(see also Mathematics(MA), Statistics(ST)) NOTES(S): FOR ALL COURSES AT LEVEL 3 WHICH ARE EXAMINED IN PART BY CONTINUOUS ASSESSMENT: STUDENTS MAY IN EXCEPTIONAL CIRCUMSTANCES BE REQUIRED TO ATTEND AND ORAL EXAMINATION. NOT ALL THE LEVEL 4 MATHEMATICAL SCIENCES SPECIAL OPTIONS WILL BE AVAILABLE IN ANY ONE ACADEMIC SESSION
Level 3
 MX 3001  REAL ANALYSIS

 Credit Points
 15
 Course Coordinator
 Dr R Kessar
Prerequisites
Overview
This course aims to put on a sound footing many of the results and procedures used in the Calculus. It starts by studying properties of the real number system, including suprema and infima, sequences and series. Then it considers the theory of continuous functions on closed bounded intervals, treating global extrema and intermediate values. These results are applied in the theory of differentiability and to the Riemann Integral.
Structure
12 week course  5 onehour lectures and 1 onehour tutorial per fortnight.
Assessment
1st Attempt:1 twohour examination (80%) and incourse assessment (20%).
Resit: 1 twohour examination (maximum of 100% resit and 80% resit with 20% incourse assessment).
 MX 3002  RINGS AND FIELDS

 Credit Points
 15
 Course Coordinator
 Dr S Theriault
Prerequisites
Overview
This is a first course in abstract algebra. The familiar, simple and useful properties of the integers places the set of integers at the core of any study of algebraic objects. But many of these properties hold for other familiar mathematical objects; for polynomials, real numbers, matrices etc. This course develops the theory of rings and fields which unifies the study of many of these objects and, at the same time, clarifies the differences between them.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination (80%) and incourse assessment (20%).
Resit: 1 twohour examination (maximum of 100% resit and 80% resit with 20% incourse assessment).
 MX 3012  MECHANICS A

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Overview
The course studies the Newtonian theory of the motion of a particle. Newton's laws of motion are introduced and illustrated through the study of dynamical problems such as projectile motion, air resistance and the theory of vibrations. Theoretical work is done on topics such as energy, linear and angular momentum and the role of inertial frames in Newtonian mechanics.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination (80%) and incourse assessment (20%).
Resit: 1 twohour examination (maximum of 100% resit and 80% resit with 20% incourse assessment).
 MX 3017  SET THEORY

 Credit Points
 15
 Course Coordinator
 Prof. G Hall
Prerequisites
Overview
This course is a basic introduction to the theory of sets. It proceeds axiomatically and includes the concepts of union, intersection and complementation of sets, Venn diagrams and the de Morgan laws. Mention will be made of Russell's paradox. Also included are relations, functions and order as applied to sets. The course then turns to a brief introduction to the construction of the integers, the rational numbers and the real numbers. The idea of cardinality is also discussed.
Structure
2 one hour lectures and 1 one hour tutorial per week
Assessment
1st Attempt: 1 two hour examination (80%), incourse assessment (20%).
Resit: 1 three hour examination (100%) (CAS mark based on the Maximum of Exam mark and Exam mark (80%) plus incourse assessment mark (20%)).
 MX 3018  ANALYSIS AND ALGEBRA 1

 Credit Points
 30
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Overview
This is a combined course covering the material in MX 3001 Real Analysis and MX 3002 Rings and Fields.
Structure
9 one hour lectures and 4 one hour tutorials per fortnight.
Assessment
1st Attempt: 1 three hour examination (80%), incourse assessment (20%).
Resit: 1 three hour examination (100%) (CAS mark based on the Maximum of Exam mark and Exam mark (80%) plus incourse assessment mark (20%)).
 MX 3019  MECHANICS AND SET THEORY

 Credit Points
 30
 Course Coordinator
 Prof. G Hall
Prerequisites
Overview
This is a combined course covering the material in MX 3012 Mechanics and MX 3017 Set Theory.
Structure
4 one hour lectures and 2 one hour tutorials per week.
Assessment
1st Attempt: 1 three hour examination (80%), incourse assessment (20%).
Resit: 1 three hour examination (100%) (CAS mark based on the Maximum of Exam mark and Exam mark (80%) plus incourse assessment mark (20%)).
 MX 3502  GROUPS AND GEOMETRY

 Credit Points
 15
 Course Coordinator
 Dr J Grbic
Prerequisites
Overview
Numbers measure size, groups measure symmetry. Many groups occur naturally as symmetry groups of solids, patterns and other geometrical objects. This course will develop the basic ideas of group theory through such examples of groups acting on sets.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination (80%) and incourse assessment (20%).
Resit: 1 twohour examination (maximum of 100% resit and 80% resit with 20% incourse assessment).
 MX 3521  JUNIOR HONOURS PROJECT

 Credit Points
 5
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Available only to candidates for Honours Degrees involving Mathematics or Statistics.
Notes
The assessment of this course does not count towards Honours classification. This course is not available in 2005/06.
Overview
The student will undertake a project specified by the department. The work may be done individually or in teams. The end result of the work is to be a report and presentation by the student or team. The work will be supervised by a member of the department and will be assessed on the quality of the report and its presentation.
Structure
12 week course  Classes as appropriate.
Assessment
Assessed on the report.
 MX 3522  COMPLEX ANALYSIS

 Credit Points
 15
 Course Coordinator
 Dr J R Pulham
Prerequisites
Overview
This is an introductory course on Complex Analysis. Holomorphic functions and power series, Cauchy’s throrem and its consequences, contour integration and the calculus of residues are discussed.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination (80%) and incourse assessment (20%).
Resit: 1 twohour examination (maximum of 100% resit and 80% resit with 20% incourse assessment).
 MX 3526  MATHEMATICAL METHODS

 Credit Points
 15
 Course Coordinator
 Dr R Kessar
Prerequisites
Overview
An introduction to the vector calculus leading to the divergence theorem and some of its applications; a brief treatment of Fourier series and their applications; an introduction to partial differential equations, their behaviour and solution.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour written examination (80%) and incourse assessment (20%).
Resit: 1 twohour examination (maximum of 100% resit and 80% resit with 20% incourse assessment).
 MX 3528  OPTIMISATION THEORY

 Credit Points
 15
 Course Coordinator
 Prof. R Levi
Prerequisites
Overview
Basic nonlinear optimisation techniques for multivariable real valued functions, including the second derivative test, constrained optimisation and the method of Lagrange multipliers. Following this, the course will specialise to linear optimisation problems. The simplex algorithm will be introduced and studied, including applications to matrix games. Computations will be done using a computerbased algerbra package, as well as manually.
Structure
2 onehour lectures per week and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour written examination (80%); incourse assessment (20%).
Resit: 1 twohour written examination (maximum of 100% resit and 80% resit with 20% incourse assessment).  MX 3529  ANALYSIS AND ALGEBRA 2

 Credit Points
 30
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Overview
This is a combined course covering the material in MX 3502 Group Theory and MX 3522 Complex Analysis.
Structure
4 one hour lectures and 2 one hour tutorials per week.
Assessment
1st Attempt: 1 three hour examination (80%), incourse assessment (20%).
Resit: 1 three hour examination (100%) (CAS mark based on the Maximum of Exam mark and Exam mark (80%) plus incourse assessment mark (20%)).
 MX 3530  APPLICABLE MATHEMATICS

 Credit Points
 30
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Overview
This is a combined course covering the material in MX 3526 Mathematical Methods and MX 3528 Optimisation Theory.
Structure
4 one hour lectures and 2 one hour tutorials per week.
Assessment
1st Attempt: 1 three hour examination (80%), incourse assessment (20%).
Resit: 1 three hour examination (100%) (CAS mark based on the Maximum of Exam mark and Exam mark (80%) plus incourse assessment mark (20%)).
Level 4
 MX 4008  TOPOLOGY

 Credit Points
 15
 Course Coordinator
 Dr A Libmann
Prerequisites
Overview
An introduction to metric and topological spaces, including a discussion of connectedness, compactness and the continuity of mappings.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination (80%) and incourse assessment (20%).
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4020  PROJECT

 Credit Points
 15
 Course Coordinator
 Prof. R Levi
Prerequisites
MX 3521 or permission of Head of Mathematical Sciences.
Overview
The student will be given a mathematical topic on which to write and submit a report. The work will be supervised by a member of staff.
Structure
12 week course – Assessed on the project report and the oral presentation (the presentations are given during the second halfsession).
Assessment
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4021  EXTERNAL PROJECT

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
MX 3521. Available only to candidates for Honours in Mathematics, Mathematics with French, Mathematics with Gaelic, Mathematics with German, and Mathematics with Spanish.
Notes
Not available in session 2005/06.
Overview
The student will undertake a parttime placement in some company, external institution or other university department to work on a project approved by the department. The placement will extend over all or part of the halfsession as appropriate. Both an onsite supervisor and a departmental supervisor will be appointed to monitor the student’s progress. The assessment of the course will be based on a report written by the student and on assessments by the supervisors. The course will only be available for selected students and if suitable placements can be found.
Structure
12 week course – Classes as appropriate.
Assessment
Assessed on the report and on the supervisors’ report.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4029  EXTENDED MATHEMATICAL PROJECT

 Credit Points
 30
 Course Coordinator
 Professor G Hall
Prerequisites
MX 3521. The course is available only to students accepted into the Joint Honours Programme MathematicsPhysics (MA or BSc) or the single Honours Programmes Physics (BSc) or Natural Philosophy (MA).
Notes
This course is run over the full session.
Overview
The student will be given a Mathematical topic on which to write a report. The work will be supervised by a member of staff. The assessment of the project will be based on the report and an oral examination based on the material relevant to the assigned topic.
Structure
24 week course – 1 tutorial per week.
Assessment
Assessed on the project report and on the oral examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4033  NUMBER THEORY

 Credit Points
 15
 Course Coordinator
 Professor M Linckelmann
Prerequisites
Overview
Number theory is the study of integers and has three main branches: Elementary, Analytical and Algebraic. This course consists of a selection of topics from these branches. The topics will include some of the following: the theory of quadratic congruences, continued fractions, pseudoprimes, primitive roots, Diophantine equations, the distribution of prime numbers, algebraic integers in quadratic number fields.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination (80%) and incourse assessment (20%).
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4034  ELECTROMAGNETISM

 Credit Points
 15
 Course Coordinator
 Dr J Pulham
Prerequisites
Notes
Not available in session 2005/06.
Overview
A course on the mathematical theory of electromagnetism, including electrostatics, potential theory and applications of the wave equation. The course exploits the mathematical techniques developed in MX 3526 (Mathematical Methods).
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour written examination (80%) and incourse assessment (20%).
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4037  ORDINARY DIFFERENTIAL EQUATIONS

 Credit Points
 15
 Course Coordinator
 Dr A J B Potter
Prerequisites
Overview
An introduction to the qualitative theory of systems of ordinary differential equations. Topics covered will include: existence and uniqueness theory, linear systems, equilibria and their stability, periodic solutions. Various particular examples will be analysed in detail.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per week.
Assessment
1st attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4505  CHAOS AND FRACTALS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
A course on some mathematical aspects of the theories of fractals and discrete dynamical processes. It will normally include a treatment of fractal dimension and the use of iterated function systems to generate fractals.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour written examination (80%); incourse assessment (20%).
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4507  GALOIS THEORY

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Available in session 2005/06.
Overview
The roots of a quadratic polynomial are given by a formula involving the coefficients. Similar formulae exist for the roots of polynomial equations of degrees 3 and 4, but not for higher degrees. The precise relationship between a polynomial and the type of roots it has emerges as one of the consequences of Galois Theory, which is a unification of ideas embracing polynomials, fields and group theory. The course will also consider the classical ruler and compass constructions.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4509  GEOMETRIC TOPOLOGY

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
An introduction to the topology associated to a variety of basic geometric spaces, including a discussion of topological invariants and applications to geometric problems.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination (80%) and incourse assessment (20%).
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4510  GRAPH THEORY

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
MA 2002 and MA 2003 and 2504 and either MA 2503 or ST 2003.
Notes
(i) Special Option. Not available in session 2005/06.
(ii) Available only to students in programme year 3 or above.
Overview
An introductory course on the theory of graphs. Topics covered will include: elementary properties of graphs, Eulerian and Hamiltonian circuits, some matching theory including Hall’s theorem.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4512  INTRODUCTION TO FUNCTIONAL ANALYSIS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
Whereas earlier work in analysis tended to focus on single functions, this course deals with functions collectively, as elements of vector spaces or function algebras.
The course will cover topics from: normed spaces, Banach spaces, Hilbert spaces (with emphasis on sequence spaces and function spaces), linear functionals and operators, HahnBanach theorem, principle of uniform boundedness, open mapping and closed graph theorems, the algebra of continuous functions on a compact Hausdorff space, StoneWeierstrass theorem and Gelfand theory.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4520  PROJECT

 Credit Points
 15
 Course Coordinator
 Dr R Levi
Prerequisites
Overview
The student is given a mathematical topic on which to write and submit a report. The work will be supervised by a member of staff.
Structure
12 week course  Assessed on the project report and oral presentation.
Assessment
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4523  HILBERT SPACES

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
A Hilbert space is a vector space which is complete with respect to the metric arising from a given inner product. This setting permits the development of geometric ideas, taken from Euclidean space, which can then be applied to spaces of functions arising naturally in the theory of differential equations. The course will cover topics from: norms, inner products and Hilbert spaces, orthogonality, orthogonal expansions and Fourier series, dual spaces, linear operators.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4528  ALGORITHMS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
The course studies computer algorithms, considering their construction, validation and effectiveness. After a general introduction to the subject a number of specific topics will be covered. These may include: the problem of sorting data sets into order, the use of abstract data types to formalise interactions, the theory of formal grammars and problems such as the parsing of arithmetic expressions, the construction and use of pseudorandom numbers. (If there is insufficient demand this course may be taught as a reading course in which case there will be no lectures and one tutorial per week).
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per fortnight.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4529  NONLINEAR ANALYSIS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
The course is concerned with the analysis of functions of several variables, in particular the differentiability and integrability of such functions. Appropriate background material will be discussed in order to prove some important theorems of analysis, for instance the inverse and implicit function theorems, Fubini’s theorem and convergence theorems of integration.
Structure
12 week course  2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4531  SPECIAL FUNCTIONS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
A study of some important Special Functions of mathematics, providing practical illustrations of many important techniques and methods of analysis.
Structure
12 week course  2 onehour lectures and 1 tutorial per week.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4533  APPLICATIONS OF ALGEBRA

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Available in session 2005/06.
Overview
Traditional applied mathematics is centred in the area where calculus and its developments are used to solve problems in the physical sciences. This course looks at another and more recent set of problems deriving from such things as digital communication and the design of efficient statistical experiments. The course is primarily an introduction to the algebraic theory of errorcorrecting linear codes.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4534  APPLIED ANALYSIS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
This course studies Fourier Series and their applications to the solution of boundary value problems associated with certain linear partial differential equations. In particular the wave equation, heat equation and Laplace’s equation will be studied using the technique of separation of variables. Various aspects of the theory of Fourier series will be discussed, for instance Bessel’s inequality, Parseval’s formula and the convergence and differentiability of Fourier series.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per fortnight.
Assessment
1st Attempt:1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4535  MECHANICS B

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
This course is a continuation of Mechanics A (MX 3012). The ideas and methods of that course are extended to study such topics as: Galilean transformations, systems of particles, the kinematics and dynamics of rigid bodies, analytic mechanics.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per fortnight.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4536  SPECIAL RELATIVITY

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Either: (a) MA2003, MA 2503 and MA 2504; or: (b) MA 2003 and PX 2012.
Notes
(i) Special Option. Not available in session 2005/06.
Overview
The failure of the Newtonian model of physics. The basic principles of the Special Theory of Relativity. The Lorentz transformation and its applications, including length and time dilation. The kinematics of particles. 4vectors and Minkowski space. The dynamics of particles, momentum, energy and force. Relativistic optics. Collision problems.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per fortnight.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4537  TRANSFORMS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
This course is concerned with the application of the Laplace and Fourier transformations to differential and integral equations. It begins with a brief discussion of differential equations. Then the theories of Laplace and Fourier transforms are developed and applied to various problems arising in the study of ordinary differential, partial differential and integral equations.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per fortnight.
Assessment
1st Attempt: 1 twohour examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4539  DIFFERENTIAL GEOMETRY OF SURFACES

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Not available in session 2005/06.
Overview
An introduction to the differential geometry of surfaces. The emphasis will be on explicit local coordinate descriptions of surfaces, allowing the introduction of explicit examples throughout the course. The course will include Gauss’s Theorema Egregium, that the Gaussian Curvature, originally defined in terms of a particular embedding of the surface in space, is an intrinsic property of the surface.
Structure
12 week course  2 onehour lectures per week and 1 onehour tutorial per fortnight.
Assessment
1st Attempt: 1 twohour examination paper.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4540  KNOTS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Available in session 2005/06.
Overview
An introduction to knot theory. The course will include a study of elementary invariants via Reidemeister moves and associated topological objects such as the fundamental group of a knot complement.
Structure
12 week course  2 onehour lectures and 1 tutorial per week.
Assessment
1st Attempt: 1 twohour written examination.
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4542  MATHEMATICS EDUCATION

 Credit Points
 15
 Course Coordinator
 Mr Allan G Duncan
Prerequisites
Pass on 60 credits at level 2 mathematics.
Corequisites
None
Notes
Special Option. Available in 2005/06.
Overview
 Theories of learning: Piaget, Bruner, Gardner (multiple intelligences), Learning styles, constructivism (radical and social)
 Theories of learning mathematics: Dienes, Skemp (relational, instrumental understanding), Thompson (mental arithmetic strategies)
 Methods of teaching: direct interactive, exposition, investigative approach, problem solving, group work and discussion
 Contribution of technology (graphic calculators, graph drawing software, CAS, dynamic geometry, PowerPoint animation, internet)
 Lesson planning and preparation, presentation skills
 Research on learning and teaching school mathematics
 Project (choice of subject matter)
Structure
12 two hour lectures/workshops and 12 one hour tutorials
Period of school experiance  1 week
Presentation sessions
Assessment
1st Attempt: Assessment will have three components:
 report on the School Project
 essay on one topic drawn from the lectures
 presentation to the class (peers)
Resit (for Honours students only): Candidates achieving a CAS mark of 68 may be awarded compensatory level 1 credit. Candidates achieving a CAS mark of less than 6 will be required to submit themselves for reassessment and should contact the Course Coordinator for further details.
 MX 4543  INTRODUCTION TO LIE ALGEBRAS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Notes
Special Option. Available in 2005/06.
Overview
Definition of Lie algebras; first properties and examples. Nilpotent, solvable and semisimple Lie algebras. The Killing form. Cartan subalgebras and the JordanChevalley decomposition of linear transformation. Representations of sl(2). Root systems and Dynkin diagrams. The classification of complex semisimple Lie algebras. Elements of representation theory: highest weight modules. Weyl's character formula and applications.
Structure
2 onehour lectures and one 1hour tutorial per week.
Assessment
1st Attempt: 1 twohour written examination (80%); incourse assessment (20%).
Resit: If required and permitted by Regulations, there will be 1 twohour written examination. The CAS mark will be based on the maximum of examination (100%) and examination (80%) together with incourse assessment (20%).
 MX 4544  REPRESENTATION THEORY OF FINITE GROUPS

 Credit Points
 15
 Course Coordinator
 Head of Mathematical Sciences
Prerequisites
Overview
Some revision of group homomorphisms, vector spaces, and linear transformations. The complex group algebra of a finite group. Modules and representations, equivalence of matrix representations, Irreducibility. Maschke's Theorem on complete reducibility, Schur's Lemma. Complex characters; the ring of generalized characters of a finite group and its natural inner product. Irreducible characters, character tables, and orthogonality relations for group characters. Examples of construction of small character tables.
Algebraic integers, divisibilty of the group order by degrees of irreducible characters. Burnside's p^aq^btheorem and other sample applications to group structure.
Structure
2 onehour lectures and 1 onehour tutorial per week.
Assessment
1st Attempt: 1 twohour written examination (80%); incourse assessment (20%).
Resit: If required and permitted by Regulations, there will be 1 twohour written examination. The CAS mark will be based on the maximum of examination (100%) and examination (80%) together with incourse assessment (20%).