Course Overview: Quota: The maximum number of students that can be accepted is 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:
\(\bullet\) an appreciation of university mathematics in its historical context;
\(\bullet\) an enriched understanding of the mathematical content of the topics covered by the course;
\(\bullet\) a broader, multicultural view of mathematics
together with skills in:
\(\bullet\) reading and analysing primary historical mathematical sources;
\(\bullet\) reading and analysing secondary sources;
\(\bullet\) efficient note-taking;
\(\bullet\) essay-writing (from 1000 to 3000 words);
\(\bullet\) construction of references and bibliographies;
\(\bullet\) oral discussion and presentation.
Course Synopsis: Lectures
The Michaelmas Term lectures will cover the following material:
\(\bullet\) Introduction: ancient mathematical knowledge and its transmission to early modern Europe; the development of symbolic notation up to the end of the sixteenth century.
\(\bullet\) Seventeenth century: analytic geometry; the development of calculus; Newton's Principia.
\(\bullet\) Eighteenth century: from calculus to analysis; functions, limits, continuity; equations and solvability.
\(\bullet\) Nineteenth century: group theory and abstract algebra; the beginnings of modern analysis; rigorous definitions of real numbers; integration; complex analysis; set theory; 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. Students will also be expected to present the content of their essays to the whole class.
Reading course
The Hilary Term part of the course is run as a reading course during which we will study a selection of primary texts in some detail, using original sources and secondary literature. Details of the materials to be read in HT 2025 will be made available towards the end of MT 2024. Students will be expected to write three essays (2000 words each) during the first six weeks of term.
Assessment
The Michaelmas Term material will be examined in a two-hour written paper during 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% of the marks for the course. The Reading Course 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 submission of an electronic version of the essay to Inspera will also be required by midday on Monday of Week 10. The essay will account for 50% of the marks for the course.
