Must Have Math Books(That aren't "Text Books")

[E01]

I was thinking about adding to my collection of math literature and I was wondering what you all consider must have reading material. I just recently got Math It's Contents, Methods, and Meaning and the Princeton Companion to Mathematics. I was thinking things at that level of must have (I might include Polya's How to Solve It as something that's pretty up there to).

 

[RLBrown]

Mathematical Thought from Ancient to Modern Times, Vols. 1,2 and 3 by Morris Kline

 

[Ackbach]

The Art of Mathematics. Also, Mathematics in 10 Lessons has to be good, though, unlike the first book, I haven't read it.

I agree with RLBrown, and would simply add that anything by Morris Kline is good. Polya's great. There's a really fun successor to his book: How to Solve It: Modern Heuristics, by Michalewicz and Fogel. I enjoyed that book very much.

 

[E01]

Thanks for the suggestions. Do you think those sorts of problem solving books can actually make a significant difference in one's problem solving skills?

 

[Ackbach]

That's a great question! I would say yes, to certain aspects of problem-solving. Problem-solving, to my mind, sort of has two parts. One part is discipline in learning a standard toolbox, what I call the "administrative side" of problem-solving. "What percent of 40 is 30?" kinds of problems. This can, and most definitely should, be learned thoroughly. Books like the How to Solve It books can definitely help you learn this side of it.

The other side is the imagination, easily the most important faculty a good mathematician can possess. For more difficult problems, you may be able to set it up, but to finish, often it's required simply to "see" the solution. You need your imagination for that. The imagination will not be trained merely by reading books like How to Solve It. The best way to train the imagination, hands down, is to read great books. I'm talking here about Jane Austen, Charles Dickens, Leo Tolstoy, Mark Twain, etc. I've mentioned only books in the Western canon. Naturally, there are great books in other traditions as well. Reading trains the imagination. Watching TV, movies, or playing video games, to my mind, can have a tendency to weaken the imagination. Beware the TV! It will not give your imagination a workout, precisely because it provides the images for you. You need to engage in activities that force you to come up with your own images. That's the literal definition of imagining.

So, to sum up: read How to Solve It, and the like. http://mathhelpboards.com/advanced-applied-mathematics-16/advanced-problem-solving-strategies-421.html I've posted on general problem-solving strategies that you might find helpful - really just a pointer to various resources. Then you should read great books, ones that stretch you. Don't read the latest thrillers, at least not exclusively. Read the great books.

 

[Math Amateur]

I was thinking about adding to my collection of math literature and I was wondering what you all consider must have reading material. I just recently got Math It's Contents, Methods, and Meaning and the Princeton Companion to Mathematics. I was thinking things at that level of must have (I might include Polya's How to Solve It as something that's pretty up there to).

If you are interested in gaining an understanding of algebra, then it helps to gain some understanding of the history of algebraic thought ...

Some books that may help you in this quest are as follows:

"From Cardano's Great Art to Lagrange's Reflections: Filling a Gap in the History of Algebra" by Jacqueline Stedall

"Modern Algebra and the Rise of Mathematical Structures" by Leo Corry

"The Beginnings and Evolution of Algebra" by Isabella Bashmakova and Galina Smirnova

"Taming the Unknown: A History of Algebra from Antiquity to the Earliest Twentieth Century" by Victor J. Katz and Karen Hunger Parshall Peter