Useful textbooks to study from

Forum for the GRE subject test in mathematics.
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Useful textbooks to study from

Post by rsk » Tue Sep 16, 2014 4:57 pm

After reading some of the posts on this site, I've noticed a sizable portion of people wanting to go to grad school in math who either : 1) didn't/aren't getting an undergrad degree in math, or 2) went to a small school that didn't offer many higher-level math courses. To help those of you in this conundrum, I'm going to suggest a few good books and links to help prep for the higher-level subjects on the Math GRE.

For Abstract Algebra, a lot of people have recommended Dummit and Foote, but I can see how this book could be very imposing to people who've never seen much, if any, abstract algebra before. A really nice book for beginners is Visual Group Theory by Nathan Carter. My abstract algebra professor used it as a supplement for my class, and it did wonders for helping me understand what all that stuff was about. This book introduces you to the subject of abstract algebra using lots of pictures to help you gain an intuition for the material. The only caveat, I think, is that ring theory isn't really mentioned, so you'd have to supplement that in (which wouldn't be hard at all after getting through the book). If you'd like an idea what it's like, my professor has a link with a lot of information on it, including his lecture notes, here (under "Teaching", "Abstract Algebra"):

For Complex Analysis, a similar kind of book is Visual Complex Analysis by Tristan Needham, which pretty much does the same thing for complex analysis that VGT above does for abstract algebra. Here's a link you might find useful for that (and other things...):

For other topics, a good, quick, no-nonsense introduction/review to multivariate calculus, differential equations, fourier analysis, complex variables, and probability can be had from Mathematical Methods in the Physical Sciences by Mary Boas: ... dition.pdf. I used it in my math methods sequence as a physics major.

For the less advanced stuff, I have to agree with everyone and recommend Stewart's Calculus text: ... entals.pdf.

At any rate, hope this info helps.

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