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How to Prove It by Daniel J. Velleman

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(1) How to Prove It by Daniel J. Velleman
(2) Fundamentals of Algebra and Trigonometry by Swokowski&Cole
(3) Calculus vol.1&2 by Tom M. Apostol
(4) Introduction to Linear Algebra by Gilbert Strang
(5) Mathematical Analysis by Tom M. Apostol
(6) Introductory Functional Analysis with Applications by Kreyszig
F. William Lawvere and Stephen H. Schanuel, Conceptual Mathematics: a First
Introduction to Categories, Cambridge University Press, 1997. (A great place to start.)
Saunders Mac Lane, Mathematics, Form and Function, Springer-Verlag, New York, 1986.
(More advanced.)
Jean Dieudonne, A Panorama of Pure Mathematics, as seen by N. Bourbaki, translated
by I.G. Macdonald, Academic Press, 1982. (Very advanced - best if you know a lot of math
already. Beware: many people disagree with Bourbaki's outlook.)
Calculus:
Gilbert Strang, Calculus, Wellesley-Cambridge Press, Cambridge, 1991. Also available free
online at http://ocw.mit.edu/ans7870/resou.... (Another classic, with lots of applications
to real-world problems.)
Multivariable calculus:
James Nearing, Mathematical Tools for Physics, available
athttp://www.physics.miami.edu/~ne.... See especially the sections on multvariable
calculus, vector calculus 1, and vector calculus 2. (Very nice explanations!)
George Cain and James Herod, Multivariable Calculus. Available free online
at http://www.math.gatech.edu/~cain...
Linear algebra:
I don't have any favorite linear algebra books, so I'll just list some free ones:
Keith Matthews, Elementary Linear Algebra, available free online
athttp://www.numbertheory.org/book/.
Jim Hefferon, Linear Algebra, available free online athttp://joshua.smcvt.edu/linalg.h....

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(1) How to Prove It by Daniel J. Velleman (2) Fundamentals of Algebra and Trigonometry by Swokowski&Cole (3) Calculus vol.1&2 by Tom M. Apostol (4) Introduction to Linear Algebra by Gilbert Strang (5) Mathematical Analysis by Tom M. Apostol (6) Introductory Functional Analysis with Applications by Kreyszig F. William Lawvere and Stephen H. Schanuel, Conceptual Mathematics: a First Introduction to Categories, Cambridge University Press, 1997. (A great place to start.) Saunders Mac Lane, Mathematics, Form and Function, Springer-Verlag, New York, 1986. (More advanced.) Jean Dieudonne, A ...
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