Department of Mathematical Sciences,
Tsinghua University, Beijing 100084, China
Comments are welcome to: jxie@math.tsinghua.edu.cn
Game Theory and its Applications (advanced course, for senior and graduates)
(Course notes are only available to the students enrolled in this course)
1. Introduction
2. Static games with complete information;
3. Dynamic games with complete information;
4. Static games with incomplete information (Beyesian games);
5. Dynamic games with incomplete information;
6. Mechanisim design and principal-agent theory;
7. Evolutionary game theory and behavioral game theory;
8. Cooperative game theory.
Network Optimization (for senior and graduates)
Course
Notes (Chinese version, in PPT-format)
2. Minimum Spanning Tree (Kruskal Algorithm; Prim Algorithm; Sollin Algorithm); Minimum Arberosence and Maximum Branchings (Edmons Algorithm)
3. Introduction to Integer Programming: Cut-Plane, Branch and Bound, Totally Unimodular Matrix
4. Introduction to Dynamic Programming
5. Shortest Path Problem: Topological Sorting; Label-setting Algorithm; Label-correcting Algorithm; Dijkstra Algorithm; Bellman-Ford; Floyd-Warshall
6. Maximum Flow Problem: Ford-Fulkerson; Maximal Capacity Argumenting; Capacity Scaling; Shortest Path Argumenting; Highest-label Preflow-push
7. Minimum Cost Flow: Cycle-Canceling; Primal-Dual Algorithm; Out-of-kilter Algorithm; Relaxation Algorithm; Network Simplex Algorithm
8. Maximum Matching and Wighted Matching: on Bipartite Graphs; on
General
Graphs
2. Recurrence: Solving methods and example; Master Theorem
3. Randomized algorithm and Probability analysis
4. Sorting algorithms
5. Dynamic Programming
6. Greedy algorithms
7. Graphs: DFS and BFS etc.; Spanning tree; Shortest Path
8. Network flow: Maximum Flow; Minimum Cost Flow
9. Computational Complexity: NP-Complete Theory
10. Approaximate Algorithms: Introduciton and Examples
Experiments in Mathematics (for undergraduates)
Course
Notes (Chinese version, in PDF-format)
Mathematical Modeling (for undergraduates)
Course
Notes (Chinese and /or English version, in PPT-format)
Introduction to Production and Operations Management (POM):
Deterministic Models and Algorithms
Course
Notes (Chinese and /or English version, in PPT-format)
Introduction to Supply Chain Management (SCM): Stochastic Models and
Algorithms
Course
Notes (Chinese and /or English version, in PPT-format)
2. Neural Networks
3. Simulated Annealing
4. Taboo Search
5. Evolutionary Computation (GA, EP, ES)
6. Lagrangean Relaxation
Optimization Methods / Linear and Nonlinear Programming
(for undergraduates and graduates of any level)
2. Introduction to Convex Analysis
3. Simplex method and Its Extensions
4. Duality Theory for Linear Programming
5. Introduction to Computational Complexity
6.Introduction to Inter-Point Algorithm
7. Unconstrained Nonlinear Programming
8. Constrained Nonlinear Programming
9. Multi-Creteria Programming
10. Goal Programming
Numerical Analysis (for undergraduates and graduates
of any level)
2. Interpolation
3. Approaximation
4. Numerical Intgration
5. Numerical Solutions for ODE
6. Numerical Solutions for Nonlinear Equations
7. Numerical Solutions for Linear Equations: Direct methods and Iterative methods
8. Numerical Solutions for Charateristic Values and Charateristic Vectors of Matrices
Linear Algebra and Analytical Geometry (for freshmen)