MATH 3015 Groups and Symmetry
Credit Points 10
Description This unit develops abstract algebraic thinking to a higher level. The abstract concepts introduced in the unit, the theory of groups and abstract symmetry, have many applications in science and technology. Symmetry plays a role in many different contexts: in crystals, in visual arts, in music and in architecture, to name a few. Analysing and exploiting the symmetries of a particular problem often is the first step towards finding a practical solution to the problem. Group theory is the study of symmetry. This unit develops the language of groups and techniques to understand the structure of groups.
School Computer, Data & Math Sciences
Student Contribution Band HECS Band 1 10cp
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Level Undergraduate Level 3 subject
Pre-requisite(s) MATH 1006
Equivalent Subjects MATH 3001 Abstract Algebra
Logic, proof techniques: direct proof, proof by division into cases, proof by contradiction, proof by induction.
- Apply fundamental structures in abstract algebra: groups, subgroups, and permutation groups.
- Apply concepts from group theory to the study of the symmetry of objects, such as polygons.
- Formulate proofs involving groups, subgroups, and permutation groups.
- Communicate mathematical arguments effectively in both spoken and written format.
- Introduction to groups
- Examples of groups and basic properties of groups
- Finite groups and subgroups
- Cyclic groups
- Permutation groups
- Cosets and Lagrange?fs Theorem
- Normal subgroups and factor groups
- Group homomorphisms and group isomorphisms
- Cayley graphs of groups
- Applications of groups