About

I’m a student at Clemson University studying for prelims.  This blog is an attempt to write down what I’m studying to help make sure that I understand things well enough to explain them to someone else.  I’m happy to say that since starting this blog I’ve passed my analysis and stochastics prelims, and am studying for algebra this coming summer.

I try to keep this blog fairly self-contained when I can, meaning that I prefer to start off with posts on basic definitions and axioms, and work up from there.  Of course, this gets to be a bit overwhelming, and so whenever there are “jumps” between posts I’ll try to include links to the articles on Wikipedia or Planet Math that describe the things I haven’t posted on yet.

Pretty much everything on here is being paraphrased from some other source.  Rather than mention those sources in each post, I’ll just do it here.  Most of the real analysis and general analysis stuff is coming from Principles of Mathematical Analysis by Walter Rudin and Real Analysis: A First Course by Russell Gordon.  Functional analysis stuff is primarily from Erwin Kreyszig’s Introductory Functional Analysis with Applications, while measure theory is from Measure, Integral and Probability by Marek Capinski and Peter Kopp.  If and when I reference other material, I’ll include it in the post, and if it happens that I start referencing something a lot, I’ll put it here.

For stochastics and probability, I’m using A Modern Approach to Probability Theory by Bert Fristedt and Lawrence Gray; Probability by A. N. Shiryaev; Introduction to Probability Models by Sheldon Ross; and Adventures in Stochastic Processes by Sidney Resnick.  Occasionally I’ll use the Capinski and Kopp book on measure theory mentioned above as well.

The books I’m using for topology are Topology by James Munkres, Algebraic Topology by Allen Hatcher (this is also available online for free, legally, from Dr. Hatcher’s homepage) and Essential Topology by Martin Crossley.

My resources for abstract algebra are Algebra by Larry Grove; Algebra by Thomas Hungerford; Abstract Algebra by David Dummit and Richard Foote; and (an older edition of) Contemporary Abstract Algebra by Joseph Gallian.  For linear algebra I’m using Matrices and Linear Transformations by Charles Cullen;  Theory of Matrices by Sam Perlis; and Matrix Analysis by Roger Horn and Charles Johnson.

Posts on category theory typically reference material from the algebra books above, class notes, and the book Category Theory by Steven Awodey.