Mathematical Statistical Mechanics (MAST90060)
Graduate courseworkPoints: 12.5Not available in 2020
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
About this subject
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
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The goal of statistical mechanics is to describe the behaviour of bulk matter starting from a physical description of the interactions between its microscopic constituents. This subject introduces the Gibbs probability distributions of classical statistical mechanics, the relations to thermodynamics and the modern theory of phase transitions and critical phenomena. The central concepts of critical exponents, universality and scaling are emphasized throughout. Applications include the ideal gases, magnets, fluids, one-dimensional Ising and Potts lattice spin models, random walks and percolation as well as approximate methods of solution.
Intended learning outcomes
After completing this subject students should:
- have learned how the ensembles and methods of classical statistical mechanics apply to a variety of problems in applied mathematics and mathematical physics;
- appreciate the role of critical phenomena in modern thermodynamics and to be able to use the principles of critical exponents, universality and scaling to describe the behaviour of complex systems;
- understand the basic concepts of phase transitions as applied to fluids, magnets, lattice spin models, random walks and percolation and appreciate their applicability;
- be familiar with the basic mathematical techniques of statistical mechanics including transfer matrices, real-space renormalization group and approximate methods and their applications;
- have the ability to pursue further studies in these and related areas.
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.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
The following subject, or equivalent.
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20009 | Vector Calculus |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
Corequisites
None
Non-allowed subjects
No disallowed subject combinations among new-generation subjects.
Recommended background knowledge
It is recommended that students have completed the following, or equivalent.
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20026 | Real Analysis |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
No prior knowledge of physics or thermodynamics is assumed.
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
| Description | Timing | Percentage |
|---|---|---|
Up to 50 pages of written assignments (two assignments worth 20% each, due mid and late in semester)
| Second half of the teaching period | 40% |
A written examination
| During the examination period | 60% |
Last updated: 3 November 2022
Dates & times
Not available in 2020
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Ph.D.- Engineering Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022