Eligibility

You will need an aptitude for mathematics for our Statistics MSc programmes and should have done some mathematics including basic statistics and probability as part of your university degree. The following is the type of mathematics you will encounter on the programme. It is important that you have mastered the items in bold before starting the programme.

• Statistics:

  • Estimation (including maximum likelihood estimation)
  • Significance testing
  • The normal distribution
  • Sampling distributions of means and related quantities
  • Significance tests using the normal distribution
  • Estimation of intervals and parameters
  • Hypothesis tests using the chi squared distribution
  • The Poisson distribution
  • Correlation
  • The analysis of variance
  • Simple linear regression

• Probability (sections from the book by S.Ross are given in brackets - see background reading section below):

  • Conditional Probability, Bayes's formula (3.1-3.3)
  • Independence (3.4-3.5)
  • Discrete random variables, expectation, variance (4.1-4.5)
  • Bernoulli, binomial, Poisson, geometric, negative binomial RVs (4.6-4.9)
  • Sums of RV's, Continuous RVs (4.9-5.3)
  • Uniform, normal, exponential, gamma RVs (5.4-5.6)
  • Joint and independent RVs (6.1-6.2)
  • Sums of independent RVs, Limit theorems: Markov and Chebyshev inequalities, weak law of large numbers, Moment generating function (6.3-8.2)
  • Central limit theorem (8.3-9.1)

• Algebra:
  • Rearranging and simplifying expressions
  • Equalities and inequalities
  • Sequences: limits and series  
• Matrices:
  • Matrix operations: multiplication, transposition, inversion
  • Determinant of matrix, nonsingularity  
• Linear Algebra:
  • Solving systems of simultaneous linear equations
  • Scalar product, norms
  • Linear dependence  
• Functions of one variable:
  • Plotting graphs of functions
  • Linear, quadratic, logarithmic and exponential functions
  • Differentiation: critical points; classifying minimizers/maximizers
  • Taylor expansion
  • Integration: area under a curve
  • Continuity
  • Differentiability  
• Functions of several variables:
  • Differentiation, partial derivatives
  • Taylor expansion
  • Gradient, Hessian, necessary and sufficient conditions for a minimizer/maximizer  
• Convexity:
  • Convex sets
  • Convex and concave functions

Desirable existing computing skills for Statistics and Operational Research students:

A familiarity with MS Windows or Unix (use of spreadsheets and word processing) would be helpful. You will do some computer programming on the course and you will have an easier start with this if you already have some programming experience. A knowledge of any of the high-level programming languages like C, FORTRAN, F90, Visual Basic or Java will be helpful. However, if you have no programming skills then you will be given a chance to develop them within this MSc.

Students' projects may have a programming component and Java will be used as the computing language for algorithmic work in the MSc. Java is a well structured object oriented language which is less error prone than C++ and provides a ready route to producing web applications.

The core of the taught component of the Operational Research content contains a course on programming with Java. This course does not assume that you have previous programming experience. However if you have not used any programming language before, you will have less work to do in this course if you do some preliminary work before the start of the course. A good public tutorial on Java is the SUN Java Tutorial.

Desirable existing computing skills for Statistics with Data Science students:

A familiarity with Windows or Linux (use of spreadsheets and word processing) would be helpful. You will have to work with the statistical computing package R on the programme. Although no prior knowledge of R is assumed, if you have no experience of formal programming (C, Java, Python etc) or software such as Matlab, it would be valuable to begin studying R before starting the programme.

R is available for free download.

You must demonstrate a level of English language competency at a level that will enable you to succeed in your studies, regardless of your nationality or country of residence.

Full details of the English language requirements are provided in the "Entry requirements" section of the Postgraduate Degree Finder:

• MSc Statistics and Operational Research
• MSc Statistics with Data Science

The books below offer valuable background reading and preparation for the Statistics MSc programmes.

Background Mathematics

The two Engineering Mathematics texts below are written in a relatively readable style. The editions below are the most recent, although older editions are just as good. If you are not confident of your mastery of some of the basic mathematics and statistics skills above then you are advised to work on the corresponding material in these books.

• Advanced Engineering Mathematics, E. Kreyszig, John Wiley & Sons, 9th edition. ISBN-10: 0471728977
• Modern Engineering Mathematics, G. James, Prentice Hall, 4th edition. ISBN-10: 027373413X

Background in Statistics and Probability

The books below cover prerequisites for the statistics courses on the Statistics MSc programmes. The topics are listed in the mathematical and statistics skills section above.

• A First Course in Probability, S.M. Ross, Pearson, 8th Edition. ISBN-10: 0136079091
• A Basic Course in Statistics, G.M. Clarke and D. Cooke, Hodder Arnold. ISBN-10: 0340814063
• Mathematical Statistics and Data Analysis, J.A. Rice, Cengage Learning. ISBN-10: 0534399428

Background to Operational Research

Both of the books below cover large amounts of the core Operational Research courses, as well as other fundamental Operational Research skills. If you are studying the Statistics and Operational Research MSc it may be valuable to have started looking at this material before you begin the programme.

• Introduction to Operations Research, F. S. Hillier and G. Lieberman, McGraw-Hill Higher Education, 9th edition. ISBN-10: 0071267670
• Operations Research: Applications and Algorithms, W. L. Winston, Brooks/Cole. ISBN-10: 0534423620