A course of study in mathematics

topic text pages
General Equations and Inequalities Herman etal
General Number Systems and the Foundations of Analysis Mendelson
Algebra Linear Algebra Done Right Axler
Differential Geometry Advanced Calculus of Several Variables Edwards
Topology Introduction to Topology Gamelin and Greene
Real Analysis Principles of Mathematical Analysis Rudin
Differential Geometry Differential Geometry of Curves and Surfaces Do Carmo
Fourier Analysis Fourier Analysis and Its Applications Folland
Numerical Analysis Numerical Analysis: Mathematics of Scientific Computing Kincaid and Cheney
Algebra Abstract Algebra Dummit and Foote
Real Analysis Real Analysis Folland
Complex Analysis Complex Analysis Gamelin
Topology Algebraic Topology Hatcher
Differential Geometry Introduction to Smooth Manifolds Lee
Differential Equations The Qualitative Theory of Ordinary Differential Equations Brauer and Nohel
Differential Equations Partial Differential Equations: Methods and Applications McOwen
Probability A First Course in Probability Ross
Probability Stochastic Processes Ross

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.



Differential Geometry


Real Analysis

Fourier Analysis

Complex Analysis

Differential Equations


Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License