AS1C-Mathematical Methods for Statistics
Module Provider: Applied Statistics
Number of credits: 20 [10ECTS credits]
Level:
4
Terms in which taught: Autumn, Spring and Summer
Module Convenor: Dr
HJ
Kimber
Pre-requisites: AS Mathematics advisable
Co-requisites:
Modules excluded: MA11B MA11C
Module version for: 2009/0
Email: h.j.kimber@reading.ac.uk
Aims:
This module covers the mathematical topics that are essential for a proper understanding of the material in many statistics modules. It is primarily intended for those students who wish to pursue a degree course in Statistics, Applied Statistics or Business Statistics & Marketing, but who do not have a sufficient technical knowledge to be able to cope with modules which involve mathematics.
Assessable learning outcomes:
On completion of this module students will have acquired:
Additional outcomes:
Outline content:
Material covered
The module introduces mathematical notation and some algebraic manipulation including inequalities. The concepts of convergence, limits and continuity of functions are covered. Methods are formulated for the summation of arithmetic and geometric series. Taylor series expansions are considered.
A substantial part of the module is differential and integral calculus. Maxima and minima of functions of one and two variables are obtained by differentiation. Integration is introduced as anti-differentiation. Techniques such as change of variable and integration by parts are used. Definite integrals are described in terms of areas under curves.
In many applications of statistics, we need to be able to deal with numerical quantities laid out in a rectangular array of rows and columns, known as a matrix. Methods for manipulating such arrays are described and illustrated.
Structure of module
Mathematical notation for sums, products and inequalities.
Functions: linear equations, monotonic functions, quadratic functions, exponential functions, logarithmic functions; graphs; convergence; limits; continuity.
Summation of arithmetic and geometric series.
Differentiation: chain, product and quotient rules; derivatives of exponential and logarithmic functions; use of second derivatives to identify the nature of stationary points of functions.
Integration: by substitution; by parts.
Expansions: Binomial, Taylor and Maclaurin.
Functions of two variables; partial derivatives, minima and maxima.
Introduction to vectors and matrices.
Construction of a matrix; matrix addition and multiplication; singular matrices.
Inverting matrices; determinants.
Quadratic forms.
Solutions of systems of linear equations.
Required book
Sadler, A J & Thorning, D W S (2004). Understanding Pure Mathematics. OUP.
Recommended reading
Ayres, F (1992). Theory and Problems of Differential and Integral Calculus. (Schaum's Outline Series). McGraw-Hill.
Bostock, L and Chandler, S (1994). Core Mathematics for A-Level. Cheltenham: Thornes.
Healey, M J R (1988). Matrices for Statisticians. Clarendon Press, Oxford.
Martin, A et al. (2000). Pure Mathematics. Stanley Thornes, Oxford.
Stephenson, G (1973). Mathematical Methods for Science Students. Longman.
Brief description of teaching and learning methods:
Primarily lectures, with some self-study.
Contact hours:
| Autumn | Spring | Summer | |
| Lectures | 20 | 20 | |
| Tutorials/seminars | 4 | ||
| Practicals | |||
| Other contact (eg study visits) | |||
| Total hours | 20 | 20 | 4 |
| Number of essays or assignments | 9 | 8 | |
| Other (eg major seminar paper) |
Assessment:
Coursework
Seventeen weekly exercise sheets
Relative percentage of coursework : Weight 35%
Penalties for late submission
Penalties for late submission of course work will be in accordance with University policy.
Examination
One paper of 3 hours duration : Weight 65%
Requirements for a pass
An overall mark of at least 40%
Reassessment arrangements
One examination paper of 3 hours duration
Last updated: 23 November 2009