Synopsis for O1: History of Mathematics

Level: H-level
Assessment: 2-hour written examination paper for the MT lectures and 3000-word essay for the reading course.
Weight: Whole unit.

Recommended prerequisites:

None.
Quota: The maximum number of students that can be accepted will be 20.

Learning outcomes

This course is designed to provide the historical background to some of the mathematics familiar to students from A-level and the first four terms of undergraduate study, and looks at a period from approximately the mid-sixteenth century to the end of the nineteenth century. The course will be delivered through 16 lectures in Michaelmas Term, and a reading course consisting of 8 seminars (equivalent to a further 16 lectures) in Hilary Term. Guidance will be given throughout on reading, note-taking, and essay-writing.

Students will gain:

• an understanding of university mathematics in its historical context;
• an enriched understanding of the mathematical content of the topics covered by the course
  
  together with skills in:
  
• reading and analysing historical mathematical sources;
• reading and analysing secondary sources;
• efficient note-taking;
• essay-writing (from 1000 to 3000 words);
• construction of references and bibliographies;
• oral discussion and presentation.

Lectures

The Michaelmas Term lectures will cover the following material:

• Introduction.
• Seventeenth century: analytic geometry; the development of calculus; Newton's Principia.
• Eighteenth century: from calculus to analysis; functions, limits, continuity; equations and solvability.
• Nineteenth century: group theory and abstract algebra; the beginnings of modern analysis; sequences and series; integration; complex analysis; linear algebra.

Classes to accompany the lectures will be held in Weeks 3, 5, 6, 7. For each class students will be expected to prepare one piece of written work (1000 words) and one discussion topic.

Reading course

The Hilary Term part of the course is run as a reading course during which we will study two or three primary texts in some detail, using original sources and secondary literature. Details of the books to be read in HT 2013 will be decided and discussed towards the end of MT 2012. Students will be expected to write two essays (2000 words each) during the first six weeks of term. The course will then be examined by an essay of 3000 words to be completed during Weeks 7 to 9.

Assessment

The Michaelmas Term material will be examined in a two-hour written paper at the end of Trinity Term. Candidates will be expected to answer two half-hour questions (commenting on extracts) and one one-hour question (essay). The paper will account for 50 will be examined by a 3000-word essay at the end of Hilary Term. The title will be set at the beginning of Week 7 and two copies of the project must be submitted to the Examination Schools by midday on Friday of Week 9. This essay will account for 50\

Jacqueline Stedall, Mathematics emerging: a sourcebook 1540–1900, (Oxford University Press, 2008).
Victor Katz, A history of mathematics (brief edition), (Pearson Addison Wesley, 2004), or:
Victor Katz, A history of mathematics: an introduction (third edition), (Pearson Addison Wesley, 2009).
Benjamin Wardhaugh, How to read historical mathematics, (Princeton, 2010).

Supplementary reading

John Fauvel and Jeremy Gray (eds), The history of mathematics: a reader, (Macmillan, 1987).