The Best of Dover Books (a.k.a the best cheap mathematical texts)

Question

Perhaps this is a repeat question -- let me know if it is -- but I am interested in knowing the best of Dover mathematics books. The reason is because Dover books are very cheap and most other books are not: For example, while something like Needham's Visual Complex Analysis is a wonderful book, most copies of it are over $100.

In particular, I am interested in the best of both undergraduate and graduate-level Dover books. As an example, I particularly loved the Dover books Calculus of Variations by Gelfand & Fomin and Differential Topology by Guillemin & Pollack.

Thanks. (P.S., I am sort of in an 'intuition-appreciation' kick in my mathematical studies (e.g., Needham))

EDIT: Thank you so far. I'd just like to mention that the books need not be Dover, just excellent and affordable at the same time.

Answer 1

In my opinion the best nooks are:

"Ordinary Differential Equations" by Tenenbaum.

"Partial Differential Equations for Scientists and Engineers" BY Farlow

"Fourier Series and Orthogonal Functions" by Harry Davis

"Concepts of modern Mathematics" by Ian Stewart

There is a nice introduction to mathematics "Mathematics for the Nonmathematician" by Morris Kline. You will find also lots of books on maths for fun like "The Moscow Puzzles" which is great. And don't forget the classic "Flatland" -it's just a story of two dimensional creatures-.

Answer 2

Just out in Dover is Applied Analysis by the Hilbert Space Method, an undergraduate text on 2nd order linear differential operators by Prof. Sam Holland. I took his class at UMass Amherst when I was a sophomore in the late '80's/early '90's, and this text was then a bunch of typewritten notes. It is very inexpensive compared to the original Marcel Dekker version. I cannot recommend this text highly enough as a gateway to higher applied mathematics.

Answer 3

Though it lacks any treatment of cardinal functions, Stephen Willard’s General Topology remains one of the best treatments of point-set topology at the advanced undergraduate or beginning graduate level. Steen & Seebach, Counterexamples in Topology, is not a text, but it is a splendid reference; the title is self-explanatory.

Answer 4

I really like François Trèves's Topological vector spaces, distributions and kernels. I always give this book as reference when I answer some questions on TVS here or elsewhere.

Torgny Lindvall's Lectures on the coupling method is also a good book if you like probability theory.

Answer 5

Pinter's A Book of Abstract Algebra is a great introductory text!

Answer 6

Nathan Jacobson's Basic Algebra I is pretty good, along with the sequel for the more brave of heart. (Disclaimer I haven't read II, but I imagine it is also good).

Answer 7

I have picked up quite a few of those Dover editions over the years, and these are some currently on my bookshelf, together with my (probably very biased opinions):

Riesz & Nagy - Functional Analysis (dated but superbly well-written)

Katznelson - Introduction to Harmonic Analysis (also a bit dated, but very good)

Knopp - Theory and Application of Infinite Series (very dated, but still useful as a reference for anything to do with series)

Cohn - Advanced Number Theory (very useful as additional reading for anyone interested in the material covered by Cox's book on primes of the form $x^2+ny^2$)

Edwards - Riemann's Zeta Function (still worth reading for anyone interested in analytic number theory)

Pollard - Theory of Algebraic Numbers (might have been good in its day, but there are many better modern treatments)

Cassels - Rational Quadratic Forms (a very detailed treatment by a real master, but a tough read)

Answer 8

Chartrand Introductory Graph Theory

Suppes Axiomatic Set Theory

Kamke Theory of Sets - Nice introduction.

Smullyan Satan, Cantor and Infinity - Anything by Smullyan!

Rosenlicht Introduction to Analysis

Answer 9

I really like Goldblatt's book Topoi: The Categorial Analysis of Logic. I think it's a good introduction to category theory.

Answer 10

I do have a soft spot for Flanders's Differential Forms with Applications to the Physical Sciences myself. Also Hoffman's Banach Spaces of Analytic Functions.

Answer 11

Jech The Axiom of Choice is probably the book I have used the most in the last two years, and the best 15 USD I ever spent, not including beer (I even got my advisor and another professor from the department to order copies).

Now I ordered Moore's book about the axiom of choice, but that one is more of an historical overview. I didn't get the book yet, so I don't know how much I am going to use it, but it was definitely worth the 12 USD.

Answer 12

Theodore J. Rivlin, An Introduction to the Approximation of Functions

Zeev Nehari, Conformal Mapping

Answer 13

For a cheap non-Dover text, there is the new edition of Kunen's Set Theory. The first edition was published by North Holland/Elsevier and is almost prohibitively expensive (the softcover version still has a list price of over US\$100), except it was the standard text for graduate-level set-theory. The new edition is completely revised, slightly expanded, and sold at Dover-like prices.

Answer 14

Since it hasn't been mentioned yet: the Dover book that is most useful to me is none other than Abramowitz and Stegun's handbook. Though we now have the DLMF, there are still pieces of useful information within the Handbook, and even the DLMF still sometimes refers to it.

Otherwise, I have liked the numerical methods textbooks that have been republished by Dover: Ralston/Wilf and Hildebrand are among the nicer ones.

Answer 15

coming from more of a computer science angle I find Fielder's "Special Matrices and Their Applications in Numerical Mathematics" really useful.

Answer 16

After many unsuccessful attempts at self-learning, my real progress in tensor calculus developed from Lovelock's Tensors, Differential Forms,....-a Dover book. I really love that book.

Answer 17

Rosenlicht's Intro to Analsysis was an awesome read, but the real learning took place in the excersises. It was cheap, and just as rigorous as the introductory analysis course I took the following semester!

Answer 18

Here's my personal best of, omitting things already mentioned:

• The Undecidable, ed. Martin Davis -- collection of reprints of classic papers on computability and undecidability including Gödel, Turing, Church, Rosser, Kleene, Post
• Nonstandard analysis, Robert. Intro to nsa using Nelson's internal set theory.
• Regular polytopes, Coxeter. Lots in there that's hard to find elsewhere even after so much time.
• Asymptotic methods in Analysis, de Bruijn
• Asymptotic expsansions, Erdélyi (spelled wrongly on the spine)

There are Dover editions of Heath's Euclid and Archimedes, and lots of problem books (Mosteller's 50 challenging problems in probability, Dorrie's One Hundred Great Problems of Elementary Mathematics, Jacoby's Intriguing Mathematical Problems, Kratchik's Mathematical recreations,...).

Honourable mention also for Dubins and Savage How to gamble if you must, boringly retitled Inequalities for stochastic processes in its Dover edition.

I $\heartsuit$ Dover books.

Answer 19

Number Theory, by George E. Andrews is a wonderful introduction to the subject for the beginner, especially the theory of partitions.

Answer 20

Elements of the Theory of Functions and Functional Analysis - Kolmogorv and Fomin This by far the best for me! (includes both the volumes!)

Answer 21

I'm a few years late to this party, but I found these books to be extremely helpful in the past and regularly find myself going back to them:

• Robert R. Stoll, Set Theory and Logic
• V. K . Balakrishnan, Introductory Discrete Mathematics
• George E. Andrews, Number Theory
• Richard J. Trudeau, Introduction to Graph Theory