MATHEMATICAL TRIPOS
Monday 11 June 2007
Part III
1.30 to 4.30
PAPER 29
MODULAR FORMS
Attempt FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
For any =
a
c
b
d
SL2 (Z) we write f |[]k ( ) = (c + d)k f ( ).
STATIONERY RE

MATHEMATICAL TRIPOS
Tuesday 12 June 2007
Part III
9.00 to 12.00
PAPER 2
QUANTUM GROUPS
Attempt FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Script paper
SPECIAL REQUIR

MATHEMATICAL TRIPOS
Thursday 29 May 2008
Part III
9.00 to 12.00
PAPER 75
APPROXIMATION THEORY
Attempt no more than FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
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Treasury Tag
Script

MATHEMATICAL TRIPOS
Monday 2 June 2008
Part III
9.00 to 12.00
PAPER 81
FUNDAMENTALS OF ATMOSPHEREOCEAN DYNAMICS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
Clarity and explicitness of reasoning will attrac

MATHEMATICAL TRIPOS
Friday 1 June 2007
Part III
1.30 to 4.30
PAPER 16
ALGEBRAIC TOPOLOGY
Attempt FOUR questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Script paper
SPECIAL REQ

MATHEMATICAL TRIPOS
Friday 8 June 2007
Part III
1.30 to 4.30
PAPER 23
ALGEBRAIC CURVES
Attempt THREE questions.
There are SIX questions in total.
The questions carry equal weight.
In answering any question, you may assume any result that
you would have pr

MATHEMATICAL TRIPOS
Thursday 7 June 2007
Part III
9.00 to 12.00
PAPER 30
ADDITIVE NUMBER THEORY
Attempt THREE questions, exactly ONE of these being from Section A.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS

3
3
G.
Let p be an ODD prime and let G be a pro-p group. Define the lower p-series of
Let G be a finitely generated powerful pro-p group. Denote the lower p-series of G
by Pi (G), and for H a subgroup of G let d(H) denote the minimal number of elements
ne

MATHEMATICAL TRIPOS
Tuesday 3 June 2008
Part III
9.00 to 11.00
PAPER 87
TURBULENCE
Attempt TWO questions.
There are THREE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
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Script paper
SPECIAL REQUIREME

MATHEMATICAL TRIPOS
Wednesday 4 June 2008
Part III
1.30 to 4.30
PAPER 80
NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
Attempt no more than FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS

MATHEMATICAL TRIPOS
Friday 1 June 2007
Part III
9.00 to 12.00
PAPER 15
DIFFERENTIAL GEOMETRY
Attempt THREE questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
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Treasury Tag
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SPECIA

MATHEMATICAL TRIPOS
Tuesday 5 June 2007
Part III
9.00 to 11.00
PAPER 12
COMBINATORICS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
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Treasury Tag
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SPECIAL REQUI

MATHEMATICAL TRIPOS
Thursday 5 June 2008
Part III
1.30 to 3.30
PAPER 90
ENVIRONMENTAL FLUID DYNAMICS
You may attempt ALL questions, although high marks
can be achieved by good answers to THREE quesitons.
Completed answers are preferred to fragments.
The q

MATHEMATICAL TRIPOS
Tuesday 5 June 2007
Part III
9.00 to 11.00
PAPER 32
ROUGH PATH THEORY AND APPLICATIONS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Scrip

MATHEMATICAL TRIPOS
Friday 30 May 2008
Part III
1.30 to 4.30
PAPER 88
WAVES IN FLUIDS
Attempt no more than FOUR questions.
There are FIVE questions in total.
Completed answers are substantially preferred to fragments.
The questions carry equal weight.
STA

MATHEMATICAL TRIPOS
Thursday 7 June 2007
Part III
1.30 to 4.30
PAPER 11
RIEMANN SURFACES AND DISCRETE GROUPS
Attempt FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
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Treasury Tag
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MATHEMATICAL TRIPOS
Monday 2 June 2008
Part III
1.30 to 4.30
PAPER 78
SYMMETRIC DYNAMICAL SYSTEMS
Attempt no more than THREE questions
There are FOUR questions in total
The questions carry equal weight
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Scri

MATHEMATICAL TRIPOS
Monday 11 June 2007
Part III
9.00 to 12.00
PAPER 3
MODULAR REPRESENTATIONS OF FINITE GROUPS
Attempt THREE questions.
There are SIX questions in total.
The questions carry equal weight.
In this paper G is a finite group. In the usual no

MATHEMATICAL TRIPOS
Thursday 7 June 2007
Part III
9.00 to 12.00
PAPER 34
QUANTUM INFORMATION THEORY
Attempt FOUR questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
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MATHEMATICAL TRIPOS
Tuesday 5 June 2007
Part III
1.30 to 4.30
PAPER 6
NOETHERIAN ALGEBRAS
Attempt FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
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Treasury Tag
Script paper
SPECIAL REQ

MATHEMATICAL TRIPOS
Friday 1 June 2007
Part III
9.00 to 12.00
PAPER 8
INTRODUCTION TO FUNCTIONAL ANALYSIS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
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Treasury Tag
Script

MATHEMATICAL TRIPOS
Thursday 31 May 2007
Part III
1.30 to 4.30
PAPER 10
ANALYSIS OF OPERATORS
Attempt THREE questions.
There are EIGHT questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Script paper
SPEC

MATHEMATICAL TRIPOS
Wednesday 4 June 2008
Part III
9.00 to 12.00
PAPER 74
STELLAR AND PLANETARY MAGNETIC FIELDS
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet

MATHEMATICAL TRIPOS
Friday 30 May 2008
Part III
9.00 to 12.00
PAPER 83
SOFT MATTER
There are FOUR questions in total.
Attempt questions one AND two,
and EITHER question three OR four.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
T

MATHEMATICAL TRIPOS
Thursday 31 May 2007
Part III
9.00 to 12.00
PAPER 25
CATEGORY THEORY
Attempt ONE question from Section I and TWO questions from Section II.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cov

MATHEMATICAL TRIPOS
Wednesday 6 June 2007
Part III
9.00 to 11.00
PAPER 24
THREEMANIFOLDS
Attempt THREE questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Script paper
SPECIAL RE

MATHEMATICAL TRIPOS
Thursday 31 May 2007
Part III
9.00 to 12.00
PAPER 1
SMOOTH REPRESENTATION
THEORY OF P -ADIC GROUPS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
In the following questions, F always denot

MATHEMATICAL TRIPOS
Thursday 7 June 2007
Part III
1.30 to 4.30
PAPER 19
COBORDISM
Attempt FOUR questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Script paper
SPECIAL REQUIREMEN

MATHEMATICAL TRIPOS
Wednesday 6 June 2007
Part III
1.30 to 3.30
PAPER 28
LOCAL FIELDS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
Qp denotes the field of p-adic numbers, Fp the field with p elements, and n

MATHEMATICAL TRIPOS
Wednesday 6 June 2007
Part III
9.00 to 11.00
PAPER 13
COMBINATORIAL PROBABILITY
Attempt THREE questions,
At most ONE from any one of the THREE parts.
There are SIX questions in total.
The questions carry equal weight.
The results you q