UnitLevel 3Undergraduate

MTH3141 Algebra 1: Group theory

Faculty of Science

MTH3141 Algebra 1: Group theory is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2023 in Semester 1 at Clayton. It needs MTH2025, MTH2137 or MTH2021 and unlocks 6 units, leading on to 14 units in all.

Credit points
6
Offered in 2023
Semester 1
Clayton
Assessment
Exam 60%
and 1 other task

This is the 2023 handbook entry. See the 2027 entry.

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Requisites

Overview

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

Offerings in 2023

Teaching periodCampusMode
First semesterClaytonOn campus

Assessment

  • Continuous assessmentOther
    40%
  • Examination (3 hours and 10 minutes)ExamThreshold hurdle
    60%

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

    Describe the power of the generality of the concepts in group theory;

  6. 6

    Pursue further studies in abstract algebra and pure mathematics more generally.

Workload and teaching

  • Lectures36 hours
  • Applied sessions22 hours
  • Teaching approachProblem-based learning
  • Teaching approachPeer assisted learning
  • Teaching approachActive learning
  • Three 1-hour lectures
  • One 2-hour applied class (in weeks 2-12) 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.

Where it fits

MTH3141 is part of 7 areas of study in the 2023 handbook.

Contacts

Unit Coordinators
Dr Norm Do
Chief Examiners
Dr Norm Do

Common questions

What are the prerequisites for MTH3141?

You need MTH2025, MTH2137 or MTH2021 before you enrol.

What can I take after MTH3141?

MTH3141 is a prerequisite or corequisite for 6 units, including MTH2137, MTH3130, MTH3137, MTH3150, MTH3170 and MTH4141. Those lead on to 14 units in all.

When is MTH3141 offered?

In 2023, MTH3141 runs in Semester 1 at Clayton.

Does MTH3141 have an exam?

Yes. The exam is worth 60% of the final mark, alongside 1 other task.

Which majors and minors include MTH3141?

MTH3141 is part of Applied mathematics, Mathematical statistics, Mathematics and Pure mathematics.

More details

Credit points
6
Level
3
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