National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
UNIVERSITY OF J
CAMBRIDGE 5
:4 Let G be a simple Lie group of N x N unitary matrices cfw_hub with hermitian
igenerators cfw_Ta (2 = 1, 2, . . . ,M . You may assume that for h an element of G
h = exp cfw_iGQTa ,
for parametervalues cfw_Ba and that the gene
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Friday 7 June 2002 9 to 11
PAPER 51
STOCHASTIC MODELS OF TRANSPORT AND MIXING
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
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Monday, 7 June, 2010 9:00 am to 11:00 am
PAPER 50
CONTROL OF QUANTUM SYSTEMS
Attempt no more than TWO questions.
There are THREE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
SPECIAL
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Tuesday 8 June, 2004 9 to 11
PAPER 51
SOLITONS AND INSTANTONS
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
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Wednesday 6 June 2001 1.30 to 3.30
PAPER 51
LOCAL AND GLOBAL BIFURCATIONS
Attempt TWO questions. The questions are of equal weight.
You may not start to read the questions
printed on the subsequent pages until
instructed to do
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Thursday, 4 June, 2009 9:00 am to 11:00 am
PAPER 53
QUANTUM INFORMATION,
ENTANGLEMENT AND NONLOCALITY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIR
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Wednesday 7 June, 2006 9 to 12
PAPER 52
THE STANDARD MODEL
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet None
Treasury Tag
Script paper
SPECIA
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Friday 1 June 2007 1.30 to 4.30
PAPER 52
SYMMETRY AND PARTICLE PHYSICS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREMENTS
Cover sheet 10 s
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Tuesday 5 June 2007 9.00 to 12.00
PAPER 51
ADVANCED QUANTUM FIELD THEORY
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet None
Treasury Tag
Scrip
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Wednesday 7 June 2006 1.30 to 4.30
PAPER 53
STRING THEORY
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
Minor errors in numerical factors will not be heavily penalized.
The covar
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Monday, 31 May, 2010 9:00 am to 12:00 pm
PAPER 53
COSMOLOGY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
SPECIAL REQUIREMENTS
No
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS Part III
Wednesday 4 June 2008
9.00 to 12.00
PAPER 54
THE STANDARD MODEL
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS SPECIAL REQUIREMENTS
Cover shee
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Thursday 7 June 2007 9.00 to 12.00
PAPER 54
STRING THEORY
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
Minor errors in numerical factors will not be heavily penalized.
The covar
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Tuesday 10 June 2003 9 to 11
PAPER 53
SUPERSYMMETRY
Answer ALL questions in Section A.
Answer any ONE of the three questions in Section B.
Sections A and B carry equal credit.
You may not start to read the questions
printed on
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Thursday 5 June 2008 9.00 to 12.00
PAPER 50
STATISTICAL FIELD THEORY AND APPLICATIONS
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover she
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Thursday 27 May, 2004 1.30 to 3.30
PAPER 53
INTRODUCTION TO QUANTUM COMPUTATION
Attempt THREE questions.
There are four questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on t
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Wednesday 13 June 2001 9 to 11
PAPER 53
RENORMALISATION IN DYNAMICAL SYSTEMS
Answer any TWO questions. The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until
instructed
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Thursday 5 June 2008 1.30 to 4.30
PAPER 52
STRING THEORY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
Minor errors in numerical factors will not be heavily penalize
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Friday 3 June, 2005 9 to 12
PAPER 50
SYMMETRY AND PARTICLE PHYSICS
Attempt THREE questions.
There are FOUR questions in total.
The questions are of equal weight.
STATIONERY REQUIREMENTS
Cover sheet None
Treasury tag
Script pap
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Friday 6 June 2003 9 to 12
PAPER 50
STRING THEORY
Attempt THREE questions. There are five questions in total. The questions carry equal
weight.
Candidates should note that trivial errors in numerical factors will not be penali
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Thursday 30 May 2002 9 to 11
PAPER 50
MECHANICS OF COMPOSITES
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 u
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Tuesday 14 June, 2005 9 to 11
PAPER 51
STATISTICAL FIELD THEORY
Attempt TWO questions.
There are THREE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet None
Treasury tag
Script paper
SP
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Monday 3 June 2002 9 to 12
PAPER 49
FUNDAMENTALS OF ATMOSPHEREOCEAN DYNAMICS
Attempt THREE questions
There are four questions in total
The questions carry equal weight
Clarity and explicitness of reasoning will attract more cr
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Tuesday 12 June 2001 9 to 11
PAPER 50
ACOUSTICS AND STABILITY
Attempt no more than THREE questions.
Little credit will be given for fragments.
You may not start to read the questions
printed on the subsequent pages until
instr
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Friday, 5 June, 2009 9:00 am to 11:00 am
PAPER 51
QUANTUM COMPUTATION
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
SPECIAL REQUI
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Tuesday, 9 June, 2009 9:00 am to 11:00 am
PAPER 52
CONTROL OF QUANTUM SYSTEMS
Attempt no more than TWO questions.
There are THREE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
SPECIA
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Friday 1 June 2007 9.00 to 12.00
PAPER 50
QUANTUM FIELD THEORY
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet None
Treasury Tag
Script paper
SP
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Wednesday 4 June 2003 9 to 12
PAPER 51
CONFORMAL FIELD THEORY
Attempt FOUR 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
National University of Computer and Emerging Sciences, Chiniot, Faisalabad
Artificial Intelligence
COMPUTER S 401

Spring 2016
MATHEMATICAL TRIPOS
Part III
Tuesday 5 June 2001 9 to 11
PAPER 49
NONNEWTONIAN FLUID MECHANICS
Attempt any TWO questions. The questions carry equal weight.
The following definitions may be quoted:
r
DJ
T
J
Jrv rv
J,
Dt
r
J J +J E + E J ,
4
J J +J E + E