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.

books...

[Yodason (526266)]

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.

Re:books...

[bmwm3nut (556681)]

6 easy pieces is cut from the full "feynman lectures on physics." this is a great series of books. unfortunately they're quite expensive, but they are lectures that feynman gave to an incoming group of physics majors at cal tech, so they start of very basic. if you're looking to get just a basic understanding of physics and a little chemistry and biology thrown in for fun, try reading volume 1 of the lectures. volumes 2 and 3, while great references for physists are probably not great if you're just trying to understand concepts. but if you have the money, there's no reason not to buy the whole set. and as the parent said, all of feynman's books are great (beware, some of them are high level graduate level books). i also recommend the feynman lectures on computing.

Re:books...

[cybermace5 (446439)]

I just wanted to reply concerning the cost issue. If you find something you think will work, and can learn easily from it, it's worth the price. You'd be surprised what a good foundation of scientific principles can do for you, at work and at home.

It's not only the facts you know about things; those give you the ability to carry on a discussion with a specialist in any given field. It's also the process of discovery and fact-checking. Every time you work a problem, or follow the progression of a historical great discovery, you teach yourself how to apply your natural curiosity in a productive way. Invaluable.

Re:books...

[JonathanBoyd (644397)]

I misspoke. Being lazy with my words. He certainly understnad the stuff well, but I didn't find it particularly useful for learning the stuff from. Found other textbooks much clearer. I think they're good to go back and look at once you've learnt a subject and have some understanding of it, but in my experience, they just don't cut it when it comes to learning for the first time.

Re:books...

[MuParadigm (687680)]

I like the Feynman books as well, but I'd start with "Surely, You're Joking Mr. Feyman" first. The reason I say that, especially if you want to share them with your kids - I'm assuming they're about adolescent in age - is that I find it's easier to develop an understanding in these subjects by hearing stories in them first, then moving on to more theory-oriented works.

For math, I'd recommend:

G. H. Hardy - A Mathemetician's Apology
E. T. Bell - Men of Mathematics (some people have problems with this book in terms of historical accuracy, but I'v always found it a lot of fun)
Courant & Robbins - What is Mathematics? (nice grounding in general theory)
Nagel & Newman - Godel's Proof
Georg Cantor - Transfinite Numbers
Alan Turing - On the Computable Numbers (fantastic essay, don't know where you can find it though)
J. E. Thompson - Algebra / Calculus for the Practical Man
Silvanus Thompson & Martin Gardner - Calculus Made Easy

For physics:

Feynman - QED (Quantum Electrodynamics)/ The Character of Physical Law
Galileo - Two New Sciences (Much more readable than you'd think)
Fermi - Thermodynamics / Elementary Particles (these might be a little too technical)
Brian Greene - The Elegant Universe
Einstein - Relativity / The Principle of Relativity / The Meaning of Relativity / The Theory Of Brownian Movemnent

Highly Unrecommended:

The Tao of Physics - Fritjof Capra
The Dancing Wu-Li Masters - Gary Zukav

I cannot emphasize enough how lousy these last two books are. I can't understand why they are still in print. Atrocious new age speculation.

Re:books...

[Hatta (162192)]

I'd add to the math list: 1, 2, 3... Infinity. by George Gamow. Also to the physics list: Einsteins Theory of Relativity by Max Born. A wonderful primer on relativity using nothing more than HS algebra.

Calculus

[rblancarte (213492)]

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

Totally on the mark

[ebuck (585470)]

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.

Re:Totally on the mark

[Joey7F (307495)]

Area of a sphere? 4 pi r ^2...no calculus needed ;-)

Of course a (an astute) calculus student would notice that when you derive the volume formula for a sphere (4/3 pi r^3) with respect to the radius you get the area.

My dad is an engineer (I will be too soon...hopefully ) and he has a novel way of find an oddly shaped area.

As long as what you are looking at has a scale of some kind you can actually cut out that area and weigh it on a (sensitive) scale. Then cut out a known square dimension from the same paper. Now you know what that area is relative to a certain weight...well now finding the original area just takes a little knowledge of proportions.

Granted it is not exactly going to score any points in the rigorous category, but it will get the answer with uncanny accuracy, which is the only category engineers have anyway :-P ::silence::

Yeah I am lucky they don't have -1 geek as a moderation...

--Joey

Areas of Odd Shapes

[BigBlockMopar (191202)]

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.

Learn How To Prove Things!

[kramer2718 (598033)]

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.

math:

[Pandora's Vox (231969)]

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

Hawking

[endquotedotcom (557632)]

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

[DarkVein (5418)]

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'll second that, and I'm an engineer

[John Jorsett (171560)]

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.

Infinity

[rf0 (159958)]

One article that I found interesting A Guide to Infinity [kuro5hin.org]

Rus

Isaac Asimov

[Esion Modnar (632431)]

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...)

ArsDigita University

[by Anonymous Coward]

You might check out some of the materials on display at ArsDigita University [aduni.org], 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.

Math texts

[plalonde2 (527372)]

Math texts rarely manage to give insight into what's going on at a level sufficient to solve problems. The reason is that it's hard to get the insight until you understand the mechanics, and hard to want to get the mechanics without an understand - a nasty education catch-22.

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.

I disagree.

[bgalehouse (182357)]

I could never do that. I need the explanation of why and always have. Quite frankly, I can't be bothered to learn facts without understanding. Furthermore, I claim that this need to understand relationships is absolutly key to being a scientist or mathematician.

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 [wff-n-proof.com].

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 [canonicaltomes.com] I made a few contributions when it first started, and would assume that it has only grown.

Re:I disagree.

[dillon_rinker (17944)]

I could never do that. I need the explanation of why and always have.
I doubt that. Ever learn to eat? Or walk? =)

I'll acknowledge that you are much more motivated to learn the WHAT if you've a notion that a WHY will follow, but I'd suggest that you CAN'T learn the why without first learning the what. For example...in 1776, the United States declared its independence from England. Why, you ask? It's impossible to explain WHY without first explaining WHAT occurred in the years leading up to 1776. I'm not sa

Re:Math texts

[Monkelectric (546685)]

I can't speak to high school, but at my university courses like calculus, physics and chemistry were "flunk courses". Courses designed to fail a maximum number of students. The professors had *NO* interest in making the subject interesting or accessable. As a whole the university (UCR) had a graduation rate of 60%, whereas the engineering college had an horrific graduation rate of 30%.

There are several reasons for wanting to fail students, the most frequently mentioned is that theres "not enough room" in the upper courses. But the real reason is they are simply elitist bastards, they figure, "I had to go through it, you do to." The worst abuse I ever saw was a chemistry course I was in. 250 Students, the teacher spent the entire quarter lecturing about the heart medicine he was working on, and how steel refineries worked (his other interest). No problem -- if the tests are on heart medicines and steel production, but, he gave standardized tests and flunked 90% of the class.

Flunk courses also create some strange strange acedemic relationships. For instance, I was getting 15s and 16s (out of 100) on my physics tests and, with the curve I was getting a nice fat C. The problem with this is two fold ... It sounds great right? get a 15 and get a C? First problem, I'm not getting the education I paid for. Secondly, it encourages cheating because all you have to do is "beat the curve". The thrid and most intriguing problem deserves its own paragraph.

For me to get a C with 15 out of 100 points. That means, about HALF of the students scored worse then me. The students who scored WORSE then me *financed* my C by getting D's and F's. If they weren't the cannon fodder, *I* would have failed the course. Now here's where things get tricky. Sometimes, you are the sacrifical lamb, and sometimes you are the priest. If you are the lamb, you take the course over -- but this time you're the priest because you've taken the course before and it's finally starting to make sense. So the first timers are competing on a curve with people who have taken the course before. This wouldn't be a problem with a normal distribution of scores, but with poor instruction causing scores to center around 15%, that advantadge *REALLY* counts.

So now that I've written a diseratation here, what I really mean is, in your post you assume that mathbooks are even designed to help students, when most of the time, they aren't.

Re:Math texts

[Maul (83993)]

I took a physics course at UCSD in a similar vein. The mean wasn't quite as bad, though as 30-35% was the average on most quizzes. The professor often went out on tangents, etc. and deferred all questions to his T.A., who was just as disinterested in teaching a bunch of Freshmen and Sophomores.

I got a B in the class, something which was difficult to comprehend considering that I never got above a 50% on any of the tests.

Looking back, though, it just depends on the prof. I took other physics classes whe

Re:Math texts

[drlock (210002)]

The reason is that it's hard to get the insight until you understand the mechanics

I agree, I just finished 3 years of college level Calculus and Differential Equations. I found that I didn't really get Calc I until I was in Calc II and it didn't all come together until Calc III. Grade wise I did great in all three, but the 'why' of it all took a while to build. The more you use/practice it the more you will begin to connect the concepts and really understand.

All that said, don't be discouraged fro

For mathematics highly recommend 2 books

[dydxjessedydt (590130)]

"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")

Most Universities...

[OS24Ever (245667)]

...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.

What is Mathematics?

[Monkey-Man2000 (603495)]

I just got a copy of this and it seems really good so far. It also got good reviews on Amazon [amazon.com].

Suggestions for Math and Physics

[CBNobi (141146)]

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 [sciam.com] - 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 [mcgraw-hill.com]
Research & Education Association's Problem Solvers series [rea.com]
CliffsNotes [cliffsnotes.com] and SparkNotes [sparknotes.com]

textbooks are references, not teachers

[SuperBanana (662181)]

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.

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).

University Book Store

[UniverseIsADoughnut (170909)]

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.

Anything by Douglas R Hofstateler.

[bons (119581)]

A list of his books [fetchbook.info]

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.

I learned plentyfrom my teachers...

[erroneus (253617)]

...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.

Re:I learned plentyfrom my teachers...

[michael_cain (66650)]

This comment raises a good point -- different people learn things differently. Some do well by reading, some do better if they can listen. What situation fits you best? While I can learn and have learned math strictly from a textbook, I find that it is easier when I can listen to someone doing the explanation while I look at the figures and/or equations. If you're a person who needs to listen, definitely look into a local community college. Try to find out about the instructor first, though -- I've se

John Allen Paulos

[kurosawdust (654754)]

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.

My favorites

[digitalhermit (113459)]

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.

My High School Math Program (IMP)

[Not Quite Jake (315382)]

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.

Good suggestions for Math Textbooks...

[Pollux (102520)]

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 al

Godel Escher Bach - An Eternal Golden Braid

[Cordath (581672)]

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?

Find a tutor/mentor

[Ninja Programmer (145252)]

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. :)

A Realistic Approach

[AdamHaun (43173)]

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!

Really good ones for Math

[photon317 (208409)]

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.

Isaac Asimov's Realm of Algebra

[lamz (60321)]

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.

Gonick's "Cartoon Guides" (Seriously)

[NoData (9132)]

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.

popular science reviews

[danny (2658)]

You might find my popular science book reviews [dannyreviews.com] useful.

Danny.

"Forgotten Algebra" and "Forgotten Calculus" by...

[Sergeant Beavis (558225)]

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.

Re:Calculus Texts

[digitalhermit (113459)]

"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 o

Re:The Dover Books

[digitalhermit (113459)]

The mathematical/physics books put out by Dover Books are decent. They give you a good overview and background of the subject. The subjects range from Number Theory, Information Theory, Magnetism, Mathematics, Physics, Probablility,etc.

The Dover books are usually inexpensive, and some are good references. As a text for the non-mathematician, they're probably inappropriate. What they do cover is usually in depth but also don't pull punches. For example, the opening chapter of "Modern Algebra" jumps directl

COMMUNITY college is not about education.

[HanzoSan (251665)]

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.

AC what exactly are you talking about?

[HanzoSan (251665)]

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 d

Calculus Made Easy by Sylvanus Thompson

[BigBlockMopar (191202)]

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:

• Sylvanus P. Thompson's 1910 classic Calculus Made Easy is still in print and remains as relevent as ever. It's funny ("To Deliver you from the Preliminary Terrors" is the title of the first chapter) and it's full of interesting tidbits. (Do you know where the time units of minutes and seconds got their names? [glowingplate.com]) Hit Amazon.com or Bibliofind to get a copy.
• Applied Calculus - an Intuitive Approach is great, too. Faber, Freedman and Kaplan. Starts with First Principles and takes you to fairly advanced integration in an easy-to-read format.

Remember: Do the problems, succeed. Don't do the problems, fail. It's that simple.