Mathematics: History and Culture - 2023 entry

Over the course of its history, mathematics has been shaped both by the subject’s own internal logic, as well as by the nature and needs of the society it which it was developed and transmitted. This module gives you the opportunity to see how the mathematics studied today has evolved over the centuries, and how mathematics relates to wider issues in culture and society. Through a mixture of lectures, student-led presentations and guided study involving the research and writing of essays, you will become familiar with selected aspects of the development of mathematics and its applications throughout history.

Pre-requsite modules: MTH1001 or COM1012.

The aim of this module is to give you an appreciation of the historical development of mathematics and of its place within the wider culture. By studying a number of specific topics, you will become familiar with the changing nature of mathematics and its role throughout history. This includes how various cultures have been influenced by numbers, geometry, algebra, calculus and the full range of mathematical ideas. Topics will be drawn from particular areas of mathematics, such as numbers, geometry, algebra, calculus, as well as from the philosophy and foundations of mathematics.

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

1 demonstrate a general appreciation of the history and philosophy of mathematics and its role in human history and culture;

2 reveal in-depth knowledge of a selection of topics, and demonstrated knowledge and critical appreciation in these topics.

Discipline Specific Skills and Knowledge:

3 show an understanding of how mathematical ideas have emerged and evolved;

4 appreciate how mathematical thinking has contributed to human history and culture;

5 display an understanding of the original historical context of material found in other modules within the mathematics degree programme.

Personal and Key Transferable/ Employment Skills and  Knowledge:

6 exemplify research, self-study, critical thinking and writing skills through essay writing;

7 illustrate oral presentation skills by participation in seminars and oral presentation;

8 demonstrate teamwork skills by researching and presenting one of the topics in a group seminar;

9 show IT skills by research and presentation of your work.

In any year a selection of four topics will be taken from the following list:

- the Greek legacy: Pythagoras, Euclid, Apollonius, Archimedes - aspects of geometry and number theory;

- ancient mathematics: a selection of ancient Egyptian, Babylonian, Greek, Chinese, Indian and Arabic/Persian Mathematics;

- geometry: Euclid's fifth postulate, non-Euclidean geometries, the Kleinian view, finite geometries, fractal geometry;

- algebra: from geometric algebra to symbolic algebra, Arabic developments, solution of polynomials by radicals, Gauss and the Fundamental Theorem of Algebra, Galois theory;

- history of numbers: history of the representation, arithmetic and use of numbers, development of number systems;

- the development of calculus: history of the foundations and emergence of calculus. From Newton/Leibniz to rigorous approaches;

- women in mathematics: a study of the experience of women in mathematics;

- what probability is: a history of the development of the ideas of probability and its applications;

- mathematical ideas in western cultural thought and history;

- philosophy and the foundations of mathematics: Frege, Hilbert, Russell, logicism, intuitionism;

- philosophy of science: empiricism, logical positivism, Popper, Kuhn;

- contemporary topics in the philosophy and culture of mathematics.

*Please refer to reassessment notes for details on deferral vs Referral reassesment 

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped. 

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 40%. 

ELE: https://ele.exeter.ac.uk

Reading list for this module: