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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

Overall Impression

1. How did you find out about the network maths programme?

2. What is your overall rating of the programme? (1 = poor, 5 = excellent)

Fundamentals of Probability

Please indicate how strongly you agree or disagree with each of the following four statements by ticking the appropriate box. (1 = strongly disagree, 5 = strongly agree)

1. The material covered in this module was relevant to my own research

2. The Lectures helped me to understand the material of the module.

3. The Lecture notes were clearly written and comprehensive.

4. The applications talks for this module were topical and appropriate.

5. Have you any specific comments or suggestions regarding this module and how it could be improved in your opinion?

Introduction to Dynamic Systems

Please indicate how strongly you agree or disagree with each of the following four statements by ticking the appropriate box. (1 = strongly disagree, 5 = strongly agree)

1. The material covered in this module was relevant to my own research

2. The Lectures helped me to understand the material of the module.

3. The Lecture notes were clearly written and comprehensive.

4. The applications talks for this module were topical and appropriate.

5. Have you any specific comments or suggestions regarding this module and how it could be improved in your opinion?

Positive Systems

Please indicate how strongly you agree or disagree with each of the following four statements by ticking the appropriate box. (1 = strongly disagree, 5 = strongly agree)

1. The material covered in this module was relevant to my own research

2. The Lectures helped me to understand the material of the module.

3. The Lecture notes were clearly written and comprehensive.

4. The applications talks for this module were topical and appropriate.

5. Have you any specific comments or suggestions regarding this module and how it could be improved in your opinion?

Optimisation I

Please indicate how strongly you agree or disagree with each of the following four statements by ticking the appropriate box. (1 = strongly disagree, 5 = strongly agree)

1. The material covered in this module was relevant to my own research

2. The Lectures helped me to understand the material of the module.

3. The Lecture notes were clearly written and comprehensive.

4. The applications talks for this module were topical and appropriate.

5. Have you any specific comments or suggestions regarding this module and how it could be improved in your opinion?