# Math books for mathematically-inclined graphics students

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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.
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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 :-). Oh...you should also have Coxeter,
"Introduction to Geometry," not for the diff'l geom., but for everything
else.
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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.
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Topology

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.
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Calculus

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!
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Multivariable Calc.

No good suggestion.
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Probability

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!
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ODEs

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

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

Zwillinger again, and Numerical Recipes.
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Others

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