Mathematics

This course explores both theoretical and practical aspects of cryptography, authentication, and information security. Students learn the relevant mathematical techniques associated with cryptography, the principles of cryptographic techniques and how to perform implementations of selected algorithms in this area, and explore the application of security techniques in solving real-life security problems in practical systems.

This interactive course revolves around problem-solving and both playing and analyzing mathematical games. Throughout the course, students are given a sequence of carefully selected problems to solve individually. Students are given ample time to think about the questions - with hints from the instructors as needed - and they receive follow-up problems after each problem solved. Later in the course, the solutions and key learnings are presented by the instructors. Topics include mathematical games, graph theory, chapters from combinatorics, information theory, and invariants.

This is a first course in combinatorics and graph theory and covers graphs, Euler's V-E+F=2 Theorem, Kuratowski's Theorem, counting sets, generating functions, matching, Hall's Marriage Theorem, Polya counting, and counting paths in graphs.

In this course, students develop concepts such as convergence, continuity, completeness, compactness, and convexity in the settings of real numbers, Euclidean spaces, and more general metric spaces.