Group Theory and Linear Algebra

Subject MAST20022 (2012)

Note: This is an archived Handbook entry from 2012.

Credit Points: 12.50
Level: 2 (Undergraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2012:

Semester 2, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable

Lectures and practice classes

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 3 x one hour lectures per week, 1 x one hour practice class per week
Total Time Commitment: Estimated total time commitment of 120 hours
Prerequisites:

One of

Subject
Study Period Commencement:
Credit Points:
  • MAST10013 UMEP Maths for High Achieving Students
  • 620-122 Mathematics B Advanced (prior to 2008)
  • 620-211 Mathematics 2 Advanced (prior to 2008)
Or
Subject
Study Period Commencement:
Credit Points:
Summer Term, Semester 1, Semester 2
12.50
and one of
Subject
Study Period Commencement:
Credit Points:
Semester 1, Semester 2
12.50
  • 620-121 Mathematics A Advanced (prior to 2008)
  • 620-120 UMEP Maths for High Achieving Students (prior to 2008)
Or

A grade of H1 in

  • 620-142 Mathematics B (prior to 2009) with additional reading
Corequisites: None
Recommended Background Knowledge: None
Non Allowed Subjects:

Students may only gain credit for one of

  • MAST20022 Group Theory and Linear Algebra
  • 620-222 Linear and Abstract Algebra (prior to 2009).
Core Participation Requirements: For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements of this entry.
The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

Coordinator

Assoc Prof Paul Norbury, Prof Arun Ram

Contact

Second Year Coordinator

Email: sycoord@ms.unimelb.edu.au

Subject Overview:

This subject introduces the theory of groups, which is at the core of modern algebra, and which has applications in many parts of mathematics, chemistry, computer science and theoretical physics. It also develops the theory of linear algebra, building on material in earlier subjects and providing both a basis for later mathematics studies and an introduction to topics that have important applications in science and technology.

Topics include: modular arithmetic and RSA cryptography; abstract groups, homomorphisms, normal subgroups, quotient groups, group actions, symmetry groups, permutation groups and matrix groups; theory of general vector spaces, inner products, linear transformations, spectral theorem for normal matrices, Jordan normal form.
Objectives:

On completion of this subject, students should

Understand the concepts of:

  • abstract groups, homomorphisms and quotient groups;
  • abstract vector spaces, inner product spaces and linear transformations;

Be able to:

  • do calculations in modular arithmetic and apply these to RSA cryptography;
  • find eigenvalues, eigenvectors, minimal polynomials and normal forms for linear transformations;
  • analyse groups of permutations, symmetries, and matrices;
  • prove simple results in group theory and linear algebra.
Assessment:

Three written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).
Prescribed Texts:

Lecture Notes for Group Theory and Linear Algebra, Department of Mathematics and Statistics.
Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills:

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time management skills: the ability to meet regular deadlines while balancing competing commitments
Notes: This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
Related Majors/Minors/Specialisations: Science credit subjects* for pre-2008 BSc, BASc and combined degree science courses
Science-credited subjects - new generation B-SCI and B-ENG. Core selective subjects for B-BMED.
Related Breadth Track(s): Accelerated Mathematics

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