MATH4231: Statistical Mechanics IV

• Analysis in Many Variables (MATH2031) AND [Mathematical Physics (MATH2071) OR Theoretical Physics 2 (PHYS2631)] AND additional Mathematical Sciences modules to the value of 60 credits in Levels 2 and 3, with at least 40 credits at Level 3.

• None

• None

• To develop a basic understanding of the dynamics and behaviour ofsystems with a large number of constituents.
• To develop approximation techniques and calculational methods tounderstand collective dynamics of large particle ensembles.

• Thermal equilibrium, laws of thermodynamics, equations ofstate, ideal gas law.
• Probability distributions and random walks.
• Classical statistical mechanics.
• Distributions and identical particles.
• Black-body radiation, magnetisation, neutron stars.
• Phase transitions.
• Reading material on one or more aspects of theRenormalization Group.

Subject-specific Knowledge:

• The students will: learn to deal with systems wherestatistical ideas give a good picture of the essential dynamics.
• have learnt to develop approximation methods necessary tosolve problems involving large systems.
• have mastered knowledge of the subject through one or more ofthe following subject areas: thermodynamics, probabilitydistributions, statistical ensembles, phase transitions.
• have a knowledge and understanding of a topic in the renormalization group approach.

Subject-specific Skills:

• The students will have specialised knowledge and mathematicalskills in tackling problems in: statistical modeling of large systems.
• Ability to read independently to acquire knowledge and understanding of aspects of the Renormalization Group approach.

Key Skills:

• The students will have an appreciation of StatisticalMechanics and its utility in the real world in the study of variouscomplex systems and solutions thereof.

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Subject material assigned for independent study develops theability to acquire knowledge and understanding without dependence onlectures.
• Assignments for self-study develop problem-solving skills andenable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in theapplication of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

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