MA103     
Introduction to Abstract Mathematics

This information is for the 2024/25 session.

Teacher responsible

Prof Peter Allen and Prof Martin Anthony

Availability

This course is compulsory on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science and BSc in Mathematics with Economics. This course is available on the BSc in Actuarial Science, BSc in Data Science and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Pre-requisites

Students should have taken, or be taking concurrently, the course Mathematical Methods (MA100), or the course Methods in Calculus and Linear Algebra (MA108). In Winter Term students will need basic knowledge of Python. Students who do not have this, and who are not attending MA160P, should contact the course convenor at the beginning of AT.

Course content

The course is an introduction to the use of formal definitions and proofs in mathematics, and to basic results of elementary set theory, number theory, linear algebra, algebra and analysis. Specific topics covered are as follows: Logic, sets and functions, relations, real numbers, infimum and supremum, sequences, limits and continuity, integers, prime numbers, greatest common divisor and modular arithmetic, algorithms and running time, complex numbers, groups and vector spaces.

Teaching

This course is delivered through a combination of classes and lectures totalling a minimum of 80 hours across Autumn Term and Winter Term.

Formative coursework

Students will be expected to produce 20 problem sets in the AT and WT.

Written answers to set problems will be expected on a weekly basis.

Indicative reading

Students may wish to have one of the recommended textbooks: N L Biggs, Discrete Mathematics (2nd edn) or P J Eccles, An Introduction to Mathematical Reasoning, but these are not required. Further background reading can be found in R Allenby, Numbers and Proofs; M Liebeck, A Concise Introduction to Pure Mathematics; V Bryant, Yet Another Introduction to Analysis; R Bartle & D Sherbert, Introduction to Real Analysis and H Anton, Elementary Linear Algebra.

Assessment

Exam (90%, duration: 3 hours) in the spring exam period.
Continuous assessment (10%) in the AT and WT.

Key facts

Department: Mathematics

Total students 2023/24: 168

Average class size 2023/24: 29

Capped 2023/24: No

Value: One Unit

Guidelines for interpreting course guide information

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills