Math books for mathematically-inclined graphics students

Lin Alg.

I've gradually decided I like Strang, "Linear Alg. and its Applications," for the overview and intro. numerical stuff. But for understanding vector spaces, etc., it's not very satisfying. For that, I prefer the book by Hoffman/Kunze (pretty heavy going), or Curtis (a little easier). I also like the book by Mike O'Nan, but it may no longer be in print.

Differential Geometry

There doesn't seem to be a good book. I like "Elementary Diff'l Geom," by Barrett O'Neill (spelling?) as a first book -- it's definitely the way to go. Do LOTS of problems, and you get a good feel for things in 3D. After that, Spivak's 5-volume series is a great reference, except that looking up anything takes about 2 hours of pointer-chasing, and the typsetting's not pretty. I also have a book by Varadarajan on "Lie Groups, Lie Algebras, and their Representations," whose first 20 pages or so are really excellent :-). should also have Coxeter, "Introduction to Geometry," not for the diff'l geom., but for everything else.

Projective Geometry

I love Hartshorne's little book (Intro to Proj Geom or something), published ca. 1970. After it, though, you should probably read some other, more concrete book, and I don't know which one.


Homology Theory, by James Vick, is an excellent intro to (you guessed it) homology theory -- at least for 4 chapters. Another wonderful intro is " Algebraic Topology: An Intro." by Massey. This is where I really learned a lot of what I know.


The winner here is "Calculus", by Mike Spivak, plus whatever book you used in your course, because looking things up there will be easier. But get Spivak's book, and read it, and do as many of the starred problems as you possibly can. It'll raise your level of understanding of everything!

Multivariable Calc.

No good suggestion.


Feller, "An Intro to Prob/ Theory and its Applications" is the classic, but dry. Mosteller's "50 hard probability problems" (or something like that) is a real treasure. Worth doing every single one!


Boyce and DiPrima is the classic. It's OK.


I like Dan Zwillingers "Handbook of Diff'l Equations"; it's got wonderful short summaries and good pointers to other material.


Zwillinger again, and Numerical Recipes.


Theory of Lie Groups, by Chevalley; Topology of Fiber Bundles, by Steenrod. Both probably well beyond what you'll ever need, but good to have on your list of "last resorts".
John F. Hughes
Last modified: Tue Nov 7 15:22:17 EST 2000