# 2007/08 Taught Postgraduate Module Catalogue

## MATH5310M Mathematical Review

### 15 creditsClass Size: 100

Module manager: Klaus Reiner Schenk-Hoppé
Email: K.R.Schenk-Hoppe@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2007/08

### Pre-requisite qualifications

The qualifications to gain entrance to the MSc in Financial Mathematics are sufficient.

This module is not approved as an Elective

### Objectives

This module aims to provide students with a thorough and formal treatment of fundamental concepts and techniques in real analysis, linear algebra and probability theory. The course also covers basic concepts of mathematical finance, simple numerical simulations and an introduction to LaTeX. On completion of this module, students will be able to ...

- find the limit of simple sequences, test for convergence of sequences;
- apply basic results on limits, continuity and differentiation;
- understand basic concepts from linear algebra and solve linear equations;
- identify ordinary and partial differential equations and solve simple ODEs;
- describe difference equations and illustrate the dynamics of one- and two-dimensional systems;
- state and use the basic rules of probability;
- apply fundamental concepts of statistics to simple problems;
- understand the mathematical models of choice under uncertainty and stochastic financial asset payoffs;
- use simulation tools to solve and visualise simple mathematical-finance related tasks;
- write reports in LaTeX.

### Syllabus

An understanding of fundamental mathematical concepts and methods as well as familiarity with their application to simple problems is a prerequisite for a successful study of any topic in financial mathematics. Beside analytical skills, it is mandatory to have knowledge of numerical simulations using mathematical software and the proper use of text editors for mathematics. The aim of this module is to equip students with these skills.

This module reviews the basic concepts of limits, continuity, differentiability, series and convergence, complex numbers, linear algebra, ordinary and partial differential equations, elementary probability and statistics. It also provides an introduction to LaTeX.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 10 2.00 20.00 Tutorial 10 1.00 10.00 Private study hours 120.00 Total Contact hours 30.00 Total hours (100hr per 10 credits) 150.00

### Private study

5 hours per lecture: 50 hours;
5 hours per tutorial: 50 hours;
Preparation for assessment: 20 hours.

### Opportunities for Formative Feedback

Exercises will be handed in for assessment on a bi-weekly basis.
Progress will further be monitored by contributions made to tutorials.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Assessed exercises 30.00 Total percentage (Assessment Coursework) 30.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 70.00 Total percentage (Assessment Exams) 70.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated