MATH 432Discrete Mathematics

Discrete mathematics deals with mathematical structures that can be counted. These structures can describe, for example, the pairwise relationships between a set of objects (forming graphs) or discrete symmetries of crystals (forming groups). Another example is a matroid, which describes a notion of dependence of a set of objects. This course combines ideas from graph theory, linear algebra, coding theory, and problems in combinatorial optimisation. It investigates properties of these various mathematical structures, and the underlying notions of duality. 

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MATH 432 is not offered in 2022. We're showing course information for 2025.

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Trimester One of three teaching periods that make up the academic year—usually March to June, July to October, and November to February.
CRN A unique number given to a single version of a course. It differentiates between courses with the same course code that are taught in different trimesters or streams, or in different modes (for example, in person or online).

Course details

Dates
7 Jul 2025 to 9 Nov 2025
Starts
Trimester 2
Fees
NZ$1,278.60 for
International fees
NZ$5,357.55
Lecture start times
  • Tuesday 3.10pm
  • Thursday 3.10pm
Campus
Kelburn
Estimated workload
Approximately 150 hours or 8.8 hours per week for 17 weeks
Points
15

Entry restrictions

Prerequisites
Corequisites
None
Restrictions
None

Taught by

School of Mathematics and StatisticsFaculty of Engineering

Key dates

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You'll be told about assessment dates once the course has begun.

Key dates

About this course

Matroids are abstract mathematical objects that we use to understand certain aspects of space. In this respect, the study of matroids is like group theory (which we can use to understand symmetries of space). Matroids are used to understand the dependence properties of discrete sets of points in space. A set of three points that lie on a common line, or a set of four points that lie on a common plane, is geometrically dependent. Matroid theory studies this type of dependence. Matroids are like groups in another way: they arise from many disparate areas of mathematics. Some of the most important examples of matroids arise from considering notions of dependence from graph theory and from linear algebra. MATH 432 is an introduction to the foundational definitions and results of matroid theory.

Course learning objectives

Students who pass this course will be able to:

  1. Know the major definitions and results in elementary matroid theory, as defined by the content of the course notes.

  2. Demonstrate your knowledge by stating definitions and results, and constructing proofs of simple theorems.

How this course is taught

During the trimester there will be two lectures per week, each of ninety minutes.
This course is designed for in-person study, and students are strongly recommended to attend. All assessment items will require in-person attendance.

Assessment

  • Final test Type: IndividualMark: 20%
  • Assignment 1 Mark: 20%
  • Assignment 2 Mark: 20%
  • Assignment 3 Mark: 20%
  • Assignment 4 Mark: 20%

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Mandatory requirements

There are no mandatory requirements for this course.

Lecture times and rooms

What you’ll need to get

The course is self-contained, and printed notes will be provided. The textbook Matroid Theory by James Oxley is an additional resource that you may wish to consult. Copies are available on request.

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Selected offering

MATH 432

7 Jul–9 Nov 2025

Trimester 2 · CRN 7673

2025 course optionsOptions (1)