19 votes

What books are like Knuth's Surreal Numbers?

Flatland by Edwin Abbott Abbott It's a story about a 2-dimensional being's encounter with a three-dimensional being. (Well, there's a class(?) allegory at the beginning, but you can skip that.)
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19 votes

What books are like Knuth's Surreal Numbers?

Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter is a book about Mathematics, Art, Music, Computer Science and Artificial Intelligence. It alternates story chapters and descriptive ...
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12 votes

Extremely "hard" books (or handouts) for undergrad studies

My pick would be Volume 1 of Richard Courant and Fritz John's Introduction to Calculus and Analysis. For discussions of how Courant/John compares with Spivak, Apostol, and other books, see the math ...
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12 votes

What are some great books for exploring mathematics? (not kids' books and not textbooks)

For a recent suggestion, check How Not to Be Wrong by Jordan Ellenberg. Lying in the "simple and profound" quadrant, the book also gives deserved attention to Condorcet, in addition to providing a ...
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11 votes

Problem books at undergraduate level

There are certainly many more. The following list is not meant to be exhaustive but meant just to give you a selection of the many more books that you have missed: Halmos: Linear Algebra Problem Book,...
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  • 577
11 votes

Inspirational Mathematics Books for Teenager

If you looked at those other topics, you saw the links to the books page at my blog, Math Mama Writes. There are a number of books there that would work for a teen. One of my favorites is Carry On, Mr....
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10 votes

What are some great books for exploring mathematics? (not kids' books and not textbooks)

I highly recommend Paul Lockhart's Measurement
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  • 905
10 votes

Teaching math in an engaging way

One recommendation that I have also given in response to similar questions, check out Jo Boaler's edX course: How to Learn Math for Parents and Teachers. It's currently in progress, but I'm sure it ...
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  • 7,385
9 votes
Accepted

Books that every aspirant mathematician should read

Here goes nothing. I have many other suggestions that are not listed; there is always one more example of a great math book: "The enjoyment of Mathematics" H. Rademacher, O. Toeplitz. You can't beat ...
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9 votes

What is a good book to learn all of prealgebra?

This California college has a no-frills $602$-page textbook available for free PDF download: College of the Redwoods Mathematics Prealgebra Textbook. 2012-13. (PublisherLink). There was a free ...
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9 votes

What books are like Knuth's Surreal Numbers?

Math Girls! It gave me a small taste of generating functions, and I want more! Very challenging math. Surreal Numbers might be the best way to learn about Conway's system. Math Girls does not have ...
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  • 17.3k
9 votes
Accepted

Material on tutoring university level math classes

I am very fond of the book by Steven G. Krantz, How to Teach Mathematics, published by the American Mathematical Society (AMS), now in its 3rd edition. The book is mostly aimed at professors and ...
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9 votes
Accepted

What are examples of math-themed sci-fi appropriate for students?

On the off-chance you don't know about it, I recommend looking through entries at Alex Kasman's website Mathematical Fiction. This has been around quite a while. I don't know when I first learned ...
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8 votes
Accepted

Recommendations for inquiry based/aided discovery textbooks

I am going to copy and paste my answer from another question on this site, because I think one would be hard pressed to beat it in terms of the number of suggestions it covers, and the general quality ...
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  • 455
8 votes

Recommendations for inquiry based/aided discovery textbooks

Check out http://jiblm.org. There are lots of scripts here, some better than others. A nice book in this style is "Distilling Ideas" by Brain Katz and Michael Starbird. I also recommend the ...
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  • 5,877
8 votes

Books that every aspirant mathematician should read

Two very good books, inspiring autobiographies: 1) "A mathematician grappling with his century", by Laurent Schwartz. Another great french mathematician. This book is even better, in my opinion than ...
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  • 81
8 votes

Books that every aspirant mathematician should read

I recommend How to Solve It by George Polya. I merely glanced at it in high school and it helped me to work on math problems. More recently I bought it and now read the whole thing annually, and it ...
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  • 2,496
8 votes

What does it take to find a good math book for self study?

Permit me to recommend the answers to this MO question: Are there other nice math books close to the style of Tristan Needham?. The emphasis here is on readable, interesting expositions, a rather ...
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7 votes

''Deep'' maths books

I think of myself as a "geometer" so let me try to offer suggestions for books that I take to be entries to geometry at different levels. Let me first mention that geometry is a huge field and I tried ...
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7 votes

How to teach calculus (book recommendation)

There are so many Calc 1, 2, and Multi video lectures online now. Watch a few... take notes on what you think are some good traits of the person teaching. MIT's Calc course (super fast) might be ...
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7 votes

What books are like Knuth's Surreal Numbers?

The Diamond Age, a science fiction novel by Neal Stephenson, includes a subplot that involves mechanical Turing machines that are described in great detail and that are used in solving key puzzles ...
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  • 221
7 votes

Inspirational Mathematics Books for Teenager

"(Books in German or with German translation are a plus)" and "she is particularly interested in geometry." The OP's notes suggest: Ziegler, Günter M. Do I Count?: Stories from Mathematics. CRC ...
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7 votes

What do I study in calculus beyond the minimum required for undergraduate engineering?

There is a big old textbook Advanced Engineering Mathematics by Kreyszig. Maybe looking at its table of contents HERE will show you what mathematics he thought was useful for engineering students. (...
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  • 6,211
7 votes

What does it take to find a good math book for self study?

If you're looking to fill in a deficient high-school education then I might recommend the OpenStax series, which has free, open-resource books for everything from arithmetic through calculus and ...
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7 votes

Textbook to study group theory as a part of Discrete Mathematics

The list of topics you want to study corresponds rather to abstract algebra than group theory. You did not say why you are interested specifically in group theory, but I believe that acquaintance with ...
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  • 249
7 votes

Introductory book or other resource on $p$-adic numbers/number theory/analysis

A few recommendations: Fernando Q. Gouvêa's $p$-adic numbers: An Introduction. This text gives a good introduction to the $p$-adic number system and the properties of the space of $p$-adic numbers, ...
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6 votes

Books that every aspirant mathematician should read

As a counterpoint to Polya: The psychology of invention in the mathematical field by Hadamard. As much as we all love Polya, Hadamard's study indicates that mathematicians don't often think in ...
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  • 5,877
6 votes
Accepted

Teaching a very enthusiastic and bright 5 year old

I would recommend "math enrichment" instead of straightforward math acceleration. (1) Here is one source from the US Florida school system: Math SuperStars (a.k.a. Sunshine Math). It covers grades K-...
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