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2013/14 Taught Postgraduate Module Catalogue
MATH5310M Mathematical Review
15 creditsClass Size: 100
Module manager: Prof K Schenk-Hoppe
Email: K.R.Schenk-Hoppe@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2013/14
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
The module aims to provide students with a thorough and formal treatment of fundamental concepts and techniques in linear algebra, real analysis, constrained optimization and differential equations. The module also provides students with a thorough grounding in computer programming (C++).On completion of this module, students should be able to demonstrate an understanding of fundamental mathematical concepts and methods as well as familiarity with their application (both analytically and numerically) to simple problems in the context of financial mathematics. This module reviews the basic concepts of limits, continuity, differentiation, integration, linear algebra, constrained optimization, ordinary and partial differential equations. The module also provides instructions to support self-studies in the programming language C++.
On completion of this module you should be able to:
-understand basic concepts from linear algebra and solve linear equations
-test for convergence and find limits of sequences and series
-understand the concept of continuity and its implications
-differentiate uni- and multi-dimensional functions, find their local and global extrema
-solve optimization problems with constraints
-compute single and multiple integrals
-identify ordinary and partial differential equations and solve simple ordinary differential equations
-write algorithms for solution of mathematical and finance related tasks
-write simple programmes in C++ for solution of mathematical and finance-related tasks
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.
This module reviews the basic concepts of limits, continuity, differentiability, linear algebra, constrained and unconstrained optimization, ordinary and partial differential equations. It also provides an introduction to the programming language C++
Session 1: Linear Algebra
Session 2: Algorithms and C++
Session 3: Limits of sequences and series
Session 4: Continuity
Session 5: Differentiability in one dimension
Session 6: Unconstrained optimization
Session 7: Optimization with constraints
Session 8: Integration
Session 9: Ordinary differential equations
Session 10: Partial differential equations
Teaching methods
| 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 on a weekly basis- Assessed assignments
- Contributions made to tutorials
Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| In-course Assessment | Assessed exercises. | 40.00 |
| Total percentage (Assessment Coursework) | 40.00 | |
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 00 mins | 60.00 |
| Total percentage (Assessment Exams) | 60.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 17/02/2014
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
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