UnitLevel 2Undergraduate

MTH2141 Algebra 1: Group theory

Faculty of Science

MTH2141 Algebra 1: Group theory is a level 2, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2027 in Semester 1 at Clayton. It needs MTH1030, MTH1035, MAT1830 or ENG1005 and unlocks 7 units, leading on to 15 units in all.

Credit points
6
Offered in 2027
Semester 1
Clayton
Assessment
Exam 50%
and 1 other task

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Requisites

Overview

Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups and quotient groups; homomorphisms, isomorphisms and isomorphism theorem; group actions; Sylow theorems, group presentations.

Offerings in 2027

Teaching periodCampusMode
First semesterClaytonOn campus

Assessment

  • Continuous assessmentDemonstration
    50%
  • Final assessment - Exam (3 hours and 10 minutes)Examination
    50%

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Learning outcomes

When you finish this unit, you should be able to:

  1. 1

    Communicate the beauty and the power of pure mathematics;

  2. 2

    Capture the mathematical notion of symmetry via group theory;

  3. 3

    Apply the fundamental concepts of abstract algebra;

  4. 4

    Explain the notion of proof in mathematics and be able to carry out basic proofs;

  5. 5

    Communicate mathematical arguments effectively, both orally and in writing, and collaborate to solve abstract algebra problems.

Workload and teaching

  • Applied sessions22 hours
  • Seminars36 hours
  • Teaching approachActive learning
  • Teaching approachProblem-based learning
  • Teaching approachPeer assisted learning
  • Three 1-hour seminars;
  • One 2-hour applied class and
  • 7 hours of independent study per week.

Primary content is delivered through traditional lectures (which will be recorded, and available for review via the Moodle page). Applied classes will be active learning. Small groups of students will work together around a whiteboard to solve problems. A key aspect is that this component involves writing your solutions on the board and critiquing the solutions of others, meaning that both written and spoken communication of mathematical ideas are developed (with input from your tutor). You also develop strategies for solving the questions together, meaning this is peer-assisted learning. Assignments will be problem-based learning. The questions will involve techniques from recent lectures and applied classes, but sometimes in settings or formats that are not immediately familiar. Thus, part of the challenge is adapting what you previously knew or have just learnt to a new setting.

Contacts

Chief Examiners
Professor Heiko Dietrich
Unit Coordinators
Professor Heiko Dietrich

Common questions

What are the prerequisites for MTH2141?

You need MTH1030, MTH1035, MAT1830 or ENG1005 before you enrol.

What can I take after MTH2141?

MTH2141 is a prerequisite or corequisite for 7 units, including FIT2014, MTH2137, MTH3115, MTH3130, MTH3137 and MTH3150. Those lead on to 15 units in all.

When is MTH2141 offered?

In 2027, MTH2141 runs in Semester 1 at Clayton.

Does MTH2141 have an exam?

Yes. The exam is worth 50% of the final mark, alongside 1 other task.

More details

Credit points
6
Level
2
Study level
Undergraduate
Faculty
Faculty of Science
Organisational unit
School of Mathematics
Type
Coursework
EFTSL
0.125
Student contribution
SCA Band 1
Study abroad
Available
Handbook years
202220232024202520262027