| Unit name | Introduction to Proofs and Group Theory |
|---|---|
| Unit code | MATH10010 |
| Credit points | 20 |
| Level of study | C/4 |
| Teaching block(s) |
Teaching Block 4 (weeks 1-24) |
| Unit director | Dr. Mackay |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
A in A Level Mathematics or equivalent |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one | |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Lecturers: Jos Gunns and John Mackay
Unit Aims
This unit aims to to introduce students to fundamental concepts in Mathematics including set theory, techniques of proof and group theory.
Unit Description
The first half provides an introduction to logical propositions, basic set theory and cardinality, functions and relations, and proof techniques. These notions are exemplified with some topics from elementary number theory, such as the Fundamental Theorem of Arithmetic, Euclid’s algorithm, modular arithmetic.
The second half explores the area of group theory. In the past, certain systems studied in various parts of mathematics have turned out to have common features, and these have been formalised into the definition of a group. Some of the earliest examples arose in connection with the solution of polynomial equations by formulae, and involved what we would now call groups of permutations. Other examples arise in trying to pin down mathematically what it means to say that a geometrical figure is symmetric and to quantify just how symmetric it is. It makes sense to study in one go all the systems which have the same general features. We shall start from the formal definition of a group and derive important general results from it using careful mathematical reasoning, but throughout there will be an emphasis on particular examples in which calculations can be performed relatively easily. The unit aims to introduce students to basic material in group theory, including examples of groups, group homomorphisms, subgroups, quotient groups, basic theorems on groups (such as Lagrange’s Theorem, Fermat’s Little theorem, 1st Isomorphism Theorem) and their applications.
At the end of the unit, the students should:
The unit will be taught through a combination of
Assessment for learning/Formative assessment:
Assessment of learning/Summative assessment:
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. MATH10010).
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 Faculty 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.
If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs
(this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
