Mathematics

This course provides an introduction to numerical linear algebra, including methods and principles for solving fundamental problems in linear algebra. The course covers matrix and vector norms, orthogonalization, projection, matrix factorizations, direct and iterative solvers, condition numbers, stability of a method, and complexity of an algorithm. Students learn to solve problems and are trained in implementing numerical methods in code. This course prepares students for further studies in numerical analysis, statistics, computer science, and image analysis.

This course provides an introduction to modern cryptography with a mathematical focus. It covers the basics of abstract algebra and number theory, and introduces cryptocurrencies such as Bitcoin, BlockChain, and FinTech. Topics include data security, stream ciphers, Data Encryption Standard (DES) and alternatives, Advanced Encryption Standard (AES), block ciphers, public-key cryptography, RSA Cryptosystem, elliptic curve cryptosystems, digital signatures, hash functions, Message Authentication Codes (MACs), and key establishment.

This course introduces students to a variety of applicable mathematical methods for solving real-world problems. It is intended for students interested in how further mathematics can be used to solve hands-on problems. The economically-minded will be interested in optimizing based on constrained resources, and computer scientists will be interested in the various network algorithms explored. Physicists will find the material at the end of the course indispensable for solving classical problems. The game theory section of the course includes a discussion of the assumptions made about how rational agents act, which may interest psychologists and philosophy students.