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

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The discussion centers on essential reading materials for math literature enthusiasts, highlighting key titles that contribute to a deeper understanding of mathematics. Participants recommend foundational texts such as "Math: Its Contents, Methods, and Meaning," "The Princeton Companion to Mathematics," and Polya's "How to Solve It." Morris Kline's works are also praised for their value. The conversation emphasizes the importance of problem-solving books, noting that they can enhance specific skills but should be complemented by reading literature to foster imagination. Engaging with classic novels is suggested as a way to develop creative thinking, which is crucial for tackling complex mathematical problems. Additionally, historical perspectives on algebra are mentioned, with titles that explore its evolution and significance in mathematical thought. Overall, the thread underscores the balance between technical problem-solving resources and imaginative literature for a well-rounded mathematical education.
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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).
 
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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?
 
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.
 
E01 said:
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
 
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TLDR: is Blennow "Mathematical Methods for Physics and Engineering" a good follow-up to Altland "Mathematics for physicists"? Hello everybody, returning to physics after 30-something years, I felt the need to brush up my maths first. It took me 6 months and I'm currently more than half way through the Altland "Mathematics for physicists" book, covering the math for undergraduate studies at the right level of sophystication, most of which I howewer already knew (being an aerospace engineer)...

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