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 ...
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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.)
- 3,810
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....
- 20.1k
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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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 ...
- 24.4k
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
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 ...
- 29.5k
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 ...
- 24.4k
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, ...
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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 ...
- 29.5k
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 ...
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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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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 ...
- 29.5k
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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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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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 ...
- 20.1k
6
votes
What are examples of math-themed sci-fi appropriate for students?
Flatland is a classic and very short/readable.
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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 ...
- 221
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 ...
- 221
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-...
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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 ...
- 2,075
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 ...
- 2,075
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.
...
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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.
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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 ...
- 2,820
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 ...
- 20.1k
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 ...
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4
votes
What books are like Knuth's Surreal Numbers?
The Phantom Tollbooth (1961) by Norton Juster is a children's fantasy story that mixes wordplay and mathplay somewhat in the style of Lewis Carroll. It's suitable for anyone, but resonates well with ...
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4
votes
What books are like Knuth's Surreal Numbers?
Incandescence by Greg Egan describes how a technologically unsophisticated alien civilisation, under the right circumstances (in this case, closely orbiting a neutron star) might discover general ...
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