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Mathematical Statistical Mechanics (MAST90060)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Overview

Year of offer2019
Subject levelGraduate coursework
Subject codeMAST90060
Campus
Parkville
Availability
Semester 1
FeesSubject EFTSL, Level, Discipline & Census Date

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.

Eligibility and requirements

Prerequisites

The following subject, or equivalent.

Code Name Teaching period Credit Points
MAST20009 Vector Calculus
Semester 1
Semester 2
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 1
Semester 2
12.5

No prior knowledge of physics or thermodynamics is assumed.

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

Assessment

Additional details

Up to 50 pages of written assignments (40%: two assignments worth 20% each, due mid and late in semester), a 3 hour written examination (60%, in the examination period).

Dates & times

  • Semester 1
    CoordinatorThomas Quella
    Mode of deliveryOn Campus — Parkville
    Contact hours
    Total time commitment170 hours
    Teaching period 4 March 2019 to 2 June 2019
    Last self-enrol date15 March 2019
    Census date31 March 2019
    Last date to withdraw without fail10 May 2019
    Assessment period ends28 June 2019

Time commitment details

170 hours

Further information

Last updated: 12 June 2019