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Options for Adults with Renewed Interest in Math?
Internet Ninja asks: "After only doing mathematics in high school level and in my first year of University, I've suddenly developed an interest in mathematics. Since that was now almost 10 years ago I'm a little rusty. Anything past pythagoras is a little tough for me :) but I know I could get back up to speed quickly. I could probably steal my daughters math textbooks and start reading but I'm wondering if there is a better way. I considered a part-time University paper at US$495 each and you need to do two as bridging courses in order to even start on undergraduate courses. A bit pricey when you have a home and family to look after as well. Another option was a night courses but I'm kept pretty busy with work. Does anyone have any advice or good resources?"
community college -- cheap and laid-back courses that'll give you the background you want.
2) If you don't have grey hairs, you can probably pass for a student with a little creative wardrobe work.
Given premises 1) and 2) above... well, do the math.
(The best part? You don't even have to show up for the exams!)
but here in the US I would take a community college course or two, they are WAY cheaper than the 'real' universities. (and just as good in my opinion, all the learning with none of the liberalism)
"I could probably steal my daughters..."
To answer your question I need to know more about this... what grade is she in? How old is she?
Brunette, red head, blonde? Please, I would love to help you but you're not giving me much to go on...
dmarien
What are you planning to do with this education in Mathematics?
Do you want this for information's sake, or do you want to plan a career out of it?
These questions are important because if you are doing it for education's sake, the first time you look into a college-level Multivariable Calculus book might result in a little voice giving you a sudden desperate need to close the book and never open it again.
Course, if you plan to make a career out of it, the above situation will probably still occur, but you'll at least have a strong reason to ignore that little voice and give it a serious try.
-Matt
well, I read a lot. I do mean a lot. I graduated w/a degree in History. You can learn a ton from reading books about History but books about Math are more difficult to learn from IMHO.
I never had difficulty learning the examples. I could do any problem pretty much that relied on the examples in the book. When I needed to apply something else that wasn't taught to the T in the book I had a bit of a hard time w/that.
Math for me is something that would have to be taught in a classroom not from a book.
Damn, I messed up the link. That should have been this one instead. Sorry!
Personally, I was in a similar bind a few months ago. A co-worker was going to school for CIS and I read over his shoulder while he did his homework. More came back to me in those few months while watching him work and helping each other out than if I'd read the book by myself.
Learning works better with two people.
i reccommend What Is Mathematics by Courant, Robbins, Stewart. This covers just about everything in modern math until the 1940's or so (and the newer version have updated sections on Fermat's last theorem). Plus there's a blurb from Albert Einstein praising the book on the back. You can't ask for much more than that.
-BlueLines
--BlueLines "The cost of living hasn't affected it's popularity." -anonymous
As Euclid said, "there is no royal road to mathematics". Go to university, take the courses they tell you to take, and expect to spend a lot of time and money.
Either that, or don't bother. Quite seriously, I doubt you'll be able to learn much whatever you do -- mathematics is a subject which people find incredibly hard to pick up late in life.
Tarsnap: Online backups for the truly paranoid
Look at the syllabus for courses at your favorite university web site. From there you can look up topics on the web or in books.
Why not just get a tutor? It would definitely be less expensive than actually going to school again. Also, you get the 1 on 1 atmosphere which is usually the best. I think anyone who actually 'wants' to take math is crazy, but whatever floats your boat
http://mathworld.wolfram.com/
This isn't completely what you want, but it is a very good reference site for mathematics, from the fine people who brought us Mathematica. And it's free, and as we all know, free is good.
-twb
A lot of university professors post their tests or nots online.
Try google...
or go to the math dept.'s site and click on professors. You'll find something like this: LSU Prof's
From there you can get their personal sites that have tons of information.
This is how Passed Dif. Eq. Got most of the information from google and lots of different university's notes.
Make sure it's not just by reading posts in Slashdot about the Riemann Zeta Function and associated hypotheses...
Mathematics for the Million (ISBN 0-393-31071-X) Even Albert Einstein had good things to say of this book.
11*43+456^2
Then there was the crackpot category theoretician
who thought he was a catamorphism operation. He'd walk around the psych ward with a pair of bananas, which he'd hold up around the other patients and giggle maniacally.
Once he did this to the resident hypochondriac (who was convinced he was in the final stages of inoperable brain cancer), but it didn't seem to bother him.
"What are you doing?" he asked.
"I'm constructing a unique arrow," said the crackpot, "with YOU as its target!"
"So what's the big deal about that?" said the hypochondriac. "I'm terminal."
(Of course, this joke is only funny if the mental hospital is Cartesian Closed...)
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to we
Hi, I'm 38. I have a similar situation. From my experience, there is only one thing stopping you - time.
I am a family man (two kids) and trying to get anything done with a family to take care of too has been very tough for me. So, slowly I realize I will eventually end up as yet another mathematician-wannabe... |sigh|
Recommendations? Get a family, skip the intellectual masturbation. When you're approaching forty years you will thank me. No algorithm beats a bed-time story.
I guarantee you will go back to hating math after taking a single class.
But seriously university classes in math tend to be rather boring because they tend to reduce even complicated fields into a few formulas that can be memorized and a few problem types for which you can memorize which formula to use.
Also they tend to assign a lot of dull homework.
So classes seem to be geared towards those that cant understand math but are willing to tackle it with brute memorization.
Or maybe i just went to a bad university.
Become friends with Math Professors or Math Teachers. or some other people who are good at math and talk about it a lot. When you hang around them for a while you pick stuff up. And espectly if they are a professor they will probly give you little helps and tips for free.
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
I have found that doing these USAMTS competition problems have pushed me forward a lot this past year of my high school career (not to mention an honorable mention finish). Try it and see what you learn. For those high schoolers out there, its a nice competition to get into, the only thing you pay is postage to send your answers in.
I'm the Devil the Windows users warned you about.
I believe it's Dover anyways...they publish a really great series of math books on a variety of subjects, available at Barnes and Noble for $10-15. A real bargain if you ask me! I bought "Math for Nonmathematicians," for a refresher, but it is more of a history book--aninteresting read nonetheless. I haven't done high-level math in about 7-8 years either, so I broke out my old calculus books too. I enjoy studying number and graph theory, very useful for programmers.
Some colleges have courses on TV. In Portland, PCC (Portland Community College) they have 'telecourses' on Math. Unfortunately, I failed to keep up on the class. However, if I get renewed interest in taking the course I can fire up the PCC channel and watch it.
I imagine this is available in SOME other areas too. It's worth a view and doesn't cost you anything.
Here are a couple of other ways to use your local university:
(1) You can register as an official auditor. That means you can go to lecture, and usually take exams and have them graded. You won't be able to use the lab, if there is one. This gives you a more official status, and makes it easier to get your exams graded, and so on.
(2) You can enroll in summer school. A lot of universities have summer sessions that are open to everyone who is over 18, or who has a high school diploma, or who has permission from their high school principal. They charge full rate but you get 6-10 weeks of intensive academic whoop-ass.
It's up to you whether you can go the independent study + book route. That works fine for math, but it's a personal character thing whether you can discipline yourself to do it.
Web sites, et cetera, are hokum. A good book is much much better. Just go down to your college bookstore and browse some. If your math is at high school level, browse the "freshmen bonehead math" books.
It sounds like the real problem is going to be creating a space in your life to work on the math every damn day. Math is hard and takes a lot of sweat. Learning calculus is like, say, running a 10k race -- you are not going to get there with an earnest attitude or even just by buying the magic equipment. You get there by training every day for weeks or months.
And similarly (speaking as a big math geek and a horrible runner who can barely make 10k) -- don't worry one bit about other people you encounter who are way better than you. When I see some elite runner go by me, I just congratulate myself that I'm on the same path as them, propelling my fat geek ass under my own muscle power. It's okay to be a newbie, especially at something tough. Just get in the game and stay in the game.
Get ready to mod this -1 redundant.
As an undergraduate I had a minor in mathematics. I've been out of school for a few years and was interested in taking the GRE. In order to prepare for the quantitative section of the GRE I enrolled in a 5 week summer evening math course at my local community college. The course was titled "college algebra", it was basically stuff you should already know coming out of high school. However, it was wonderful. A perfect refresher for somebody who hasn't writen a proof or solved a quadratic since college. I enjoyed the experience so much that I'm enrolling in more classes this fall. I have found that community colleges are wonderful resources, but more importantly tuition is dirt cheap. $67.00 a credit hour here. I can't stress this enough, tuition doesn't get any cheaper than that anywhere in the US.
Check out my podcast: DreamStation.cc Video Game Show
The Teaching Company has great audio and video lectures on all subjects by reknown professors. Though they may seem a bit expensive, try requesting your local public library to order a set. I know I've ordered them for people when I worked in a library.
a sp?Sbj=10
Here's a link to their Science & Math courses: http://www.teachco.com/ttcstore/CoursesBySubject.
Mathematics is one of those fields where there's a huge variety of topics covered by a single label. What does "math" mean to you, and what are you interested in?
If you're interested in calculus (differential equations, dynamic systems, chaos, etc.), you would probably be best served by getting a current university calculus book and Maple/MathLab/Mathematica/whatever and working through it. The software handles the mechanical aspects of the process and you'll probably find the material easier to pick up than before.
Same thing if you're interested in number theory (cryptology, matrices, etc.) If you get an introductory text designed to work with one of these programs it will handle the mechanical grunt work and allow you to focus on the concepts.
If your interest is precalculus (algebra, trig, etc.), you may be better off working through the problems by hand. You want the software to be a tool, not a crutch, and one of the main reasons for the usual introductory sequence (up through PDQ) is just to train the students how to reliably perform the necessary work.
For every complex problem there is an answer that is clear, simple, and wrong. -- H L Mencken
Seriously, what subject matter interests you. That makes all the difference.
A: None. The Universe spins the bulb, and the Zen master merely stays out of the way.
I was in the same position as you about a year ago...I had done advanced calculus stuff in high school about 12 years ago, and really enjoyed it, but somehow let it drop when I got to university. I bought a couple of calculus text books for a refresher and took off for a train ride across the country with them (!). I found it came back to me fairly well, but it was difficult without the structure of a classroom w/required assignments, etc.
If you're just interested in exploring some (fairly) current math theory and less in the mechanics of solving problems, I highly recommend a book called "mathematics: the new golden age" by Keith Devlin. It covers such topics as primes and factoring them, set theory, topology, etc. It was a little over my head, but in the good way -- it forced me to stretch and although there were things I didn't quite get, it was really enjoyable.
just my 2c, hope it's helpful...good luck!
:wq
I would try doing the books first and see if I could find a math brain friend or two who would be willing to help me over the rough spots. I've done this before. Between hs and college I took 7 years to "find myself". When I decided to to college I brought my math back up to speed and taught myself two semesters of calculus to boot. I started with second semester calculus in college (and a linear algebra course also) and aced both of them. But then I've always been a math nut. YMMV
All right, so a lot of the replies to you thus far have said that reading a book is a good way to do it, but I think for a lot of the higher level stuff, it'll be hard to learn it from a book.
I think programming/development/etc are differenct since you can actually apply those concepts in the real world, but from the sounds of the original poster, the amount of math he'll actually use is minimal . . . sounds like he wants to learn it for the sake of learning, and more power to him for that, but without some sort of application/repetition, it'll be real hard to learn it . . . which is why I think a college classroom is probably the best way for him to go . . . and like many others have posted, community college is a good option . . .
While SOSmath is a nice reference for finding old formulas, it's really quite horrible for learning Math. It has the same problem 90% of Math textbooks have, when they introduce new topics they tend to just give it a name (like say Laplace Transform) and give you the formula (with plenty of implicitly defined single letter greek variables) and tell you to go with it. There is no discussion on what it is useful for, when you need to use it, or even what problem domain this solution exists in. Heck, I don't think SOSmath even tells you how to intrepret any of the arcane syntax common in any high level math.
I read the internet for the articles.
...some of us are opposed to putting computers in every classroom...
Thanks to file sharing, I purchase more CDs
Thanks to the RIAA, I buy them used...
hey, here's an idea: try working some math problems. there are tons of resources on the web from math contests that were originally given to high school students all the way up through graduate students. try working some of them - you can often find elegant solutions published right along the problems after you have tried to solve them. here's a couple of links to good problem repositories:
/ pr oblemarchive.html
/ pu tnam/index.html
n .h tml
http://www.unl.edu/amc/a-activities/a7-problems
http://www.unl.edu/amc/a-activities/a7-problems
and to order copies of easier (though still very interesting) exams:
http://www.unl.edu/amc/d-publication/publicatio
good luck,
jeff.
I'm a math prof at a small private college. My students who have taken courses at community colleges repeatedly tell me that the classes are so much better at our school than at community colleges. At small private colleges, your math courses are taught by real, professional mathematicians with Ph.Ds. The Ph.D. is not always directly relevant, but it does give your professor the authority to look far ahead of your current coursework and tell you what is relevant and what is not.
Community college professors are usually masters (or less) degree instructors, perhaps working part time teaching while also doing other jobs. They have far fewer rigorous evaluations of their teaching, and they do absolutely no real mathematics research, so they don't really know what mathematics is actually important and what isn't.
Professors at big universities also have Ph.Ds and do research, of course, but they are paid primarily to conduct research and teach graduate students; undergrads are the lowest priority for them.
Forgotten Algebra
Barron's
0812019432
Apologies if you're beyond this, but it is EXCELLENT if you're thinking of going to a
college level algebra class. Takes a few weeks
to work through. You'll be ready for intermediate
algebra or precalc when done.
-fb Everything not expressly forbidden is now mandatory.
Personally, I'd start by proving the Riemann Hypothesis. At that point you can take the million dollar prize and hire a few Nobel Laureates as tutors.
This tagline is umop apisdn.
Many are even school professors and book writers!
;-)
You'd probably be surprised how many of those people are 14 year old girls in other rooms...
The guys whole point is he's trying to re-learn math AFTER COLLEGE. Who gives a fuck about the 'college experience'. He wants to learn math. Not hook up with drunk co-eds and go to 'protest marches'. Go back and re-read the post...
I lost my concept of community when my community lost all concept of me.
And by this I mean- see if you can do your learning at work. I don't know what you do so I'm not sure how practical this is for you. But I can totally relate to your situation.
I've got 2 toddlers, I don't spend enough time w/them and my wife as it is and I don't have spare cash or time for school.
So what I do when I want to put some decent time in learning something I try to find a way to make it a function of my job.
I'm a programmer- when I want to learn something new I start working on a way to make it fit into the company's needs. Now that is kind of an easy thing to do sometimes I'll admit. Sometimes I have to be creative.
If you work for a company w/better employee policies than mine they may pay for you take classes on the clock. That, I would think, would be ideal.
But say these ideas are just way out there- you're a night security guy. Well if you are allowed to read while you are gaurding whatever- the book ideas come in handy.
I've found that when there is little leeway in my personal life I just need to look hard at ways to create that leeway on the job. (I justify my time on slashdot when I find out about current computing issues that affect the company- happens more often than you would think- and my boss is cool w/it)
.
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?
A good general book that I picked up a few years ago and am slowly working my way through is 'Mathematics From the Birth of Numbers' by Jan Gullberg.
It provides a very intelligent of the whole topic of Mathematics, from the point of view of an adult reader wanting to learn more. The author goes into a lot of the interesting historical and cultural background behind the math.
It's truly a book that belongs in everyone's library.
Rather, you should begin your study of mathematics by reading the Ancient mathematicians. Begin with Euclid. In reading the Elements, you'll quickly discover that Euclid has presented a complete science (from self-evident first principles to logical conclusions) that includes truths about geometry (continuous quantity), number (discrete quantity), even the foundations of algebra (Elements, Book II). The Elements culminates with the constrution of the Five Perfect (or Platonic) Solids, the proofs of which are marvelous to behold.
In reading Euclid you'll not only create a rock-solid mathematical foundation for yourself, but you'll also:
After you've finished with Euclid, move on to Apollonius' Conics, a beautiful work, a thousand times more complete and wonderful in its treatment of conic sections than you'll find in any modern analytic geometry textbook. You may also want to look at works by guys like Archimedes, whose early work on the infinite inspired the Classical develompent of the Calculus.
With this firm foundation, you'll be able to read and understand the mathematics of Descartes, whose treatment of geometry (notably the solution of the four-line locus) was key in the development of algebraic notation. And if you stick with it, you can probably read Newton's Principia, Leibniz, and other later Classical mathematicians. I'd stay away from 20th century mathematics, at least at first. There's lots more joy for the amateur mathematician in reading and understanding these Ancient and Classical works than there is in trying to decipher some of the work that has been done recently (within the past 100 years).
Whatever you do, read original works. They are infinitely more understandable than textbooks and other secondary sources. Find someone or a small group of people to discuss them with. Ask each other what each author is doing, what assumptions he has made, what he thinks he has proven (if anything). Memorize proofs, especially with Euclid.
There is lots more that you can do, just with the authors I've named here, but at the very least, even if you ultimately decide to take a college course or something, get yourself a copy of Euclid's Elements. It's a singularly wonderful work, and you'll be very glad you did.
Belloc
I got more rhymes than Jamaica got Mangoes.
There are great Cliff's Notes for math. I picked up the one for Calculus before taking the course. It came with a CD that had great visualizations, etc. The book was great. It had quick reference cards, was well organized, and was short and to the point. I preffered it to my actual text for that class.
The version of the CD that I have doesn't work under OS 9, much less X, but I'm sure they've updated it by now. I don't know what kind of support it has for Linux or Windows. I know it did work with some version of Windows, but Linux support is probably poor.
t'nera semordnilap
You should start by looking at every single function in the header file "math.h" in ANSI C (Appendix B of Kernigan & Ritchie) and for each of them ask yourself "what exactly does this function do?"
Then you need some math programs. You only really need one from each of two categories. You need one serious number crunching program, and one serious algebra program.
For number crunching, I recommend "Octave" (which is free but hard to compile correctly unless there is already a binary for your platform), "Matlab" (which will run you several hundreds of dollars but you can probably get a used copy with a want ad or an auction site), or a spreadsheet with a sufficient coverage of library functions, such as Excel. I recommend them in that order.
In addition to a number cruncher, you will want a computer algebra system (which will also do calculus and "higher" math): Maple, Matlab, and Macsyma; again, I recommend them in that order.
I am a math professor at a liberal arts university and we have a "non-traditional" student (he hates it when I call him that) who went back to school for reasons like the one you mention. However, he has is doing it full time; he was a fairly successful consultant/businessman and took early retirement. Sounds like you don't have that option.
If you have a fairly week background in mathematics, you are going to need to "go to school". By this I do not mean that you have to register for a class. I mean that you need to be around people who are learning mathematics and talk with them - a lot. Students will typically tell you that they learn most of their mathematics not from the classroom setting, but talking with other students. Especially at the early levels, learning mathematics is very similar to learning a foreign language; to really learn it you must surround yourself with people who speak the language.
Our non-traditional student has learned this lesson well. For all intents and purposes, he lives in the math lounge across from the department. He even does non-math homework there just so he can be around when someone comes in to study math. He also gets the bonus the faculty come in and talk to him when they need a break. We don't always talk about the material he his studying; sometimes we talk about something that was in the news or something we are working on. But whatever we talk about increases his math vocabulary and exposes him to the important concepts in mathematics.
If all you do is night classes, you will not get this, even if you go to some of the best teaching schools in the country. And you certainly won't get this from reading books. So what is there to do? Many good liberal arts universities have math clubs that are intended to "popularize mathematics" and draw in new majors to the department.
A lot of times, these clubs pull in speakers to talk about jobs in mathematics. However, these clubs also farm for Putnam contestants (the big undergraduate mathematics competition) and hence sometimes work on problems. Putnam problems can often be understood with very little mathematics (though their solution is far from simple).
So, if you have a liberal arts university in your area, you might want to check if they have a math club (And whether it actually does math, or is just a social club). These typically meet in the evening and would give yourself an opportunity to surround yourself with other people learning math. This is not a substitute for learning math, however. You will still need to start either reading or taking night courses in order to learn the basic "grammar".
I was kinda in the same boat. Due to lousy math innstruction in HS and a dumbass mistake on a placement test in said HS, I barely got out with algebra. Not good for someone going into physics. I took a remdial self paced course in trig and analysis as freshman. There are a several good books written as college level remedial math course. Check your local community college bookstore for some of these. Meanwhile, my science book club sent me a really fun book. The title is something like _Mathematics_Through_History_. The author develops mathematical concepts as mankind discovered them through time. It takes you all the way from math as homo erectus might have done all the way to pre calc and some calculus as well. It's a big thick book that gives you a decent work out as you take it from the shelf and replace it. The book was designed as text book and has exercises. I pick it up from time to time and read a chapter or two just for fun. I dunno if I would teach from this book or even use it as a serious text book, but it's darned interesting read.
...sort of... when he got out of the service. He decided he wanted to do something different (he was a Navy engineer, IIRC - he told us this story like 12 years ago when I was one of his students) and started going through his old books from school to figure out what he liked. Eventually, he found one on algebra (group theory) and picked a hard problem in the book he had never understood. Starting with page 1, he worked through everything in the book until he'd solved it - completely - by himself - working alone - with no timetables. When he finished, several months had passed and he was having the time of his life. He started taking formal classes at the University, and is now (was at the time) a full Professor at BGSU.
I guess the point is that math still needs you if you still need math.
"Lawyers are for sucks."
- Doug McKenzie
Mathematical Atlas
Statistics Every Writer Should Know
Why is it called COMMON sense when so few people have it?
I take it that you're interested in math itself, not necessaarily interested in pursuing a degree in math. Trying to learn most things through formal education is like trying to paint a barn with a brush that only has 10% of its bristles. You'll get it done eventually, but boy is it inefficient.
One of the few advangates that formal education provides, at least in terms of learning, is the step-by-step programmed nature of it. If you're trying to learn something and you don't know how to approach it or what to study, then formal instruction can work. However when you know what it is you should be studying and learning, then formal schooling is usually a hinderance because you can learn things more quickly and more thoroughly on your own, assuming of course that you have some degree of discipline. The forced nature of formal education is its other advantage, and it is a dubious one at that.
Formal education is geared towards the stupid and lazy. For someone who is intelligent and industrious it usually gets in the way more than anything else.
Primary and secondary school spends twelve years teaching those of average intelligence what those whose IQ ranges in the top 10% can easily learn in six. I should know because when I was in sixth grade my "achievemnt" test scores were on par with most college students. My IQ is about 130, or in the top 10%. Of course my teachers all thought I was much brighter, but then they're not used to dealing with someone like me and are, by and large, not too far above the 50% percentile themselves.
College courses are better in that the instructors aren't there to babysit anyone. Also anyone who is either stupid or lazy doesn't usually stick around for long. The pace of study and depth in which the subject is explored can vary greatly however. There have been courses I've had to work pretty hard at, of course those have almost always been the ones that were worth taking.
But anyway, my point is don't spend money to take a course when independent discipline and effort will get you farther in your pursuit of knowledge. Spend money on courses only when they are required for some other purpose independent of learning, such as a job. Don't rely on them as your sole or even primary form of education. Rely on yourself and you'll always be ahead of curve.
Lee
Muslim community leaders warn of backlash from tomorrow morning's terrorist attack.
Too many posts basically tell the OP not
;-)
to go to college! There's no doubt some truth to that. The school part of the experience is not,
as you may naievely surmise, to "be taught", rather to provide the opportunity to teach yourself (ostensibly with guidance and supervision), then be tested.
The goal of the university experience is part education for its own sake, and part quest for a framable document! Myriad problems arise when an individual seeks one part without the others!
My university catalog actually says you'll not be admitted if you have more than 15 hours without a degree plan. (I think that's pretty harsh).
Community colleges don't do this, but once you get a degree from one, it's somewhat a waste of effort to keep studying there.
I have a certain amount of contempt for the whole system, which was put there BY the system (been to 5 colleges!) So excuse my hostility today
-fb Everything not expressly forbidden is now mandatory.
Ask [your daughters] to teach you.
This is the best advice so far, because it will help you and your daughters. One of the things I learned while I was a math tutor was that I didn't know dick about math until I started tutoring. Sure, I had made it to Calculus, and I could keep up at that level, but I didn't know math. It has been said that the best way to really learn something is to try and tech it to someone else, and I've found that it really is true.
Having your daughters teach you the math they're studying will help you relearn the things you've forgotten (or maybe even teach you new things, depending on where they are at), but it will help them even more through the increased understanding they will gain by trying to teach these concepts to someone else, and perhaps as your memory is refreshed you can teach them concepts that don't seem to be presented to them otherwise (the way Kramer's Rule is presented currently is a prime example of this. It is more much more difficult to understand the mechanics of it with the current method, even though (or maybe because) it is more consistent with matrix mechanics).
A better understanding of math can only open more and better opportunities to them, which is a noble pursuit for any parent. Also, the time spent will help strengthen the bonds between you.
So, don't steal their books, ask them to teach you. This is by far the most beneficial solution for all involved.
Under capitalism man exploits man. Under communism it's the other way around.
I throw out a little caution here. Not too long ago I was helping a roomate through a remedial math class he was taking at community college. The text books were horrible. Without me, the poor guy would never have gotten the idea of negative numbers. I'd look for a good alternate text book. Still, this approach is a very good idea.
CCs are designed for adults returning to college. You might find that most CC profs are your age and so they will be easy to talk to and learn from.
Not funny. Here's funny:
Did you hear about the constipated mathematician? He worked it out with a pencil.
Graduate school. Take these classes at a community college:
1) Algebra
2) Trigonometry
3) Calculus
4) Differential Equations
5) Linear Algebra
6) Prob/Stat
7) Abstract Algebra
8) Numerical Methods/Analysis
Then send your applications for grad school off. If you pass those seven classes you will be a shoe in.
The middle mind speaks!
So, one night whilst out for a drink I grabbed the little packets of sauce that were on the table. I laid down three packets of tomato sauce and said that these three packets could be represented by a single packet of tartare. Then I put down two packets of tartare and asked how many packets of tomato sauce that represented.
That was her first exercise in symbolic representation for about thirteen years. She passed it, and has gone on to take access courses before studying for four years to be a dispensing optician. She's now done her finals, involving such things as ray tracing and equations of quite ridiculous lengths that usually had to be re-arranged and substituted into other equations. We're waiting to hear the results, though she's passed everything else so far.
So there you go. My small contribution to the world of teaching - applied mathematics using packets of sauce in a pub. Not the most conventional maths lesson of all time, but it worked.
Cheers,
Ian
Your teacher's name wan't Masey was it? I may have the name spelled wrong, but this is identical to a guy I knew in the Navy who decided he wanted to teach math. We were Nuclear Machinist's Mates on the USS Enterprise at the time.
"God fights on the side with the best artillery." - Napoleon, Marshal of France - speaking truth to power
Computers have made it much easier to experiment with mathematical ideas, and experimenting helps you learn better. I'd suggest buying a copy of Mathematica and one of the companion books. It will do you more good than college courses until you're back in the swing of things.
For the more adventuresome, I'd try J from JSoftware. It's terser, and more intellectually challenging, but it's free and also has advantages over Mathematica in some respects. Ken Iverson has some on-line papers that make a good companion (one of which comes with the J distribution).
One option is community college
Yup, that's exactly what I'm doing. I've been feeling the same way as the article submitter for a while now, and finally got off my ass and did something about it. Just applied for a mathematics course at my local community college.
The nice thing is that it lets me get a second degree at my own pace whilst still working. Either I can just take the courses at the CC, "cash in" the credits and come out with an AA degree, or can transfer the credits over and finish up at a "full" university to get a BA, still part-time.
Good luck, whatever you choose.
What would Lemmy do?
I'm going to take this wildly off topic, because something flashed inside my brain.
;)
.. the official recognition and accredation as their stats, whether they be a history grad or an official fan. Your suggestion is the corollary but demonstrates an exciting point - its clearly benificial to society in this case to let you sit in on class, since there will never be a shortage of paying folks there for the 'official gear' to support the industry financially. Any 'run-off' like sitting in or copying a CD is simply a bonus - free info back to the people, free advertising for the content creator, and everyone saves on card scanners, security gaurds, and DRM OSes!
----
I'm waiting for the anti-piracy posters to flame all over your post - your stealing your proffessors IP! How can he make a living - you're one less might-be student to extort!
This is tongue and cheek of course, but hey, those 'then everyone will steal the CD, theyll just go without the paper CD insert' people should be chiming in 'then nobdy will pay for school, theyll just go without the tests' any minute now, right?
Okay, I gather the next thing someone might say is that a school gives you official accredation. A piece of paper that means, "We think that this person knows their stuff, so we vouch for them." So, a diploma is, in many ways, a brand. Its not just that you completed your courses, its that that school says you're as capable as the other folks they've turned out, which employers presumably have some sort of track record with.
Now, with CDs, the 'brand' is the official gear. The official CD. The official 'making of' CD. Its a diploma, from the school of "I'm a fan of so-and-so".
Anyhow, I've long since felt that people don't buy music/art/culture because they want the cold hard media - they want to get the 'diploma'
"Old man yells at systemd"
A local community college is your best bet. You can pay for classes "a la carte".
Here's a good starting point:
You need algebra to start....without algebra you can't do anything. After that:
Calculus I & Calculus II: Integration and differentiation.
Statistics: Very important...means, medians, confidence intervals...etc.
Like computer science? Take discrete math. This is extremely important if you want to understand the "digital" world, and the foundations of logic...truth tables etc.
That should be plenty to keep you busy. Calc III and differential equations are really hard-core engineering maths. I was an EE major before switching to CS...let's just say that Diff EQs, helped me make the switch.
Have fun and good luck!
-ted
$67/credit? How do you arrive at that figure? At the community college I'm going to the fees breaks down basically like this:
$11/(unit|credit)
$12/session in other fees
$60-120 for books
$40/session for parking (or $1 per day, which may be cheaper)
For the Calculus series I took it works out to about $40/credit (3 semesters at 4 credits each, plus parking, plus $150 in books to cover the whole series). Even for a one semester class I estimate $44/credit.
The cost goes up if you consider your time, of course. 4 hours of class a week plus 2-3 times that for homework can add up pretty quick. Also it would be more if I had a degree. For CA CCs tuition is $11/credit normally for residents, and up to $125/credit for non-residents and people with 4-year degrees (I don't remember the exact breakdown, as it doesn't apply to me, but I do remember the upper cap, as it seemed like a lot).
Anyway, just curious how you arrived at that figure.
Under capitalism man exploits man. Under communism it's the other way around.
That sounds suspicious...are you sure its not illegal?
"(Man) tries to live his own life as if he were telling a story. But you have to choose: live or tell." --Sartre
This was also my experience also. When I took advanced calculus in college the professor repeatedly asked me to change majors (I was getting straight As). When she asked the reason why, I put it as best I could. I said I had no problems remembering formulas but there was some part of calculus I wasn't quite understanding. Kind of like seeing seeing a part of a picture and almost being to the point of guessing what the rest of the picture was but not getting anywhere. Very flustrating. She couldn't help me either because she had simply memorized the formulas and gone on.
"God fights on the side with the best artillery." - Napoleon, Marshal of France - speaking truth to power
If you have access to the PBS-U channel on TV or can find the tapes, you might want to check out a group called "Standard Deviants" and their eponymous show.
It's basically high school curricula, at several levels, but they have a way of making some pretty dry material memorable. I was really surprised at what I retained after watching a few of their shows on physics and math. (They teach all kinds of subject matter.)
The girls are frequently cute too.
If you're reasonably intelligent, you'll learn the subject as you teach. I've been doing this as sort of a refresher course in Spanish. When their maths level gets to the point where it would start to challenge me, that's when I intend to take over. The learning materials I buy for them will help me as well. :)
These are my friends, See how they glisten. See this one shine, how he smiles in the light.
Not too long ago I was helping a roomate through a remedial math class he was taking at community college. The text books were horrible. Without me, the poor guy would never have gotten the idea of negative numbers.
They let him out of high school? Holy crap!
Change and Motion: Calculus Made Clear. Prof. Starbird is an exceptional instructor who illustrates insights into calculus using layman's terms. I took three calculus related courses during the course of high school and college, yet found these six tapes to be incredibly enlightening.
Be sure to buy them when they're on sale! They're $54.95 today (2 Jul 02) but retail for as high as $199.95, I believe.
Enjoy,
Helevius
Surely you mean imaginary and not negative numbers. I can't imagine someone completing high school without knowing what negative numbers are.
I know public schools are bad, but they aren't that bad, are they?
The world is neither black nor white nor good nor evil, only many shades of CowboyNeal.
1. You say you have developed an interest in math. Does that mean you like the idea of yourself knowing a lot of math or you are interested in a field that you want to know more of.
2. If it is the first one, then pay lots of money to learn lots of math that you will never use and halfway thru give up. At least you won't have regrets.
3. If it's the other one, then you know what fields of mathematics that you need to study in order to further understand the subject that you are interested in. Find the things that don't make sense or topics that don't make sense and make a list of subjects that you need to learn. You can go the local university library and read some of the books there which will lead you to other question and so on. That will be the true fun way of doing it.
2) If you don't have grey hairs, you can probably pass for a student with a little creative wardrobe work.
Here's some pointers on blending in:
GMD
watch this
I've found that Schaum's study guides are great for learning mathematics on your own. Clear concise descriptions of how and why things work, and lots of sample problems. Oh, and do the problems man, do them all. You won't get good at math without lots and lots of problem solving experience.
Another great tool is Mathematica. It will do the problems for you, which you don't want to make a habit of. But, when you're stuck, it really helps out, and it will show you all the work. Mathematica helped me through many high-level math courses, but it's pretty spendy. If your daughter is in college, she can probably get you the student version for around $100 or so. I worked in the Mathematics department at a large university, so I had the full version to use for free since it was installed on all of their machines. It runs on Windows, Linux, and Mac OSX.
Need Free Juniper/NetScreen Support? JuniperForum
I was an undergraduate math major (graduated 5 years ago). I was excellent at it, but unfortunately in the "real world" there is little opportunity to use abstract mathematics.
So of course it's easy to miss out on doing math unless you have the time and patience for doing it in your "spare time". Even then, there are certain hurdles that I'd like to overcome. Perhaps some of you can help.
I can also confidently say that it is nearly impossible to really learn advanced math (beyond 3rd year undergraduate) from books alone. The major problem is that math is a very highly compressed field. The notation is usually different from book to book, and the notation is extremely terse. There is rarely any reasonable prose describing why or what motivated a step along the way. Combine this with difficult ideas, and you find that having someone who can help explain why and how to go forward is infinitely more helpful than going alone.
with beginning undergraduate topics like calculus or differential equations, you have comparatively expansive textbooks to describe what and why and how the math was developed along with how it works. It's also usually very applied mathematics. There are plenty of example "real world" problems where you can see how they work. Try that with n-sphere packing or coding theory and it just doesn't work.
However getting access to teachers for advanced courses (beyond 2nd year undergrad) is usually very hard. First, they aren't taught except at universities, (even the small colleges rarely have more than 3 or 4 courses for post 3rd year undergrad) then second they have 1 section and sometimes only tought every other year or every 3rd semester or whatever.
So it's actually hard to even find a place and time to do things like knot theory, algebraic topology, or complex variable analysis.
Has anyone else who has an undergraduate math major been able to go on to do more math other than as a graduate student? I'd love to hear some suggestions as to how to do it.
I was going to take a number theory course at UC berkeley summer session, but it was too much time commitment (commute to berkeley and back, plus 2 hrs lecture 4 times a week)
Has anyone been successful at finding a mentor outside of these channels?
thanks if you can help
((lambda (x) (x x)) (lambda (x) (x x))) http://www.endpointcomputing.com a scientific approach to custom computing.
If I were you, I'd tutor my daughter first. See if you can keep up with her! It won't be easy, because any school pushes hard. Don't be discouraged, but realize that your memory fades and you have to push a little to get a coherent body of information in you mind all at once to see the interrelationships. You have two advantages over your daughter: you have seen the material before and you can concentrate on it alone.
The next step, if you don't have time for night class, is to find a peer who is reviewing for some kind of test. An engineer studying for the Engineer in Training Exam (EIT, formerly FE) will be boning up on all sorts of practical tricks. This will be less than satisfying, but it can establish a relationship that works in the future. Who knows, you might find someone who just wants to study. Teaching others is what graduate students are forced to do. It's a great way to learn becuase the holes in your knowledge stand out sharply when you try to explain things to others =:] This is probably the best means you have to expand your knowledge in the short term.
If you decide to go it alone, and you can do this, try to follow a college course. Go to any university web page and get the course curriculum that interests you. Then find out what the professor recomends for the course where you are. If it's not on a web page, go to their bookstore and see what book is on the shelf. It's generally the best, and at least represents much careful thought. Try to follow the class sylabus. The pace is usualy challenging and involves much homework every night! If you are interested in engineering math, I strongly recomend the CRC Math Handbook as general reference and the appropriate Schwam's Outline for the course you try.
Earning an ordinary undergraduate degree while working takes an effort few people are willing to make. You will be forced to study stuff you don't like under people you like even less. Imagine your least favorite grade school English teacher and give them ten times the power over your future. If you are willing to risk poverty, divorce and great disatisfaction you could quit your job. Don't expect to finish in less than four years. If you keep your job, don't expect to finish in less than eight. If you push too hard you will end up loathing the very thing that now entertains you. All that said, people have done it and done very well.
Friends don't help friends install M$ junk.
Calculus Primer:
7 5/ qid=1025647279/sr=1-1/ref=sr_1_1/002-8828002-34688 55
8 5/ qid=1025647399/sr=1-2/ref=sr_1_2/002-8828002-34688 55
http://www.amazon.com/exec/obidos/ASIN/09132324
Read it. Work the problems. Have fun.
While you're doing that also read David Berlinski's 'A Tour of the Calculus:'
http://www.amazon.com/exec/obidos/ASIN/06797478
This is an English language history of the calculus that is simply supurb.
If you get stumped by some of the algebra, ( which you really shouldn't), then grab that textbook of your daughter's, if you've done math before you don't need a class, just to work some problems to bring you back up to speed.
By the time you're through with these two books you'll either have sated your current mathmatical bent or have a much better idea of what you want long term.
Be warned though, Berlinski's book is likely to set you off on a math 'jag' that you may never recover from.
KFG
Im sure you could find a job at Arthur Anderson. Theyre looking for adults with interest in math now, after their "Hire adults with no math skills" program didnt pan out.
(not saying that my dad is some super-parent, but this is one of the fonder memories I have of my childhood)
My father was in college when I was young (until I was 7 or 8). Sometimes he would read his college-level textbooks to me. Since I didn't know any better, and I thought Dad was God (partly because he always told me, "I'm God, I know everything"), I didn't realize that the college textbooks were supposed to be over my head. Bottom line, for me anyway, was that it didn't especially matter what we were doing together for quality time so much as that we were spending quality time together. I am NOT an advocate of pushing your child to learn things that are beyond what is appropriate to fulfill your own fantasies, I just believe that kids are capable of understanding and enjoying a lot more than we give them credit for, especially when the teacher is a loving parent who is sharing their time with them instead of sending them off for lessons with someone who doesn't know them and doesn't have an emotional investment.
Two books that I remember fondly from my childhood, and that still serve as good reference books for number theory, are Mathematical Circus and Mathematical Magic Show, both by Martin Gardner. These were both really fun books that are also challenging reading for an adult. I originally picked them up because I thought they had cool names (kids love magic shows and circuses, ya know), and I picked them up again a few years ago and still found them entertaining and very informative. The author doesn't just write math books either--he is a well-known creator of puzzles and brainteasers and has done some annotated versions of literary classics. He seems to teach critical thinking rather than rote mathematics.
Denver Isuzu Suzuki
More physics than math, but a great place to start. If you buy the series (or tape it off PBS), you can watch it again and again until you finally learn the concepts. It opens a whole new world in math and physics. It was recorded and animated (by Pr. Blinn, no less!) in the mid-80s, and is still relevant.
-S
https://www.accountkiller.com/removal-requested
- G.H. Hardy wrote several books on math for the interested layperson: A Course of Pure Mathematics, A Mathematician's Apology, and one titled something like Mathematics for the Common Man.
- Lancelot Hogben's Mathematics for the Million is a standard of this sort; Hogben's ideology gets a bit in the way--he, very much unlike Hardy, has very little truck for pure mathematics.
- Isaac Asimov's Realm of Numbers and Realm of Algebra are classics--and, alas, darned hard to find.
- Jagjit Singh wrote several books on technical and mathematical matters for the layperson, including a very good one on information theory.
As someone else has mentioned, Dover reprints a LOT of good books on many subjects, especially mathematics.Now...a lot of the popular mathematics books concentrate on analysis. Internet Ninja didn't specify a particular interest--algebra (in the abstract sense, i.e. groups, rings, fields, and the like), topology, category theory, and so on. Knowing whether IN has specific interests would help.
Talk to the professor first. They'll generally be thrilled to have someone there who is genuinely interested in learning. I had a few dropins when I was TA'ing and found them a nice break from pre-meds. (My favorite was the dog who attended a genetics class every day with his surfer dude owner. It was a 75 minute class period and the students mostly dozed off after 40, but the dog paid careful attention to every word.)
If you want to get graded, though, auditing is probably necessary.
What I'm listening to now on Pandora...
You can learn a ton from reading books about History but books about Math are more difficult to learn from IMHO.
This is true, but it is due to the difficult nature of the material being presented. There is a huge difference between reading *and deeply understanding* "George Washington was the first president of the US", and "A Function F from A to B is called continuous on a set A if and only for every open set C in F(A) ( a subset of B ) the inverse image of C under F is open in A."
The first is a simple statement of fact, the second is simply a definition. To understand the first takes almost no effort. To understand the second, you have to know and understand the definition of Set, Open set, Function, Domain, Range, Inverse Image, and Subset. You also have to put these concepts together in a new way and form some sort of picture in your mind of something it's impossible to take a picture of.
I'm not bagging on history, and I know that there are much more difficult concepts than my example.
The point is that you can't "read" a math book. If you want to get anything out of it you have to take time to understand every subtle concept. Every sentence depends critically on almost every previous sentence in not just that book, but every book that came before. I took a graduate class in real analysis my senior year, and our book was about the size of The Catcher in the Rye. We got through about a third of it in the entire year. I spent a week understanding a single page from the book at times.
I never had difficulty learning the examples. I could do any problem pretty much that relied on the examples in the book. When I needed to apply something else that wasn't taught to the T in the book I had a bit of a hard time w/that.
This is the point of that thing called "learning". High school is one thing, but at college level, the point is that you are presented with concepts and you take those and apply them to new ideas in new ways. I know you are just doing it out of personal interest, rather than for a degree or something, but if you do want to take a step past books about math for the lay person, it does take a certain level of commitment.
Math for me is something that would have to be taught in a classroom not from a book.
A classroom setting might help somewhat in some areas, but even then it requires quite a bit of work to wrap your head around some of the concepts. Having other people to discuss it with makes a huge difference, but there is no way around spending time wrestling with some very abstract concepts.
I gotta stop multitasking - that's 6 and 24, not 6 and 4. The '...4' becomes '...40' and we need to add 24 (not 4) to get it back to a '...64' pattern.
For every complex problem there is an answer that is clear, simple, and wrong. -- H L Mencken
Poster #1: "I'm a Ph.D. in Math at the University of Zimbabwe. Applied math is a waste time. You should learn nothing but theory and proofs. If you try and do anything useful with math, then you're a fuckin' sellout. PS: I love Goedel."
49%: Right on!
Poster #2: "You don't need any college at all! I make $600,000 a year coding VB, and all I did was get a pirated copy of VB and bought a book of Teach Yourself Visual Basic ASP.NET.COM+.ActiveX In 42 Days For Dummies. PS. Math is for weenies.
Another 49%: Right on!
Me: Theory and practice are both important in the world. Ignore one at your peril. Learn both, and you will be better off. Tilt the mix to either end according to your interest.
The remaining 2%: -1, Flamebait
I can explanate how to administrate your network. You must configurate and segmentate it, so it can computate.
They're very much an "engineer's" view of math; their emphasis is more on results than on process or proof, but they're a great buy and very much emphasize the learn it by doing it approach.
One site I like to visit is grey labyrinth. They semi-regularily put up new puzzles and a lot of them use some applied math. Not really a whole solution, but something to look over and point you in a few areas of math you can research on the net (like probability, induction, and others).
-no broken link
I have to wonder if this sudden interest in Math is do to recent drug use like LSD.
Everytime you look at porn a devil gets their horns.
Poor and almost uneducated, Ramanujan used that one book to teach himself and became on of the world's greatest mathematical minds. An outsider, he began corresponding with mathematicians at Oxford. They eventually brought him to England where the food killed him, I think.
The link is to a pretty good background on him - I think it's pretty inspiring to anyone about to undertake what you are - Here's a bit from the site:
Yes, this is the same guy who gets a mention in 'Good Will Hunting' - Back in high school in the early '80s, my math teacher had his picture above the blackboard and began each year by telling us about him - His personal hero.
Cheers,
Jim in Tokyo
-- My Weblog.
Community colleges vary in quality wildly from location to location. I wouldn't trust Burlington County Community college (Burlington County, NJ, where I currently live) with anything more advanced than introductory single variable calculus. On the other hand, the Philadelphia Inquirer did a story a few years back where they had some students attending the University of Pennsylvania come out to Montgomery County CC for a few classes of freshman physics and calculus. The community college students were using the same text as the ivy leaguers, and were proceeding at the same pace. Also, the sudents found the quality of instruction higher at the CC.
As a basically uninformed guess, I'd assume that community colleges in tech. boom areas that do a lot of night-school business are better able to fund the more advanced courses (and hire the better teachers) than community colleges in areas that don't provide lots of night-class business.
Towards the end of my mathematics degree I discovered the greatest secret for ***REALLY*** enjoying and getting into any mathematical subject -- simply ask the other students who there favourite math lecturers were.
In my final year I only took courses that were taught by those individuals which were regarded as gifted lecturers or who could enjoy themselves in class with their students. It was the VERY BEST year I ever had in school and one which even today (15 years afterwards) brings a smile to my face. I have shared this secret with a dozen young students (co-op students, children of friends and co-workers, etc) and each and every one has repeatedly thanked me for it. Ask other students who they really enjoyed being with and why and try to make your decision based on their answers. You might be pleasantly surprised
Of course, some places (like MIT) put their lectures on the web now. You can view Strang's linear algebra lectures on the web--you can't do much better than that (I leave out the link--no need to burden his site, but if you really care, it's easy to find).
There are lots of "mathematical recreations" and "math puzzles" that are fun to try solving, in the same way that it can be fun solving other puzzles. And sometimes you may see a variation on that puzzle that's fun (and truly new). Not all of them are truly critical from the point of view of furthering the advancement of mathematics, but they help develop the mind, and if your purpose is to have fun, start now!
For example, I learned about the ``four fours'' problem as a kid (using exactly 4 fours, create legal mathematical expressions to compute 0, 1, 2, 3, etc.). Recently I created a definitive list of answers for the four fours problem. I also played with various really weird bases. Will these change the universe? No. But in the process I learned more than I knew before, and I enjoyed the process.
If nothing else, if you enjoy the process, you're more likely to continue doing it.
- David A. Wheeler (see my Secure Programming HOWTO)
Anyway, if you're serious about learning mathematics but scared of the cost, go to your nearest University and just sit in on the class. Listen to the lecture, ask questions, take notes, do homeworks, take tests, just don't pay. I teach mathematics at the college level... if a students showed up in my classroom who seriously wanted to learn, but didn't want to pay tuition, I would be more than supportive of his/her presence in my class. A number of my colleagues feel the same way -- learning should transcend economic boundaries. (On the other hand, though, some of my peers in our University's Physics department like the fact that tuition weeds out the middle-aged crackpots with their pseudo-scientific TOEs). For math books freely downloadable online, dig around at http://www.math.umn.edu/~garrett
All the math professors here are great. Lots of applications, of course, but if you pay attention, you can learn a lot of theory as well.
Same at my CC.Instruction is generally focused on application, but if you ask they'll go as deep into the theory as you care to.
One thing I've noticed, though, is that the more focused an instructor is on application, the more the students seem to learn, and that also corelates with a lower drop rate.
Under capitalism man exploits man. Under communism it's the other way around.
Anyway, I can't speak for someone who tackled Calculus, but I picked up a book called "Forgotten Algebra", which starts off really light, and ends up somewhere between where my grade 11 and 12 years left off. I take a commuter train to work and back, which gives me an hour and a half of math joy, and I manage to plug in a couple hours on the weekend.
So far, it's been a very rewarding break from all those programming books I've been cramming into my head. I plan on taking on some trig next.
I'm a self taught geek, and my strongest means of learning has always been books. I thought math might be an exception, and it may be at a higher level, but so far it's worked out excellently for myself. I can't wait to go in to work tomorrow and do more.
I found when I teac someoen else anything I learn it better than the person I am teaching. I learn at least three programming languages. This way I did it in all my math courses when I sit down and try to explain something to someone it sticks better in my mind. Also find someone who is willing to teach you what you cannot understand on your own.
Have fun
For linear algebra, calculus, etc. It's the only way to go. Every problem has integer eigenvalues, the proofs are hard but doable, and it is just about as rigorous as you can get.
It's more important than the bible.
----------
I am an expert in electricity. My father held the chair of applied electricity at the state prision.
Stealing your daughters' textbooks is almost what you want to do. Sit down with (one of) them and ask them what they're doing. Ask them to teach you. It'll be a wonderful learning experience for both you and your daughter(s).
Precisely. There's a taxonomy of understanding called Bloom's Taxonomy:
Knowledge
Comprehension
Application
Analysis
Synthesis
Evaluation
It progresses from Knowledge to Evaluation. Most students really only learn to the knowledge level in class. They memorize for an exam, and that's about it. But anyone who really knows what they are doing has achieved all of these levels of abstraction of understanding.
By working with your daughters and having them teach you, they'll progress to comprehension, they'll have to. You can continue to work with them, and challenge them to show you how things are done - advancing both of your understanding.
And you can do this at almost any age. I challenge my son to explain how he makes certain things out of Legos. He's 4. And he's good at it. And every time he explains how he build a bridge or a car or something, he gets better at it. Sometimes he did something clever, but didn't realize why it was clever until the explanation happens.
It's a good trick in a knowledge workplace as well. Have employees or teams explain what they are doing, how they solved a problem, or addressed a challenge to the larger community. Not only will it build the community and help everyone understand the whole widget, but the presenters will learn a great deal more about what they did and why though the presentation.
Unfortunately, online, Borders *is* Amazon.
Java is the blue pill
Choose the red pill
A mathematician, a physicist, an engineer went again to the races and laid their money down. Commiserating in the bar after the race, the engineer says, "I don't understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run..."
..."
.haeger
The physicist interrupted him: "...but you didn't take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning..."
"...so if you're so hot why are you broke?" asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret.
"Well," he says, "first I assumed all the horses were identical and spherical..."
An chemist, a physicist, and a mathematician are stranded on an island when a can of food rools ashore. The chemist and the physicist comes up with many ingenious ways to open the can. Then suddenly the mathematician gets a bright idea: "Assume we have a can opener
A mathematician is asked to design a table. He first designs a table with no legs. Then he designs a table with infinitely many legs. He spend the rest of his life generalizing the results for the table with N legs (where N is not necessarily a natural number).
A Mathematician (M) and an Engineer (E) attend a lecture by a Physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The M is sitting, clearly enjoying the lecture, while the E is frowning and looking generally confused and puzzled. By the end the E has a terrible headache. At the end, the M comments about the wonderful lecture.
E: "How do you understand this stuff?"
M: "I just visualize the process"
E: "How can you POSSIBLY visualize something that occurs in 9-dimensional space?"
M: "Easy, first visualize it in N-dimensional space, then let N go to 9"
A mathematician, an engineer, and a chemist were walking down the road when they saw a pile of cans of beer. Unfortunately, they were the old-fashioned cans that do not have the tab at the top. One of them proposed that they split up and find can openers. The chemist went to his lab and concocted a magical chemical that dissolves the can top in an instant and evaporates the next instant so that the beer inside is not affected. The engineer went to his workshop and created a new HyperOpener that can open 25 cans per second.
They went back to the pile with their inventions and found the mathematician finishing the last can of beer. "How did you manage that?" they asked in astonishment. The mathematician answered, "Oh, well, I assumed they were open and went from there."
Mathematician U. was a great friend of his five-year old grandson. They discused everything including math and U. was very proud of the boys math talents. The child went to kindergarden; In two weeks the he ask U.to help with the difficult math problem: "There are four airplanes flying, then two more airplanes join them. How many airplanes are flying now? U. was very disappointed by the simplicity of the problem. "What confuses you?" he asked. The child says: " I know, of course, that 4 + 2 =6, but I cannot figure out what the airplanes have do with this!"
These days, even the most pure and abstract mathematics is in danger to be applied.
"The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again."
The shortest math joke: let epsilon be 0
A Neanderthal child rode to school with a boy from Hamilton. When his mother found out she said, "What did I tell you? If you commute with a Hamiltonian you'll never evolve!"
How many topologists does it take to screw in a lightbulb??
Just one. But what will you do with the doughnut?
Q: What's the contour integral around Western Europe?
A: Zero, because all the Poles are in Eastern Europe!
Addendum: Actually, there ARE some Poles in Western Europe, but they are removable!
Noah's Ark lands after The Flood and Noah releases all the animals, saying, "Go forth and multiply." Several months pass and Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" asks Noah. "Cut down some trees and let us live there," say the snakes. Noah follows their advice. Several more weeks pass and Noah checks up on the snakes again. He sees lots of little snakes; everybody is happy. Noah says, "So tell me how the trees helped." "Certainly," reply the snakes. "We're adders, and we need logs to multiply."
Q: What's a polar bear?
A: A rectangular bear after a coordinate transform.
I'm sorry, I just couldn't help myself.
You are not entitled to your opinion. You are entitled to your informed opinion. -- Harlan Ellison
It's almost too bad that I saw this so late. Given how much the math books of John Allen Paulos have entertained me. I really could have done some good karma whoring.
Many of them are about the bastardization of statistics, others not. My favorite is Mathmatics and Humor, short, interesting. Most are similar in that respect and pretty much all of them are written for the layman who doesn't have time for homework. All the ones I have were easy, quick, reads. And some of them I even paid full price for (normally I just pick up interesting looking stuff from half price books).
Most things have a qualitative and a quantitative aspect, the difference between how and how much. Math really isn't any different.
In that way, math with history might intersect with the history of Pi, and the solution of Fermat's Last Theorem (Unlocking the Secret of an Acient Mathmatical Problem, by Amir D. Aczel), both of which have been turned into interesting books.
But why math? Physics can certainly have a similar bent. And there are quite a few books that seek to explain the mysteries of quantum mechanics, and relativity in simpler, less rigorous, and less tedious, terms. Many of them aren't even written by kooks! To say nothing of those books that cronicle some of the more interesting discoveries that are crying to be made into a Nova special if not an actual movie. The book about the COBE experiment, I think it was called First Light, comes to mind. The personal drama is engaging enough to keep someone interested even if one finds the science, impenetrable, which I would think unlikly.
For whatever reason I dislike the vast majority of fiction, so I browse at Half Price Books and buy $30 or so of math and science books.
But it's all about what one hopes to gain. I don't hope to build a supercollider in my back yard, even if I could afford it and the DOE would sign off on it (and they might!). I seek more illumination about the world, and larger universe I get to live in, that, I can get from a book.
--Jimmy has fancy plans; and pants to match.
She went back to evening school, got a Masters degree all while taking care of 3 children (with the help of my dad of course).
A lot of work? Yeah.
A good excuse? Bollocks.
IANAL but write like a drunk one.
To get a good intuition, it is necessary to develop your own math images in your head and to test them against other people and to see how they see/visualize the same theorem. In time, this will vastly expand your toolbelt of techniques and your intuition. If you read one book, you will certainly miss out on conversations with other math enthusiast and will miss the additional input. A small example: I was once in a class where everyone was challenged to present a proof of pythagoras theorem of "a^2+b^2=c^2". I think I saw 7 or 8 different proofs, while I came up with "only" 2 myself.
Once you do have a solid math basis, then working and studying math in solo fashion is possible, although my own experience with complex function theory has taught me that you will learn more then twice as much from studying with other students then going solo.
That said, I can advise the following books for introduction:
- Vector calculus by Marsden en Tromba
- Algebra by Hungerford
- Elementary Topology by Munkres
- Groups and symmetry by M. Armstrong
Good luckI intend to live forever, so far so good.
Firstly sorry I'm posting here, but I should like the original requestor to read this...
Mathematics, at least pure mathematics, is more of a mindset that a knowledge set. It is incredibly hard to learn the mathematical way of thinking from books alone, that said once this mindset is acquired the books are the only thing you'll need.
My advice would be to find yourself a mentor who's willing to assist you in acquiring this mindset, you'll probably be succesful asking around the various maths newsgroups.
You need to be able to interact in real time with this person occasionally, but there is no reason not to do this over IM or IRC.
As for what to learn / which books to read Calculus by Micheal Spivak is an excellent book, it brings in rigour gently and covers all of the main points of analysis. Covering its contents alone would set you up for a college / uni course, though you might also what to get a basic grip of [say] group theory and a very basic idea of sets [doesn't have to be above the venn diagram level]
One word of warning do not let a physicist, on engineer or anyone else who 'thinks' they know maths teach you maths, find a mathematician
My interest is actually in advanced physics, but that requires a pretty serious math background. I went to a local university bookstore and bought up some textbooks on calculus. I also bought books at my local bookstore on calculus, and topology.
I study on my own. I use the internet as a resource, as there are quite a few sites that have tutorials on math.
I tend to learn best on my own, if I have a source of asking questions. Again, the internet comes in handy there. Google Groups sci.math is also a good source for asking questions.
If I feel I have what it takes, my goal is to go back and get a graduate degree in Physics, but it's hard to do when you have a full-time job and other responsibilities. I'll get as far as I can on my own first, though.
Or, if you want to pay the LOWEST price (and don't care which souless corporation you're giving money too), go to bestbookbuys.com. It's a meta-search comparative shopping site that checks 10 or so sites for the book you're looking for by ISBN.
Im a Physics/Economics double major graduating senior, going to gradschool in Economics next year...
I would advise not going for exclusively a physics major, if you're unsure whether that's what you really want to do. Out of all the physics majors i know, very few are in there to actaully do physics research as a career, or many of us start with that intention, then realize how difficult/strange/boring/uninteresting/etc that we think it really is. We have a very large amount of double majors, (Physics/math, physics/finance, physics/chem, some premeds even), where we use the physics courses to teach us how to think, not necessarily for the physics itself.
Unless you really really want to know/study stuff like the boundary conditions of the fields of a conductor in an oscillating magnetic field, I would stay away from physics as a pure major; but if you wanted to do something like a M.S in Physics w/ a PhD in Economics, your analytic skills for something like IndustrialOrganization or GameTheory (maybe even theoretical econometrics) would be awesome.
Don't give my roomate too bad a time. He was basically doing HS over again at community college after royally screwing up when he was younger. You gotta admire someone who realizes they made a mistake and actually goes out and tries to put things right. I know a lot of people who are content to just take easiest path down. This guy on the other hand was trying and succeeding at pulling himself out of the hole he was in. He was also working his butt off with two jobs and school at the same time.