MA103 One Unit
Introduction to Abstract Mathematics
This information is for the 2025/26 session.
Course Convenor
Prof Peter Allen
Dr David O'Sullivan
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 Actuarial Science (with a Placement Year), BSc in Data Science, BSc in Mathematics, Statistics and Business, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.
Requisites
Mutually exclusive courses:
This course cannot be taken with MA102 at any time on the same degree programme.
Co-requisites:
Students must complete MA108 or MA100 either before taking this course or in the same year as this course.
Additional 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 Autumn Term.
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
20 hours of lectures, 10 hours of help sessions and 20 hours of classes in the Autumn Term.
20 hours of lectures, 10 hours of help sessions and 20 hours of classes in the Winter Term.
The 10 hour help sessions will be Extra Examples Lectures.
Formative assessment
Problem sets weekly
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: 180 Minutes in the Spring exam period
Continuous assessment (10%) weekly
Key facts
Department: Mathematics
Course Study Period: Autumn and Winter Term
Unit value: One unit
FHEQ Level: Level 4
CEFR Level: Null
Total students 2024/25: 179
Average class size 2024/25: 30
Capped 2024/25: NoCourse 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