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20 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 ...
Stig Hemmer's user avatar
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.)
David Steinberg's user avatar
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....
Sue VanHattum's user avatar
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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 ...
Sue VanHattum's user avatar
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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 ...
Daniel R. Collins's user avatar
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 ...
Dave L Renfro's user avatar
8 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 ...
eipi10's user avatar
  • 231
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 ...
Joseph O'Rourke's user avatar
8 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 ...
Daniel R. Collins's user avatar
8 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, ...
Xander Henderson's user avatar
  • 8,225
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 ...
Joseph O'Rourke's user avatar
7 votes

What books are like Knuth's Surreal Numbers?

To follow up on David's recommendation of Flatland, how about Ian Stewart's Flatterland.        An amazon.com review says, Along his fictional path, Stewart touches ...
Joseph O'Rourke's user avatar
7 votes

What books are like Knuth's Surreal Numbers?

"The Number Devil" by Hans Magnus Enzensberger is right up your alley. It is written for and is 100% accessible for children and introduces many math concepts such as recursion, infinity, and ...
celeriko's user avatar
  • 5,070
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. (...
Gerald Edgar's user avatar
  • 7,607
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 ...
beroal's user avatar
  • 279
6 votes

High school maths textbook for talented students

You will find textbooks for all of these at artofproblemsolving.com. They formed in order to help students like you. I have used their number theory book, while tutoring a young student (who was ...
Sue VanHattum's user avatar
  • 20.8k
6 votes

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

Flatland is a classic and very short/readable.
guest's user avatar
  • 99
6 votes

Book recommendations for Math for Biochemistry Course

[Edit: if there is some moderator-approved way to cross post this to Biology Stack Exchange and/or Chemistry Stack Exchange, you might get some good additional feedback.] It is a great question. I ...
guest troll's user avatar
5 votes

What books are like Knuth's Surreal Numbers?

You might want to consider the books of Raymond Smullyan. They often take the form of a sequence of puzzles tied together loosely by a narrative. The puzzles are typically intended to work towards ...
Dan Piponi's user avatar
5 votes

What books are like Knuth's Surreal Numbers?

The Mathematical Fiction web site, maintained by Alex Kasman of the College of Charleston, has summaries of hundreds of stories and movies that in some way include or discuss mathematics. It is ...
eipi10's user avatar
  • 231
5 votes
Accepted

Inspirational Mathematics Books for Teenager

For your particular case, I highly recommend "The Joy of X" by Dr. Steven Strogatz. And although you didn't request it, for higher level students and adults I also recommend "Mathematics for Non-...
Axiomaric's user avatar
  • 106
5 votes

High school maths textbook for talented students

To supplement Sue's great suggestion: Another advantage of the artofproblemsolving.com is that it provides a whole lot of support for students like you, whether or not you purchase or use the ...
amWhy's user avatar
  • 2,095
5 votes

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

Are you an undergrad majoring in aerospace engineering, or are you interested prerequisites from graduate programs in aerospace engineering? In either case, the following syllabus may help you ...
amWhy's user avatar
  • 2,095
5 votes

Textbook to study group theory as a part of Discrete Mathematics

To repeat my comments: I can recommend Fraleigh's classic introduction. It is easy to read for beginners, with many exercises, from easy to difficult, on which self-learners could check themselves. ...
Joseph O'Rourke's user avatar
5 votes

Arithmetic books for adults

You might check out the OpenStax Prealgebra text. It seems to have much of what you’re looking for.
Nick C's user avatar
  • 9,639
5 votes

Programming and computation-focused textbook for introductory linear algebra

You may be interested in Application-Inspired Linear Algebra by Heather Moon, Thomas Asaki, and Marie Snipes. It covers all of the general topics you’ve listed, and there are exploratory programming ...
Justin Hancock's user avatar
5 votes

Programming and computation-focused textbook for introductory linear algebra

I don't know if any of what I do will be helpful information for you, but maybe? I teach at a community college, and most of my students certainly aren't into proof. But that feels like an important ...
Sue VanHattum's user avatar
  • 20.8k
5 votes

Demarcated "Proof Idea"

I'm not sure if this is what you're looking for, but "How to Read and Do Proofs: An Introduction to Mathematical Thought Processes" by Solow is an intro-to-proof-writing book that frequently ...
Aeryk's user avatar
  • 8,021
4 votes

What books are like Knuth's Surreal Numbers?

The ultimate for this, which is an entire curriculum, is "The Life of Fred" book series. It is fantastic, and you can get an entire math education, elementary to undergrad, just through Fred ...
johnnyb's user avatar
  • 1,249

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