Math Resources

Note: I only link to pages that I use myself. I'm being selective to avoid overwhelming people with too many choices, and I'm not going to link to other pages just so someone can get more traffic. But the fact that I haven't linked to a page doesn't mean I think badly of it.

Notes and pages on topics in math

[August 24, 2022] I'm slowly revising the notes - currently, most of the revisions are for the linear algebra notes, though I fix other things on a spot basis if someone points out a typo, or I have an idea for something. I may at some point put some of the exercises I wrote online, but they need substantial work before they'll be ready, so this won't happen anytime soon. (Check the review sheets linked below if you want some practice problems.) I had a number of videos on MU Video, which I took down when I retired because I wasn't sure if I'd be allowed to leave them there. I don't want to put them back up without a lot more work.

The notes are web pages, usually accompanied by PDF files for printing.

I appreciate hearing about mistakes, which I'll correct as soon as I can. Some of the notes are very incomplete; there may be a few worked-out examples, with little exposition.

• Calculus
• Notes on calculus 1 - Single variable calculus: Limits, derivatives and differentiation, applications of derivatives, integrals and antiderivatives
• Notes on calculus 2 - Single variable calculus: integration techniques, applications of integration, numerical series and power series, parametric equations, polar coordinates
• Notes on calculus 3 - Multivariable calculus: Vectors and vector algebra, lines and planes, curves in the plane and in space, calculus of functions of several variables, multiple integrals, vector calculus (Green's theorem, the Divergence Theorem, Stokes' theorem)
• Math proof
• Linear algebra
• Abstract algebra
• Elementary number theory
• Topology

Review Sheets

The Review Sheets contain practice problems with solutions. Usually, there are 3 review sheets corresponding to the three tests I gave during the term, and a final review sheet for the final exam. They are arranged by course, and I'll try to put more of them online in the future.

Note that if you're taking a course, your instructor will probably cover different topics than I did, and will teach those topics in different ways. Be sure you know what your instructor expects!

Free mathematical software

• Maxima is a GPL-ed symbolic mathematics program. It does (among other things) algebra, calculus, and graphing in 2 and 3 dimensions.
• GAP is a free system for doing computational discrete algebra. It is best known as a tool for doing computational group theory.

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