Dorky Poll: Favorite Math Book

Forever Undecided: A Puzzle Guide to Godel by Raymond M. Smullyan.

In college (back in the dark ages) I really liked "Advanced Engineering Mathematics", by Wylie and Barrett.

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There are so many great math books, it's hard to choose just one. I think Concrete Mathematics by Knuth is excellent. I wasn't too big a fan of Serge Lang's Undergraduate Algebra in college.

For math textbooks, I like Strang's Linear Algebra. It's great for a birds-eye view of the subject and its explanation of the FFT.

There's also Spivak's monumental differential geometry series. If only for Spivak's paintings on each of the five volumes. The text is fun, too, but there's *so much*.

I.N.Herstein's Topics in Algebra was the first pure math book I had that I regarded as something more than just a textbook.

If computer science books count, then I would include Michael Sipser's Introduction to the Theory of Computation.

Silvanus P. Thompson's "Calculus Made Easy" (Martin Gardner's New Edition)

I'm fond of Shankar's "Basic Training in Mathematics: A Fitness Program for Science Students". A helpful note about writing sin and cos in terms of complex exponentials appears in bold: "Forget these and you are doomed." Instead of Arfken I've always preferred Kaplan's "Advanced Calculus" book as well as F.B. Hildebrand's "Advanced Calculus for Applications". For an exposition on differential forms I really like Bamberg & Sternberg's "A Course in Mathematics for Students of Physics". Stretching things a bit, I also like Tinkham's "Group Theory and Quantum Mechanics", although I don't know if that counts as a physics book or a math book. Finally, I can't imagine being without Numerical Recipes, Abramowitz & Stegun, or Gradshteyn & Ryzhik.

I second Gradshteyn & Ryzhik. Often more useful than Mathematica if you need to do integration.

I should also add Butkov's book (http://www.amazon.com/Mathematical-Physics-Eugene-Butkov/dp/0201007274/…) as a wonderful alternative to Arfken, although it's frighteningly expensive for such an ancient book.

I've always loved Korner's book on Fourier Analysis. To me, the subject is beautiful because of its various applications in so many fields. Korner does an excellent job of presenting these. I wouldn't recommend this book as an introduction to the subject, though.

Artin's Algebra is an easy favorite.

'Applied Cryptography' by Bruce Schneier, or any of Donald Knuth's books - Computer Science mightily supported by fun Mathematics :)

How about "The Annotated Flatland" by Edwin Abbott? Does that count? :)

There's so many!

I read Osserman's _Minimal Surfaces_ for fun. So that should count. I remember, when preparing for my orals, liking Kra's _Automorphic Forms and Kleinian Groups_. Recently I've been impressed by Borwein and Bailey's _Mathematics by Experiment_.

My favorite reference book is definitely Abramowitz and Stegun. While I also find Numerical Recipes in C useful for numerical algorithms, Press et al. is the premier example of how not to write C code: lack of whitespace, lack of comments, obfuscatory shortcuts, and (worst of all) a gratuitous insistence on indexing arrays from 1 to n even when the algorithm would be just as clear with array indices following the preferred C convention of running from 0 to n-1.

If you mean books written for the non-mathematician, I second Melissa's nomination of Flatland.

I'm a big fan of Bender and Orszag's Advanced Mathematical Methods. Every page is eloquent, not too terse or too wordy. And the subject matter is really useful.

I'm also rather fond of Herstein's little blue algebra book and Concrete Mathematics.

Favorite overall:

I second Silvanus P. Thompson's "Calculus Made Easy" This really helped me when I was learning it. "Considering how many fools can calculate it is surprising that it should be thought difficult for any other fool to do the same."

Favorite textbook:

Differential Equations, First Edition, by Blanchard, Devaney, Hall. Published by Brooks/Cole Publishing Co., 1998. ISBN 0-534-34550-6.

This was my Diff Eq textbook and I love it. The only math textbook I've ever had with humorous word problems.

Favorite mathematical fiction book:

Fantasia Mathematica, edited by Clifford Simak. Includes short stories by everyone from Aldous Huxley to Robert Heinlein, not to mention naughty limericks and poetry by Edna St. Vincent Millay. This book helped make me who I am today.

Favorite math book that is marketed to kids but is entertaining even for adults:

"The I Hate Mathematics Book"

http://www.amazon.com/Brown-Paper-School-book-Mathematics/dp/0316117412

Strangely entertaining excercises and experiments involving ice cream, popcorn, and pidgeons, lots of interesting little riddles and brainteasers, and even math pranks.

Favorite? That's much too hard.

Conics, by Kendig is nice.

So is Visual Complex Analysis by Needham.

This has killed me for the last ten years, because I can remember the book, but I'm not completely sure of the title or author. I believe however it was Principles of Mathematical Analysis by Walter Rudin.

The course was Introduction to Analysis (Math 104) and it totally kicked my butt. I had never been challenged so much in a class, but it was enormously stimulating. I spent hours and hours trying to wrap my brain around how to do the proofs, finding one gap in my logic and trying to push it around, until I could either jump over it... or find an inconspicuous place to hide it.

I couldn't say whether it is a good or bad book. But it was a constant companion for a semester, and I was never as proud as when I was able to make it out of that course with a B. I think the failure rate on that class was about 50%... over all sections, in any given semester. (So it goes in the big state school.) That book for me marked both my top academic challenge as well a deep insight into what math really means.

In a later moment of college poverty, I sold that book back. It was probably $50 even then which kept me in soba for a couple weeks. But I deeply wish I'd gone hungry instead.

Postscript: Two years later, my prof won the Fields Medal.

Milnor's Topology from the Differentiable Viewpoint: it's short and astoundingly clear.

For a really good (and accessible) introduction to differential geometry, it is very hard to beat Barrett O'Neill's "Introduction to Differential Geometry". I also quite like "Semi Riemannian Geometry with Applications to Relativity" by the same author as well, for pretty much the same reasons.

My favorite calculus text: Michael Spivak's Calculus (not to be confused with his Calculus on Manifolds, also an excellent little book). I'm also rather fond of Miles Reid's Undergraduate Commutative Algebra and Undergraduate Algebraic Geometry -- he has an odd but entertaining sense of humor.

My personal favorite math book (assuming people count it as a math book) is How to Solve It: Modern Heuristics, which does for search/optimization what Poyla's text did for heuristics in pure math. I also can't do without Knuth's The Art of Computer Programming, all three complete volumes are essential reading IMO, and the fascicles for volume 4 have also been showing a lot of promise for the final edition.

As for a Calculus text, I prefer Richard Silverman's Modern Calculus and Analytic Geometry. It's oldie but goodie, accomplishing the rarely accomplished task of being both unusually comprehensive and unusually engaging.

I second the nomination for the 'little' Rudin: Principles of Mathematical Analysis, but I'd also like to add V.I. Arnold's Ordinary Differential Equations. Differential equations is a bag of tricks, but Arnold concentrates on the bag itself. His Mathematical Methods of Classical Mechanics is also a masterpiece; I hope I can understand it someday.

There are some good books by Whitaker and Watson on special functions but in general I get my math from physics books.

Of course, as others said, both Gradshteyn/Ryzhik and Abramowitz/Stegun are very useful; but this is because they are references and not trying to teach you anything.

Peter Szekeres "A Course in Modern Mathematical Physics", although that's probably because I'm reading it now.

It's got pretty much all the background you need to get past the undergraduate level in physics.

All time favorite? Maybe Flatland

Could mention various books by (among others) Martin Gardner, Ian Stewart, Ivars Peterson, or Clifford Pickover.

Think I'll just mention two books that give a broad overview of the field: "Mathematics, The Science of Patterns" by Keith Devlin and the much longer "Mathematics, From the Birth of Numbers."

I second Barrett O'Neill's books. I'm looking through Elementary Differential Geometry as we speak. I also love Spivak's Calculus on Manifolds.

I know it's a classic, but I hate Munkres' Topology.

Sorry I got here late, because this book is way cool: The Mathematical Experience by Philip Davis and Reuben Hersh. It isn't a dorky how-to textbook, but a fascinating look under the metaphysical skirt of mathematics: about abstraction, Platonism, intuitionism and constructivism, weird stuff like surreal numbers and non-standard analysis, set theory paradoxes and contradictions, proving that some things can't be proved, infinities, etc.

Second choice in like vein: Mathematics: The Loss of Certainty by Morris Klein. Either one leaves you feeling like math is Alice's Wonderland, not a crisp sensible toy for anal-retentive logicians.

I'm very found of the Shaggy Steed of Physics by David Oliver It was my introduction to the Principle of Least Action and it changed the way I view the world. I also very much like Fulton and Harris' book on Representation Theory. As far as worst goes... hmmm... hmmmm.... I'll have to think about that some more. The titles appear to have been completely driven from my head.

When I chimed in earlier I was just thinking about reference books or textbooks. But upon further thought, the book that got me especially interested in mathematics is more of a popular book: "Journey through genius" by William Dunham. It's a fun little book with math history and proofs of fun problems of historical interest.

Favorite(S): MacRobert's Functions of a Complex Variable, anything by Ruel Churchill, Korn & Korn, Stegun and Abramowitz, Gradshteyn & Rhyzik
Unfavorites: anything where the proof volume exceeds the application volume.

"Winning Ways for Your Mathematical Plays" by Berlekamp, Conway & Guy. If only for the title, although the content is great fun too.

For standard texts - Jacobsen, "Basic Algebra".

Probably the most fun course i had as an undergrad was based on Bondy & Murty's "Graph Theory with applications".

Wikipedia.

Stewart's Calculus: Early Transcendentals.

Tough call, since it depends on the criteria used.

Nostalgia: My dad's College Algebra textbook that I worked through while in 4th grade. Awesome story problems that were lots of fun to solve.

My Precious: "Calculus and Analytic Geometry" by Thomas (4th ed), the first 'real' math textbook I learned from, but maybe that is part nostalgia. If so, the choice would be "Real Analysis" by Royden, where I learned how to use topology and Lebesque measure theory to integrate a function defined on the Cantor set defined by casting out middle thirds.

Fun: "One Two Three Infinity" by Gamow, where I first learned about the crazy properties of different infinities, such as the one that allows Cantor's ternary set to have zero measure while having the same number of points in it as a set of measure 1. You just gotta love that stuff.

R. Churchill's Fourier Analysis

We have been taught using Boas' Mathematical Methods for the Physics Sciences, and it's a decent one-stop shop, but lately I've been turning towards Mathematical Methods for Physics and Engineering by Riley and Hobson, which is unfortunately so large that I would cripple myself carrying it around.

Div Grad Curl and All That is also quite cute.

Oh yes! One more! How to Ace Calculus: A Streetwise Guide (books I and II) really helped me out in the beginning. I really liked the style of it and the good simple examples.