Core Mathematics III module (MA21001)

Core Mathematics III takes you deeper into the structure and logic of university mathematics. You will move beyond familiar two- and three-dimensional ideas into higher-dimensional algebra, while developing the rigour needed to understand calculus at a more advanced level. 

You will study vectors and matrices in greater depth, leading to powerful ideas such as vector spaces, linear independence, basis, dimension, eigenvalues, and eigenvectors. These concepts are central to pure mathematics and essential in physics, data science, modelling, algorithms, and many areas of applied mathematics. 

You will also strengthen your understanding of limits and continuity. A key step is learning to work with precise mathematical definitions, including epsilon-delta arguments, and extending calculus from one variable to functions of two variables. 

By combining abstraction with problem-solving, this module develops your mathematical maturity, precision, and independence, preparing you for advanced mathematics, physics, and careers that rely on high-level analytical thinking.

What you will learn

In this module, you will:

• study vectors, matrices, and systems of linear equations 
• explore vector spaces, linear independence, basis, and dimension 
• calculate eigenvalues and eigenvectors 
• deepen your understanding of limits, differentiation, and integration 
• explore functions of two variables, critical points, and double integrals

By the end of this module, you will be able to:

• solve problems using linear algebra and matrix methods 
• understand and apply key ideas in vector spaces 
• use eigenvalues and eigenvectors in mathematical problems 
• construct simple epsilon-delta arguments 
• apply calculus to functions of one and two variables

Assignments / assessment

• Coursework (40%) 
• Final, written exam (60%) 

Teaching methods / timetable

You will learn through a combination of lectures and tutorials designed to build confidence and problem-solving ability. 

Lectures introduce the key ideas, methods, and worked examples, supported by clear online lecture notes. 

In tutorials, you will apply these ideas by solving problems individually and in groups, with guidance and feedback from lecturers.