The Princeton Companion to Mathematics

Of the books mentioned in this thread so far I think I'd have been most excited about the Princeton Companion to Mathematics as a birthday present. Here's why: - Your goal of the gift is something more than a plain textbook. The Princeton Companion is something your child will return to throughout their math career. It will be an anchor book that will remind them of your support for them when they were still a budding mathematician. - Relatedly, the book is far too broad to be consumed as a textbook. Hence it will be more like a friend (or companion :) ) on their journey. Even a really amazing textbook (like Baby Rudin) in contrast is just a snapshot of where they are now.

The Princeton Companions to Mathematics and Applied Mathematics are beautiful to leaf through at the library. They're also hardcore heavy-weight (physically) and unlikely to be read twice, so don't buy them. My personal take is that good linear algebra books at any level are great "tours of mathematics". Start with Strang and never stop. In a few years you'll be balled up with Kreyszig scribbling proof attempts in receipts, flaming unkempt hair and everyone around you will think you're weird but you'll be so, so happy.

In terms of depth and breadth, the Princeton companions get close to Feynman.[1][2] A more formal approach appears in handbooks.[3][4] [1] Gowers et al., The Princeton Companion to Mathematics. https://press.princeton.edu/books/hardcover/9780691118802/th... (https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics) [2] Higham and Dennis, The Princeton Companion to Applied Mathematics. https://press.princeton.edu/books/hardcover/9780691150390/th... (https://press.princeton.edu/books/hardcover/9780691150390/the-princeton-companion-to-applied-mathematics) [3] Zwillinger, CRC Standard Mathematical Tables and Formulae. https://www.crcpress.com/CRC-Standard-Mathematical-Tables-an... (https://www.crcpress.com/CRC-Standard-Mathematical-Tables-and-Formulas/Zwillinger/p/book/9781498777803) [4] Bronshtein, Handbook of Mathematics. https://www.springer.com/gp/book/9783540721222

I read almost all of it cover to cover when I was an undergrad in math, when I still had intention of going to grad school, to get a sense of which area(s) of math I'd like to pursue further. It is incredibly illuminating and I also recommend it highly.

"Best" is a vague metric, but one textbook I am always happy to recommend is the Princeton Companion to Mathematics. The book is a selective review of the most significant ideas in maths and mathematical research. The great editorial process is what sets this book apart from the rest: each chapter is authored by an outstanding expert in his/her particular field (among which several fields medalist the likes of Terence Tao) and the editing by Timothy Gowers does an amazing job of uniforming the tone, notation and rigor across the whole text. The authors were evidently chosen also for their communication skills since the articles come across as quite discoursive and really convey the beauty of modern maths. In the book you'll find not only the articles on mathematical concepts, but also an introduction to modern mathematics, chapters on the relationship of maths with other sciences, a thorough history of mathematics and a collection of biographies of famous mathematicians. Well recommended to anybody with an interest in maths. My background is in CS and I found it approachable (except minor sections) and illuminating!

The Princeton Companion to Mathematics [1] is good if you want to gawk at the breadth and depth of the field. For actual education I would just suggest looking at a math department's syllabus, e.g. at http://ocw.mit.edu/. As a CS grad you should start with analysis, as that's probably your most looming dark spot. My warning as a math student is that a lot of book recommendations are just a tad bit elitist. Don't stick with a single book too long if it isn't cutting it for self-study. Exercises are good. [1] http://press.princeton.edu/titles/8350.html

I dunno about SICP-like, but here's some good book lists https://github.com/ystael/chicago-ug-math-bib (updated Univ of Chicago bibliography http://math.ucr.edu/home/baez/books.html http://www.maths.cam.ac.uk/undergrad/course/schedules.pdf ______________________ and 2 i got from HN and /r/machineLearning http://www.reddit.com/r/MachineLearning/comments/1jeawf/mach... (http://www.reddit.com/r/MachineLearning/comments/1jeawf/machine_learning_books/) https://github.com/vhf/free-programming-books/blob/master/fr... (https://github.com/vhf/free-programming-books/blob/master/free-programming-books.md#machine-learning) ________________________ finally, the "Maths for PHysics" texts http://www.scribd.com/doc/156523189/Boas-mathematical-Method... (http://www.scribd.com/doc/156523189/Boas-mathematical-Methods-in-the-Physical-Sciences-pdf) http://www.goldbart.gatech.edu/PG_MS_MfP.htm http://www.scribd.com/doc/91670553/Arfken-Math-Physics ___________________ (if i had to recommend only one book, it would be the Boas, or maybe Princeton Companion: http://press.princeton.edu/titles/8350.html

I haven't picked it up yet, but I remember reading about "The Princeton Companion to Mathematics" on here a while ago. It looks like a pretty complete guide to all of modern mathematics and sounded like it was easy enough for a beginner to get through while still being able to teach math experts some new things. Thanks for reminding me about it - I think I'm going to order my self a copy!

It's an encyclopedia of essays on math topics. It's very comprehensive and well edited. However, while it's a cool book, speaking as a former math tutor, it isn't the most helpful from a self study perspective.

The Princeton Companion to Mathematics.

I'm trying to do a similar thing. I've purchased "The Princeton Companion to Mathematics" (http://press.princeton.edu/titles/8350.html). I've not read a huge amount so far, but what I've read so far has been well-written and understandable.