Math Books

My favourite math books

  1. Abraham and Shaw for the Dynamics "colouring books". These provide the clearest and most straightforward introduction to dynamics that I have ever seen.
  2. Abramowitz and Stegun. This is not really a `favourite', but it is hands down the most useful book I own. Thank you, Mr. Dover, for printing it so cheaply.
  3. E. J. Barbeau, for `Polynomials'. This book is intended as a text for people between Grade 13 and first year university. It succeeds at all levels. Very useful facts about polynomials, contained in no other source that I know.
  4. Bender and Orszag, for `Advanced Mathematical Methods for Science and Engineering.' I took a course solely because this was the textbook for the course---I have rarely made a wiser decision. This book is readable and contains material that I still use. Definitely a classic.
  5. Birkhoff and Rota for Ordinary Differential Equations. A classic in the classic style.
  6. Bishop and Goldberg Tensors on Manifolds.
  7. Colin Clark, for `The Theoretical Side of Calculus'. He later wimped out and changed the title to some standard-sounding thing like `Elementary Introduction to Analysis' or something, but this was the first analysis book I ever saw. It's very clear (and he's a good prof, too---but then I have to say that, as he may very well read this!).
  8. Cox, Little, and O'Shea, for ``Ideals, Varieties, and Algorithms.'' A very deep book, lucidly written. A delight to read.
  9. Golub and van Loan Matrix Computations is the numerical linear algebraist's bible. My copy of the 2nd edition is signed by Golub; my first edition is falling apart; my third edition sits proudly on my shelf. I've never bought all the editions of a book before, but Matrix Computations is special.
  10. Jack Dongarra et al. for the Lapack User's Guide. This book is a concentrated exercise in professional linear algebra. There are no words.
  11. Graham, Knuth, and Patashnik: Concrete Mathematics. What a book! Beautifully typeset, charmingly written, jam-packed with interesting and useful mathematics, complete with murderously difficult exercises (with answers), and containing brilliant marginalia. My copy is signed by Knuth; with luck I'll collect the other author's signatures too.
  12. John Guckenheimer and Philip Holmes for Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. An extraordinary collection of useful material.
  13. William W. Hager Applied Numerical Linear Algebra. With Golub and Van Loan to compete with, how could any numerical linear algebra book make this list? Well, Hager has an exciting treatment of Rayleigh quotient methods, and lots of other stuff (including eigenvalue conditioning) that is very worth while. Excellent.
  14. Hairer, Norsett, and Wanner for their delightful books on the numerical solution of initial-value problems.
  15. R. W. Hamming. His book `Numerical Methods for Scientists and Engineers' is iconoclastic and dated, but still useful. His book `Methods of Mathematics applied to Probability, Statistics, and Calculus' is the finest calculus text in existence. Unfortunately it is too far away from the `standard' text so it went out of print. If the standard calculus course was built around this book, we'd all be better off.
  16. G. H. Hardy Pure Mathematics.
  17. Hardy and Wright Introduction to the Theory of Numbers.
  18. J. P. den Hartog, for `Mechanics' and `Mechanical Vibrations'. Old books but very useful.
  19. Peter Henrici's `Applied and Computational Complex Analysis', volumes 1 through 3. I have to admit I've not got beyond chapter 1 of volume 3 (whew). But these books will be permanent additions to the mathematics literature---clearly written and brilliantly selected topics.
  20. Roger A. Horn and Charles R. Johnson, for Matrix Analysis. Why didn't I get Horn to sign this book when I met him? Because I hadn't bought it yet! Next time. This book taught me that commuting matrices were important (see my research papers).
  21. J. H. Hubbard and B. H. West, for ``Differential Equations, A Dynamical Systems Approach.'' A superb text, which is the real model for how to teach differential equations with technology.
  22. Jeffries and Jeffries Methods of Applied Mathematics. English applied mathematics written in the old style.
  23. Mark Kac, `Statistical Independence in Probability, Analysis, and Number Theory'. Or some such title, anyway---it's in the M.A.A. Carus Mathematical Monographs series. Beautiful.
  24. Donald E. Knuth for The Art of Computer Programming, volumes one through three; we are awaiting the inevitable volume four, as one awaits the majestic motion of an ice mountain: it will be serene and profound.
  25. D. F. Lawden's Elliptic Functions. Dense, deep, delightful.
  26. Benoit Mandelbrot for The Fractal Geometry of Nature. My copy went missing somewhere, which was very irritating, because I missed my chance to get it signed (got a note from Benoit instead which I will glue into my copy whenever whoever has it gives it back. Meanwhile Matt Davison's copy is on my shelf---now that Matt's back in the country I'll have to give it back I suppose---and that's also signed.) I wasn't sure whether to put this book in the "math" section or the "nonfiction" section---it's a lovely book either way.
  27. Misner, Thorne, and Wheeler Gravitation. Deep, lucid, precise.
  28. Ivan Niven. `Maxima and Minima Without Calculus'. Fun and useful!
  29. C. D. Olds Continued Fractions. A wonderful book.
  30. Papadimitriou and Steiglitz for Combinatorial Optimization. Uri Ascher taught the course for which this was the text; brilliant choice. I'm told the book is dated now (no wonder, with all the developements in optimization), but it's still wonderful.
  31. Arnold Reimann for his three-volume work on Physics. (Ok, so it's not a math book---close enough, already). Extremely clear, aimed at the fundamentals not the superficies.
  32. T. J. Rivlin for Chebyshev Polynomials. My copy is signed. A brilliant book, containing nearly everything anyone could ever want to know about Chebyshev polynomials. Of course Rivlin had an easy time of it because the Chebyshev polynomials are so inherently interesting.
  33. Roberts' book `Number Theory'. As a text it is merely excellent, but the fact that it is done in calligraphy makes it unique, and a real pleasure to simply read.
  34. Walter Rudin for all his wonderful analysis texts. They are very, very dense, but this is analysis as it should be: clear, correct, and clean.
  35. Sachs and Wu General Relativity for Mathematicians. Also very funny.
  36. Colin Sparrow for The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. An excellent compendium of accessible and interesting dynamical systems results, focussed on nearly the simplest example possible.
  37. Gilbert Strang for many of his books, but especially for Introduction to Applied Mathematics, which achieves a useful grand synthesis of an extraordinary range of problems. In some parts it can be read by junior undergraduates; I recommend that my colleagues read it, as well as our grad students. And of course Gil's personal charm shines clearly through.
  38. Charles F. Van Loan for Introduction to Scientific Computing. I am using this as the text for a course I am teaching. It does not do things as I would do them. Van Loan makes me like it. There is material new to me (particularly about parallel and vector computing), but mostly I like it because it says so many very useful things about numerical analysis, in such a short space.
  39. L. C. Young for Calculus of Variations and Optimal Control---Frank Clarke's candidate for `funniest textbook of all time'.