modules

This module is designed to develop an understanding of the nature of mathematics and mathematical thinking. It takes you on a voyage of exploration of how mathematics was invented and developed. For millennia BC, mathematics was used for various purposes such as in the study of planets and their motions as well as in construction and trading, and since then the study of mathematics was expanded and new branches were explored. The module aims to enhance your ability to use mathematical reasoning, abstraction and logic while enjoying the process of learning and performing mathematical procedures. In its first theme, it focuses on the concept of number sets and cardinality, where notions like, ‘infinity’ are discussed and explored through examples and simple proofs. The second theme develops an understanding of the mathematical language through an illustration of symbolic representations, patterns and relationships, such as the relationship between the number of spirals in a pine cone (a natural pattern) and the famous Fibonacci sequence (a number pattern), showing how those patterns are linked to other parts of mathematics such as geometry, arithmetic and probability. This is followed by a third theme about Euclidean geometry featuring some of its intriguing theorems and properties including simple geometrical proofs as well as some special geometric shapes (e.g. Kepler triangle), it also covers some aspects of coordinate geometry and transformations.

 

Each theme will be covered over three weeks with scheduled weekly sessions led by the module instructor/convenor. During those sessions you will be introduced to the topic of the theme through lecture presentations, learning materials and provided exercise worksheet. In this module you will learn how to: use theories and definitions; analyse and critique mathematical claims; perform simple proofs; formulate examples and communicate results. This will be achieved by encouraging you to develop solutions for the weekly formative exercises in the class while working in small groups, as well as through effective management skills and self-directed study outside scheduled hours. You will be assessed through a combination of summative assessments: in-class tests (3 tests – a test per theme), coursework and presentation (a mini-project), and a final exam. Each in-class test will take place during the end of the third week of the subject theme; the coursework will be in the form of a mini-project consisting of two components selected from a list of given problems – components should be selected from two different topics, and the solution of a component could be presented in the form of an essay, a recorded audio/clip, a written mathematical argument, or could be a combination of those.

 

Students are expected to have knowledge of Principles of Pure Mathematics (MTH0001 ) as a co-requisite.