MATHEMATICAL TRIPOS
Friday 30 May 2003
Part III
1.30 to 4.30
PAPER 14
DIFFERENTIAL GEOMETRY
Attempt THREE questions.
There are six questions in total.
The questions carry equal weight.
All the manifolds and related concepts should be assumed to be smooth.

MATHEMATICAL TRIPOS
Thursday 3 June, 2004
Part III
9.00 to 12.00
PAPER 76
ASYMPTOTIC METHODS IN FLUID DYNAMICS
Candidates may attempt ALL questions.
There are five questions in total.
The questions are of equal weight.
A distinction mark may be obtained b

MATHEMATICAL TRIPOS
Monday 31 May, 2004
Part III
9 to 12
PAPER 75
ENVIRONMENTAL FLUID DYNAMICS
Attempt BOTH questions in Section A and THREE in Section B.
There are six questions in total.
Questions in Section A carry half the weight of questions in Secti

MATHEMATICAL TRIPOS
Tuesday 3 June 2003
Part III
1.30 to 4.30
PAPER 7
RESTRICTION AND KAKEYA PHENOMENA
Attempt ONE question from each of sections A, B and C
There are six questions in total.
The questions carry equal weight.
The notation o(1) refers to a

MATHEMATICAL TRIPOS
Wednesday 2 June, 2004
Part III
1.30 to 3.30
PAPER 79
SEISMIC WAVES
Any number of questions may be attempted.
Full marks can be obtained for one complete answer or its equivalent.
There are three questions in total.
The questions carry

MATHEMATICAL TRIPOS
Wednesday 4 June 2003
Part III
9 to 12
PAPER 24
MODULAR FORMS
Attempt FOUR questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until
in

MATHEMATICAL TRIPOS
Monday 9 June 2003
Part III
1.30 to 4.30
PAPER 25
ADDITIVE AND COMBINATORIAL NUMBER THEORY
Attempt THREE questions.
There are six questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on

3
3
In an imposed vertical magnetic field, two-dimensional Boussinesq convection in a
liquid metal confined to the region 0 6 x 6 L, 0 6 z 6 1 is governed by the reduced
nondimensionalised PDEs
2 (, 2 )
2
+
= 4 + R
Q 2 ,
t
(x, z)
x
z
(, )
+
= 2 +
,
t
(x

MATHEMATICAL TRIPOS
Monday 31 May, 2004
Part III
9 to 12
PAPER 55
GENERAL RELATIVITY
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
Candidates may make free use of the information on the attached sheet.
You m

MATHEMATICAL TRIPOS
Thursday 27 May, 2004
Part III
1.30 to 3.30
PAPER 64
ASTROPHYSICAL FLUID DYNAMICS
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
Candidates may bring their notebooks into the examination.

MATHEMATICAL TRIPOS
Wednesday 2 June, 2004
Part III
1.30 to 4.30
PAPER 71
APPROXIMATION THEORY
Attempt FOUR questions.
There are seven questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent

MATHEMATICAL TRIPOS
Monday 31 May, 2004
Part III
1.30 to 4.30
PAPER 74
SLOW VISCOUS FLOWS
Attempt at most THREE questions.
There are four questions in total.
The questions carry equal weight.
Substantially complete answers will be viewed more favourably t

MATHEMATICAL TRIPOS
Monday 2 June 2003
Part III
1.30 to 4.30
PAPER 16
GLOBAL RIEMANNIAN GEOMETRY
Attempt THREE questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequen

MATHEMATICAL TRIPOS
Tuesday 1 June, 2004
Part III
1.30 to 4.30
PAPER 73
LARGE-SCALE ATMOSPHERE-OCEAN DYNAMICS
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
Cartesian coordinates (x, y, z) are used with z den

MATHEMATICAL TRIPOS
Tuesday 3 June 2003
Part III
9 to 12
PAPER 1
FINITE DIMENSIONAL LIE ALGEBRAS AND THEIR REPRESENTATIONS
Attempt QUESTION 1 and THREE other questions.
There are six questions in total.
The questions carry equal weight.
You may not start

MATHEMATICAL TRIPOS
Friday 30 May 2003
Part III
1.30 to 4.30
PAPER 18
CATEGORY THEORY
Attempt SIX questions.
There are ten questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until

MATHEMATICAL TRIPOS
Thursday 5 June 2003
Part III
9 to 12
PAPER 4
CLASSICAL GROUPS
Attempt THREE questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until

MATHEMATICAL TRIPOS
Thursday 29 May 2003
Part III
1.30 to 4.30
PAPER 11
TOPOLOGICAL GROUPS
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent page

MATHEMATICAL TRIPOS
Thursday 29 May 2003
Part III
9 to 11
PAPER 8
ORDINARY DIFFERENTIAL EQUATIONS IN THE COMPLEX DOMAIN
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
You may not start to read the questions
p

MATHEMATICAL TRIPOS
Friday 30 May 2003
Part III
9 to 11
PAPER 10
CLASSICAL BANACH SPACES
Attempt THREE questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages

MATHEMATICAL TRIPOS
Friday 6 June 2003
Part III
9 to 12
PAPER 5
GEOMETRIC GROUP THEORY
Attempt THREE questions.
There are five questions in total.
The questions carry equal weight.
Notation and Conventions Let A be a finite set, A is the set of all finite

MATHEMATICAL TRIPOS
Friday 28 May, 2004
Part III
9 to 11
PAPER 56
COSMOLOGY
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until
instruc

MATHEMATICAL TRIPOS
Monday 2 June 2003
Part III
9 to 12
PAPER 6
INTRODUCTION TO BANACH SPACES AND ALGEBRAS
Attempt THREE questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the

MATHEMATICAL TRIPOS
Tuesday 3 June 2003
Part III
1.30 to 4.30
PAPER 2
NOETHERIAN ALGEBRAS
Attempt THREE questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages

MATHEMATICAL TRIPOS
Thursday 3 June, 2004
Part III
9 to 12
PAPER 58
APPLICATIONS OF DIFFERENTIAL GEOMETRY TO PHYSICS
Attempt FOUR questions.
There are seven questions in total.
The questions carry equal weight.
You may not start to read the questions
prin

MATHEMATICAL TRIPOS
Monday 7 June, 2004
Part III
1.30 to 3.30
PAPER 61
BOUNDARY VALUE PROBLEMS FOR INTEGRABLE PDEs
Attempt TWO questions.
There are three questions in total.
The questions carry equal weight.
You may not start to read the questions
printed

MATHEMATICAL TRIPOS
Friday 4 June, 2004
Part III
9 to 12
PAPER 57
BLACK HOLES
Attempt THREE questions.
The are four questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until
instruc

MATHEMATICAL TRIPOS
Monday 7 June, 2004
Part III
9 to 11
PAPER 77
FLUID MECHANICS OF SWIMMING ORGANISMS
Attempt TWO questions.
There are three questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the sub

MATHEMATICAL TRIPOS
Friday 4 June, 2004
Part III
1.30 to 4.30
PAPER 59
ADVANCED COSMOLOGY
Attempt THREE questions.
There are six questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages

MATHEMATICAL TRIPOS
Tuesday 1 June, 2004
Part III
9 to 12
PAPER 62
STELLAR MAGNETOHYDRODYNAMICS
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
Candidates may bring their own notebooks into the examination.
Yo