3
Fluid and Solid Mechanics
3.4
Convection of Magnetic Flux
(10 units)
This project concerns a magnetohydrodynamic problem, studying the effect of differential rotation of a conducting fluid on a magnetic field. Knowledge of the Part IB Fluid Dynamics cou
2
Waves
2.2
Dispersion
(7 units)
This project assumes only the elementary properties of dispersive waves, covered in the Part II
course Waves
1
Introduction
This project illustrates the way in which a disturbance in a dispersive system can change its
shap
2
Waves
2.11 Fishers Equation for Population Dispersal
Problems
(9 units)
This project is essentially self-contained, and does not directly rely on any Part II lecture course.
However, attendance at a Part II Numerical Analysis course may be of some help,
1
Numerical Methods
1.6
Multigrid Methods
(10 units)
Knowledge of Part II Numerical Analysis would be advantageous for this project.
1
Solution of Poissons Equation by Relaxation Methods
We consider the problem of solving Poissons equation in a square dom
1
Numerical Methods
1.1
Fourier Transforms of Bessel Functions
(6 units)
This project assumes only material contained in Part IA and Part IB core courses. Other
than that, the project is self contained (although the Part II courses on Numerical Analysis,
3
Fluid and Solid Mechanics
3.10 Smoke Rings
(8 units)
This project discusses a simple model of the motion of smoke rings. Knowledge of Part IB
Fluid Dynamics is required and knowledge of the Part II course Classical Dynamics will help
with Question 2. Th
9
Dynamic Programming
9.1
Policy Improvement for a Markov Decision (4 units)
Process
This project is self-contained mathematically; background information is provided in the Part II
course on Optimisation and Control.
1
A Car Replacement Problem
Car owner
16
Algebra
16.5 Permutation Groups
(7 units)
This project is self-contained, building on theory covered in the Part IA course Groups. Some
knowledge of the groups part of the Part IB course Groups, Rings and Modules would be useful.
1
Introduction
We are
15
Number Theory
15.10 The Continued Fraction Method for
Factorization
(8 units)
This project is related to material in the Part II course Number Theory.
1
Factor bases
In this project N will be a (usually large) integer, that we would like to factor, and
15
Number Theory
15.1 Primality Tests
(9 units)
This project is related to material in the Part II course Number Theory.
A primality test is an algorithm used to determine whether or not a given integer is prime.
In this project we consider several differ
9
Dynamic Programming
9.4
Option Pricing in Mathematical Finance
(6 units)
This project is connected with material in the Stochastic Financial Models course. Students who
are not taking that course but who wish to attempt the project will find the necessa
16
Algebra
16.1 The Galois Group of a Polynomial
(7 units)
This project is related to material in the Part II course Galois Theory.
1
Introduction
The Galois group G(f ) of a polynomial f defined over a field K is the group of K-automorphisms
of the field
17
Combinatorics
17.1 Graph Colouring
(7 units)
This project is based on the material found in the Part II Graph Theory course.
In this project you will need to be able to generate graphs from G(n, p) and Gk (n, p). The space
G(n, p) is that of graphs wit
17
Combinatorics
17.3 Hamiltonian cycles
(5 units)
This project is based on the material found in the Part II Graph Theory course.
In this project you will need to be able to generate graphs from G(n, p), the space of graphs with
n labelled vertices, edge
19
Communication theory
19.1 Random codes
(5 units)
Background material for this project is given in the Part II course Coding and Cryptography.
The (binary) Hamming space cfw_0, 1n consists of all possible n-tuples of 0s and 1s. We define a
code C of len
If
is approximately equal to 1, then
approximately equal to:
Incorrect
Incorrect
2440
is
Incorrect
(True Answer )Correct
Use the following reproduction curve for a population
to answer the question(s). Units are in thousands.
Reference: Ref 23-2
The maxim
0.994 (True Answer )Correct
2452
A population grows according to a logistic growth
model, with population parameter
? = 1.3 and x = 0.7 for the first year. The value of x
after the second year is:
0.273 (True Answer )Correct
0.546 Incorrect
0.608 Inco
2484
Suppose the world demand for aluminum is about
16,800,000 tons per year. The known global reserves
are 1,700,000,000 tons. The demand for aluminum is
increasing at a rate of 6.4%. What is the exponential
reserve for aluminum?
32.43
2485
Suppose the
2414
The population of the state of Texas in 1993 was about
17,778,000. In 2001, the population was about
21,325,000. What was the average growth rate over
that period of time?
0.3% Incorrect
1.2% Incorrect
1.9% Incorrect
2.3% (True Answer )Correct
24
Using the FreeRTOS
Real Time Kernel
PIC32 Edition
Richard Barry
Contents
List of Figures . v
List of Code Listings .vii
List of Tables . x
List of Notation. xi
Preface
FreeRTOS and the PIC32 . 1
Multitasking on a PIC32 Microcontroller . 2
An Introduction
20
Probability
(9 units)
20.5 Percolation and the Invasion Process
This project requires general knowledge of probability theory, at the level of IA Probability. It
also requires competency in programming.
1
Introduction
This project concerns certain prob