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Science and Math For Adults?
Peter Trepan writes "Like most Americans, I made it through high-school and college without a thorough understanding of major scientific and mathematical concepts. I'm trying to remedy this situation both for personal betterment and so I can supplement my *own* kids' education. The problem is, most textbooks are not designed to convey an understanding of the subject, but to squeeze in all the 'facts' required by state law. I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science?" This is similar to an earlier question, but with a broader focus.
Feynman has 6 easy/not so easy peices on physics... I enjoyed those. On A whole I will recomend any of his books... Math I'm not sure... I'd like to try and find a math book (that teaches you as much as a text book) thats not as dry as one... For calculus for the easy stuff Learn Calculus the easy way is a interesting concept, its taught through a story.
zero, the biography of a dangerous idea by charles seife (sp?)
the god particle, by leon lederman
the particle garden, by someone whose name i can't remember.
good math and good physics. enjoy!
-Leigh
Try enrolling in some night classes at your local Community College if you have the time. It's pretty cheap, and you may be able to get your employer to pay for it.
Stephen Hawking's "Universe in a Nutshell" is a good start on physics and relativity. I've never taken any physics and was able to understand it fairly well.
Calculus Made Easy by Silvanus P. Thompson and Martin Gardner. This is exactly the sort of book you're looking for, in the subject of Calculus. To quote from the preface, on the subject of modern math textbooks: Their exercises have, as one mathematician recently put it, "the dignity of solving crossword puzzles." The purpose of this book is to explain the philosophy of Calculus, and teach you how to differentiate and integrate simple functions. I recommend reading the Preface in a bookstore, skimming the first few chapters. I think you'll like it.
I'm as mimsy as the next borogove but your mome raths are completely outgrabe.
One article that I found interesting A Guide to Infinity
Rus
Cheap UK and US VPS
Any of his non-fiction books, and there's a ton. All subjects, from algebra to the brain to chemistry. (He even wrote about the Bible...)
They say the first thing to go is your penis. Well, it's either that or your brain. I forget which...
You might check out some of the materials on display at ArsDigita University, they have lectures online and a critique of each course, together with a list of texts...personally, Sispser's text for Theory of Computation was very helpful in explaining a lot of the higher-level CS Math.
The solution that most math texts take then is to give you *lots* of problems/drills so that the mechanics get ingrained, allowing the insight to come later.
When I screwed up my second year calculus course *really* badly (like 6% on the midterm...) I used a Schaum's Outline to get back on track (and eventually ace the final). It's main benefit is *heaps* of problems to work through. That made me a convert to the problems approach to math teaching.
The key is to do all the problems, in order.
That said, I can't really recommend one math text over another, just so long as there are lots of problems, and hopefully a solution key in the back for at least half the excercises.
"Foudations of Mathematics" by Denbow and Goedicke (old, but an amazing book for the understanding of most math concepts) "Mathematical Sorcery" by Clawson (More of a "evolution of modern math concepts")
I've always found it easier to learn something when I know the history of how/ it was developed.
For math, I can definitely recommend "A History of Mathematics" by Carl Boyer
For Physics I would recommend the Feynman lectures highly. In these, he mixes theoretical development with modern application.
Not sure what to tell you about chemistry or other sciences!
KRL
...teach some form of 'Math 002' or Science 101 of some kind. Find your local university and see if they have a weekend/evening program (if you're working) and then go to it, work hard. reading books for betterment is a good thing too, but sometimes it helps to have someone to talk to about it.
As a rock-in-roll Physicist once said, No matter where you go, there you are.
I just got a copy of this and it seems really good so far. It also got good reviews on Amazon.
This post was generated by a Cadre of Uber Monkeys for Monkey-Man2000 (603495).
There are "for Dummies" books that cover many of the topics you've listed. I was never fond of them, but you may want to take a look at them.
The biggest problem when you're undertaking a self-study endeavour is that most books that are available are either
- Very specialized topics (What does pi mean?)
- Refresher-course books (Lots of problems, few explanations)
The specialized topics books - commonly reviewed in magazines such as Scientific American - are fun to read, but I'm not sure if they serve the purpose of what you're seeking.
How much of algebra do you know? If you can look through the table of contents of a textbook for Algebra I and II and are confident in all the topics, then I'd move on to geometry/trigonometry before calculus.
Also, keep in mind that conceptual physics texts are divided between algebra-based and calculus-based reasoning. Take whichever you're more comfortable with.
Some 'refresher-course' books that will come in handy with the conceptual books that others may suggest:
Schaum's Outlines
Research & Education Association's Problem Solvers series
CliffsNotes and SparkNotes
The problem is, most textbooks are designed to be companion references, with all the 'facts' squeezed in so the teacher can spend time helping everyone understand the concepts etc. The two work together.
Simple answer is, you need to take adult education classes. I left college barely half-way through, and ended up taking night classes- intro to calculus was one; another was an intensive Economics class. I found them worthwhile; I probably would have enjoyed the class more if I wasn't young enough to be most of the other student's kid(you would fit in FAR better, from the sounds of it.)
Without the classes, you don't get the benefits of peer learning, in-class interaction("Did everybody get that?" [blank stares] "Heh, ok, let me explain it a different way...") the discipline that testing creates, nor the resource of having a Really Smart Person(professor) to go to when you need help. There are also other benefits- making friends(you're probably all in similar 'boats' so to speak, so people socialize pretty readily), and networking. My old boss decided to do part-time classes for an MBA, and got a lot of networking out of it(granted, those were business classes, more prone to networking activities, but you get the idea).
Please help metamoderate.
Go to the nearest university book store, or even just find the web page for a universities math department and find the text book for the subjects you want and order it online.
I don't think very many text books just give you a equation and say use this. My HS was a poor ass sucky redneck school and didn't do that, we just didn't have much of a variety in subjects. Also I think saying books just do what the states require only applies to states with said systems. Many, maybe most, just say you need to have a class in this that and the other thing.
Also once you get into learning the hows and whys of lots of math you will see why people tend to just want the equation, far less frustrating and confusing for learning. Learning how to do it and then going back for the why is often better for subjects like math. Same for say engineer, it seams a whole lot more fun till your actualy doing it and find out 99% of it sucks big time and is not what you think engineers do.
One book to stay away from if calc. is you game is Thomas Finny, that book sucks beyond belief.
A list of his books
Since what you're looking for is about as broad as the universe, I figured I'd point you to the man who set me straight back in 8th grade. Godel, Escher, Bach not only taught me much about the arts, sciences, and mathematics, but it rekindled a passion for learning that the education system had done it's best to beat to a pulp. And that's a passion I still have today thanks to him.
No Zen is good zen
...and very little from the books.
I suppose it depends on the type of learner you are, but frankly, I imagine seeing and using the information being delivered to me. Rather than simply "knowing" the things I learned, I understood them and used what I learned to add more peices to the puzzle I call "reality."
In more simple terms, everything you (should have) learned should be assimilated into the way you operate within your environment. Ever heard "you use it or you lose it"? There's a lot of truth to that.
Rather than try to get what you missed from books, perhaps it's time to make a much more grand display by going back to school. It doesn't have to be thought of as "remedial" but rather as a "brush-up" or simply continuing education. If you show your children that learning only ends when you die, their minds will be open for life with the expectation that they can grow and improve themselves at any point in their lives... not just during the beginning phases. By the time they reach it, "middle aged" will be 50-something anyway.
Best advice? Go back to school and pay attention this time.
Mastering Technical mathematics, by Norman Crowhurst A Tour of the Calculus, by David Berlinski The Calculus Tutoring Book, IEEE The Feynman Lectures in Physics (3 vols), Richard P. Feynman Asimov on Chemistry, Asimov on Physics, by Isaac Asimov e - The Story of a Number, by Eli Maor I didn't get much education in high school, and ended up supplementing many college textbooks with the books above, among others. For Calculus, there is a book called "The Concept of Limits" that is an excellent guide to the first hurdle encountered by students of calculus, but I can't remember the author. Good Luck!
A Tour of the Calculus is a particularly comendable book. It only covers the more basic tenants and theorems of Calculus, but gives you an immense sense of the power behind such theorems and of the near-glacial process which has formed them and the calculus as a whole. Reading it gave me a much deeper understanding of the particular topics it covered, as well as the Calculus and math in general.
~metal_llama out.
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move every sig!
I hope I spelled his name correctly - read his books Innumeracy and Beyond Numeracy, excellent introductions to practical mathematics and advanced mathematics, respectively. I tutored math in college, and by *far* the best way I have found to explain calculus to students who "just don't get it" is using Paulos's "driving on the turnpike" analogy.
In each book, there is a bibliography of the sources that it used, in case you want to do additional research on the subject.
As an added bonus, each book is less than $15, and they can be picked up at any Barnes & Noble. So its worth picking up to see if you are interested in a certain subject.
Hope it helps, I've enjoyed them.
010_digital_100
I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science.
This is broad. My own list that you might find useful (or not):
algebra -- a good introduction is Earl Swokowski's "Fundamentals of Algebra and Trigonometry". It's often available in used book stores, campus book sales, etc.. It is a text book, though, and you may or may not enjoy this method of learning. If you want more of an overview of math, take a look at Paulos' "Innumeracy". If you want some lighter reading, try stuff by Martin Gardner.
calculus -- builds upon algebra so you need to know your algebra, especially limits, before you tackle calc. Know the limits well because it will help in many ways. I often refer to Elliot Gootmans' "Calculus" from Barron. For fun, also try "A Tour of the Calculus". Many chapters in "A History of Pi" are interesting (and approachable) also. Stay away from the Dover books until you have a pretty good grasp. They're cheap, but their approach is sometimes a little heavy-handed.
physics -- Feynman's "Six Easy Pieces".
For general reading, also try:
Godel, Escher, Bach (Douglas Hofstadter)
Islands of Truth (??Ivars Peterson??)
BTW, I'm a big proponent of using mathematics software as an addition to traditional study. There are programs such as MuPAD, GnuPLOT, Octave and Maxima that are available for free that can really help in the understanding of concepts. Many people are more visual so a graph is eminently useful.
The math program I was a part of in high school, at Whitney Young Magnet School in Chicago, was called IMP, or Integrated Mathematics program but it could have just as easily stood for Interactive Mathematics Program.
Basically the way it was structured was that instead of the traditional math program where one learns algebra the first year, geometry the second, trig the third and then moves onto precal, we learned a litte bit of each every year.
Furthermore, instead of them just shoving facts down our throat and saying here, memorize these (such as all the proofs from traditional geometry) we were actually guided along in discovering them for ourselves.
Every problem was given to us in word problem format. Each unit, which represented a major concept such as the quadratic equation or some of that other stuff, was presented as one big word problemm and it was broken up into smaller pieces which slowly led up to the solution of the actual problem.
So instead of coming out of it with simply memorizing the quadratic equation, pythagorean theorem, pi, geometric proofs and the like, we were actually able to discover these on our own.
It's just too bad the teachers weren't all that great and the program didn't much fit into the "flash/bang" you need to know this information right now that most high school classes are based around. God forbid students actually understand and can apply the information they are learning.
I also can't seem to recall who published the books we used but I'm sure a bit of googling can solve that.
Douglas Hofstadter won a pulitzer for this little gem. This is a fantastic book to read for anyone remotely interested in the mathematical principles behind some of the more glamorous aspects of computing. Hofstadter's "Achilles & the Tortoise" dialogues are a frequently hilarious tribute to Lewis Carol that remain some of my most favorite things in print.
If you're lacking a basic understanding of algebra then this book may be a tad over your head, but if you can get into it you will find it immensely rewarding.
P.S. Algebra? ALGEBRA?!!?? You made it through college without algebra?
"Keep in mind that during the 80s-90s (I think), there was a revolution of sorts in the way calculus was taught in colleges. Professors supporting this reform movement wanted students to understand the concepts instead of memorizing the formulas."
The concept of "new math", and the resultant ill effect on thousands of mathematics students, was a corruption of some really good ideas. There's no doubt that some bureaucracy was at fault in this madness. They took the idea that mathematics students should not only think about the "how", but also the "why", and corrupted it into the notion that students really don't need to learn their multiplication tables or memorize trigonometric identities. It was tried before in the 1800's, the 1900's, and recently in the 80's and early 90's. Every single time the message of learning "why" got corrupted.
Given that you, yourself, are not very math/physics savvy, text books alone may not be enough. You might easily end up in a situation of the blind leading the blind when trying to help your kids. Understanding math/physics will often go beyond what any textbook can tell you. You might do a lot better from a person you can interact with who can see how well you are grasping a concept.
:)
If you literally want to go to the trouble of hiring a tutor, then you'd get him/her for your kids obviously, but I don't know what to recommend for adult education. Given the current economy I'm sure the tutor might be willing to help you out as well in a package deal.
Real math involves proofs. In fact, for mathematicians that is the definition of mathematics. The rest is "just" application. Since the original poster is complaining about the lack of explanation why, I suggest that he look into proofs and other creative aspects of real mathmatics. If you haven't learned that math is a creative art you haven't learned jack. Ok, so I'm opinionated, but this is slashdot and what else is new.
Anyway I suggest that anybody of any age interested in math check out equations and wff-n-proof from the wff-n-proof people.
Regarding books, he had a vague request so I'll make some vague suggestions. Springer Verlag publishes lots of great mathbooks, as well as quite a few not so great. Some of them I can even read, and they do have a some series and books advertised for undergraduates. Look for yellow in any self respecting University library or technical bookstore.
Actually, going through a university library or bookstore is probably the best advice I can give under the teach a man to fish philosophy. Learning to go through a stack and pick out books that are readable but challenging is basically the secret to scholarhood. That and faith in the fact that once you've ground through one the rest will be a smidgen easier.
Oh, and you can also check out the math section of Cononical Tomes I made a few contributions when it first started, and would assume that it has only grown.
For what you do, it might be useless, but for people in Engineering and other fields, calculus is a VERY important subject. As a current CS major, I agree with what you say about descrete math and linear algebra, but I think you are discounting the need for Calculus.
RonB
It is human nature to take shortcuts in thinking.
What is the point of avoiding difficult but important classes simply to preserve your GPA? Are you in school to get an education or to simply achieve some arbitrary GPA? I've been in the position of hiring people for technical positions and I've always been far more impressed by a mediocre GPA in a substantial curriculum then a high GPA in an easy curriculum.
I recently returned to school myself, so I do have sympathy with amount of work required to do really well in a course, and I do understand that those planning to continue to a four year school or go on to graduate school need to match minimum requirements, but in my opinion you'll be better served by reducing the number of classes you take in a given term then by trying to ditch the challenging courses.
Speaking of slackers, what's with this question? Right, everybody wants to be Ptolemy, 'cause It Is Good To Be King. Except when the revolution is coming for you, dragging a frehly greased Guillotine to enliven the show. But most of you probably don't have clue number one what this bit is all about either, do you? Of course you don't! You're Slack-dotties, you can't be expected to have learned anything in school. You spent all your time trying to pretend you weren't in school, fuckheaded idiots that you were. I was like that too, but back in my day they'd tie you to the desk and keep you after school until... well, no, they didn't really do that. And that cliche about the rulers and your knuckles? Hardly ever. Really. Of course they didn't HAVE to rap most kids across the knuckles to get their attention back then. No one with that million-miles-away glazed look that says hey yeah, I like school so much better when I stuff the earbuds in and crank the mindless, mind-shredding noise up. Anything to avoid having to use the mind you've spent half your life trying to lose, right Slackies?
You young pukes make me sick!
But that's not what I came here to sing about. No, I came to sing the praises of some Good Books. I did see a few nods to Feynman, and a few of his essays are simple enough for even Slackdots to get the feeling that they sort of understood, or at least appreciated, whatever exactly he was going on about. But mostly you gotta have math, and to get math you gotta WORK AT IT.
'cause there still ain't no bloody god-be-damned royal road to mathematics. No Easy Street slide for slackers, neither.
You want to learn calculus? I mean learn it well enough to be able to start to learn about how it (and some harder maths as well, but calc will get you in the door of understanding; arithmetic and its yuppie cousin algebra just let you turn the cranks that were designed by people who had the chops) truly is the language of science, which ain't just a cute turn of a phrase, though it is that, but it's like a real, no false analogies here, metaphor for the way our understanding of the entire fucking universe has developed over the last few centuries. As oppposed to how you slackwits have closed your minds to any deeper understanding than the ability to catch a fly ball, and that, though you haven't the understanding to know it, has more to do with a few eons of evolutionary development of your central nervous system than it does with your brain, so called.
So You Want To Learn Math And Science?
Get thee to your community college; odds are damned good that they'll have the courses you need to fill in those gaps in your mental toolkit. Of course it's harder now - old brains are less flexible than young, but if you've reached the point that you can see the utter stupidity of your younger self who squandered those golden years, learning to be a twit instead of something worthwhile, something that might be useful for more than impressing your half-drunken friends that you're a wit - it's half true, after all - why, at that point you might be about to find that maturity does bring some compensation for the things you have to give up getting to it. If you haven't blanched and run away yet, back to your comfortable, mindless, slacking drift through life, you may be able to find the gumption to exert yourself and go to school in order to learn what you missed the first time around.
I mean, the odds aren't very good - if you're reading this, you're probably in the slacker half of the population, more inclined to rant and rail on the
Karukstis, Kerry and Van Heck, Gerald. Chemistry Connections: The chemical basis of everyday phenomena. (ISBN: 0124008607)
Anything in the Commentaries on the Fascinating Chemistry of Everyday Life series by Dr. Joe Schwarcz:
On the topic of calculus, don't learn anything past calculus I (well, bits of calculus II are useful). The rest is completely useless and you'll forget about it all in a couple of years anyway because of its uselessness. If you want something that's useful go for discrete math and/or the good bits of linear algebra. Your comment is completely offbase. Actually, Linear Algebra is about as important as Calculus in many scientific/engineering disciplines.
More importantly, you claim that anything more advanced will be forgotten, but the later courses often serve to reinforce earlier material. For example a course on Fourrier theory reinforces both Linear Algebra and Calculus.
Most math departments have a course somewhere after the introductory sequence which teaches basic proof techniques often by studying the definition of numerical systems from logical axioms.
These basic proof techniques are the very basis of mathematics. The reason so many people get through high school with little understanding of math is that they are never forced to do any proofs outside of Geometry.
In short, if you cannot prove anything, you know practically nothing about mathematics.
http://yetanotherpoliticalrant.blogspot.com
Concepts of Modern Mathematics - Ian Stewart
Mathematical Mysteries -- The Beauty and Magic of Numbers
He proceeds in explaining the interesting connections numbers play in our world similar in which Paul Hoffman portrays in his book, Archimedes' Revenge, except without so much of the story-telling. Semi formula book but can be read without the slightest clue of understanding them.
[rant]
I believe Stephen Hawking to be extremely overrated. I picked up one of his books at a bookstore and threw it done in utter disgust. I personally have a bitter dislike of dumbing everything down for the layman and glitzing all the empty space with fancy graphics...okok, that is a bit harsh as I think his books are great for children.
[/rant]
Anyways for the highschool/college folk crowd I definitely ever so highly recommend
People go to community college to transfer into a good university and get cheap credits, not get an education.
If they wanted me to focus on an education perhaps they wouldnt make the GPA so damn important.
What is the point of avoiding difficult but important classes simply to preserve your GPA? Are you in school to get an education or to simply achieve some arbitrary GPA? I've been in the position of hiring people for technical positions and I've always been far more impressed by a mediocre GPA in a substantial curriculum then a high GPA in an easy curriculum.
Ok say I do take a few math classes and get a few Cs, well then my GPA goes under 3.0 and I can forget about transfering into a good 4 year university, I can also forget about scholarships and grants which also require a high GPA of above 3.0 or 3.5, I really cannot afford any Cs and I know for a fact that its simply impossible for me to get an A or B in math. I take classes which I know I can/will get an A or B in.
This isnt about the jobs, this is about getting a degree from an elite private university.
I recently returned to school myself, so I do have sympathy with amount of work required to do really well in a course, and I do understand that those planning to continue to a four year school or go on to graduate school need to match minimum requirements, but in my opinion you'll be better served by reducing the number of classes you take in a given term then by trying to ditch the challenging courses.
I never take more than 4 classes per semester, and I never get anything below a B in grades, those are the rules I follow.
Maybe if universities werent so strict and competitive on the GPA issue I could actually focus on learning but right now I have a goal, that goal is to get into Harvard, Tufts, Boston College,Boston University or North Eastern, all which are ELITE private universities which will NOT let you in with a sub 3.0 GPA, you most likely wont get in with a sub 3.5 GPA, so no its not about "learning" right now, its about moving up the ladder, it will be about learning once I get into university, thats when I'll take math clases, get a C or two, and learn something.
If you use Linux, please help development of Autopac
I confess that I made it through 3 semesters of college calculus and an engineering degree pretty much not understanding the underlying concepts of calculus. It's surprising what you can accomplish by rote. This book was a real forehead-slapper for me, and I can't recommend it highly enough. Many years after graduating, I've finally learned what I should have back then. If it were up to me, this would be the first book anyone learning calculus ever read. I wish Sylvanus Thompson were still alive (I think Calculus Made Easy was published in 1919) so I could give him a big smooch.
While I'm sure that the people recommending GEB and Hawking have your best interests at heart, they're answering the wrong question. If you want to learn math, you're going to have to start at the beginning and work your way up. "Popular" math and science books won't help you with the basics.
What you'll want to do instead is what they do in school. Start with some basic number theory(nothing fancy, maybe just enough to know the difference between integer/real/rational/etc). After that, assuming you understand how to add, subtract, multiply, and divide, you're going to want to get into some basic algebra, then calculus, then geometry or whatever else you want. Unfortunately, I learned algebra way back in middle school so I don't have a textbook to name, but I do have some advice that applies at all levels:
* Do the problems in the book. Then do some more. Then do even more, just for good measure. Some of the other posters have complained about doing problems. Ignore them. Nothing will give you a better feel for how algebra and calculus work than actualy *doing* them.
* Understand each piece of information before you move on and how it relates to the whole. Any decent textbook should offer problems that use both new and previously gained knowledge. Make sure your textbook of choice has lots of examples and that those examples are worked out well. Never underestimate the value of a fully worked out problem. It may be worth it to get multiple textbooks, look them over, and then return the ones you don't want.
* Be persistant. Children learn math by doing it every(other) day for years. You're an adult. You can learn faster and better, but that doesn't mean you get to be lazy. Do a bit every day, even if it's just working one or two problems. Daily practice will ingrain concepts in your brain and also make it easier to pick up a book and start on something new.
* Don't get too formal. Wanting to know "why" is great, but "why" must often take a backseat to what is being learned. Often, the reason for doing something may not be obvious until you already know how to do it.
* Have I mentioned doing problems?
Now I do have one actual book to name, and that's:
Calculus by Larson, Hostetler, and Edwards
This book has tons of examples and illustrations, as well as excellent problems. It even features a two chapter algebra/pre-calc review!
Some people have mentioned the calc book by Stewart. We use that book at my college, and given the number of people who seem to have problems with it I cannot recommend it for self-teaching.
Good luck!
Visit the
Mathematics for the Million - Lancelot Hogben
ISBN: 0-393-31071-X
(This ISBN is from a 1993 printing of the 4th (last I believe) edition, originally published in 1895. The first edition was circa 1862).
This book is hands down one of the best adult math texts around, as shown by how it has endured over time. It covers all the practical branches of math one should know including calculus, and starts out at a very basic level. Throughout it explains the real meaning of the math, this is not a fact memorization book at all.
Also, if you're further interested in calculus, I'd recommend:
Calculus Made Easy - Silvanus P. Thompson and Martin Gardner
ISBN: 0-312-18548-0
(Original by Thompson was from 1851, the ISBN here is an updated version (by Martin Gardner) published in 1998).
Covers (again, with real explanations, not memorization of facts) the real meaning and understanding of calculus, both differential and integral.
11*43+456^2
Calculus is INCREDIBLY important, and from a philosopical point of view it might even be dangerous. :)
Imagine a field of mathematics that explicitly has at it's underpinnings the hypothesis that as you break up a line into smaller segments, eventually if you make each segment have no length, they still all add up to a lenght.
Philosopy aside, it's an INCREDIBLE tool for particular applications. Need the area of a sphere, no problem. A cone, still no problem. An oddly shaped object that looks like a art-deco running shoe? BIG problem, that is unless you use calculus.
I read Isaac Asimov's Realm of Algebra when I was in grade 6, and didn't learn anything beyond it until around grade 10. Actually, I didn't even finish reading Realm of Algebra -- if I did, who knows how many grades worth of math I would have learned in one sitting!
Unfortunately, it is out of print, and has been for some time. I have seen people asking outrageous sums of money for it used, upwards of $300 U.S. This is truly a book that is crying out to be open-sourced/pirated. Maybe someone who owns one would scan it into a tidy little pdf or something. Do the same to Realm of Numbers too.
Mike van Lammeren
It will challenge your head, your brain, and your mind.
I have found Larry Gonick's "Cartoon Guides" charming, accurate (if sometimes kinda understandibly rushed), and very compelling. Gonick is most famous for his "Cartoon History of the Universe," but he also has a "Cartoon Guide to Physics" and a "Cartoon Guide to Statistics" among other science titles. It's perfect for the adult novice and the young student as well. The cartoons illustrate abstract concepts visually, while maintaining a great sense of humor and fun.
The parent poster points to one of the few well-developed Mathematics textbook series that offer students a braod understanding of mathematics. If you are looking for a textbook series that actually let's you understand why the math works the way it does instead of just accepting it as truth, then I have one of two suggestions. Both of these series were actually rated as exemplary by the Untied States Department of Education.
IMP: Integrated Mathematics Program. IMP (as the parent poster said) takes all the mathematics taught in high school and blends it together in a format which is VERY GOOD at showing how mathematics develops logically. Subjects are not isolated lessons which involve repeated "practice of skills." Each lesson involves only two or three (at most) complex math problems which are set up specifically for students to do so that they can learn why math works. The only thing you may want to consider though is that this textbook series does not specifically say how the math works; only by actually doing the lessons does one gain an understanding of the math involved. If you're looking for a more direct detailing of the math, I would suggest this next series.
CPM: College Prep. Math. This textbook series is divivided into the traditional "Alg. I, Alg. II, Geom/Trig, Calc" classes, though it too does a very good job of making each lesson a logical progression of the last two or three (in fact, it actually gives a "guide bar" at the end of each chapter showing how much each "portion" of Alg / Trig / whatever has been conceptually developed). The biggest difference compared to IMP however is that it explains what the mathematics is doing as it develops in the textbook. Also, there are a lot more practice problems. One drawback is that the book is not the most reader-friendly...many of the text pages are rather cluttered, plus the book is only printed in black & white.
By the way, avoid the Saxon series like the plague. If you want to know why, or if you want to discuss anything else about what I've mentioned, just drop me an email.
(And if you're wondering, I am a Math teacher...this isn't just another geeks advice that you're getting.)
In my own experience (from grade school math through grad school math), I have almost always found that the texts aren't terribly helpful until *after* you've learned (at least to some basic level) the mathematics. In one of the posts above, SuperBanana notes this problem, and suggests that you try adult ed courses. I agree that the human interaction with a professor and fellow students can be invaluable. In fact, some of the biggest mathematical ah-ha moments I've had have been when I've been trying to work through an idea with friends. Only then did the stuff in the textbook really make sense.
... and how to find them before the teacher does
Now, that's not to say that there aren't good books out there to help you learn about mathematics. It's just that the ones that are written as textbooks (particularly in the traditional theorem-proof style) don't seem to be written with a learner in mind. By presenting all of the mathematics in a *mathematically* logical progression, many of them end up hiding the kinds of thinking that has to happen in order for someone who doesn't already know the math to learn it. After all, mathematicians don't do their work by smoothly going from stating fixed definitions to giving a theorem with proof- there's a lot of work going on there that we don't see in the formal presentation. I should be careful, though, not to exaggerate. Most textbooks try to give some exposition to help the reader along. However, this usually doesn't do enough to change the fundamental problem of structure that comes with using the mathematically logical sequence to guide the organization of a book intended for learners.
You may find that some of the newer so-called "reform" materials may be closer to what you are looking for. Many of them do make an explicit effort to focus on the ideas and concepts underlying the mathematics (though some complain that they don't focus enough on developing fluency with procedures). The trick with these is that, when used in schools, they generally work best with teachers who themselves have this kind of deep understanding and thus know where the materials are pointing. There has been quite a bit of venom circulating around these newer materials. My suggestion is to try a few different kinds of materials in both the "traditional" and "reform" styles, and see what works for you.
So, here are a few suggestions of books that I found useful in making sense of mathematics, its ways of thinking, and how it can relate to the world. The first several aren't really textbooks, but rather books about mathematics.
Philip J. Davis & Reuben Hersh - The Mathematical Experience
George Polya - How to Solve It
John Allen Paulos - A Mathematician Reads the Newspaper
John H. Conway & Richard K. Guy - The Book of Numbers
Barry Cipra - Misteaks
The Calculus Consortium at Harvard has developed several textbooks, including Functions Modeling Change: A Preparation for Calculus (Eric Connally, Deborah Hughes-Hallett, Andrew Gleason) and Calculus, Single and Multivariable (Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum)
Mr Tompkins in Wonderland and Mr. Tompkins Explores the Atom are both fictional narratives that demonstrate relativity through greatly exaggerated examples-- apparently Mr. George Gamow has written an umber of other physics books as well.
They're fun to read, and definitely helped me in high school AP physics.
I would recommend Mas-Colell, Whinston, and Green's "Microeconomic Theory" and Obstfeld and Rogoff's "Foundations of International Macroeconomics" Both presume only a limited background in mathematics (and economics) and have generous explanations of the mathematical tools being used.
Sig (appended to the end of comments you post, 120 chars)
Danny.
I have written over 900 book reviews
Not everyone by birth is a genius at math, some people must work for YEARS to get the B in math.
"If you can't even get a B in a community college undergraduate math class,"
I'm not a Math person.
"you're not going to make it at Harvard or any truly "ELITE" university, private or not. Sorry."
Thats exactly why I wont major in math or science at Harvard.
"Getting a real education takes work on your part, not simply gaming the system for least effort per credit or slapping the right label on a bogus degree. It's not something other people do to you, it's something you do for yourself."
I am working, but I also know the system is not a very fair system, and the system does not reward hard work, it rewards those who "game" the system. So yeah I could learn math, get a C in math, have a bad GPA and never get into an elite private university, or I can get a good GPA, find some way into an elite university, and then take the math classes when I'm there.
I see no reason why I should take them now and get bad grades now when my grades actually matter when I can get bad grades later. And what you said doesnt make any sense, you act like a person must get a B in every single class they ever took in college, we all know that this is very unlikely as most people are humans who have strengths and weaknesses. I might get a C in Algebra and Calculus, but I'll never have to take those two classes again once I actually go ahead and do it, so for you to tell me that because I cant get a B in calculus that I'll never be able to handle university is pretty ignorant, I mean sure if I were majoring in math and science you'd be right, but I suppose you didnt do a good job looking at the list of possible majors which do not require you take tons of math classes.
If you use Linux, please help development of Autopac
http://www.math.com/
http://homeschooling.about.com/cs/math/index.htm?t erms=math
http://homeschooling.about.com/cs/science/
http://physics.about.com/
What is Science?
Even on the off chance that the About network doesn't have all the information you need, they have a large number of links to sites with relevant information across the Web, so there's a very good chance that you will be able to use them to find what you are looking for.
Also...although these are not strictly an answer to your question, I would still heartily encourage you to follow the links to these (listed in a suggested order of reading...my probably misguided opinion only) text files, web pages, and books, as I think they could be of enormous benefit to both your children and yourself...indeed, anyone who wishes to read them. Although I understand that several of these could possibly only be understood at tertiary level, they also as far as I know are not normally included in *general* curriculums, and IMHO they should be.
It used to be in the past that the education systems of most nations didn't want us to know the why (philosophy, religion, history, political theory) of life, but were content enough to let us know the how. (Science without analysis, numeracy and literacy skills, etc) Now however we are seeing that primarily in America, but also in other places, government education departments no longer even want to allow people to know the how.
Mathematics is part of the how - a means to an end, a way of solving problems - but it is not a destination in itself. The material I've given you links to in my second section is concerned with finding out *why* - "Why am I here? Who am I? How do I know what reality is? What do I want to do with my life? What moral values do I believe in?"
The answers to these questions are far more important than becoming merely literate or mathematically capable for their own sake. Figure out what your purpose is first, and the rest, although still requiring work, will be relatively easy. That is what the links in the second list will help you do, and it's not something you'll be taught to do in any contemporary public school, either...Governments consider people with purpose to be highly dangerous.
Barbara Lee Bleau Ph.D. are excellent books. I was in a similar situation in that I decided to go back to college at age 32. Being that I was educated in Louisiana (worst in the nation) I never was properly taught many math principles. I was very fortunate when friend pointed me to these books. Both book start under the assumption that your math understanding is at an elementary level (basic addition, subtraction, multiplication, and division.) It is a truly great teaching guide and workbook which was so successful for me that I passed the math placement test at The Univ. of North Texas and will be taking Pre-Calc this semester. As for physics, I have seen several great books recommended so far. I'm reading Dr. Hawking's book right now.
There is nothing inherently safe about liberty. That's why so many people died protecting it.
Physics: The Human Adventure, Gerald Holton and Stephen Brush
Nice, historical look at how well known physical concepts of today were discovered.
Physics for Scientists and Engineers, Paul Fishbane and Stephen Gasiorowicz
First few chapters good if you have a basic knowledge of calculus. For the later chapters (ie, Electricity and Magnetism, basic quantum mechanics) good idea to have a calculus book handy, I reccomend
Calculus: Early Transcendentals, James Stewart
First chapter is a good review of algebra, precalculus, and analytical geometry. Through chapter 7, fairly straightforward. Chapter on sequences and series is kind of fuzzy, though it mostly makes sense.
Hope this helps!
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Okay, I'm going to overlook the fact that the primary poster of the thread is pursuing personal edification, and not a particular educational track, so the fact that grades are given doesn't seem to be a relevant concern in his case.
Let me see if I can be helpful in this sub-thread. I'm an adjunct faculty member at a community college, I've taught for going on two years now. I'll speculate that I'm teaching in the same region you're going to school, based on the 4-year institutions you're looking at.
If I could give one crucial insight to my students, that I usually have to bite my tongue on, it's this. 4-year schools have expectations which are an order of magnitude beyond those of 2-year community colleges. My biggest challenge in teaching now is to take my experiences at a 4-year (state) school and dial them way down to a level where my students can pass the course, with some getting A's. Maybe my two best students in a class of 20 seem to be doing work that would be appropriate at a 4-year school.
I would encourage you to not shy away from any courses at a community college. The hardest class in your school will be just a taste of what you'll be asked to do at any 4-year school. You need to find this out about yourself, if you can function at this level, sooner rather than later. If you're worried about passing a math course at a community college, the honest truth is, Harvard is not in the cards. My guess is that a school like Harvard is not going to distinguish much past "4.0 or not 4.0?" when looking at a GPA from a community college.
Not to say that other colleges you mention are not a possibility. I write quite a few recommendations for my students to go to Northeastern and BU, but even those are generally just my "A" students.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
Guidelines:
1. If you really want to understand mathematics, stay away from suggestions made my engineers; in particular, eschew books that dumb down mathematical theory in favor of the 'this is how you compute the solution' approach. Silvanus Thompson I find to be especially egrigious in this regard (those who try to learn calculus from Thompson will never understand the rigorous notion of a Limit, which is hardly pedantic since the derivative is itself a limit and the Riemann integral is the limit of a Riemann sum).
2. Be patiant with yourself. Geometry, Analysis (which includes what is called calculus) and Algebra have required centuries of constant effort to develop. If you go for the 'fast and cheap' approach to learning it, you will aquire nothing more than skills, when what you really want is knowledge.
Books:
Preliminary topics: Before you can think, you must memorize certain things and learn other things by rote. This will be hard and painful, but these fundamental topics are to mathematics as the alphabet and grammar is to Shakespeare, Milton, and Joyce. They are: the notion of a function, the laws of exponents, elementary trigonometry (sine, cosine, tangent, and their inverses), the binomial theorem, the definition of a polynomial, factoring polynomials, setting up applied problems in algebra, linear equations and their graphs, simple nonlinear equations and their graphs, slope and area, the Pythagorean Theorem. Most of these basic noitions are covered in Forgotten Algebra (which is published by Barrons for people just like us, and College Algebra, by Michael Sullivan.
Fundamental Notions:
By fundamental notions I mean ideas that form the basis for other ideas. Mathematics is all about definitions, and definitions are all about ideas; you cannot learn complicated ideas without understanding basic ideas (if you don't believe me, try explaining why every vector space has a basis to someone who doesn't understand what linear independence is). Unlike preliminary topics, fundamental notions are actually fun to learn--you get to think instead of just memorize and drill! I know of one wonderful book for this sort of thing, for someone in your position:
1. A Tour of the Calculus, by David Berlinski. This will make you think about what 'continuity' is. Good preparation for calculus, which is all about continuous functions, and good because it presents mathematics as a branch of philosophy (which it is).
Single Variable Calculus
Single variable calculus is where you will find most of the major concepts in the subject; the next time you will think this much is in linear algebra, when you study why the derivative for a n-dimensional vector space is actually representable in terms of matrix multiplication (the derivative is a linear map.) Here are some good books on calculus:
1. Calculus, Thomas and Finney. This text features a superb fusion of theory and application. The exercises are challenging, but doable for an independent student, and solution guides are available (these are indispensable as you search, at 2AM, for the mistake in your integration by partial fractions problem that required nine pages and is off by a constant).
2. Calculus, by Michael Spivak. My favorite calculus book. A brilliant synthesis of upper division real analysis and run-of-the-mill calculus. Reading it is like feeling awestruck by the beauty of someone you have known for years and years. This also has a solution manual (which you will need, because here there are proofs).
Advanced Mathematics
Don't stop learning math just because you
"Oh, the tragedy of math gone wrong. I can't even talk about it." -Wil Wheaton http://www.wilwheaton.net
A much better book is Riordan's, The Hunting of The Quark.
George Gamow's One, Two, Three... Infinity is an irreplaceable classic combining the author's deep understanding with jokes and whimsical stories about numbers and physics. An absolute joy, one of my favorite books since age twelve.
Sigmund
For a literate and entertaining look at the concepts of calculus, I highly recommend David Berlinski's A Tour of the Calculus. It won't teach you how to solve problems, but it will teach you the concepts behind limits, differentiation, and integration along with the important theorems and their proofs.
It is or is not accurate.
;)
That's an old indian trick; a statement of totalogy
--Joey
is 'Mathematics for the Millions -- How to Master the Magic of Numbers' by Lancelot Hogben. ISBN 0-393-30035-8.
If you are looking for a book that explains why the various matematical properties and axioms are what they are, only a text for a graduate degree course would explain that stuff. However if you are looking for a "why'd they do that" then this book is for you.
Originally written in 1937 this is an awesome book. I found this book a godsend while I was in college. It is basically a history of mathematics. By giving a historical perspective, most of those mathematical "WHY" questions get answered because you can see how the mathematics evolved step by step.
It covers the basics: how numbers developed and why, how geometry developed and was used, how trigonmetry sprang from geometry, how spherical geometry/astronomy came from applying trig to navigation problems, how improvements in technology linked motion to geometrical figures that could be described by algebra, and how problems in describing motion lead to the developement of calculus. Throw in statistics being developed to try to predict games of chance for good measure.
The material is layed out with quite a bit of detail and has plenty of examples and diagrams.
With this book under your belt, much of the reading suggested by others will be far more understandable.
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The key to really mastering these subjects is to have a good teacher.
By all means, get some of the books recommended by fellow Slashdot readers. I'm familiar with many of them and a lot of them are great.
But at some point, no matter how good the books are, you'll get stuck on some point - and that's where you need to find a good teacher you can turn to. It doesn't have to be someone you see in person - someone you correspond with via email or over the phone would be fine.
It doesn't have to be someone with any sort of credential - but ideally it should be someone who is either currently a student (studying math/science at a much higher level than you) or someone who uses these subjects in their work. The main key, though, is to find someone who really loves math/science, and someone who's really patient.
I love helping people who really want to understand math or science. It gets old fast if the person just wants to know how to get the right answer and doesn't care why. If they really care, and they're really patient enough to take the time to learn it really well, then I'm always more than happy to take the time to help. It's fun! I really love it when the light bulb comes on in somebody's head! (Feel free to email me - I'm great with Trig, Calc, & Discrete Math.)
How to tell a good student: The bad student asks, "how do you solve this problem?", but the good student asks, "I tried to solve it this way, but it didn't work...why?"
How to tell a good teacher: The bad teacher, in response to the good student's question above, responds, "that's the wrong way to solve it; here's the right way". The good teacher responds, "interesting approach - let's figure out why it didn't work".
The best piece of advice I can give anyone trying to learn from a textbook is to tell them to work through the problems. Anyone should be able to pick up many of the textbooks listed below and work though as many of the problems as time allows (limited either by patience or by real life events). Most textbooks provide answers to selected problems, so you can check your progress.
Absolutely, 100%. Nobody is born with the ability to take a triple scalar product or multiply two matrices (both happening in your video card when you're playing Doom!). As a great Calculus teacher once announced to his class through a thick French Canadian accent, "Math is not a spectator sport." (Actually, it came out as "Matt ees not a spectator sport.")
Having said that, Calculus is my favorite kind of math. It's incredibly elegant and probably the most useful advanced math, as it touches everything you do. Consider your car. If you calculate your speed using a watch and the odometer, you have an idea how fast you were going, but your speedometer is actually showing you the value of the derivative at any instantaneous time. Your speedometer shows the rate of change of position (distance travelled) at any instantaneous time. That's calculus.
Don't be afraid. "Calculus" (besides being a formal term for tartar the dentist scrapes off your teeth) means small stones in Latin... small stones as used for counting.
Two *great* books on the subject:
Remember: Do the problems, succeed. Don't do the problems, fail. It's that simple.
Fire and Meat. Yummy.
Math is a very important thing in High School... But not in the way that a lot of you think... There are two uses for math in High School...
1) To teach the concepts of basic math and calculus.
2) *The most important* To exercise the students
brain and to keep them mentally alert.
When a student graduates from school it is a huge shock to them because the world is a lot slower then it is in school (at least it should be if they were working hard). Suddenly you don't have home work every day... You don't have tests every week and there are no such things as exams... Work is very much different. Now some businesses do testing on there employees... but it's not as bad as school...
When you drop math... you drop creativity, the ability to learn other subjects, to stay focused, and most importantly... to stay curious...
--
There I finally was smart enough to save this as plain text lol.
How. I understand the area under a graph is the intergral of the formula of the graph, but if you have an everyday shape, chances are its not created by a known mathematical formula. how do you work out the area using calculus?
Ahh... Now we discover the joy of Infinite Series. Infinite series allows you to do all sorts of things to (arbitrary) precision. (Arbitrary in that it won't spit back an answer to 300 decimal places unless you make the program you write run through the loop 300 times...)
Basically, here's the idea. You can do a regression of the known points on the graph to come up with a function (formula) to describe the relationship. Regressions come from infinite series, but are used in a plug-and-play format in statistics courses. Also annoyingly, Excel 95 and up includes the capability to do them in the Data Analysis tools, OpenOffice does not yet [grumble grumble]. Anyway, once you have a function, you simply integrate it to find the area.
My favorite part of all this is that the series usually gives you a nice long sum of little polynomial expressions, which are individually and collectively easy to integrate.
Practical applications? Fourier Transforms and Fast Fourier Transforms. They allow you to express any function (audio waveform?) as a sum of different overlapping sinewaves. From there, you can do all the math you want on them. MP3 and Ogg codecs do this.
Fire and Meat. Yummy.
For maths you might want to try the books of Ian Stewart.
The desire to understand the world and the desire to reform it are the two great engines of progress -- Bertrand Russell
ISBN: 0-19-513427-3, 1998, Oxford University Press. This is a concise and readable summary of the history, philosophy and theories of science. I had a bit more science and math education than you claim, but it was a long time ago. This book really helped me to appreciate the accomplishments of those who contributed to the scientific endeavor. It won't teach you the particulars of any one of the sciences, but it will help you to put them all into a context for further study.
Hopefully someone will find these interesting:
CALCULUS
Quick Calculus by Kleppner and Ramsey.
This book is designed to teach you step by step all the calculus you would learn in 2+ semesters of college calculus classes. It is workbook style. That is they teach you something and then have you work individual problems. I tought myself calculus in 10th grade by using this book.
PHYSICS:
The Feynman Lectures on Physics:
I've only read volume 1 but I have 2 and 3 queued up. These are good for getting an understanding of how and why physics works if you know a fair amount about calculus and you've taken some physics (high school at least). THESE WILL NOT teach you how to solve physics problems (as far as I can tell they don't publish the problem set anymore).
Schaum's Outlines: Physics for Scientists and Engineers by Michael E Browne
This one will give you practical problems to solve and practice with, plus a concise explanation of topics that Feynman blew past you too quickly.
STATISTICS and DATA ANALYSIS:
It's hard to recommend anything specifically here because it's a hard subject to teach and I've never found a great book.
Principles of Statistics by M.G. Bulmer (dover)
It's an inexpensive paperback and it gives a very good overview of the basic concepts of statistics.
An introduction to error analysis by John R Taylor
I haven't read this book but I've had it recommended. If you want to understand why you need to be skeptical of numerical data, you at least need to know something about this subject.
Statistics for Experimenters by Box Hunter and Hunter
This is another one that's supposed to be a great book. If you want to do experiments and analyze the results you need to study this subject.
MATHEMATICS:
Mathematics books are often aweful, and what makes a good mathematics book is very personal (ie. your learning style), so here's a general list of subjects and why you should study them.
Calculus and differential equations Without calculus you can't do physics effectively. see my recommendation for Quick Calculus above. Differential equations are effective for modelling the behavior of physical systems.
Linear Algebra This topic forms the basis of several important fields, such as signal processing, statistics, differential equations, and much of numerical analysis.
Topology This is a field that will teach you more about important properties of functions, and of sets. It's basically about invariance: properties that do not change when you transform something (continuously)
Combinatorics or discrete math This is about counting, probability, and sequences of numbers. It's entertaining and important for computer science.
AS FOR MATH BOOKS:
The thing to know is that there is a huge variability in math books. I'd recommend starting with cheap Dover paperbacks and trying several in a particular field. Once you've exhausted those (either too poorly written or too complicated for you) at least you haven't spent a lot of money.
If you need more after the Dover paperbacks, move on to something hardback and expensive but sit down in the book store and read through it first. Does the author take pains to explain things, or just use a flurry of symbols?
Remember you can't start at the top. Work your way up a mathematical subject, preferrably with some application or core reason that drives you.
((lambda (x) (x x)) (lambda (x) (x x))) http://www.endpointcomputing.com a scientific approach to custom computing.
Just wonder if there are any good online sites that can help adults who aren't fortunate enough to have the opportunity to properly learn math, science, or whatnots that most think are _basic_skills_ ?
Thank you !
Muchas Gracias, Señor Edward Snowden !
One of the subjects that really put it all together for me was Linear Algebra. It doesn't require calculus so much as a certain mathematical sophistication. The book that made it interesting for me was "linear algebra and its applications" by Gilbert Strang
All generalizations are false, including this one. Mark Twain
I wonder if there are good books on math and physics for game developers?
O'Reilly publishes a book called "Physics for Game Developers" and Charles River Media publishes a book called "Mathematics for 3D Game Programming and Computer Graphics." Both are quite good.
I happen to like Stewart's Calculus with Vectors book. Covers from precalc (quick review) all the way through 3-d vector calculus. Lots of problems and decent examples. I used this book as an undergrad to learn calc, but even as a grad student I often find it invaluable as a reference.
Don't become a regular here, you will become retarded. -- Yoda the Retard