# Mathematical Explorations

## Overview

• Credit value: 15 credits at Level 4
• Convenor and tutor: Brad Baxter
• Assessment: problem-based assignments (70%) and a 1000-word essay (30%)

## Module description

In this module we will:

• look at some of the many ways that mathematics can give us insights and understanding in a wide range of real-world situations, from music and harmony to the way nature adapts to large and small scales
• get practice in problem solving, explaining our reasoning, structuring our thinking and writing solutions to problems in a clear and coherent way
• increase awareness of the social and cultural context in which mathematics is done, through biographical information on a diverse range of mathematicians embedded into the course content.

### Indicative module syllabus

• Games and strategies: starting with simple games and moving on to real-life problems of strategy, we’ll look at how simple mathematical ideas can help us make decisions.
• Sound and music: how are sounds made? Why do some notes sound pleasing together and others don’t? This unit explores the mathematics of sound, music and harmony.
• Large and small: why are large animals not just small ones scaled up? Could giants really exist? Why were insects so much larger in prehistoric times? We’ll explore the mathematics of size and scale.
• Time and space: we’ll explore the mathematics of clocks, calendars, maps and navigation and see how humanity has solved these problems over history.

## Learning objectives

By the end of this module, you will have:

• knowledge and understanding of, and the ability to use, mathematical and/or statistical techniques
• knowledge and understanding of a range of results in mathematics
• appreciation of the need for proof in mathematics, and the ability to follow and construct mathematical arguments
• awareness of the use of mathematics and/or statistics to model problems in the natural and social sciences, and the ability to formulate such problems using appropriate notation
• understand the importance of assumptions and have an awareness of where they are used and the possible consequences of their violation
• the ability to present, analyse and interpret data
• appreciation of the historical and cultural aspects of mathematics.