MA4SMA-Statistical Mechanics and Applications

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Terms in which taught: Spring term module
Pre-requisites: MA2MPH Mathematical Physics or MA2MM Mathematical Modelling or MA1MM Mathematical Modelling
Non-modular pre-requisites:
Modules excluded: MA3SMA Statistical Mechanics and Applications
Module version for: 2017/8

Module Convenor: Prof Valerio Lucarini


Summary module description:
This module will introduce the concepts of statistical mechanics and their mathematical formulation.

To introduce the concepts of statistical mechanics and their mathematical formulation; to apply these concepts in studying the equilibrium properties of simple physical systems.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

• acquire basic concepts of statistical mechanics, including entropy, ensemble, partition function and free energy, and their mathematical formulation;

• solve problems related to the equilibrium properties of simple physical systems.

This module will be assessed to a greater depth than the excluded module MA3SMA.

Additional outcomes:

Solve real world problems, such as physical properties of weakly out-of-equilibrium systems.

Outline content:

Statistical mechanics applies the mathematical tools of calculus and probability theory to study the macroscopic properties of large physical systems from the properties of their individual components. In a self-contained manner, this module covers:

• background knowledge of mathematics, probability distributions and thermodynamics;

• basic concepts in statistical mechanics, such as entropy, free energy, ensembles and partition functions, and their mathematical formulation;

• application of statistical mechanics in studying the equilibrium properties of some model systems, such as ideal gas and simple van der Waals liquids and Ising model; 

• (optional) Investigation of simple out-of-equilibrium forced and dissipative systems.

Brief description of teaching and learning methods:
Lectures supported by problem sheets.

Contact hours:
  Autumn Spring Summer
Lectures 20
Guided independent study 80
Total hours by term 100.00
Total hours for module 100.00

Summative Assessment Methods:
Method Percentage
Written exam 75
Report 25

Other information on summative assessment:

One examination paper and a 6-8 pages report on a chosen topic agreed with the instructor (6-8 pages in pdf format, Page size: A4, Fontsize: 11 or 12, Linespacing: 1.15-1.5 lines.)

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

  • where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
  • where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

  • The University policy statement on penalties for late submission can be found at:
    You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

    Length of examination:

    2 hours

    Requirements for a pass:
    A mark of 50% overall.

    Reassessment arrangements:

    One examination paper of 2 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (75% exam, 25% coursework).

    Additional Costs (specified where applicable):
    1) Required text books:
    2) Specialist equipment or materials:
    3) Specialist clothing, footwear or headgear:
    4) Printing and binding:
    5) Computers and devices with a particular specification:
    6) Travel, accommodation and subsistence:

    Last updated: 31 March 2017

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