What are some good books on number theory, combinatorics and probability for beginners - people who haven't studied calculus yet? There must be some really clear, *fun* books like this. But I don't know them! Someone needs them... now! Thanks. https://twitter.com/kid_wolfe/status/1186417111054184449 …
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Replying to @johncarlosbaez
A Friendly Introduction to Number Theory: https://amzn.to/31AEiXl Integer Partitions: https://amzn.to/33PQyEH Proofs that Really Count: https://amzn.to/2J8YwkA Probability Theory: A Concise Course:https://amzn.to/2MyKzyg
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Replying to @johncarlosbaez
Oh, yes, absolutely. They're pedagogically sound. I'm especially fond of Silverman and Andrews/Eriksson. Another book worth considering is "The Magic of Numbers" by Gross and Harris: https://amzn.to/2BxUBtg
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Replying to @MathPrinceps @johncarlosbaez
(A small point, though: I'm not warranting any of these books as the solution to the specific problem posed by the person who applied to you for advice and recommendations. I don't know what sort of "math club" he or she has in mind, but such things make me a little queasy.)
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Replying to @MathPrinceps @johncarlosbaez
How well does the 'Integer Partitions' book explain how the Rademacher formula is derived? I ask because I've had Tom Apostol's on modular functions since last week, and I am finding his chapter on that topic tough sledding. (Not giving up on it yet, though.)
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Replying to @HiramPurkeypile @johncarlosbaez
The Integer Partitions book attempts no proof of the asymptotic formula for the number of partitions of n. The intended audience for this book is more or less complete beginners, and the asymptotic formula requires some pretty subtle calculus (specifically, the "circle method.")
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Replying to @MathPrinceps @HiramPurkeypile
Neat! Of course my request was for books that assume no calculus, so this will be too hard for the intended kids. But it sounds good for me.
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Let me be clear: the "Integer Partitions" book assumes NO CALCULUS. Even the infinite series it includes and discusses are really just formal power series. It is essentially an algebra book, readily accessible to smart high school students (and even smart middle-schoolers.)
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The same is true of Silverman's book, and of the book by Gross and Harris.
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