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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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
Taught by
School of Mathematics and Statistics—Faculty of Engineering
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:
Know the major definitions and results in elementary matroid theory, as defined by the content of the course notes.
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%
Assessment dates and extensions
Once you've signed up to this course, you can use to see due dates for assessments and information about extensions.
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.
Who to contact

Selected offering
MATH 432
7 Jul–9 Nov 2025
Trimester 2 · CRN 7673