| Unit name | Introduction to Pure Mathematics |
|---|---|
| Unit code | MATH10027 |
| Credit points | 20 |
| Level of study | C/4 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Dr. Bouyer |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
None |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Why is this unit important?
This unit will introduce students to some of the core ideas in Pure Mathematics, covering fundamental concepts such as sets, functions, logic, numbers and groups. The unit will emphasise the central importance of mathematical proof, and several proof techniques will be introduced and developed with the aid of concrete examples. The unit will equip students with the skills to confidently present clear and accurate mathematical arguments. Topics from elementary number theory, including the Fundamental Theorem of Arithmetic, Euclid’s algorithm and modular arithmetic, will be used to exemplify some of the key ideas. In addition, students will learn about groups, which are fundamental algebraic structures that arise naturally throughout mathematics.
How does this unit fit into your programme of study?
This unit covers core material that is essential for all units in Pure Mathematics. It has a natural connection with the level C/4 units Linear Algebra and Analysis.
An overview of content
Students taking this unit will be introduced to many fundamental ideas in Pure Mathematics, with the concept of mathematical proof acting as a unifying theme throughout. They will study basic properties of familiar number systems such as the integers, rational numbers and real numbers, laying some of the foundations for level C/4 Analysis. Core ideas from set theory and logic will then be introduced, which leads naturally to the idea of a function between two sets. Groups then arise as sets with some additional structure and their basic properties will be investigated with the aid of concrete examples. This includes the notion of isomorphism, as well as Lagrange's theorem on subgroups of finite groups. The unit also covers some elementary topics in number theory, such as modular arithmetic and Euclid's algorithm, and it concludes by introducing students to the concepts of cardinality and infinite sets.
How will students, personally, be different as a result of the unit?
At the end of the unit, students will have improved their logical thinking and have increased the range and scope of their problem-solving techniques. These are essential skills in all areas of mathematics and its applications. They will also appreciate the importance of rigour in Pure Mathematics and they will have the skills and confidence to apply different proof techniques in a wide range of settings.
Learning Outcomes
After completing this unit successfully, students will be able to:
The unit will be taught through a combination of:
Tasks which help you learn and prepare you for summative tasks (formative):
Guided independent activities such as problem sheets and/or other exercises, with regular feedback from tutors.
Tasks which count towards your unit mark (summative):
90% timed examination; 10% coursework
When assessment does not go to plan
If you fail this unit and are required to resit, then reassessment is by a written examination in the Resit and Supplementary exam period.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH10027).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
