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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
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
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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.
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
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?
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.
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.