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MATH4231: Statistical Mechanics IV

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 4
Credits 20
Availability Available in 2023/24
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • 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.

Corequisites

  • None

Excluded Combinations of Modules

  • None

Aims

  • 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.

Content

  • 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.

Learning Outcomes

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.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • 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.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week in Michealmas and Epiphany; 2 in Easter1 Hour42 
Problems Classes8Fortnightly in Michaelmas and Epiphany1 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 hours100none

Formative Assessment

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

More information

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