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MATH-410 Applied Combinatorics
Fall only
We focus on "Internet mathematics" which includes the following topics: the web as a graph, use of the web for collecting information, access to online databases and formulation of queries and questionnaires, network structure and social analysis, random graphs and preferential attachment models, the page rank algorithm, and analysis of malware. Tools will be reviewed and developed as needed - topics in basic graph theory (trees, bipartite graphs, complete graphs, Hamiltonian cycles) including sufficient material on probability (Markov chains, expectation, variation, Martingales, concentration of measure) to support extension of the graph theory
to stochastic and uncertain networks. Connections with neural network and analytic models will be considered as time permits. Emphasis is on the understanding of basic techniques and ability to apply them to actual problems. Course level is suitable for
graduate and advanced undergraduate students.
Ideally, students ought to have had one of the following courses: Graph theory, combinatorics, linear algebra, probability theory, neural networks, database analysis, combinatorial optimization, or number theory. However, the course will be self-contained so a very diligent student could take the course without background.
Credits: 3
Prerequisites: None
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More information
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