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					Major Theme Code: CSMA004                                                                           Theme Title: Statistical Mathematics
GCSE: Maths                                                                                         A levels: Mathematics grade ‘B’
Module Code: MATH101 Title: Calculus                                                                No of Wks: 5       Terms Taught: M1       Tut/Lec/Lab: 5/20/5        exam/cwa: 50%/50%
Functions of real variable and their graphs. Compositions and inverses. Important special functions. Induction. Sequences and limits. Series. Differentiation. Product and chain rules. Maxima and
minima. Taylor series. Definite integrals as areas. Fundamental theorem of calculus. Integration by parts and substitution.
Module Code: MATH102 Title: Integration                                                             No of Wks: 5       Terms Taught: M2       Tut/Lec/Lab: 5/20/5        exam/cwa: 50%/50%
Integration over infinite ranges. Functions of two or more variables: partial derivatives, stationary points. Double and repeated integrals.
Module Code: MATH103 Title: Matrix Methods                                                          No of Wks: 5       Terms Taught: L1       Tut/Lec/Lab: 5/20/5        exam/cwa: 50%/50%
Complex numbers, the Argand diagram, polar form and De Moivre’s theorem. Matrix algebra. Systems of linear equations. Elementary row operations. Determinants. Linear programming and
maximization by the simplex method.
Module Code: MATH104 Title: Probability                                                             No of Wks: 5       Terms Taught: L2       Tut/Lec/Lab: 5/20/5        exam/cwa: 50%/50%
Set operations. Probabilities. Conditional probability and independence. Random variables and expectation. Probability models.
Module Code: MATH105 Title: Statistics                                                              No of Wks: 5       Terms Taught: S        Tut/Lec/Lab: 5/20/5        exam/cwa: 50%/50%
Exploratory data analysis, statistical model building, statistical investigation of scientific questions and statistical conclusions.
Module Code: MATH220 Title: Linear Algebra                                                          No of Wks: 10 Terms Taught: M             Tut/Lec: 10/30             exam/cwa: 85/15%
(Pre-requisite MATH103) The course begins by introducing the idea of a vector space, showing how it grows naturally out of the ideas developed for studying vectors in two and three dimensions. It
shows how the abstraction has a number of advantages, including making precise any underlying assumptions, suggesting concepts of utility in areas where their significance might not otherwise have
been recognised and simplifying matters by trimming away superfulous information. 0.67 unit [20 credits]
Module Code: MATH230 Title: Probability                                                             No of Wks: 10 Terms Taught: M             Tut/Lec: 10/30             exam/cwa: 85/15%
(Pre-requisite MATH104) Probability provides the theoretical basis for statistics and this course covers some of the main ideas required in subsequent statistical work. In the first part we review
some basic results from the first-year probability course and discuss how methods which are available for describing the properties of discrete random variables can be extended to the continuous case.
Some imprtant continuous probability distributions are investigated and their role in real-life applications illustrated. The second part of the course extends the methods to some of the more
complicated situations found in practice. We consider methods for dealing with two of more randomvariables, and functions of random variables. The important Central Limit Theorem is introduced
and discussed, and throughout we emphasise the role of the probability models as tools of genuine use in practical applications of statistics. 0.67 unit [20 credits]
Module Code: MATH235 Title: Statistics                                                              No of Wks: 10 Terms Taught: L             Tut/Lec: 10/30             exam/cwa: 85/15%
(Pre-requisite MATH105, 230) Statistics is the art of understanding patterns of behaviour from data. Our data are usually a sample from a bigger population and we know that a different sample
would have contained different data; so when we try to estimate some characteristic of the population from the data, we should recognise that different data would have given different estimates. In the
first half of this module we approach this problem by specifying a statistical model for the data, which usually includes a number of unknown parameters such as the population mean. Having
collected data, we then need to decide how to estimate these parameters. In this course we look at a number of possibilities, but focus mainly on the likelihood function. This approach is intuitive, has
nice mathematical properties and has proved to be one of the most flexible procedures for carrying out statistical estimation in both simple and very complicated situations. In this course we will
develop the theory and look at a wide range of problems which can be tackled using likelihood techniques. 0.67 unit [20 credits]
THIRD YEAR COURSES = 15 credits/0.5 unit each (Choose 2 units from the following:)
Module Code: MATH331 Title: Statistical Inference                                                   No of Wks: 5       Terms Taught: M2       Tut/Lec: 5/20              exam/cwa: 90/10%
(Pre-requisite MATH235) This course gives a comparison of likelihood and Bayesian approaches to statistical inference. The aims are for the student to understand the central role of the likelihood
in both forms of inference and to appreciate the advantages and disadvantages of both approaches. At the end of the course students should be able to demonstrate subject specific knowledge,
understanding and skills and have the ability to: compare likelihood and Bayesian approaches to statistical inference. conduct hypothesis testing using the likelihood ratio approach and Bayes Factors.
understand the importance of the asymptotic distributions and be able to use them to assist inference with multi-parameter problems. Use the predictive distribution for model checking. appreciate the
importance of the parameterisation of statistical models. compare optimality of decision making from the Bayesian and likelihood frameworks.

Module Code: MATH332 Title: Stochastic Processes                                                 No of Wks: 5     Terms Taught: L1           Tut/Lec: 5/20              exam/cwa: 70/30%
(Pre-requisite MATH230) The course aims to show how the rules of probability can be used to formulate simple models describing processes, such as the length of a queue, which can change in a
random manner, and how the properties of the processes, such as the mean queue size, can be deduced. By the end of the course the students should be able to use conditioning arguments to calculate
probabilities and expectations of random variables for stochastic processes; to calculate the distribution of a Markov Process at different time points; to determine whether a Markov process has an
asymptotic distribution and to calculate it; and to understand how stochastic processes are used as models.
Module Code: MATH333 Title: Statistical Models                                                   No of Wks: 5     Terms Taught: L2           Tut/Lec: 5/20              exam/cwa: 90/10%
(Pre-requisite MATH331, 390*) The course introduces a class of well known statistical models for regression problems. The class includes linear regression, for normal data, generalized linear
models for non-normal data and survival models for lifetime data. By the end of the course students should be able to formulate sensible models for different sets of data, taking account of the
constraints on the data, and to explore and analyse the data in R.
Module Code: MATH334 Title: Topics in Modern Statistics                                          No of Wks: 5     Terms Taught: L2           Tut/Lec: 5/20              exam/project/cwa: 70/20/10%
(Pre-requisite MATH331, MATH390*) This module aims to provide an introduction to recent developments in statistics. This may include statistical methods for analysing time series, multivariate
data with emphasis on the financial applications, change-point analysis and stochastic volatility models.
Module Code: MATH361 Title: Mathematical Education                                               No of Wks: 10 Terms Taught: M1&L1 4 essays (1 non-assessed) exam/cwa: 0/100%
Please note that this course is taught at the University of Cumbria. Mathematical concept formation. Psychology and mathematical education. Deductive and inductive thinking. The axiomatic
method. Aims and objectives of mathematical education. Purist and utilitarian approach. History of mathematics and the contribution of mathematics to historical development. Mathematical
models. Mathematics in other subjects. Computer education. Assessment in mathematics. Curriculum development. Recent changes and research.
Module Code: MATH390 Title: Project Skills                                                       No of Wks: 10 Terms Taught: S & M1 Lec/Lab: 12/11                      exam/cwa: 0/100%
Pre-requisite at least 1 of MATH220, 230. This course aims to teach and enhance skills, including both subject-related and transferable skills, appropriate to Part II students in Mathematics and
Statistics. These skills include mathematical document preparation and presentation, scientific writing and facility with a statistical software package.

* Students who do not take the whole of MATH390 should audit the practical course in R language given as part of MATH390, usually in week 26-30 of Summer term, in their second year.

Content Major Theme:        3 units or 90 credits chosen from:                               Assessment:
Second year:                MATH220, 230, 235, plus audit part of *MATH390                   Marks 1 - 4: MATH220, 230, 235
Third year:                 Four from: MATH331, 332, 333, 334, 361, 390                      Marks 5 - 8: Four from MATH331, 332, 333, 334, 361, 390


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