Mathematics

*A course of study in mathematics*

These are the books I studied from as an upperclassman and a graduate student. In a few cases I've substituted a book I think is better than the one I actually used. I used these books to pass some of the UCLA qualifying exams. I took the basic exam in 2003, the geometry and topology exam in 2004, and the algebra exam in 2005.

# General

- Equations and Inequalities Herman etal
- Number Systems and the Foundations of Analysis Mendelson

# Algebra

- Linear Algebra Done Right Axler
- Abstract Algebra Dummit and Foote

# Differential Geometry

- Advanced Calculus of Several Variables Edwards
- Differential Geometry of Curves and Surfaces Do Carmo
- Introduction to Smooth Manifolds Lee

# Topology

- Introduction to Topology Gamelin and Greene
- Algebraic Topology Hatcher

# Real Analysis

- Principles of Mathematical Analysis Rudin
- Real Analysis Folland

# Fourier Analysis

# Complex Analysis

- Complex Analysis Gamelin

# Differential Equations

- The Qualitative Theory of Ordinary Differential Equations Brauer and Nohel
- Partial Differential Equations: Methods and Applications McOwen

# Probability

page revision: 10, last edited: 23 Jun 2011 06:23