MATH429-23S1 (C) Semester One 2023

Combinatorics

15 points

Details:
Start Date: Monday, 20 February 2023
End Date: Sunday, 25 June 2023
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 5 March 2023
  • Without academic penalty (including no fee refund): Sunday, 14 May 2023

Description

Combinatorics

Matroids (combinatorial geometries) are precisely the geometric structures that underlie the solution of many combinatorial optimisation problems. These problems include scheduling and timetabling, and finding the minimum cost of a communications network between cities. Given this, it is surprising that matroid theory also unifies the notions of linear independence in linear algebra and forests in graph theory as well as the notions of duality for graphs and codes. This course is an introduction to matroid theory and is designed for mathematics and computer science students.

Topics

Definition and three fundamental examples; circuits, bases, and uniform matroids; the Greedy Algorithm; geometric representations; the rank function; matroid representation; the closure operator; duality; minors; connectivity; excluded-minor theorems; the Tutte polynomial.

Prerequisites

Subject to approval of the Head of School.

Course Coordinator

Charles Semple

Notes

This course is an introduction to matroid theory, a subject that unifies the notions of linear independence in linear algebra and forests in graph theory as well as the notions of duality for graphs and codes. Matroids are also the geometric structures that underlie the solution of many combinatorial optimisation problems.

Indicative Fees

Domestic fee $1,045.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH429 Occurrences

  • MATH429-23S1 (C) Semester One 2023
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