MATH 3015 Groups and Symmetry

Credit Points 10

Legacy Code 301376

Coordinator Roozbeh Hazrat Opens in new window

Description This subject develops abstract algebraic thinking to a higher level. The abstract concepts introduced in the subject, 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 subject develops the language of groups and techniques to understand the structure of groups.

School Computer, Data & Math Sciences

Discipline Mathematics

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

Assumed Knowledge

Logic, proof techniques: direct proof, proof by division into cases, proof by contradiction, proof by induction.

Learning Outcomes

On successful completion of this subject, students should be able to:

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.

Subject Content

- Sets and equivalence relations
- 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

Assessment

The following table summarises the standard assessment tasks for this subject. Please note this is a guide only. Assessment tasks are regularly updated, where there is a difference your Learning Guide takes precedence.

Type	Length	Percent	Threshold	Individual/Group Task	Mandatory
Quiz	20 minutes	10	N	Individual	N
Quiz	20 minutes	10	N	Individual	N
Numerical Problem Solving	3-6 pages	20	N	Individual	Y
Presentation	15 minutes	10	N	Individual	Y
Final Exam	2 hours	50	N	Individual	Y