UNIVERSITY OF DURHAM
DEPARTMENT OF MATHEMATICAL SCIENCES
2H & 2JH MATHEMATICS COURSES
1999 - 2000
SCIENCE LABORATORIES
SOUTH ROAD
DURHAM DH1 3LE
1
CONTENTS
Page
Introduction
2
The Department
3
The Degrees
3
The Degree Structure
6
The Modules
8
Teaching and Learning
11
Monitoring of Work
11
Books and Libraries
11
Calculators
11
Staff-Student Consultation
12
Useful Contacts
12
Illness and Absence
12
Examinations and Progression
13
Illness and Examinations
13
No Smoking Policy
13
Durham University Mathematical Society
14
Booklists and Module Descriptions
15
2H Core
062011: Complex Analysis II
16
062021: Linear Analysis and Applications II
18
062031: Vector Calculus and Partial Differential Equations II
20
2H Options
062061: Algebra and Number Theory II
22
062071: Mathematical Physics II
24
062051: Numerical Analysis II
26
062041: Statistical Concepts II
28
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INTRODUCTION
Welcome to 2H! This booklet is provided for second year students registered for Single
or Joint Honours degrees in Mathematics. Separate literature is available for students
registered for Natural Sciences or Combined Studies in Arts or Social Sciences (including
those taking Named Routes within these programmes).
This booklet contains information specific to your programme of study within the
Department. For information concerning general University regulations, examination
procedures etc., you should consult the Faculty Handbooks and the University Calendar,
which provide the definitive versions of University policy.
If at any time you would like to discuss aspects of your course, or if there are questions
about the Department which this booklet leaves unanswered, please contact your
Departmental Advisor or the Second Year Course Director, Dr. C. Kearton.
You may find it useful to keep this booklet for future reference.
prospective employers might find it of interest.
For instance,
It is usual for the second year to be regarded as harder than the first year. Time spent
during the vacation in catching up on first year work which was not understood, or in
browsing through some of the recommended 2H books and following the suggestions made
at the end of each module description, will be well rewarded.
Have a good vacation!
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THE DEPARTMENT
The Department has two main functions, teaching and research. This booklet gives a
guide to the academic programme provided by the Department for students taking the
second year of the degrees listed in the next section.
THE DEGREES
The following Single or Joint Honours degrees in Mathematics are available. Each one
is a first degree, eligible for local authority funding in the normal manner.
3 year B.Sc./B.A. Honours in Mathematics.
3 year B.Sc. Joint Honours in Mathematics and Physics.
3 year B.Sc. Joint Honours in Computer Science and Mathematics.
3 year B.A. Joint Honours in Mathematics and Economics.
3 year B.A. Joint Honours in Economics with Mathematics.
4 year B.Sc./B.A. Honours in Mathematics (European Studies).
4 year M. Math. Master of Mathematics.
4 year M.Sci. Master in Science Joint Honours in Mathematics and Physics.
Each of the above will qualify you for a wide range of employment and also for further
study in programmes such as the PGCE, specialised M.Sc. courses which make use of
mathematics in other areas (Operational Research, Applied Statistics, Computation etc.) or
research leading to a Ph.D.
The final two degrees in the list are particularly suitable if you wish to study your
subject in greater depth, for example with the intention of doing research. They aim to
provide a mathematical education comparable with that which may be gained elsewhere in
Europe, in terms of depth and breadth. One third of the final year will be spent on project
work, allowing an in-depth study of a particular topic.
The overall structure of the degree programmes is described in your Faculty’s First Year
Undergraduate Handbook under ‘Degree Programme Frameworks’ and summarised in the
flow chart on pages 6-7.
Entry to the third year of the M.Math., M.Sci., or B.Sc./B.A. (European Studies) degrees
usually requires a performance at II.2 level or better in the examinations at the end of year
two. Progression from year three to year four of the M.Math. or M. Sci. will normally
require a performance at II.2 level or better (2H and 3H marks combined in the ratio 2:3) at
the end of year three.
Students registered for the M.Math. who do not attain the necessary standard at the end
of year three will normally be required to terminate their studies and will be awarded a
B.Sc. honours degree of the appropriate class, subject to their having reached the minimum
standard required. With this exception, it will not be possible to change programme from
B.A./B.Sc. to M.Math. or vice versa at the end of year three. Students registered for the
three year course who may wish to follow the four year course should negotiate with their
Local Education Authority before the end of the first term of the second year. By the end
of the second year, you must finally decide whether to register for a three year or a four year
degree.
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B.Sc. Joint Honours (Mathematics/Physics) students take the three core modules in their
second year and in their third year choose three level III modules from those marked P.
Joint M.Sci (Mathematics/Physics) students take the three core modules in their second
year and in their third year choose three modules from those marked P in the list of level III
and level III/IV modules, with at least one from level III/IV. In their fourth year they take
two modules from those marked P at level III/IV and IV; at least one must be a level IV
module. They also do a Project (double module) in some area of Mathematical Physics.
Joint Honours (Computer Science/Mathematics) students take Complex Analysis II,
Numerical Analysis II and Statistical Concepts II in their second year and in their third year
choose three level III modules from those marked C.
Joint Honours (Mathematics/Economics) students take Numerical Analysis II, Statistical
Concepts II, and Operations Research III in their second year and in their third year choose
one or two level III modules from those marked E. If you choose just one you should
register for Joint Honours Economics with Mathematics, but if you choose two then you
should take Joint Honours Mathematics and Economics. Details of Operations Research III
can be found in the 3H/4H booklet, available in the Department Office.
For all joint honours degrees, timetable clashes may prevent a free choice in your third
year (and fourth year if relevant) from all available modules in each department.
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THE MODULES
Level II Modules
2H Core
062011: Complex Analysis II
062021: Linear Analysis and Applications II
062031: Vector Calculus and Partial Differential Equations II
2H Options
062061: Algebra and Number Theory II
062071: Mathematical Physics II
062051: Numerical Analysis II
062041: Statistical Concepts II
All second year modules have 2 lectures per week during the Michaelmas and
Epiphany terms together with a programme of tutorials and, where appropriate, practicals.
There is a revision programme in the Easter term.
Your choice of 2H options may limit your choice of modules in 3H and 4H. The 3H
and 4H options may vary from year to year but typically there will be 12 level III options
and 4 level III/IV options. We will ensure that, if you are a single honours mathematician,
then no matter which options you take in 2H you will have at least 9 options at level III to
choose from in 3H. The modules we plan to give are listed below, together with any
prerequisites not in the core. The exact prerequisites are given in the module descriptions in
the 3H/4H booklet.
Level III Modules
CP Analysis III
CE Approximation Theory and Solution of
Ordinary Differential Equations III
P Continuum Mechanics III
CE Decision Theory III
P Differential Geometry III
CP Dynamical Systems III
Galois Theory III
CP Mathematics Teaching III
Number Theory III
CP Operations Research III
Quantum Mechanics III
CP Reflection Groups and Lie Groups III
CE Statistical Methods III
Level III/IV Modules 2000/01
P Elliptic Functions III/IV (A)
Geometry III/IV (A)
P Probability III/IV (A)
P Solitons III/IV (A)
Prerequisites
Numerical Analysis II
Statistical Concepts II
Algebra and Number Theory II
Algebra and Number Theory II
Mathematical Physics II
First year Core Mathematics A and B
Statistical Concepts II
Prerequisites
Algebra and Number Theory II
9
Level III/IV Modules 2001/2002
P Analytic Number Theory III/IV (B)
P Electromagnetism III/IV (B)
Representation Theory and Modules III/IV (B)
P Stochastic Processes III/IV (B)
Level IV Modules
Advanced Quantum Theory IV
Algebraic Geometry IV
Bayesian Statistics IV
P General Relativity IV
Numerical Linear Algebra and Partial
Differential Equations IV
P Topology IV
Project IV
Prerequisites
Mathematical Physics II or 2H
Mathematics/Physics
Algebra and Number Theory II
Prerequisites
Quantum Mechanics III
Algebra and Number Theory II plus 3H
Mathematics
Statistical Methods III
Mathematical Physics II or 3H
Mathematics/Physics
Approximation Theory and Solution of
Ordinary Differential Equations III
3H Mathematics or Mathematics/Physics