Pure mathematics is mathematics for its own sake, focusing on abstraction, generalisations and proving. 

Imagine a hidden language that governs the patterns and structures behind everything, from the tiniest atom to the vastness of space. Pure mathematics delves into this language, revealing the core concepts that power all areas of science.

During their undergraduate studies, students will focus on two main areas, both with a rich history dating back before the 19th century, so it is mostly mathematics to be used in applications :

  • Analysis: This branch studies continuous change and its applications. You'll explore topics like limits, differentiation, and integration, forming the bedrock for calculus and advanced mathematical analysis. These concepts are fundamental tools used extensively in applied mathematics.
  • Algebra: This branch delves into the abstract structures and relationships between mathematical objects. You'll learn about functions, equations, and various algebraic structures, laying the groundwork for abstract algebra and other advanced areas. Understanding these structures is crucial for formulating the precise models used in applied mathematics.

As you progress on your mathematical journey, pure mathematics truly comes alive. Algebra transforms into the captivating world of abstract algebra, where you explore the elegant structures that govern mathematical objects. Similarly, the exploration of functions in calculus blossoms into the powerful tools of mathematical and functional analysis, opening doors to in-depth theoretical exploration with captivating sub-specialities waiting to be discovered.

Careers and Research

Careers in mathematics rarely carry the title of “mathematician” and are often coupled with a speciality or area of research interest. Students wondering what kind of career they can have with a degree in mathematics should take a look at this brochure by the South African Mathematical Foundation.

Current research in the department can be broadly divided into the following:

  • Functional Analysis
  • Ring and Near-Ring Theory
  • Mathematics Education


First Year

MATT101 Mathematics 1A

MATT102 Mathematics 1B

Second Year

MATT201 Multivariate and Vector Calculus

MATT202 Real Analysis

MATT212 Linear Algebra

Third Year

MATT301 Advanced Real Analysis

MATT311 Advanced Linear Algebra

MATT302 Modern Algebra

MATT312 Complex Analysis


MATH440 Functional Analysis

MATH450 Topology

MATH460 Abstract Algebra

MATH470 Set Theory

MATH480 Measure and Integration Theory

Undergrad Qualifications

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Postgrad Qualifications

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