Harvard Mathematics Department Quals Syllabus

Recommended books for the Harvard Mathematics PhD qualifying exam. Source.

Algebra

Abstract Algebra

Dummit/Foote

Representations of Finite Groups

Serre

Representation Theory: A First Course

Fulton/Harris

Algebraic Geometry

Basic Algebraic Geometry 1

Shafarevich

Algebraic Geometry: A First Course

Harris

Complex Analysis

Complex Analysis

Ahlfors

Algebraic Topology

Algebraic Topology

Hatcher

Algebraic Topology

Fulton

Algebraic Topology

Spanier

Algebraic Topology: A First Course

Greenberg/Harper

Differential Geometry

Differential Geometry: Bundles, Connections, Metrics and Curvature

Taubes

Manifolds and Differential Geometry

Lee

Foundations of Differential Geometry

Kobayashi/Nomizu

Real Analysis

Real and Complex Analysis

Rudin

Real Analysis

Stein/Shakarchi

Analysis

Lieb/Loss

Fourier Analysis

Stein/Shakarchi

Partial Differential Equations

Evans

Probability

Shiryayev

An Introduction to Probability Theory and Its Applications

Feller

Probability: Theory and Examples

Durrett