This course introduces students to ideas and techniques from discrete mathematics that are widely used in Computer Science. Students will learn about the fundamentals of propositional and predicate calculus, set theory, relations, recursive structures and counting. This course will help increase students’ mathematical sophistication and their ability to handle abstract problems.

This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.

This course will introduce, explain and employ both the classical and modern basic techniques of cryptography. Topics will include the Vignère cipher, affine ciphers, Hill ciphers, one-time pad encryption, Enigma, public key encryption schemes (RSA, Diffie-Hellman, El-Gamal, elliptic curves), and hash functions. The course will include an introduction to algebraic structures and number theoretic tools used in cryptography.

This course covers basic set theory, number theory, groups, subgroups, cyclic and permutation groups, Lagrange and Sylow theorems, quotient groups, and isomorphism theorems. Group Theory finds applications in other scientific disciplines like physics and chemistry.

Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.

Independent Study