Curriculum Schedule for Graduates of the Department of Mathematics, PKU ((trial implementation)
Oct. 25th, 2018
Intermediate Courses:
1. Analytics and Partial Differential Equations
Real analysis. Harmonic analysis. (offered respectively in the first and second semester)
Complex analysis.
Functional analysis II.
Second order linear partial differential equations. Hyperbolic partial differential equation. (offered respectively in the first and second semester)
Courses offered every two years:
The basis of linear analysis. Calculus of variations. The theory of functions of several complex variables.
Courses for qualification tests:
Functional analysis II. Harmonic analysis. Complex analysis. Second order linear partial differential equations. Hyperbolic partial differential equation.
2. Ordinary Differential Equations and Dynamical Systems
The Qualitative Theory of Ordinary Differential Equations. Ergodic Theory. Dynamical System.
Courses for qualification tests:
The Qualitative Theory of Ordinary Differential Equations.
3. Algebra and Number Theory
Courses offered every year:
Abstract Algebra. Commutative Algebra. (offered respectively in the first and second semester)
Number Theory I. Number Theory II. (offered respectively in the first and second semester)
Algebraic Geometry I. Algebraic Geometry II. (offered respectively in the first and second semester)
Group theory. Theory of Group Representations. (offered respectively in the first and second semester)
Homological algebra.
Lie Groups, Lie Algebras and Representations.
Theory of Geometric Representation.
Modular Form.
Courses of Basic Applied Algebra: Cryptography. etc.
Courses offered every two years:
Finite Field.
Homogeneous Flows, Moduli Spaces and Arithmetic.
Courses for qualification tests:
Abstract Algebra II. Representation Theory. Algebraic Geometry. Number Theory.
4. Geometry and Topology
Courses offered every year:
Homology Theory. Homotopy Theory. (offered respectively in the first and second semester)
Differential Manifold. Differential Topology. (offered respectively in the first and second semester)
Introduction to Riemannian Geometry.
Complex Geometry.
Symplectic Geometry.
Courses offered every two years:
Low-Dimensional Manifolds.
Introduction to Hyperbolic Geometry. Geometric Group Theory. (offered in turn)
Courses for qualification tests:
Differential Geometry. Algebraic Topology. Differential Topology.
5. Mathematical Physics
Courses offered every year:
Mathematical Methods of Classical Mechanics.
*Mathematical Methods of Quantum Mechanics.
*Gromov-Witten Theory.
Courses offered every two year:
*Introduction to Quantum Field Theory.
*Introduction to Condensed Matter Physics.
*Biomathematics.
Courses for qualification tests:
To be determined.
6. Mathematical Logic, Combination and Discrete Mathematics
Combinatorial Mathematics.
*Mathematical Logic.
Probability Theory.
*Discrete Mathematics.
*Mathematics in Information and Big Data.
Courses for qualification tests:
To be determined.
7. Other Courses
Courses offered every year:
Mathematical Skills Training.
Courses offered every two year:
History of Mathematics.
Courses of Special Topics:
Topics in Analysis: Complex Analysis, Harmonic Analysis, e.g. Function Theory of Several Complex Variables. etc.;
Topics in Partial Differential Equation: courses offered in the first and second semester;
Topics in Ordinary Differential Equation & Dynamical System: courses offered in the first and second semester, e.g. Smooth Ergodic Theory. etc.;
Topics in Algebra: courses offered in the first and second semester;
Topics in Geometry and Topology:
Algebraic Topology: Category Theory.
Geometric Topology: Introduction to Contact Topology. Foliation. etc.
Differential Topology: courses offered in the first and second semester, e.g. Morse Theory. Floer Homology Groups. etc.
Riemannian Geometry: courses offered in the first and second semester, e.g. Gromov Geometry. Geometric Analysis. etc.
Global Differential Geometry: Fiber Bundle Geometry. etc.
*Moduli Space & Gauge Field Theory: courses offered in the first and second semester.
Topics in Mathematical Physics:
courses offered in the first and second semester for two years, including Gromov–Witten Theory, Fukaya Category Theory, Mirror Symmetry, etc.
Courses of Hotly Discussed Topics:
Every year at least one course will be offered in accordance with the latest developments in mathematics.