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## ECM3719 - Mathematics: History and Culture (2015)

MODULE TITLE | Mathematics: History and Culture | CREDIT VALUE | 15 |
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MODULE CODE | ECM3719 | MODULE CONVENER | Prof Peter Ashwin (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
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DURATION: WEEKS | 11 weeks | 0 | 0 |

Number of Students Taking Module (anticipated) | 34 |
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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.

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.

Scheduled Learning & Teaching Activities | 20.00 | Guided Independent Study | 130.00 | Placement / Study Abroad | 0.00 |
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Category | Hours of study time | Description |

Scheduled learning and teaching activities | 10 | Lectures |

Scheduled learning and teaching activities | 10 | Seminars |

Guided independent study | 130 | Guided independent study |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
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Formative essay | 500 words | 6, 9 | Peer feedback |

Coursework | 40 | Written Exams | 50 | Practical Exams | 10 |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Coursework - essay 1 | 10 | 500 words | 1,3,4,5,6,9 | Written comments |

Coursework - essay 2 | 30 | 1,500 words | 1,2,3.4,5,6,9 | Written comments |

Practical oral presentation | 10 | 10 minutes during one of the seminars | 1,2,3,4,6,7,8,9 | Emailed feedback |

Written examination | 50 | 1 1/2 hours | 1,2,3,4,5,6 | Feedback sheet |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-reassessment |
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As above | Written examination | 1,2,3,4,5,6 | August Ref/Def period |

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: http://vle.exeter.ac.uk

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Katz V.J. | A History of Mathematics. An Introduction | 3rd | Addison-Wesley | 2009 | 978-0321387004 | [Library] |

Set | Grattan-Guinness I. | The Fontana History of the Mathematical Sciences | Fontana | 2000 | 978-0006861799 | [Library] | |

Set | Fauvel J. and Gray J. | The History of Mathematics: a reader | Macmillan & Oxford University Press | 1987 | 000-0-333-42791-2 | [Library] | |

Set | Dunham W. | Journey through genius: the great theorems of mathematics | Wiley | 1990 | 000-0-471-50030-5 | [Library] | |

Set | Boyer, C.B. | A History of Mathematics | Electronic | Wiley | 2011 | 0471097632 | [Library] |

Extended | Struik D.J. | A concise history of mathematics | Dover | 1987 | 000-0-486-60255-9 | [Library] | |

Extended | Kline M. | Mathematics in Western Culture | Oxford University Press | 1972 | 000-0-140-21546-8 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
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PRE-REQUISITE MODULES | None |
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CO-REQUISITE MODULES | None |

NQF LEVEL (FHEQ) | 6 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Friday 09 January 2015 | LAST REVISION DATE | Wednesday 11 March 2015 |

KEY WORDS SEARCH | History; philosophy; culture of mathematics. |
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