Geometry and Calculus for Computing

Overview

Mathematics provides the foundation for reasoning, problem-solving, and analysis in computer science. Geometry and Calculus for Computing equips you with essential tools to model shapes, describe motion, and analyse change. Across four modules, you’ll build a solid grounding in trigonometry, graph sketching, kinematics, exponential and logarithmic functions, and introductory calculus. You’ll learn to connect abstract mathematical concepts to practical computing applications, from computer graphics and simulations to optimisation and algorithm analysis. By the end of the course, you’ll have the skills to interpret functions, calculate gradients, and apply mathematical reasoning to a wide range of computational problems. This course prepares you for advanced study in computer science and data science by strengthening the mathematical toolkit you need to succeed in both academic and professional contexts.

Syllabus

Angles, triangles and trigonometry

In this module, we will look at angles, triangles and trigonometry. We will study trigonometric ratios on different triangles, we will work with triangles that are not necessarily right-angled and we will use the sine, cosine and tangent rules relating to the lengths and angles of a triangle. We will also look at Pythagoras' theorem and use it in conjunction with trigonometric ratios.

Graph sketching and kinematics

In this module, we will learn about three concepts: the definition of a function, Cartesian coordinates and the graph of a function. We will use these concepts to describe simple motion (kinematics).

Exponential and logarithmic functions

In this topic (weeks 13 and 14), we will look at exponential and logarithmic functions. This week, we will introduce the exponential functional as extension of elevation to a non-integer power, we derive its properties and plot.

Limits and differentiation

In this topic (weeks 15 and 16), we will focus on limits and differentiation. This week, we will look at limits of a function and discuss the concept of continuity of a function. We will then introduce a new tool, differentiation and derive the derivative of common functions from first principles.