M325K DISCRETE MATHEMATICS
Prerequisite:
M408D with a grade of at least C, or consent of instructor. This is a first
course that emphasizes understanding and creating proofs. Therefore, it
provides a transition from the problem-solving approach of calculus to the
entirely rigorous approach of advanced courses such as M365C or M373K. The
number of topics required for coverage has been kept modest so as to allow
adequate time for students to develop theorem-proving skills: Introductory
combinatorics: counting principles, permutations with and without repetitions,
combinations and distributions.
Course Topics:
Fundamentals of logic:
truth tables, symbolic logic, elementary set theory, laws of set theory,
Venn diagrams.
Functions:
relations, functions and their properties, Stirling numbers of the second
kind, pigeonhole principle.
Relations:
relation algebra, matrix representation of relations, directed graphs and
relations, partial orders, Hasse diagrams, lattices, equivalence relations,
partitions.
Introductory graph theory:
Euler paths and cycles, planar graphs, Hamilton paths and cycles.