B.Sc HONOURS SYLLABI

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B.Sc HONOURS


SYLLABI


2



Module Code

Module Title

MATH 4831

Mathematical Methods 2

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

Mathematical
Sciences


Module Author:

Dr. David J. McCarthy


Module Description:

The module contains a treatment of advanced mathematical
techniques applied to linear differential equations, to vector calculus and to complex
variables. The general theory of linear ord
inary differential equations is developed,
including the case of Sturm
-
Liouville systems; solution techniques for linear partial
differential equations are treated. The integral theorems of vector calculus are
covered. Integral calculus of functions of one

complex variable is treated, including
Cauchy’s Theorem, the Residue Theorem and applications.


Module aim


The aim of this module is to



introduce some basic theorems on the solutions of linear ordinary
differential equations,



develop techniques for
solving second
-
order linear ordinary differential
equations,



cover solution methods for linear partial differential equations,



investigate the properties of special functions (such as Bessel and Legendre
functions),



treat in detail the integral theorems of

vector calculus(e.g. the theorems of
Green and Stokes) and their applications and


introduce the basic theorems of contour integration, such as Cauchy’s
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Learning Outcomes:



On successful completion of this module the learner will be able to



solve second
-
order linear ordinary differential equations by using power
series or by using the Frobenius method



apply standard solution techniques to important linear partial differential
equations (such as the wave equation, the heat equation)



evaluate real integrals and sum series by the use of contour integration


apply the integral theorems of v
ector calculus to mathematical problems
which arise in science and engineering.


Learning and Teaching Methods


Lectures 24 hrs/Semester (48 over 2 Semesters)


3

Tutorials/Practical 12 hrs/Semester (24 over 2 Semesters)


Module conte
nt:

Linear Differential Equations

Inner product on a function space. Expansion of functions in series of orthogonal
functions. Mean square convergence.

Sturm
-
Liouville theory. Expansions of functions in series of eigenfunctions of

self
-
adjoint (Hermitian
) operators.

General theory of linear ordinary differential equations. Power series solutions of
second
-
order linear ordinary differential equations. Legendre and Bessel functions.

Solution techniques for linear partial differential equations, including se
paration of
variables, integral transforms, Green’s functions.


Special Functions

Gamma function. Bessel and Legendre functions. Asymptotic expansions.


Vector Calculus

Theorems of Green, Stokes, Gauss and applications.


Integral Equations

Linear equations

of Volterra and Fredholm. Singular integral equations.


Complex Analysis

Cauchy’s theorem and integrals. Taylor and Laurent series, contour integration
-

evaluation of real integrals. Uniformly convergent series of regular functions
-

expansion of a meromo
rphic function. Summation of series by residue methods.



Module Assessment


Minor projects/Problem sets 25% of final mark

End of module written examination (3 ½ hours) 75% of final
mark



Essential Reading

Arfken G. B., Weber H. J.,
Mathematical Methods for Physicists

(6
th

Ed.) 2005,
Academic Press

Supplemental Reading


Hassani S.,
Mathematical Physics


A Modern Introduction to its Foundations

(2002), Springer
-
Verlag



Further Details:


Stage 3
-

Part 7
-

Linked module over two semesters.

Weekly contact hours:


Lecture 2 hrs


Tutorial 1 hr


Date of
Academic Council approval

………………………….



4


Module Code

Module Title

MATH 4832

Topics in Analysis

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

Mathematical
Sciences


Module Author:

Dr. Susan Lazarus


Module Description:


We begin by reviewing the basic concepts of vector spaces, and then study concepts
of analysis on normed linear spaces, on which we have a notion of vector length. We
then study inner prod
uct spaces and introductory concepts of operators.


Module aim:

To provide a solid foundation in the study of analysis and to develop
the student’s ability to reason in a mathematically rigorous manner.


Learning Outcomes:

On completion of the course

the student should:


(i) be able to demonstrate a thorough understanding of convergence, completeness
and continuity in normed linear spaces and inner product spaces,

(ii) be adept at working with norms and inner products, and

(iii) be able to demonstrate

properties of linear operators on normed linear spaces and
inner product spaces


Learning and Teaching Methods:


Lectures 24hrs/Semester(48 over 2 Semesters)

Tutorial 12hrs/Semeste
r(24 over 2 Semesters)


Module content:



Normed Spaces

Review of vector spaces. Normed linear spaces, convergence, continuity, closed sets,
function spaces, completeness, compactness, Banach’s Fixed
-
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Hilbert Spaces

Inner product spaces,

orthogonality, Bessel’s Theorem, Parseval’s Relation, and the
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-
Banac栠
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-
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Theory of Operators

Bounded linear operators. The adjoint of an
operator, self
-
adjoint operators, unitary
operators. Eigenvalue problems for self
-
adjoint operators.


Module Assessment:



Assignment 25% of final Mark


End of Module written exam 75% of final mark


5



Essential Reading:

Kreyszig, Erwin, Introductory Functional Analysis with
Applications, John Wiley & Sons, 1989


Recommended Reading:

Saxe, Karen, Beginning Functional Analysis, Springer

Verlag, 2002


Supplemental Reading:

Griffel, D. H.
Applied Functional Analysis, John Wiley &
Sons, 1985



Further Details:


Stage 3
-

Part 7
-

Linked module over two semesters.


Weekly contact hours: Lecture 2 hrs/week


Tutorial 1 hr/week


Date of Ac
ademic Council approval

………………………….



6


Module Code

Module Title

MATH 4840

Differential Equations and Numerical Methods

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

Mathematical Sciences


Module Author:

Dr. Chris Hills


Module Description:

Partial differential equations occur throughout mathematical
modelling from meteorology and continuum mechanics, to financial mathematics,
quantum mechanics, mathematica
l biology and electromagnetism. The module
introduces advanced techniques to tackle partial differential equations both
analytically and via numerical methods. The learner will be able to solve practical
partial differential equations and an understanding

of their behaviour will be
developed.



Module aim:

The aim of this module is to



introduce the learner to the ideas and techniques of solving partial
differential equations



develop and analyse the suitability and effectiveness of competing
numerical m
ethods



discover which PDEs can be solved analytically, which require a
numerical approach



discuss modern applications of partial differential equations and appreciate
how models can be constructed



Learning Outcomes:



On successful completion of
this module the learner will be able to



solve first and second order, linear and nonlinear partial differential
equations occurring throughout the sciences both analytically and using
tailor
-
made numerical algorithms



analyse the effectiveness of numerical
schemes



model simple processes such as traffic flow



apply and analyse numerical techniques to solve real world problems



Learning and Teaching Methods:


Lectures 24 hrs/Semester (48 over 2 Semesters)

Tutorials 12 h
rs/Semester (24 over 2 Semesters)



7




Module content:



Introduction

to

the definitions and terminology associated with partial differential
equations and numerical modelling.

First
-
order PDEs: linear PDEs, method of characteristics; quasi
-
linear PDEs,

singularities and consistency, traffic flow; non
-
linear PDEs, Charpit’s method.

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-
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-
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Module Assessment:

Minor projects/Problem sets 25% of final Mark

End of Module written exam (3 ½ h
ours) 75% of final mark



Essential Reading

Smith G.D.,
Numerical Solution of Partial Differential Equations: Finite Difference
Methods
, 1985, Oxford University Press


Supplemental Reading


Ockendon J., Howison S. , Lacey

A. & Movchan A.,
Applied Partial Differential
Equations
, 2003, Oxford University Press

Sneddon I.M.,
Elements of Partial Differential Equations
, 1957, McGraw
-
Hill

Williams W.E.,
Partial Differential Equations
, 1980, Oxford Clarendon Press


Further Deta
ils Further Details
:

Stage 3


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-

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Date of Academic Council app
roval

………………………….



8


Module Code

Module Title

MATH 4833

Mathematical Control Theory

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

Mathematical Sciences


M
odule Author:
Dr. David J. McCarthy


Module Description:

This module introduces the learner to the techniques and
results that form the basis of control theory. The skills and methods for solving
problems in control theory are developed.



Module aim:

The aim of this module is to



introduce the learner to the concepts and techniques of control theory



ensure that the qualitative theory of differential equations can be applied to
simple dynamical systems



provide an understanding of the state
-
space approac
h



give an appreciation of optimal control theory




Learning Outcomes:


On successful completion of this module the learner will be able to



implement the state
-
space approach and solve linear control systems



use mathematical tests to determine the stabi
lity characteristics of
dynamical systems



assess controllability/observability of linear control systems


apply the Pontryagin Principle for optimal control


Learning and Teaching Methods:


Lectures 24 hrs/Semester (4
8 over 2 Semesters)

Tutorials 12 hrs/Semester (24 over 2 Semesters)



9



Module content:



Introduction

to

the mathematical formulation of control problems, state space
representation, linear systems, fundamental matrix, two
-
dimensional
systems, phase
portraits, critical points.

Stability theory for non
-
linear systems, Liapunov stability theory, almost linear
systems, periodic solutions and limit cycles.

State transition matrix, controllability and observability, state feedback, system
re
alisation.

Techniques of the calculus of variations, optimal control problems, necessary
conditions for optimality, the Bolza problem, Pontryagin’s principle, bang
-
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Module Assessment:

Minor p
rojects/Problem sets 25% of final Mark

End of Module written exam (3 ½ hours) 75% of final mark



Essential Reading

Barnett S. & Cameron R. G.,

Introduction to Mathematical Control
Theory,
2
nd

Edition 1985, Oxford University Press.


Supplemental Reading


Brauer F. & Nohel J. A.,

Qualitative Theory of Ordinary Differential Equations

1990, Dover.

Hocking L.,

Optimal Control
1991
,
Clarendon Press.



Further Details:


Stage 3


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-

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Date of Academic Council appro
val

………………………….





10


Module Code

Module Title

MATH 4834

Advanced Algebra

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

None

None

2005

15


School:

Mathematical Sciences


Module Author:

Susan La
zarus


Module Description:

The module begins with a review of important properties of
the integers. It continues to investigate the algebraic systems of groups, rings and
fields.



Module Description:
To provide a solid foundation in the area of abstr
act algebra in
order to prepare students to handle the algebra they will meet in all areas of

mathematics, and form a firm foundation for more specialized work in

algebra.



Learning Outcomes:

On completion of the module, the student will



Be able to d
emonstrate understanding of the fundamental concepts within the
areas of group theory, ring theory and field theory,



have developed the ability to reason formally and present a mathematical


argument in a fully rigorous fashion.



Learning a
nd Teaching Methods:


Lectures 24hrs/Semester(48 over 2 Semesters)

Tutorial 12hrs/Semester(24 over 2 Semesters)


11



Module content:


Preliminaries
:

Integers, Equivalence Relations,
Congruences.


Group Theory

Transformation groups, Homomorphism, Isomorphism, Cayley's theorem,

Cosets, Lagrange's theorem, Normal subgroups, Quotient groups, Isomorphism

theorems, Symmetric groups, Class equation, Sylow's theorems, Direct

products, Finit
e Abelian groups, Soluble groups.


Ring Theory

Homomorphism, Isomorphism, Ideals, Quotient rings, Isomorphism

theorems, Commutative rings, Integral domains, Fields, Principal ideal

domains, Prime ideals, Maximal ideals, Quotient field, Divisibility, Eucl
idean

domains, Polynomial rings.


Field Theory

Extension fields, Simple extensions, Finite extensions, Algebraic extensions,

Minimal polynomial, Algebraic closure, Galois group, Splitting field, Galois

correspondence, Solution by radicals.



Module As
sessment:

Module Assessment:


Assignment 25% of final Mark


End of Module written exam(3
) 75% of final mark



Essential Reading
:

Gallian J. A., Contemporary Abstract Algebr
a, 6
th

Edition,
Houghton Mifflin Co., 2006


Recommended Reading:

Herstein, I. N., Abstract Algebra, 3
rd

Edition, John Wiley
& Sons, 1996


Supplemental Reading:

Fraleigh J. B., A First Course in Abstract Algebra, 7
th

Edition, Addison Wesley, 2002.


Web re
ferences, journals and other:
www.d.umn.edu/~jgallian



Further Details:


Stage 3


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-

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Date of Academic Council approval

………………………….



12


Module Code

Module Title

MATH 4835

Operations Research

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

M
athematical Sciences


Module Author:

Dr. David J. McCarthy


Module Description:

This module introduces the learner to the concepts and basic
methods of Operation Research. Linear programming is introduced and is used to
formulate and solve applied problem
s. Scientific and industrial models are used to
apply the theory of both queuing theory and Markov processes. Software packages are
used to solve and simulate problems in each topic.



Module aim:

The aim of this module is to



introduce the learner to th
e concepts and methods of operation research,



provide an understanding of both the basic models and applications of
queuing theory and


provide the learner with sufficient theory and examples in stochastic
processes to enable models in sci
ence and industry to be formulated and
solved.


Learning Outcomes:

On successful completion of this module the learner will be
able to



formulate and solve applied problems in linear programming,



design and analyse queuing models in applied areas,



apply

the theory of stochastic processes acquired to resolve problems using
these techniques and



assess and solve models in all these areas using various software packages.



Learning and Teaching Methods:



Lectures 24 hrs/Semester (48 hrs over

2 Semesters)

Tutorials 6 hrs/Semester (12 hrs over 2 Semesters)

Laboratory 6 hrs/Semester (12 hrs over 2 Semesters)



13



Module content:

Queuing Theory

Introduction to queuing models. Poisson arrival pattern. Negative exponentia
l service
pattern. Different queuing models
-

M/M/
1 and
M/M/
S infinite models,
M/M/
1 and
M/M/
S finite models.
M/M/
1 with varying arrival patterns and service rates.
Derivation and analysis of mean queuing times, mean number of customers in the
system, etc.

for above models.

Stochastic Processes

Review of matrix analysis. Definition of primitive/imprimitive matrices,
reducible/irreducible matrices. Definition of a stochastic process and Markov chains.
First
-
order and higher order transition matrices. Classif
ications of states of a Markov
chain
-

absorbing, persistent, transient, periodic, null, non
-
null, ergodic. Theorems
relating states, long
-
term probabilities, etc. Existence of limits for irreducible ergodic
chains.

Linear Programming

Introduction to and e
xamples of linear programs. Linear programs in standard form.
Definitions of feasible, basic feasible and optimal solutions. The fundamental theorem
of linear programming (with proof). Relations to convexity. Simplex method
-

pivots,
vectors to leave and e
nter basis, determining a minimum feasible solution. Artificial
variables. Variables with upper bounds. Duality
-

dual linear programs, the duality
theorem. Simplex multipliers. sensitivity and complementary slackness. Dual Simplex
method. Primal
-
dual alg
orithm. Reduction of linear inequalities.

Practical

Use of software packages to solve problems and set up simulations.



Module Assessment:


One minor project 25% of final mark

End of modul
e written examination ( 3 ½ hours) 75% of final mark



Essential Reading

Taha H. A.,

Operations Research
-

An Introduction

(8
th

Ed.) 2006, Prentice Hall.

Luenberger D.G.,

Linear and Non
-
linear Programming
(2
nd

Edition) 2003, Kluwer
Academic
.

Supplemental Reading


Medhi J.,

Stochastic Processes

(2
nd

Ed) 2000, Wiley.



Further Details

Stage 3
-

Part 8
-

Linked module over two semesters.

Weekly contact hours:


Lecture
2 hrs


Tutorial 0.5 hrs


Laboratory 0.5 hrs


Date of Academic Council approval

………………………….


14


Module Code

Module Title

MATH 4836

Quantum Theory

ISCED

Code

Pre
-
Requisite
Modul
e Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

Mathematical Sciences


Module Author:

Dr. Emil M Prodanov


Module Description

: This module introduces the student to the main concepts of
quantum mechanics. The material provides a sound knowledge of the most important
topics from physical perspective and also through the mathematical formalism.




Module aim:

The aim of this module is to



introduce the student to the fundamental concepts

of quantum mechanics,



provide thorough knowledge of the most important areas,



promote clear, precise and analytical thinking.



Learning Outcomes:

On successful completion of this module the learner will be
able to:



Fit quantum mechanics in the general

picture of theoretical physics and
thoroughly understand the interplay between quantum mechanics and the
other major physics theories, classical mechanics in particular.



Understand the mathematical apparatus of quantum mechanics.



Formulate and solve the m
ost standard problems of quantum mechanics
including linear harmonic oscillator, potential wells and barriers, hydrogen
atom.



Demonstrate confidence when using quantum mechanics in both


the Heisenberg and Schrödinger formulations.


Lear
ning and Teaching Methods:


Lectures 24hrs/Semester(48 over 2 Semesters)

Tutorial 12hrs/Semester(24 over 2 Semesters)


15



Module content:


. THE WAVE FUNCTION


i. The Schrodinger E
quation


ii. The Statistical Interpretation


iii. Probability


iv. Normalization


v. Momentum


vi. Heisenberg’s Uncertainty Principle


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Module Assessment:


Minor projects/Problem sets 25% of final mark

End of module written examination (3 ½ hours)

75% of final mark



16



Essential Reading
:

(1) David J. Griffiths,
Introduction to Quantum Mechanics

2/e, Benjamin Cummings
(2004), ISBN
-
13: 978
-
0131118928

(2) J. J. Sakurai,
Modern Quantum Mechanics
2/e, Addison
-
Wesley (1993), ISBN
-
13:
978
-
0201539295


Supplemental Reading:

L. D. Landau and L. M. Lifshitz,

Quantum Mechanics: Non
-
Relativistic Theory
,
Butterworth
-
Heinemann (1981), ISBN
-
13: 978
-
0750635394


Further Details:

Stage 3
-

Part 8
-

Linked module over two semesters.

Weekly contact hours:



Lecture 2 hrs


Tutorial 1 hr




Date of Academic Council approval

………………………….



17


Module Code

Module Title

MATH 4837

Fluid Mechanics

ISCED

Code

Pre
-
Requisite
Mod
ule Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

Mathematical Sciences


Module Author:

Dr Brendan Redmond


Module Description:

This module presents the basic and more advanced principles
of fluid mechanics and illustrates them by application to a variety of problems of
scientific interest.




Module aim:

The aim of this module is:



To introduce the fundamental aspects of both classic and modern fluid
mechanics and to provide techniques f
or solving specific classes of fluid flow
problems.




Learning Outcomes:


On completion of this module the student should be able to



understand the phenomena which are associated with various properties of
fluids



apply appropriate mathematical techniqu
es in solving problems in fluid
dynamics.



Learning and Teaching Methods:


Lectures 24hrs/Semester(48 over 2 Semesters)

Tutorial 12hrs/Semester(24 over 2 Semesters)


18



Module conte
nt:

Preliminaries

Properties of fluids, dimensional reasoning, the continuum model, Newtonian fluids.

Fundamental Equations

Conservation laws, the rate of strain matrix. Mathematical methods


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Flow Kinematics

Acceleration of a

fluid particle, flow lines, vorticity.

Ideal Fluid Flow

Stream function, complex potential and complex velocity, complex variable
techniques, aerofoil theory.

Solutions of the Navier Stokes Equations

Couette flow, flow in a pipe, flow down an inclined pla
ne.

Slow Viscous Flows

The biharmonic equation and some solutions of it.

Water Waves

Surface gravity waves, sinusoidal waves on deep water, particle paths for travelling
waves.


Module Assessment:


Assignment

25% of final mark.

End of module written examination(3
) 75% of final mark.



Essential Reading:


Batchelor G. K., An Introduction to Fluid Dynamics, Cambridge Univer
sity Press,
2000.

Currie I. G., Fundamental Mechanics of Fluids, Marcel Dekker, 2002.


Supplemental Reading
:

White F. M., Fluid Mechanics, McGraw
-
Hill, 2008.

Young D.F., Munson B.R., Okiishi T.H., A brief introduction to fluid mechanics,
Wiley, 2004.





Further Details
:

Stage 3
-

Part 8
-

Linked module over two semesters

Weekly contact hours Lectures 2 hrs/week


Tutorial 1 hr/week




Dat
e of Academic Council approval

………………………….



19


Module Code

Module Title

MATH 4838

Financial Mathematics

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Modules

None

2005

15


School:

Mathe
matical Sciences


Module Author:

Mr Anthony Byrne


Module Description:

This module introduces the terminology of financial markets
and many relatively new mathematical techniques used in valuing financial
instruments. Stochastic methods are employed to va
lue stocks. Black
-
Scholes
analysis is introduced and used to price options. Extensive use is made of financial
packages in the formation of models and the solution of problems relating to the
valuation of options.

.


Module aim:

The aim of this module
is to



introduce the concepts and terminology of stocks and financial derivatives,



analyse the application of stochastic processes in modeling option pricing,



derive the Black
-
Scholes partial differential equation,



apply Black
-
Scholes analysis to the valua
tion of options and stock indices
and



devise models using financial packages ( e.g. Matlab) and use these
packages to determine the values of options



Learning Outcomes:



On successful completion of this module the learner will be able to



identify dif
ferent types of financial instruments and their particular
characteristics,



model option prices using stochastic processes,



apply Black
-
Scholes analysis to determine the value of options and



use financial packages to model and solve a range of problems i
n stock and
option pricing.



Learning and Teaching Methods:



Lectures 24 hrs/Semester (48 hrs over 2 Semesters)

Tutorials 6 hrs/Semester (12 hrs over 2 Semesters)

Laboratory 6 hrs/Semester (12 hrs over 2 Semesters
)


20



Module content:

Financial Markets

Introduction to financial markets. Derivatives. Forwards and futures.

Option and option positions. Margins and swaps.


Trading and Option Pricing


Factors affecting option prices, Put
-
call parity. Forward and futu
re pricing. Trading
strategies. Introduction to binomial trees and option pricing.


Stochastic Methods and Valuations

Asset price modelling. Wiener processes. Ito’s Lemma.


Black
-
Scholes Analysis

Introduction to Black
-
Scholes analysis. Put
-
call parity.
Arbitrage.

Boundary and final conditions. Derivation of the Black
-
Scholes equation.
Applications of the Black
-
Scholes equation.


Variation on the Black
-
Scholes model

Dividend paying assets. Forward and future contracts. American Options.

Free boundary
problems. Exotic and barrier options.


Software Packages

Use is made throughout the module of software packages (e.g. Matlab) to form
models and solve applied problems.



Module Assessment


One minor project

25% of final mark.

End of module written examination (3 ½ hours) 75% of final mark.



Essential Reading:

Wilmott P., Howison S., Dewynne J.,
Mathematics of Financial
Derivatives

1995, Cambridge University Press


Re
commended Reading:

Higham D.,
An Introduction to Financial Options:
Mathematics, Stochastics and Computation

2004, Cambridge University Press.

Supplemental Reading:

Capinski M., Zastawniak T.,
Mathematics for Finance


An Introduction to Financial Engineer
ing
(2005) Springer

Web references, journals and other:



Further Details:


Stage 3
-

Part 8
-

Linked module over two semesters

Weekly contact hours Lectures 2 hrs


Tutorial/Lab 1 hr





Date of Academic Council approval

………………………….



21



Module Code

Module Title

MATH 4839

Major Project

ISCED

Code

Pre
-
Requisite
Module Code(s)

Co
-
Requisite
Module Code(s)

Last Revision
Date

ECTS
Credits

461

Stage 2 Mod
ules

None

2005

15


School:

Mathematical Sciences


Module Author:

Mr. Anthony Byrne


Module Description:

This module offers the learner the opportunity of choosing a
major project as an optional module at Stage 3. The choice of topic will be chosen in
di
scussion with staff attached to the programme



Module aim:

The aim of this module is to give the learner the opportunity of
pursuing an in
-
depth investigation into a topic in which they have a particular interest.
It might also be chosen in connection
with their employment.



Learning Outcomes:


On successful completion of this module the learner will have



gained an in
-
depth knowledge of a distinct mathematical topic,



greatly enhanced their ability to research and manage a significant project
and



imp
roved their ability to coordinate and present a research document.



Learning and Teaching Methods:

The teaching method in this module will be
flexible. Regular meetings/tutorials will be provided where the learner will be assisted
and encouraged. Use
will be made of the extensive facilities of this College and,
where appropriate, other institutions.



Module content:

The content of this module will be chosen in consultation with the
academic staff on the programme. It is envisaged that, in many case
s, the choice of
topic may originate from the learner.



Module Assessment:

This module will be assessed under the following criteria


Oral Presentation 15%


Project Report 45%


Understand
ing/Conduct 40%


Understanding refers to the level of comprehension as assessed by the supervisor
and the second internal examiner.



22

Conduct refers to the candidate’s behaviour with reference to punctuality in attending
arranged meetings with the su
pervisor, promptness in carrying out supervisors
instructions, timeliness of completion, etc..

A log book will be given to the candidate which will form a record of supervision and
include details regarding agreed programmes of work, a timetable of work c
ompleted
etc.. The oral presentation will be assessed by at least three members of the

Programme team. The report in typed, bound form will be assessed by two internal
examiners (one of whom is the project supervisor). The project supervisor will report
o
n the candidate’s understanding of the material and their conduct during the period
involving the project. The project will be moderated by the external examiner.



Essential Reading

As prescribed by project supervisor


Supplemental Reading


Texts

and papers

as prescribed by project supervisor






Further Details:


Stage 3


Part 8


Linked module over two semesters

Weekly contact hours Tutorial 1 hr



Research 2 hours



Date of Academic Council approval

………………………….