Mathematics and Statistics BSc (Hons)

Module details Programme Year One

Compulsory modules

• Calculus I (MATH101) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims

  1.       To introduce the basic ideas of differential and integral calculus, to develop the basic  skills required to work with them and to  apply these skills to a range of problems.

  2.       To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.

  3.       To introduce the notions of sequences and series and of their convergence.

  Learning Outcomes

  After completing the module students should be able to:

  ·      differentiate and integrate a wide range of functions;

  ·       sketch graphs and solve problems involving optimisation and mensuration;

  ·       understand the notions of sequence and series and apply a range of tests to determine if a series is convergent.

• Calculus Ii (MATH102) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims

  ·      To discuss local behaviour of functions using Taylor’s theorem.

  ·      To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.

  Learning Outcomes

  After completing the module, students should be able to:

  ·         use Taylor series to obtain local approximations to functions;

  ·         obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables;

  ·         evaluate double integrals using Cartesian and polar co-ordinates.

• Introduction To Linear Algebra (MATH103) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims
  •      To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
  •      To develop geometrical intuition in 2 and 3 dimensions.
  •      To introduce students to the concept of subspace in a concrete situation.
  •    To provide a foundation for the study of linear problems both within mathematics and in other subjects.
  Learning Outcomes

  After completing the module students should be ableto:

  •     manipulate complex numbers and solve simple equations involving them
  •     solve arbitrary systems of linear equations;
  •     understand and use matrix arithmetic, including the computation of matrix inverses;
  •     compute and use determinants;
  •     understand and use vector methods in the geometry of 2 and 3 dimensions;
  •     calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics.
• Numbers, Groups and Codes (MATH142) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims

  ·         To provide an introduction to rigorous reasoning in axiomatic systems exemplified by the framework of group theory.

  ·         To give an appreciation of the utility and power of group theory as the study of symmetries.

  ·         To introduce public-key cryptosystems as used in the transmission of confidential data, and also error-correcting codes used to ensure that transmission of data is accurate. Both of these ideas are illustrations of the application of algebraic techniques.

  Learning Outcomes ​​

  After completing this module the student should be able to:

  1. Use the division algorithm to construct the greatest common divisor of a pair of positive integers;

  2. Solve linear congruences and find the inverse of an integer modulo a given integer;

  3. Code and decode messages using the public-key method;

  4. Manipulate permutations with confidence;

  5. Decide when a given set is a group under a specified operation and give formal axiomatic proofs;

  6. Understand the concept of a subgroup and use Lagrange''s theorem;

  7. Understand the concept of a group action, an orbit and a stabiliser subgroup;

  8. Understand the concept of a group homomorphism and be able to show (in simple cases) that two groups are isomorphic;

  9. Understand the principles of binary coding and how to construct error-detecting and error-correcting binary codes.

• Introduction To Statistics (MATH162) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims

  To introduce topics in Statistics and to describe and discuss basic statistical methods.

  To describe the scope of  the application of these methods.

  Learning Outcomes

  After completing this module students should be able

  -         to describe statistical data;

  -         to use the Binomial, Poisson, Exponential and Normal distributions;

  -         to perform simple goodness-of-fit tests;

  -         to use the package Minitab to present data, and to make statistical analysis.

Programme Year Three

Compulsory modules

• Theory of Statistical Inference (MATH361) Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims

  To introduce some of the concepts and principles which provide theoretical underpinning for the various statistical methods, and, thus, to consolidate the theory behind the other second year and third year statistics options.

  Learning Outcomes

  After completing the module students should have a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference.  The students should also gain an appreciation of the blossoming area of Bayesian approach to inference.

• Linear Statistical Models (MATH363) Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims

  ·      to understand how regression methods for continuous data extend to include multiple continuous and categorical predictors, and categorical response variables.

  ·      to provide an understanding of how this class of models forms the basis for the analysis of experimental and also observational studies.

  ·      to understand generalized linear models.

  ·      to develop familiarity with the computer package SPSS.

  Learning Outcomes

  After completing the module students should be able to:

          understand the rationale and assumptions of linear regression and analysis of variance.

  ·      understand the rationale and assumptions of generalized linear models.

  ·      recognise the correct analysis for a given experiment.

  ·      carry out and interpret linear regressions and analyses of variance, and derive appropriate theoretical results.

  ·      carry out and interpret analyses involving generalised linear models and derive appropriate theoretical results.

  ·      perform linear regression, analysis of variance and generalised linear model analysis using the SPSS computer package.

The modules listed above are illustrative and subject to change. Please refer to the department site for further information