## MA212Further Mathematical Methods

This information is for the 2017/18 session.

Teacher responsible

Prof Jozef Skokan, Prof Adam Ostoja-Ostaszewski and Dr Arne Lokka

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 Statistics with Finance. This course is available on the BSc in Accounting and Finance, BSc in Econometrics and Mathematical Economics, BSc in Economics 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 (permitting application of the Laplace transform to discrete and continuous probability distributions), 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

22 hours of lectures and 10 hours of classes in the MT. 22 hours of lectures and 10 hours of classes in the LT. 2 hours of lectures in the ST.

Formative coursework

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

A Ostaszewski, Advanced Mathematical Methods for both halves.

Useful background texts:

(i) for the calculus half: Ken Binmore & Joan Davies, Calculus, Concepts and Methods; M R Spiegel, Laplace Transforms; R A Adams, Calculus.

(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 main exam period.

Key facts

Department: Mathematics

Total students 2016/17: 292

Average class size 2016/17: 14

Capped 2016/17: No

Lecture capture used 2016/17: Yes (MT & LT)

Value: One Unit

Guidelines for interpreting course guide information

PDAM skills

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

Course survey results

(2014/15 - 2016/17 combined)

1 = "best" score, 5 = "worst" score

The scores below are average responses.

Response rate: 52%

Question

Average
response

2.8

Materials (Q2.3)

2.4

Course satisfied (Q2.4)

2.3

Lectures (Q2.5)

2.6

Integration (Q2.6)

2.1

Contact (Q2.7)

2.3

Feedback (Q2.8)

2.3

Recommend (Q2.9)

 Yes 52% Maybe 37% No 11%