Marcelo Sales

Ma 121 abc. Combinatorial Analysis. 9 units (3-0-6); first, second, third terms, 2026-27. Prerequisites: Ma 5. A survey of modern combinatorial mathematics, starting with an introduction to graph theory and extremal problems. Flows in networks with combinatorial applications. Counting, recursion, and generating functions. Theory of partitions. (0, 1)-matrices. Partially ordered sets. Latin squares, finite geometries, combinatorial designs, and codes. Algebraic graph theory, graph embedding, and coloring.
Instructors: Dong, Sales

Ma 191 abc. Selected Topics in Mathematics. 9 units (3-0-6); first, second, third terms, 2026-27. Each term we expect to give between 0 and 6 (most often 2-3) topics courses in advanced mathematics covering an area of current research interest. These courses will be given as sections of 191. Students may register for this course multiple times even for multiple sections in a single term. The topics and instructors for each term and course descriptions will be listed on the math option website each term prior to the start of registration for that term.
Instructors: Sales, Bjoern, Marcolli

Ma/CS 6/106 abc. Introduction to Discrete Mathematics. 9 units (3-0-6); first, second, third terms, 2026-27. Prerequisites: for Ma/CS 6 c, Ma/CS 6 a or Ma 5 a or instructor's permission. First term: a survey emphasizing graph theory, algorithms, and applications of algebraic structures. Graphs: paths, trees, circuits, breadth-first and depth-first searches, colorings, matchings. Enumeration techniques; formal power series; combinatorial interpretations. Topics from coding and cryptography, including Hamming codes and RSA. Second term: directed graphs; networks; combinatorial optimization; linear programming. Permutation groups; counting nonisomorphic structures. Topics from extremal graph and set theory, and partially ordered sets. Third term: syntax and semantics of propositional and first-order logic. Introduction to the Godel completeness and incompleteness theorems. Elements of computability theory and computational complexity. Discussion of the P=NP problem.
Instructors: T. Yu, Dong, Sales