Further Mathematical Methods

**This information is for the 2019/20 session.**

**Teacher responsible**

Prof Jozef Skokan and Dr James Ward

**Availability**

This course is compulsory on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business and BSc in Statistics with Finance. This course is available on the BSc in Economics, BSc in Management and MSc in Economics (2 Year Programme). This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

**Pre-requisites**

Students should ideally have taken the course **Mathematical Methods** (MA100) or equivalent, entailing intermediate-level knowledge of calculus and linear algebra, linear independence, eigenvalues, diagonalisation, and proficiency in techniques of differentiation and integration.

**Course content**

This course develops ideas first presented in MA100. It is divided into two halves: calculus and linear algebra. The calculus half explores how integrals may be calculated or transformed by a variety of manipulations, and how they may be applied to the solution of differential equations. This aim is achieved by studying the following topics: Limit calculations. Riemann integral. Multiple integration. Improper integrals. Manipulation of integrals. Laplace transforms. Riemann-Stieltjes integral, to a level of detail dependent on time constraints. The linear algebra half covers the following topics: Vector spaces and dimension. Linear transformations, kernel and image. Real inner products. Orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications to the solutions of differential and difference equations. Singular values, and the singular values decomposition. Direct sums, orthogonal projections, least square approximations, Fourier series. Right and left inverses and generalized inverses.

**Teaching**

20 hours of lectures, 10 hours of classes and 10 hours of workshops in the MT. 20 hours of lectures, 10 hours of classes and 10 hours of workshops in the LT. 2 hours of lectures in the ST.

**Formative coursework**

Written answers to set problems will be expected on a weekly basis.

**Indicative reading**

Useful background texts:

(i) for the calculus half:

Ken Binmore and Joan Davies, Calculus, Concepts and Methods (Cambridge University Press 2002);

Robert C. Wrede and Murray R. Spiegel, Advanced Calculus (McGraw-Hill Education; 3rd edition 2010).

(ii) for the linear algebra half:

Martin Anthony and Michele Harvey, Linear Algebra: Concepts and Methods (Cambridge University Press 2012).

**Assessment**

Exam (100%, duration: 3 hours) in the summer exam period.

**
Key facts
**

Department: Mathematics

Total students 2018/19: 271

Average class size 2018/19: 12

Capped 2018/19: No

Value: One Unit

**Personal development skills**

- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills