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MA212

Further Mathematical Methods

**This information is for the 2020/21 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 and BSc in Mathematics, Statistics and Business. 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**

This course is delivered through a combination of lectures, help sessions and classes totalling a minimum of 80 hours across Michaelmas Term and Lent Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.

**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.

**Important information in response to COVID-19**

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

** Key facts **

Department: Mathematics

Total students 2019/20: 283

Average class size 2019/20: 15

Capped 2019/20: No

Value: One Unit

**Personal development skills**

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