This is the second in a two-course sequence. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates.

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 prepares students for professions that use mathematics in daily practice, and for mathematics courses beyond the introductory level where it is essential to communicate effectively in the language of mathematics. It covers various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and set theory, and then moving to applications in advanced mathematics.

The course introduces students to basic techniques of classical and modern cryptography, and learn about the significant impact of codes and ciphers on historical events. Topics will include the Vignère cipher, affine ciphers, Hill ciphers, one-time pad encryption, Enigma, public key encryption schemes (RSA, Diffie-Hellman, elliptic curves), and cryptographic hash functions. The course will include an introduction to algebraic structures and number theoretic tools used in cryptography. Students in this honors course will also study and explore historical source documents to get first-hand exposure to critical aspects of cryptanalysis from the early to mid-20th century.

This course provides an introduction to the study of the set of integers and their algebraic properties. Topics include prime factorization and divisibility, linear Diophantine equations, congruences, arithmetic functions, primitive roots, and quadratic residues.

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.

This course covers the basic theory of rings, integral domains, ideals, modules, and abstract vector spaces. It also covers the key constructions including direct sums, direct products, and field extensions. These topics serve as the foundation of mathematics behind advanced topics such as algebraic geometry and various applications like cryptography and coding theory.

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

Independent Study