Mathematics

This course brings together as a coherent body of knowledge the game theoretic algorithms and models that underpin several flourishing subjects at the intersection of computer science, economics, e-commerce, and AI.

The course treats multiplicative number theoretic functions, Möbius inversion formula, properties of Euler's totient function, primitive roots and indices, quadratic residues, the Legendre symbol and it's properties, the quadratic reciprocity theorem, representations of integers as sums of squares, number theoretic properties of the Fibonacci sequence, continued fractions, Diophantine approximation.
 

This course provides research training for exchange students. Students work on a research project under the guidance of assigned faculty members. Through a full-time commitment, students improve their research skills by participating in the different phases of research, including development of research plans, proposals, data analysis, and presentation of research results. A pass/no pass grade is assigned based a progress report, self-evaluation, midterm report, presentation, and final report.

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.