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
 
For the following four books, has anyone used them in a course or for self study? Compiler Construction Principles and Practice 1st Edition by Kenneth C Louden Programming Languages Principles and Practices 3rd Edition by Kenneth C Louden, and Kenneth A Lambert Programming Languages 2nd Edition by Allen B Tucker, Robert E Noonan Concepts of Programming Languages 9th Edition by Robert W Sebesta If yes to either, can you share your opinions about your personal experience using them. I...
Hi, I have notice that Ashcroft, Mermin and Wei worked at a revised edition of the original solid state physics book (here). The book, however, seems to be never available. I have also read that the reason is related to some disputes related to copyright. Do you have any further information about it? Did you have the opportunity to get your hands on this revised edition? I am really curious about it, also considering that I am planning to buy the book in the near future... Thanks!
I’ve heard that in some countries (for example, Argentina), the curriculum is structured differently from the typical American program. In the U.S., students usually take a general physics course first, then move on to a textbook like Griffiths, and only encounter Jackson at the graduate level. In contrast, in those countries students go through a general physics course (such as Resnick-Halliday) and then proceed directly to Jackson. If the slower, more gradual approach is considered...

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