter years there I was diagnosed (perhaps incorrectly) with some vague, undefined "learning disability". They'd no doubt label it ADHD today. I do seem to have dyslexia, but personality conflicts with my teachers had a bigger impact on my learning. Their anger and frustration with my obvious ability versus my lack of performance had a very negative effect on me. It didn't matter that I had an IQ of 136 or that I scored 1390 on my SATs, my grades were always terrible because I resented having to do what I thought was pointless busy work (something I regret today). By my twelfth year I was cutting classes everyday to spend my time in the library, learning what I wanted to learn about science, mathematics, and computers. If I am interested in a subject, and have the proper material, I usually have little difficulty learning and excelling in it.
My specific problems in mathematics classes were varied. Part of it was not being presented with practical applications. Most of it was not doing the home work, which severely penalized my grades and crippled my overall retention. Although I did well on tests, I wasn't learning. Having a literal nervous breakdown during my analytic geometry finals didn't help anything. All that said, I LOVE mathematics. I love its purity, its elegance, its logic, and its lack of ambiguity.
Fast forward to today, I'm a clever and skilled programmer, graphics designer, and game developer, 26 years as a hobbyist, 10 as a professional, with no formal education in those fields. As I expand my skill set in game programming, I'm finding more and more that I don't possess enough basic mathematics ability to truly understand topics like kinematics, physics, artificial intelligence, and statistics, even if I almost blindly employ them everyday. The practical applications I craved as a child are squarely in my lap, and I'm so rusty now that I couldn't tell you the difference between a derivative and a determinant. I may know more about fractals and ray tracers than any of my friends, but I couldn't possibly explain them or think about them critically because I don't speak the language. I liken it to being able to play jazz, but not being able to read music or talk about music theory in a meaningful way. This needs to change, my lack of mathematics skills are holding me back.
So there you have it, in too many words or less. Thanks again to all the respondents, and to Slashdot for posting this topic.
+0 Meh
I worked as a math tutor to put myself through college, most of my remaining work has been in teaching programming in the industry.
Item 1: Math makes sense. If something doesn't make sense, find another explanation/teacher.
Item 2: When tutoring, I have a 95% confidence that if someone can't do topic N, they don't quite understand topic N-1 well enough.
Item 3: Practice, and indeed speed at doing problems is very important. Many topics will not make proper sense if you can't hold intermediate steps in your head.
Item 4: Learning for adults is usually best accomplished by either
(a) having a task one is trying to do, and having to learn the bits.
(b) having a live person/teacher to both help and motivate schedule-wise
http://youtube.com/watch?v=Tr1qee-bTZI
If you disagree with me on social issues, then it's pretty clear that you are a narrow-minded bigot.
In a humongous all-encompassing mathematical hypertext, start at what you need to know and work backwards until you find the place where you're comfortable and know what you're doing. Work forward diligently from there.
Heard any good sigs lately?
Here's a little secret that most math teacher should know, but don't seem to: If you know your arithmetic, you've already learned the hardest part of math. Everything else is just puzzles and game solving. Why teachers insist on making things like Algebra, Geometry, and Trig seem difficult is beyond me. Just think of them as games. It makes them a lot easier to learn and practice. JM
The problem with the linear approach is that it is necessary to understand a section of study before you move on to another section (that invariably builds on the previous section). That doesn't mean that I think that the linear approach is wrong. It just means that if you don't understand what you are being taught, you need to speak up. It definitely doesn't mean that you are stupid. It just means that the way that it was presented may not "speak to you". You may want to read different books or talk to different people. Teachers present the material in different ways and hopefully, you can find the one way that speaks to you about that particular subject. That's the reason that there are so many books on the same subject at the book store. One teacher will never speak to all people equally and what seams to be a good book to someone else won't necessarily be a good book for you. If you don't understand something, do NOT move on until you do get a grasp of it.
Just crack open a text and start going at it.
I am very small, utmostly microscopic.
... to "learn" a skill?
So far as I am able to tell, it means constructing a set of neural pathways -- connections within the brain -- that provide the wetware necessary to be able to perform specific modalities of what we call "thinking". This means that physical changes MUST occur for learning to take place, it's not quite as simple as recording a stream of bits, despite what you may have inferred from The Matrix.
The ease with which skills are "learned" depends upon the existing framework of neural connections, and the plasticity of the brain, i/e. the ease with which new connections are developed. I've read somewhere that it takes about 28 days for new neural pathways to be grown -- so much for the myth of last-minute cramming for tests. The best way to learn formulaic information (like math) is to repeatedly exercise those developing pathways over several months of time.
That's right -- boring drill work. Crank through 30-40 minutes of math problems every day (not sure whether morning or evening is better) and after a month or two, you WILL see improvement.
The younger you are, the more plasticity your brain has, and the easier it is to learn things.
But expecting to be able to read a text or observe a lecture, and pick up significant skills is simply deluding yourself. It doesn't work that way.
Maybe you shouldn't have smoked so much weed back in the day.
I ran into sort of the same thing, except in my case, I also wound up having to take first- and second-year calculus in my 40's as prerequisites for an IT class I wanted. (My situation was a little different, having a master's, but I was a newborn baby as far as math is concerned.) I found I could not remember the trigonometric functions to save my life and got a C- on the first exam. Finally, it occurred to me to code a "scientific calculator" in javascript with all the trig functions on it. Having coded them, I could remember them long enough to get through the next exam. Moral: Make the math relate to your life.
If you get as far as calculus, I recommend Calculus Made Easy by Silvanus Thompson. Alas, in my case, as the teacher remarked, "But not easy enough, huh?"
Try this book.
Yoda of Borg am I! Assimilated shall you be! Futile resistance is, hmm?
Depending on your situation, a public college or university may be right for you. Community colleges are great and really cheap, but you normally get what you pay for :). Many universities will do a much better job on the basic math classes (especially calculus), and if you already got a previous degree, entrance should be really easy. They are usually more expensive, but public universities are usually affordable, no matter what (I live near Atlanta, and teach at SPSU, one of several metro-Atlanta public universities, we charge about $450 per class for GA residents, which is not bad at all; online classes are about $700; a community college around here would be $75 to $100).
So it depends more on which options are available near you.
I always found that a good analogy for some math operation was all it took to understand what I was working with. Of course, you have to be careful that your analogy doesn't have flaws. I was lucky in algebra since I used the "move-x-to-the-other-side" analogy and I came to an understanding before the formulas got too complex for that trick to work.
I swear to God...I swear to God! That is NOT how you treat your human!
By coincidence I'm taking a machine learning course and am undergoing the same experience. Fortunately I'm just auditing the class, so I'm not under the wire to actually demonstrate class related knowledge! But I am motivated to dig out dusty tomes on differential equations, linear algebra, and calculus so that I can review the material to get a deeper understanding.
MAC | A polar bear is a cartesian bear after a coordinate transform.
You're almost certainly right, so I guess the reason math and I never got along was that I have little tolerance for rote work. I became aware of my aversion to all things mathematical at a tender age: in third grade. How well I remember the despair that would engulf me every morning when I entered the classroom, seeing the two huge blackboards entirely covered with arithmetic problems. (For those of you you who are too young to have ever seen one, blackboards are like whiteboards, but sort of dark gray and you write on them with sticks of compressed diatomaceous earth.) During the course of the day, I would have to copy those problems onto my notebook paper and solve every single one of them. Solving arithmetic problems was a horrible sort of tedium that I would put off as long as I possibly could.
My teacher had formulated a rule to encourage us to finish our arithmetic problems early: if you weren't done with them by the time afternoon recess rolled around, you didn't get recess--you had to stay inside to do your arithmetic. For a year, I never got afternoon recess. To me, it was simply less aversive to put off doing arithmetic and accept never seeing the afternoon sun, than to do those long division problems one instant sooner than I absolutely had to.
It wasn't that I couldn't do them, it was just that I hated doing them. I knew how to do arithmetic in principle; what was the point of performing the same dumb operations over and over and over again? Sure, I was lousy at it. For one thing, I didn't seem to have the ability to arrange columns of numbers in a straight line; my columns were pathetic, broken things that writhed all over the page in grotesque pain, merged with one another and perversely twisted about whenever I added them up so that I would get a different result every time. I really didn't (and still don't) think that practice would improve this condition.
Algebra and trig were just extensions of the same phenomenon. Algebra was actually pretty simple, but of course I kept making arithmetic mistakes. Trig was a bunch of arcana for which I could see no conceivable use whatever. Again, trig was rote work: I was supposed to memorize these odd terms and formulas, and then I would pass the course. But why? What was this stuff good for? I know that engineers used it for something or other, but I had no intentions of ever becoming an engineer. Basically, I couldn't motivate myself to put effort into something in which I had no intrinsic interest, and for which I could see no possible use. So I developed my ability to sleep while remaining upright to world-class level. (An ability that has proved very useful in business meetings.) Things would have gone ill with my academic career, had I not been accepted to U.C. Berkeley "by examination" (i.e., high SAT scores...mostly on the verbal part of the test). Ah, such a joyous day when I dropped that course, never again to set foot in a math class.
Am I proud of this, am I happy about it? Not really. I've felt all my life that I missed something important; I feel guilty not only about understanding so little about math, but about not understanding why it's supposed to be so interesting. In the dark nights of my soul, I fear that I wasn't paying attention during the one minute that some math teacher explained why mathematics was not only important, but also beautiful. Or perhaps I missed the class in which my third grade teacher explained something fundamental that would have made math accessible to me.
It was a good day when I realized that I could write computer problems to solve simple calculations ("Hey! It gets the same answer every time! Yowza!") Oddly enough, I don't mind doing math (the sort within my capabilities) if I can use i
Great men are almost always bad men--Lord Acton's Corollary
Actually, I think English (at least American :) puts a very low barrier to accepting new words that are created according to the standard rules. I would definitely consider memorizable a valid word.
You already know the answer to this problem. Buy some textbooks and set aside some time to study them. That's all it takes. That's more or less what everyone who's good at math has done. Posting your question on /. was just a form of procrastination. There is no shortcut, just get on and do it. It's what I'm about to do...
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
http://www.its.caltech.edu/~sean/book.html http://www.trillia.com/zakon1.html
- Mathematics for the Million
by Lancelot Hogben. This book is fun, mathematics unfolds in its historical context. It is not an easy read but I found a very good supliment for my school work, anything that makes math more interesting gets you doing more of it.Morris Kline's Calculus, An Intuitive and Physical Approach. ISBN 0-486-40453-6 From Dover Books is an excellent start on calculus. It has a CD with all of the answers worked out that is available free on-line.
Well, it was good enough for Honest Abe, and he was just a backwoods hick - Grin.
http://aleph0.clarku.edu/~djoyce/java/elements/elements.htmlEuclid's Elements
I've been reviewing this and taking notes in Freemind.
Pug
An Invisible Entity of Vast Power whose existence must be taken on faith alone: Liberal Media
I wish I had this going through college
http://www.howtodogirls.com/bikini_calculus_dvd_sale.php
(youtube mirror)
http://youtube.com/watch?v=5O5_LFJ7FtI
I'm one of those people who is naturally good at english, but had difficulty with math. The problem I had when I went to college was that even if I did all the homework, and seemed to understand it, I would still do poorly on the tests. Finally I found a method that worked for me. What I would do to prepare for a test (in addition to completing the homework) is to take a problem from each section of the homework, alter it slightly, and prepare my own practice test. Then I would close my book and try to take my test without any notes. If I did poorly, I would open my book and notes and see what concepts I needed to work on. Then I would draft up another practice test and start over. After a few iterations of this I would be able to complete a practice test and then would do pretty well on the real test when the time came. This technique got me through four semesters of calculus and a semester of differential equations.
although I must say you gave some hints with the "It takes you from early chapters on counting from one to five" part...
I had another sig before, but this one is better
I just bought a Precalculus book. I read through the whole thing and did the odd number exercises. I took my time and really absorbed the material.
YMMV,
-l
Help cure AIDS, cancer, and more. Donate your unused computer time to worldcommunitygrid.org. Join Team Slashdot!
Most public libraries have some form of book fair; they sell their retired books plus donations, usually incredibly cheap. You can usually find some older college textbooks, especially if you go to to one from a university library rather than the county one.
My county's (Cobb, in GA) was this past weekend, and I got a genetics textbook (probably 5 years old) for $1. Basic math hasn't changed that much, so a 5-10 year old book is still great, but very cheap.
As an aside, the best pricing scheme I saw was in New Orleans; they sold the books by the inch ! you stack them and they measure them !. I don't know if they still do those, but I loved it.
Symbolism, the word you are looking for is Symbolism!
Ubuntu is an African word meaning 'I can't configure Debian'
But it's only half as big as a circle of infinite diameter, natch.
"Slow down, Cowboy! It has been 3 years, 7 months and 26 days since you last successfully posted a comment."
Your that asshole thats always frontin about respect even though you are constantly talking shit!
I'll teach you the difference between your and you're.
"Your" is indicative of possession, such as in "That's your ex-girlfriend with the black guy."
"You're" is a contraction for "You are", such as in "You are an idiot."
Do you understand the difference now?
LK
"Hi. This is my friend, Jack Shit, and you don't know him." - Lord Kano
Can't believe no one has mentioned these books yet. Engineering Mathematics by K. A. Stroud was the book that got me through my maths course for my (Electronics & Computing) degree. It's probably got more of a UK bias, seeing as there are hardly any reviews on amazon.com, but more on amazon.co.uk. Links here:
http://www.amazon.com/Engineering-Mathematics-K-Stroud/dp/0831133279/ref=pd_bbs_sr_1/103-7700355-0295828?ie=UTF8&s=books&qid=1192519415&sr=8-1
http://www.amazon.co.uk/Engineering-Mathematics-6th-K-Stroud/dp/1403942463/ref=pd_bbs_sr_1/026-6301190-6658802?ie=UTF8&s=books&qid=1192519745&sr=8-1
It's also worth getting his second book, Further Engineering Mathematics.
'The best thing about deadlines is the wonderful WHOOSHing sound they make as they go by.' - Douglas Adams
That's why we need things like limits, calculus etc.
Only three things are certain; death, taxes, and apocryphal quotations - Ben Franklin.
first, i was just noting to a friend recently that i dropped out of high school and then went on to get a college degree, but i had never met anyone else who had done the same, so congrats!
i'll have to side with the community college folks here. the real trick is to work problems. it is very easy for me to read some math text and be thinking "i see, this get bigger, this gets smaller, and the whole enchilada converges to 'the answer'" but true understanding only comes with actually working a few examples, which i am far more likely to do in a structured environment.
another option is to tutor kids who are learning what you want to know and that provides some incentive to keep ahead of the material.
good luck!
cryptozoologist
There is a whole series of "___ Demystified" books, including Trig., Pre-Calc., Calc., Algebra, & College Algebra...
True enough. But since the definition of a circle depends on a comparison of distances, and you can't measure infinite distances, I can't even think of a legitimate way to define a "circle of infinite radius." Perhaps you can have an arc whose curvature reaches an infinite minimum.
Not to mention circles, by their nature, enclose a finite area, with an "inside" and "outside." How could an infinite circle do that?
"Slow down, Cowboy! It has been 3 years, 7 months and 26 days since you last successfully posted a comment."
The key to success for any math program is ability in algebra. You will use algebra constantly and you will be needing to do many types of simple algebra manipulations in your head. Concentrate on algebra and get confident in that. Once you have that down, move to basic trig. If you are very good at algebra there is really no reason why you cannot succeed in mathematics.
The quick answer is Schaum's Outlines, which provides comprehensive "outlines" for almost all college courses. Ideally, however, Schaum's works best when you're taking the course concurrently. Regarding the disclipline, however, it's entirely possible progress will be slow unless you first unlearn a few concepts or misconceptions that may be embedded in your psyche. Because of the way we were first introduced to math both in our secondary schools and by our parents, many have developed mental blocks against ever learning any useful math. It doesn't have to be that way. Like many things, all that is required for progress is a small change of attitude. Specifically: 1. Approach the subject by understanding that math is really just another language. Things start to make sense once you master the vocabulary and the symbolic way of writing declarative sentences. The rules will follow. 2. Accordingly you'll need a good math dictionary. Common words used in conversational English have a much more precise meaning in mathematics. My favorite math dictionary is the classic James & James, but it's fairly expensive compared to others that are targeted more to the non-mathematician. 3. Become motivated. For most of us, math is best learned in the context of our personal interests (e.g., music, science, art, politics, economics, sports, etc.). Self-study is the ideal venue. There are many math books devoted to specific problems in various fields of interest. 4. Pure mathematicians, on the other hand, believe that math has to be divorced from practical applications in order to achieve universal application (that which is true for all situations for all time). The world needs the special intellect belonging to pure mathematicians, but for some reason, most such mathematicians are rather contemptuous of those of a practical nature and have been responsible for a lot of grief. Much woe befalls the physics or engineering student who must take a math course from the mathematics department. So it generally behooves the math student to understand the philosophic proclivities of the teacher/author in order to avoid the arrogant purest whenever possible. 5. Understand that practical people have had an important role in mathematics as well. Historically, much significant math has been developed in response to specific needs. For example, the Calculus (differential and integral) was invented to calculate volumes and areas of irregular shapes; Riemann geometry was developed to deal with the failure of Euclidian geometry for curved space; and Tensor Analysis was extended by Einstein to describe a particular kind of geometric field useful to his theory of General Relativity. Hope this helps ...
I had the same issue when I went back to the University. When in high school, I took math courses, and was pretty good at it, I was in the highest math courses my high school offered, which was Calculus at the time. When I got out of high school, I went to the Marine Corps for four years, and I felt like I had lost a lot of what I had learned.
When I went back, I went to University of Wisconsin - Marathon County, and they offered the ALEKS program, which is excellent for someone who already learned the material, but learned it years ago. I became a Math tutor, and recommended it to everyone who was a returning student to college.
ALEKS is a Math Learning Program that is done completely online, and you take an assessment of what you know and don't know. The website for the ALEKS program is found here at aleks.com. The stuff that you know becomes part of your "Pie", and the sections you need work on still you can take by clicking on a link. It gives you reading materials online, and then a sample problem, and then 5 problems on the material. Once you pass the 5 problems you can continue onto the next part of your pie, and you continue until your "Pie" is completed, and you are done with the course.
Seeing the rules again refreshed my memory, and working on the problems was quick enough, yet long enough to teach my brain once again how to do Algebra problems. I finished the course a month and a half early, and don't regret it.
Go to Aleks.com, they have a trial offer for 24 hours where you can try it out for free. If you like it, then you need to purchase a subscription.
I thought it was worth it, and many people that I recommended it to also enjoy it.
I personally found my technical mathematics book an excellent resource; it costs a lot, I paid about $120 at the college bookstore, I think, though I got it used many years ago so I can't really remember, but it is a very good reference for everything from the crude basics (addition, subtraction, even real numbers), and goes all the way up to Calculus, though it doesn't define the core elements of integration. The title is "Technical Mathematics with Calculus" by Paul A. Calter and Michael A. Calter; the fourth edition, which is the copy I have, has more than 1200 pages, with good details, though it does have a few minor typos, particularly two incorrect formulas shown in the third appendix (though both formulas are shown in their correct forms in the text itself).
One thing I haven't seen in this thread is to read primary sources by brilliant people which will get you more excited about math than the average pre-calc book. Read Bertrand Russel, A.N. Whitehead, Feynman's chapter on vectors (in 6 not-so-easy pieces), Quine's small introductory book on logic, Aristotle, Euclid, etc. These books are more engaging than some watered down committee-produced math book. Not that there's anything wrong with math books, of course. But I think the primary sources by the minds which created math in the first place are motivating.
Schaum's Outlines ... Murray Spiegel for President ... of the world
Bill Drissel
Start from the beginning. Read carefully. Work through the example problems over and over until the concepts become obvious. When you feel comfortable do the chapter exercises. This is how to learn it.
I have, over the past year and a bit, been working on a very similar project...getting myself from a rapidly eroding grasp of high-school math and a couple semesters of mostly forgotten calculus through to a pretty solid grounding in algebraic manipulation and proofs, analysis of nonlinear dynamical systems, and the beginnings of modern algebra. And it really was like learning to read.
It's a new way of reading - and a new way of thinking - and it's one that you're unfamiliar with. Start simple and small, and work with basic algebra. I'd get a GRE prep book or something along that line (barrons is the best, IMO), and solve all the problems through algebraic manipulation, working out the arithmetic by hand. No numeric substitution or checking all the answers - you essentially want to be constructing a proof of the correct answer to each question. It helps if you have someone who knows more math than you that you can turn to when you're stuck, so you can skip the frustration of looking up the rules and staring at a problem that just doesn't work. The point is to do enough basic math that it starts to become second nature...the same way that you started out reading things like "see spot run", having to think about the meaning of every word and every step. Eventually, as in reading, you hit a "knee" of sorts, and it starts to become easier, and then effortless. If you really want to learn it quickly and well, math should be the sort of thing you could end up doing for fun after a happy hour, or when you're bored on the train on the way to work. Once the basics are solid and you can do it without effort, then everything else continues to be fun. You're free to focus on the clever plot twists and new ideas of the more advanced mathematics without having to worry about the medium in which they're conveyed - and when you do come across a new notation it's no more troublesome than a new word in a novel - if you can't figure it out from the context you can look it up and continue on your way.
The one exception to the above that I'd recommend is to study linear algebra early, probably before you even review calculus. A solid understanding of spaces, sets, transformations, and dimension helps to tie everything else together in a wonderful way.
I would simply rebuild my civilization so that mathematics was its religion.
In Repressive Burma, it's not just your connection that dies. slashdot.org/comments.pl?sid=314547&cid=20819199
A lot of technical jargon is actually useful.
If you don't name a concept it can be harder to recall it months later.
If you don't have a standard name for a concept it can be harder for someone to know what you are talking about, when you're talking about it.
Whether it's in medicine or math, it helps to have specific terms for specific things that experts in the field use often.
Sales/marketing/BS jargon is also useful I suppose, but it's used for rather different reasons. Proactively leverage synergies and all that...
FOIL. How could I forget. I just recently finished what you are trying to do. I needed to take QBA, but I hadn't done real algebra in around 15 years. the problem I see with most of the posts, is that you said you struggled, yet they are directing you to university texts. And like the math teacher says, they do things for different reasons at the high school level. So it depends on what you need. Another thing is that if you have been out of school for a while, the curriculum at the K-12 is nothing like you remember. Intro to algebra is done at the 5th and 6th level sometimes. If you know any middle/high school kids, ask them to for copies of some of their worksheets. The math tutor is also a good idea, because they will be able to customize to your needs.
But here's what I really did: I went to a book store and picked up the kind of thin workbooks you pick up for kids. They have the grade levels right on them. I actually started with grades 4, 5 and 6. Yes, you should breeze through these. I did have to practice on some areas with grades 9-12. There are dozens to choose from so pick the ones that look like they are leaning toward what you need.
The focus I think is making sure the foundation is solid before going on. There are so many 'teach yourself math' books it is crazy. One little one I really like was called 'No Fear Algebra'. It's just a tiny thing with straightforward exercises. I wish they had them for other areas. There are a couple of typos in it though that drove me crazy! Good luck! I think I will brush up at least once a year now, so that never happens again.
Then pick up a copy of Relativity for the Million, and you'll be as smart as Einstein...
Seriously, a great math book for reading pleasure is "The Nothing That is - A Natural History of Zero" by Robert Kaplan - all about the number zero. Very interesting.