Undergraduate Programme and Module Handbook 2018-2019 (archived)
Module MATH4231: Statistical Mechanics IV
Department: Mathematical Sciences
MATH4231:
Statistical Mechanics IV
Type |
Open |
Level |
4 |
Credits |
20 |
Availability |
Available in 2018/19 |
Module Cap |
|
Location |
Durham
|
Prerequisites
- Mathematical modules to the value of 100 credits in Year 2
and 3, with at least 40 credits at Level 3, and including Analysis in
Many Variables II (MATH2031).
Corequisites
Excluded Combination of Modules
- Statistical Mechanics III (MATH3351)
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
- 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.
- 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.
- 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 for 20 weeks and 2 in term 3 |
1 Hour |
42 |
|
Problems Classes |
8 |
Four in each of terms 1 and 2 |
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 |
Eight written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students.
■ 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