MAS343 History of Mathematics

Semester 2, 2021/22 10 Credits
Lecturer: Dr Fionntan Roukema Timetable Reading List
Aims Outcomes Teaching Methods Assessment Full Syllabus

The course aims to introduce the student to the history of mathematics. The topics discussed are Egyptian and Babylonian mathematics, early Greek mathematics, Renaissance mathematics, and the early history of the calculus.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

Outline syllabus

  • Introduction
  • Egypt and Mesopotamia
  • Early Greek mathematics
  • Renaissance mathematics
  • The route to the calculus


  • To introduce the student to the history of mathematics
  • To place mathematical developments into historical perspective
  • To train the student to study from a set text
  • To encourage independent study and use of the University's libraries
  • To allow students to research a topic and then write up a formal report or produce a poster on their findings, which counts towards the continuous assessment part of the course
  • To discuss developments in mathematics in various periods, including its beginnings in the Egyptian and Mesopotamian civilizations, its flowering under the ancient Greeks and its renaissance in sixteenth-century Europe.
  • To trace the pre-history of the calculus from its beginnings in Greece to its rapid expansion in seventeenth-century Europe.

Learning outcomes

  • Discuss some of the difficulties arising in studying the history of mathematics.
  • Describe the structure and scope of the set text, and comment on its weaknesses and strengths.
  • Use the University's libraries to research a topic in the history of mathematics and then to write up a formal report or produce a poster on the topic.
  • Detail the mathematics of the Egyptians and Babylonians, and the role it played in their societies.
  • Contrast the Greeks' attitude to mathematics with that of earlier civilizations and outline the main developments in Greek mathematics up to and including Euclid's Elements.
  • Relate the events leading to the algebraic solution of cubic equations in sixteenth-century Italy, appreciate the mathematics involved, and comment on Italian academic life at the time.
  • Discuss the work of Robert Recorde, Thomas Harriot and John Napier in the circumstances of the time: increasing literacy, growing trade and prosperity and developing technology.
  • Outline and apply some of the pre-calculus methods for finding areas, volumes and tangents that are associated with Euclid, Archimedes, Kepler, Cavalieri, Roberval and Fermat.

Teaching methods

20 lectures (including a speciality lecture, video and poster session), reading a set text together with a commentary on it.

20 lectures, no tutorials


Three equally weighted assignments.

Full syllabus

1. Introduction

The structure of the course and the nature of the history of mathematics.
2. Egypt and Mesopotamia
Egyptian arithmetic, algebra and geometry. Mesopotamian arithmetic, algebra and geometry.
3. Early Greek mathematics
Thales, the Pythagoreans, the three classical problems of antiquity and the Platonic School. Euclid's Elements.
4. Renaissance mathematics
The solution of the cubic equation. The beginnings of mathematics in Britain: Robert Recorde, Thomas Harriot and John Napier.
5. The route to the calculus
Greek origins: the method of exhaustion, the quadrature of the parabola, The Method of Archimedes and the volume of a sphere. Prelude to the calculus: area, tangent, and rectification problems before Newton.

Reading list

Type Author(s) Title Library Blackwells Amazon
A Boyer and Merzbach A history of mathematics 510.9 (B) Blackwells Amazon
A George Gheverghese The crest of the peacock : non-European roots of mathematics Blackwells Amazon
B Katz A history of mathematics 510.9 (K) Blackwells Amazon
C Fauvel and Gray The history of mathematics: a reader 510.9 (H) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.