Combinatorics and Graph Theory

University of Newcastle

Course Description

  • Course Name

    Combinatorics and Graph Theory

  • Host University

    University of Newcastle

  • Location

    Newcastle, Australia

  • Area of Study

    Computer Science, Information Technologies, Mathematics, Statistics

  • Language Level

    Taught In English

  • Prerequisites

    MATH1510

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • Host University Units

    10
  • Recommended U.S. Semester Credits
    3 - 4
  • Recommended U.S. Quarter Units
    4 - 6
  • Overview

    Combinatorics and Graph Theory is a blend of the mathematical techniques applicable to Computer Science, Information Technology and Statistics. This is 'discrete' mathematics as distinct from the continuous mathematics of calculus. It is a major growth area in modern mathematics, largely because of emerging applications in areas such as biotechnology and communication security.
    Much of the subject matter is a continuation of topics studied in MATH1510 such as graphs, trees, and enumeration, and additional topics such as experimental design and finite geometry are introduced. Some use is made of basic techniques from calculus and abstract algebra.
    LEARNING OUTCOMES
    1. An in-depth knowledge of one specific area of mathematics.
    2. An improved ability to communicate mathematical ideas.
    3. Some experience with applications of mathematics to the Information Sciences.
    CONTENT
    Enumeration: generating functions, recurrence relations, Polya's Theorem, inclusion-exclusion.
    Graph theory: paths and cycles, connectivity, factorisations, colouring, planarity applications.
    Combinatorial Designs: finite fields, Latin squares, Steiner triple systems, finite geometries.
    ASSESSMENT ITEMS
    In Term Test: Examination - Class
    Written Assignment: Assignments
    Tutorial / Laboratory Exercises: Group/tutorial participation and contribution: Lab exercises and group case study
    Formal Examination: Final examination

Course Disclaimer

Courses and course hours of instruction are subject to change.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.