- Lecturer: Christopher Hollings

General Prerequisites:

None.

Course Term: Michaelmas

Course Lecture Information: 16 lectures in MT and reading course of 8 seminars in HT

Course Weight: 2

Course Level: H

Course Overview:

Quota

The maximum number of students that can be accepted will be 20. Students should note, however, that numbers are unlikely to reach this level, and so there is little danger of not being accepted onto the course.

The maximum number of students that can be accepted will be 20. Students should note, however, that numbers are unlikely to reach this level, and so there is little danger of not being accepted onto the course.

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 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.

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 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 books to be read in HT 2023 will be decided and discussed towards the end of MT 2022. 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 two copies of the project must be submitted to the Examination Schools by midday on Monday of Week 10; submission of an electronic version of the essay will also be required by the same deadline. The essay will account for 50% of the marks for the course.

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 books to be read in HT 2023 will be decided and discussed towards the end of MT 2022. 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 two copies of the project must be submitted to the Examination Schools by midday on Monday of Week 10; submission of an electronic version of the essay will also be required by the same deadline. The essay will account for 50% of the marks for the course.