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August 3rd – August 6th 2009

Professor Martin Corless, Purdue University

Fundamentals of Probability

August 17th – August 20th 2009

Professor Chris King, Northeastern University

1. Review of basic probability theory;
2. Discrete-time Markov chains;
3. Markov jump processes; Markov chains and diffusion processes;
4. Communication and recurrence;
5. Invariant measures, stationary distributions and reversibility;
6. Laws of Large numbers;
7. The Central Limit Theorem;
8. Infinitesimal generators and the master equation;
9. Markov chain monte carlo

• Basic Real Analysis
• Basic Linear Algebra
• Fundamentals of Probability

Lecture Notes

To Appear

Further Reading

• Markov Chains. J. R. Norris. Cambridge University Press, 1997

1. Fundamental Concepts
   1. Directed and undirected graphs, bi-partite graphs;
   2. Paths, cycles, circuits and trees;
   3. Connectivity and diameter;
   4. The adjacency matrix
2. Basic Algorithms
   1. Breadth-first and depth-first search;
   2. Dijkstra’s algorithms;
   3. Floyd-Warshall algorithm;
   4. Spanning Trees;
3. Networks and Flows
   1. Ford-Fulkerson algorithm;
   2. Edmonds-Karp algorithm;
   3. Blocking flows;
   4. Goldberg-Tarjan algorithm
4. Coloring and related topics
   1. Edge and vertex coloring problems;
   2. Coloring in communications;
   3. Modern coloring algorithms

• Basic Linear Algebra

Lecture Notes

To Appear

Further Reading

• Graphs, Networks and Algorithms. D. Jungnickel. Springer, 2005
• Modern Graph Theory. B. Bollobas. Springer, 2002