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MATH 310 Syllabus

Discrete Structures

Revised: September 2020

Course Description

Graph Theory: planarity, Eulerian, Hamiltonian, colorings, and trees. Enumeration: permutations, combinations, generating functions, recurrence relations. Additional topics as determined by Instructor. Prerequisites: MATH 250. Three credit hours.

Student Learning Objectives

  • Use graphs to model and solve a variety of problems;
  • Identify and prove structural properties possessed by a given graph; and
  • Use combinatorial modeling to solve problems in discrete mathematics.
  • Be able to analyze and use appropriate algorithms related to graphs and combinatorial problems.

Text

Sarah-marie belcastro, Discrete Mathematics with Ducks, Second Edition. CRC Press, 2019.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

The topics below should be given roughly equal attention. Their chronological ordering is left to the instructor鈥檚 discretion.

  • Elements of Graph Theory
    Graphs, applications of graph theory, and graph isomorphisms
  • Trees, Algorithms, and Searching
    Definition and examples of algorithms. Properties of trees, depth-first and breadth-first searching, and spanning trees.
  • Circuits and Graph Coloring
    Euler circuits, Hamiltonian cycles, graph coloring, coloring theorems, planarity.
  • Counting Methods
    Basic counting principles, arrangements and selections, arrangements and selections with repetition, distributions, and binomial coefficients. Counting with Venn diagrams and the inclusion-exclusion formula.
  • Recurrence Relations and Generating Functions
    Generating function models, and calculating coefficients of generating functions. Recurrence Relation models, divide-and-conquer relations, and solutions of linear recurrence relations.
  • Additional Topics
    To be chosen based on instructor expertise and student interest. Examples include: hypergraphs, mathematics of cryptography, number theory, bijective proofs, review of induction, the use of computers in discrete mathematics, etc.