Module overview
The module provides advanced mathematics training necessary for students planning to specialise in physical chemistry, computational chemistry, spectroscopy, data sicence and quantitative finance. It also aims to provide training of rational reasoning skills in a subject-independent way: studying mathematical proofs and derivations introduces a more rigorous logical system than practical skills and applied training alone. In particular:
- Basic linear algebra (spaces, operators, matrices)
- Ordinary differential equations (uniform, non-uniform, 1st and 2nd order)
- Basic pharmacokinetics modelling
- Integration of functions of multiple variables
- Polar, cylindrical and spherical coordinates
- Algebraic foundations of quantum theory
- Basic partial differential equations
- Full solution of the Schrödinger equation for the hydrogen atom
- Definition and applications of Fourier transform
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- The use of Mathematical modelling methods in modern chemistry
- Advanced Mathematical methods for solving chemical theory and modelling problems.
- Advanced types of chemical theory and modelling problems.
Syllabus
Lecture 1: Vector and matrix spaces I
Lecture 2: Vector and matrix spaces II
Lecture 3: Vector and matrix spaces III
Lecture 4: Vector and matrix spaces IV
Lecture 5: Ordinary differential equations I
Lecture 6: Ordinary differential equations II
Lecture 7: Ordinary differential equations III
Lecture 8: Ordinary differential equations IV
Lecture 9: Functions of multiple variables: integration I
Lecture 10: Functions of multiple variables: integration II
Lecture 11: Functions of multiple variables: integration III
Lecture 12: Functions of multiple variables: integration IV
Lecture 13: Algebraic foundations of quantum theory I
Lecture 14: Algebraic foundations of quantum theory II
Lecture 15: Partial differential equations I
Lecture 16: Partial differential equations II
Lecture 17: Schrödinger’s equation for hydrogen atom I
Lecture 18: Schrödinger’s equation for hydrogen atom II
Lecture 19: Fourier transform
Lecture 20: Applications: molecular dynamics
Lecture 21: Applications: density functional theory
Lecture 22: Applications: magnetic resonance imaging
Lecture 23: Applications: crystal structure prediction
Lecture 24: Revision
Learning and Teaching
Teaching and learning methods
Lectures and problem-solving workshops with group working and tutor support. Feedback is provided:
- In workshops through assistance with the set work.
- Through generic feedback following the examinations.
- Upon request by viewing of marked examination scripts.
| Type | Hours |
|---|---|
| Practical classes and workshops | 24 |
| Follow-up work | 48 |
| Wider reading or practice | 10 |
| Preparation for scheduled sessions | 24 |
| Lecture | 24 |
| Revision | 20 |
| Total study time | 150 |
Resources & Reading list
Textbooks
E. Steiner (2008). The Chemistry Maths Book. Oxford: OUP.
P. Monk, L.J. Munro (2010). Maths for Chemist. Oxford: OUP.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Final Assessment | 100% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Final Assessment | 100% |
Repeat Information
Repeat type: Internal & External