Module overview
This module provides training in advanced mathematics and numerical methods that will allow in-depth understanding and solving of problems in physical chemistry, computational chemistry, and spectroscopy. It will also provide transferable skills that can be applied to other areas such as data science and quantitative finance. It involves learning to solve problems both “on paper” and on a computer by developing code in Python.
Aims and Objectives
Learning Outcomes
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Learn and use simple numerical methods for mathematical operations
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Apply mathematical methods to solve problems in chemistry
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Learn and explain mathematical methods for scientists
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Combine and implement numerical methods to numerically approximate solutions to problems in Chemistry
Syllabus
1Vector and matrix spaces I – definitions and properties
2Variables (integer, real, etc.), programs and subroutines
3Vector and matrix spaces II – expansions and basis sets
4Intrinsic mathematical functions, combining these to compute new functions, outputting and plotting
5Vector and matrix spaces III – linear transformations
6Arrays, loops, vector addition and dot products, matrix multiplication
7Vector and matrix spaces III – eigensystems
8Matrix diagonalization, Jacobi method
9Fourier transform
10Discrete (slow) Fourier Transform in one dimension
11Multivariate integration – line integrals
12Discretisation. Numerical derivatives and error.
13Multivariate integration – multiple integrals
14Numerical integration, trapezium rule, Simpson’s rule (prove it) and possibly higher order quadratures
15Polar, cylindrical, and spherical coordinates
16Optimisation. Methods using the objective function only (simplex)
17Multivariate integration – polar and spherical integrals
18Optimisation using gradients (steepest descents, conjugate gradients) and 2nd derivatives (Newton Raphson)
19Algebraic foundations of quantum theory I
20Matrix functions. Calculation of matrix exponentials, matrix inverse and other matrix functions.
21Algebraic foundations of quantum theory II
22Discretisation of Newton’s law of motion, molecular dynamics concepts, Verlet integrator algorithm for MD
23Partial differential equations
24Revision lecture
Learning and Teaching
Teaching and learning methods
Material will be delivered and supported in a number of ways. Some material will be provided in lectures supported by handouts, while other learning will take place in workshops which will support more extended practical exercises that will also form part of the assessment.
| Type | Hours |
|---|---|
| Follow-up work | 48 |
| Wider reading or practice | 10 |
| Revision | 20 |
| Preparation for scheduled sessions | 24 |
| Lecture | 24 |
| Practical classes and workshops | 24 |
| Total study time | 150 |
Resources & Reading list
Textbooks
William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery. Numerical Recipes. Cambridge University Press.
P. Monk, L.J. Munro (2010). Maths for Chemists. Oxford: OUP.
E. Steiner (2008). The Chemistry Maths Book. Oxford: OUP.
Gene H. Golub, Charles F. van Van Loan (1996). Matrix Computations. Johns Hopkins.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Workshop activities | 100% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Workshop activities | 100% |
Repeat Information
Repeat type: Internal & External