MTH2051 · Introduction to computational mathematics

Overview

When mathematics is used in real-world applications, it almost always involves the use of computers. This unit provides an introduction to numerical methods for solving maths-related problems on computers. Topics covered include error analysis; methods for finding roots of nonlinear equations; polynomial interpolation; numerical differentiation and integration; numerical methods for ordinary differential equations; and methods for solving linear systems. You will receive a solid introduction to the theory of the numerical methods (with derivations of the methods, error estimates and convergence proofs), and will learn to implement the computational methods in Python. The methods and techniques learned have broad applicability in areas that include the natural sciences, engineering, the biomedical sciences, finance, business, machine learning, and data science.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Demonstrate an understanding of the uses of common numerical methods, as well as their advantages and disadvantages;
2. Determine the performance of a numerical algorithm when applied to a concrete mathematical problem from the properties of problem and the properties of the algorithm, using theoretical results;
3. Apply mathematical principles and theorems to quantify the error of approximations used in numerical methods;
4. Work actively with mathematical concepts such as vector norms, matrix norms, the Lipschitz property and the one-sided Lipschitz property in a mathematically rigorous way;
5. Implement numerical methods for a variety of problems in Matlab, and test the accuracy and efficiency of an implementation;
6. Demonstrate advanced skills in the written presentation of theoretical and applied numerical mathematics problems.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.