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. Walling |
Open unit status | Not open |
Pre-requisites |
A in A Level Mathematics or equivalent |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Lecturers: Lynne Walling and Jeremy Rickard
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:
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