Course Materials: Michaelmas Term
Main content blocks
- Lecturer: Profile: Christopher Hollings
Course information
General prerequisites:
None.
Course term: Michaelmas & Hilary
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 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. The MT lecture course, delivered through 16 lectures, looks at a period from approximately the mid-sixteenth century to the end of the nineteenth century. The HT reading course involves looking in depth at one particular topic, which may be drawn from any period, and consists of 8 seminars (equivalent to a further 16 lectures). 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.
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; number theory; non-Euclidian geometry.
The MT lectures will be complemented by four intercollegiate classes in which the assigned reading will be discussed. For each class students will be expected to prepare one piece of written work (1000 words) and one discussion topic. Students may also be expected to present the content of their essays to the whole class.
Guided reading course
The Hilary Term part of the course is run as a guided 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 2026 will be made available towards the end of MT 2025. Students will be expected to write two or three essays (2000 words each) in MT 2025.
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.
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; number theory; non-Euclidian geometry.
The MT lectures will be complemented by four intercollegiate classes in which the assigned reading will be discussed. For each class students will be expected to prepare one piece of written work (1000 words) and one discussion topic. Students may also be expected to present the content of their essays to the whole class.
Guided reading course
The Hilary Term part of the course is run as a guided 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 2026 will be made available towards the end of MT 2025. Students will be expected to write two or three essays (2000 words each) in MT 2025.
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.
Section outline
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BO1.1. MT25 Slides for Lecture 3 File
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BO1.1. MT25 Slides for Lecture 4 File
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BO1.1. MT25 Slides for Lecture 5 File
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BO1.1. MT25 Slides for Lecture 6 File
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BO1.1. MT25 Slides for Lecture 7 File
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BO1.1. MT25 Slides for Lecture 8 File
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BO1.1. MT25 Slides for Lecture 9 File
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BO1.1. MT25 Slides for Lecture 10 File
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BO1.1. MT25 Slides for Lecture 11 File
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BO1.1. MT25 Slides for Lecture 12 File
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BO1.1. MT25 Slides for Lecture 13 File
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BO1.1. MT25 Slides for Lecture 14 File
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BO1.1. MT25 Slides for Lecture 15 File