Mathematics

This course covers the theory, models, and analysis of probability and basic statistics and their applications with emphasis on electrical and computer engineering problems. The main topics are: Experiments, Model, and Probabilities, Random Variables, Random Variables and Expected Value, Random Vectors, Sums of Random Variables, Parameter Estimation Using the Sample Mean, and Hypothesis Testing. Text: R.D. Yates and D.J. Goodman, PROBABILITY AND STOCHASTIC PROCESSES. Assessment: midterm exam (35%), final exam (35%), homework and problems (25%), participation (5%).

This course introduces fundamental principles and techniques in combinatorics as well as the basics of graph theory, which have practical applications in such areas as computer science and operations research. The major topics from combinatorics are: Permutations and Combinations, Binomial and Multinomial Coefficients, Principle of Inclusion and Exclusion, Generating Functions, Recurrence Relations. The major topics from graph theory are: Basic Concepts and Results, Bipartite graphs and trees.

The course covers introductory linear algebra, focusing on the eigenvalues and eigenvectors of a matrix, orthogonality, and properties of positive definite matrices. The eigenvalues and eigenvectors are considered from their definitions to their applications. Other topics include orthogonal projections, the Gram-Schmidt process, and the inner product space.