UnitLevel 3Undergraduate

MTH3121 Algebra and number theory

Faculty of Science

MTH3121 Algebra and number theory is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2021 in Semester 1 at Clayton. It has no prerequisites and unlocks 10 units, leading on to 15 units in all.

Credit points
6
Offered in 2021
Semester 1
Clayton
Assessment
Exam 60%
and 1 other task

The 2027 handbook has no page for MTH3121. This is its 2021 entry, the latest one.

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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; homomorphisms, isomorphisms and the first isomorphism theorem. The Euclidean algorithm, prime factorisation, congruences, the Euler totient function; the theorems of Fermat, Euler and Wilson, and the RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; factorisation and primality testing algorithms.

Offerings in 2021

Teaching periodCampusMode
First semesterClaytonOn campus

Assessment

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

Learning outcomes

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

  1. 1

    Appreciate the beauty and the power of pure mathematics;

  2. 2

    Recognise the fundamental concepts of algebra and number theory;

  3. 3

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

  4. 4

    Illustrate how thousands of years of pure mathematical developments have enabled secure electronic communication;

  5. 5

    Apply important number theoretic algorithms;

  6. 6

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

Workload and teaching

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

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

MTH3121 is part of 6 areas of study in the 2021 handbook.

Contacts

Unit Coordinators
Professor Ian Wanless
Chief Examiners
Professor Ian Wanless

Common questions

What are the prerequisites for MTH3121?

MTH3121 has no prerequisites, but enrolment rules apply.

What can I take after MTH3121?

MTH3121 is a prerequisite or corequisite for 10 units, including MTH3130, MTH3150, MTH3170, MTH3175, MTH4115 and MTH4141. Those lead on to 15 units in all.

When is MTH3121 offered?

In 2021, MTH3121 runs in Semester 1 at Clayton.

Does MTH3121 have an exam?

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

Which majors and minors include MTH3121?

MTH3121 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
20202021