Undergraduate Programme and Module Handbook 2024-2025

# Module MATH4231: Statistical Mechanics IV

## Department: Mathematical Sciences

### MATH4231: Statistical Mechanics IV

Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### 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 Combination of Modules

- None

#### Aims

- To develop a basic understanding of the dynamics and behaviour of systems with a large number of constituents.
- To develop approximation techniques and calculational methods to understand collective dynamics of large particle ensembles.

#### Content

- Thermal equilibrium, laws of thermodynamics, equations of state, 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 the Renormalization Group.

#### Learning Outcomes

Subject-specific Knowledge:

- The students will: learn to deal with systems where statistical ideas give a good picture of the essential dynamics.
- have learnt to develop approximation methods necessary to solve problems involving large systems.
- have mastered knowledge of the subject through one or more of the following subject areas: thermodynamics, probability distributions, 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 mathematical skills 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 Statistical Mechanics and its utility in the real world in the study of various complex 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 the ability to acquire knowledge and understanding without dependence on lectures.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application 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 acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week in Michealmas and Epiphany; 2 in Easter | 1 Hour | 42 | |

Problems Classes | 8 | Fortnightly in Michaelmas and Epiphany | 1 Hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 hours | 100% | none |

#### Formative Assessment:

Eight assignments to be submitted.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University