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Harvard Mathematics Department Quals Syllabus
Recommended books for the Harvard Mathematics PhD qualifying exam.
Source.
Contents
Algebra
Algebraic Geometry
Complex Analysis
Algebraic Topology
Differential Geometry
Real Analysis
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