|
|
| M08A |
PRE-CALCULUS |
| |
(6
P-Credits) |
Semester
I |
Level
0 |
| |
|
|
|
| Pre-requisite: |
CXC
Mathematics or equivalent |
| |
|
|
|
| Syllabus: |
Algebra:
Elementary logic, number sets, real numbers, functions, inequalities,
complex numbers, surds, logarithms, linear and quadratic equations,
fmite series, binomial theorem, mathematical induction; trigonometry:
Trignonometric functions and their inverses, addition and
multiplication formulae, identities, trigonometric equations,
solutions of triangles. |
| |
|
|
|
| Examination: |
One
3-hour paper
Written course test
|
85%
15% |
| |
|
|
|
| M08C |
CALCULUS
AND ANALYTICAL GEOMETRY |
| |
(6
P-Credits) |
Semester
II |
Level
0 |
| |
|
|
|
| Pre-requisite: |
CXC
Mathematics or equivalent |
| |
|
|
|
| Syllabus: |
Calculus:
Functions, limits, continuity, differentiability, higher derivatives
and application, anti-derivatives, and the integral. Elementary
method of integration and solution of simple differential
equations;
Analytical Geometry: Equations and representations of elementary
plane curves, applications of calculus to determine equations
of tangents, normals and computations of areas and volumes.
|
| |
|
|
|
| Examination: |
One
3-hour paper
Written course test
|
85%
15% |
| |
|
|
|
| M10A |
BASIC
INTRODUCTORY MATHEMATICS |
| |
(6
Credits) |
Semester
I & II |
Level
I |
| |
|
|
|
| Pre-requisite: |
GCE
A-Level Mathematics or MO8B and MO8C or equivalent. |
| |
|
|
|
| Syllabus: |
Elementary
logic, sets and elementary set operations, maps from sets
to sets and binary operations; an axiomatic presentation of
R, the field of real numbers; matrices and vectors, systems
of linear equations; the field of complex numbers and factorization
of polynomials; functions from R to R, continuity and its
consequences. |
| |
|
|
|
| Examination: |
One
3-hour paper
One in-course test
|
85%
15% |
| |
|
|
|
| M10B |
FUNCTIONS
OF REAL VARIABLES |
| |
(6
Credits) |
Semester
I & II |
Level
I |
| |
|
|
|
| Pre-requisite: |
M10A |
| |
|
|
|
| Syllabus: |
Sequences and series: criteria for convergence; integration
methods and the Fundamental Theorem of Calculus; Properties
of differentiable functions of one real variable, Taylor series;
ordinary differential equations; functions of two real variables;
parametric representation of curves. |
| |
|
|
|
| Examination: |
One
3-hour paper
One in-course test
|
85%
15% |
| |
|
|
|
| M10C |
MATHEMATICS
FOR PURE AND APPLIED SCIENCES |
| |
(6
Credits) |
Semester
II |
Level
I |
| |
|
|
|
| Pre-requisite: |
GCE
A-Level Mathematics or MO8B and MO8C or equivalent. |
| |
|
|
|
| Syllabus: |
One and two variable calculus, convergences of series; solutions
of ordinary differential equations; elementary vector analysis
in R^3. coordinate systems in R2 R3. |
| |
|
|
|
| Examination: |
One
3-hour paper
One in-course test
|
85%
15% |
| |
|
|
|
| M20A |
ABSTRACT
ALGEBRA |
| |
(4
Credits) |
Semester
I |
Level
II |
| |
|
|
|
| Pre-requisite: |
M10A,
M10B |
| |
|
|
|
| Syllabus: |
Elements of set theory: elements of proof theory, relations
and functions; Groups, including fine permutation groups; Rings
and the Euclidean algortihm; Homomorphisms; Fields |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M20B |
LINEAR
ALGEBRA |
| |
(4
Credits) |
Semester
II |
Level
II |
| |
|
|
|
| Pre-requisite: |
M10A,
M10B |
| |
|
|
|
| Syllabus: |
Matrices: rank and nullity; Vector spaces and bases; Linear
transformations; Determinants; Inner product spaces; Eigenvalues
and Eigenvectors. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M21A |
ANALYSIS
AND MATHEMATICAL METHODS I |
| |
(4
Credits) |
Semester
I |
Level
II |
| |
|
|
|
| Pre-requisite: |
M10A,
M10B |
| |
|
|
|
| Syllabus: |
Limits of real sequences; convergence of real series; Absolute
convergence;
Comparison, quotient, ratio, root, integral and alternating
series tests;
Power series: radius and interval of convergence;
Functions of a single real variable: continuity, differentiability,
Rolle's Theorem, Mean Value Theorem and Taylor's Theorem; Theory
of the integral of one real variable.
Functions of two or more real variables: continuity, differentiablity;
Partial derivatives, Jacobians, critical points, repeated integrals,
double integral, Fubini's Theorem, change of variables.
|
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M21B |
ANALYSIS
AND MATHEMATICAL METHODS II |
| |
(4
Credits) |
Semester
II |
Level
II |
| |
|
|
|
| Pre-requisite: |
M10A,
M10B |
| |
|
|
|
| Syllabus: |
Ordinary linear differential equations, existence and uniqueness
theorems (no proofs), Wronskians; Solution in series for first
and second order non-singular an dregular singular equations;
Methods of Frobenius.
Fourier series, two dimensional separable linear partial differential
equations; Solutions by separation of variables and Fourier
series.
Functions of a single complex variable, continuity, differentiability,
Cauchy-Rieman equations; Analyticity, power series; Cauchy's
Theorem and applications to evaluation of integrals. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M25A |
PROBABILITY
THEORY |
| |
(4
Credits) |
Semester
I |
Level
II |
| |
|
|
|
| Pre-requisite: |
M10A,
M10B |
| |
|
|
|
| Syllabus: |
Basic probability theory.
Laws of probability, conditional probability, independence,
Bayes formula, random variables, discrete and continuous distributions,
expectations, moments, moment generating functions, functions
of random variables.
Special distributions; Binomial, geometric, negative binomial,
Poisson, hypergeometric, uniform, exponential, gamma normal,
Laws of large numbers, the Central Limit Theorem. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M25B |
STATISTICAL
INFERENCE |
| |
(4
Credits) |
Semester
II |
Level
II |
| |
|
|
|
| Pre-requisite: |
M25A
or permission form the Head of Department |
| |
|
|
|
| Syllabus: |
Sampling distributions including X2, t, F; Order statistics;
Estimation of parameters, likelihood, sufficiency, significance
test, simple linear regression and correlation;
Analysis of variance; Non-parametric procedures, elementary
principles of experimental design. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M27A |
MATHEMATICS
OF FINANCE |
| |
(4
Credits) |
Semester
I |
Level
II |
| |
|
|
|
| Pre-requisite: |
M10A
and M10B
This course is available only to final year students and
to students in the Actuarial Science Option |
| |
|
|
|
| Syllabus: |
Introduction to actuarial science; Measurement of interest;
Solutions of problems in interest, basic annuities; more general
annuities, yied rates, amortization schedules and sinking funds,
bonds and other securities, practical applications. |
| |
|
|
|
| Examination: |
One
2-hour written paper
Course work (or in-course test)
|
80%
20% |
| |
|
|
|
| M27B |
INTRODUCTION
TO ACTUARIAL MATHEMATICS |
| |
(4
Credits) |
Semester
II |
Level
II |
| |
|
|
|
| Pre-requisite: |
M21A,
M25A and M27A |
| |
|
|
|
| Syllabus: |
Survival distributions and life tables, utility theory, life
insurance, life annuities, commutation functions, net premiums
and premium reserves, introduction to multiple life functions. |
| |
|
|
|
| Examination: |
One
2-hour written paper
Course work (or in-course test)
|
80%
20% |
| |
|
|
|
| M30B |
APPLIED
ALGEBRA II |
| |
(4
Credits) |
Semester
II |
Level
III |
| |
|
|
|
| Pre-requisite: |
M20A |
| |
|
|
|
| Syllabus: |
Finite fields, shift registers, algebraic coding theory. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M30Q |
MATRIX
THEORY |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M20A,
M20B |
| |
|
|
|
| Syllabus: |
Projections in Rn and Cn; The adjoint
of a matrix; special classes of matrices (Hermitian, positive
definite, normal and unitary); Polynomials of matrices; The
Jordan canonical form; The singular value decomposition, the
Moore-Penrose (pseudo)-inverse. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M31E |
APPLIED
STATISTICS |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M20B,
M25A and M25B |
| |
|
|
|
| Syllabus: |
Study is continued on the applied aspects of M25B such as analysis
of variance, regression analysis, design of experiments and
categorical data analysis, time series analysis, stochastic
processes and decision theory. |
| |
|
|
|
| Examination: |
One
2-hour written paper
Course work (or in-course test)
|
80%
20% |
| |
|
|
|
| M32A |
NUMERICAL
ANALYSIS |
| |
(4
Credits) |
Semester
II |
Level
III |
| |
|
|
|
| Pre-requisite: |
M21A |
| |
|
|
|
| Syllabus: |
Types of error, finite differences and interpolation, numerical
evaluation and integrals, numerical solution of differential
equations; root of equations; linear systems and matrices; construction
of algorithms for computation. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M32B |
OPTIMIZATION
THEORY |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M20B |
| |
|
|
|
| Syllabus: |
Linear programming and duality; A mathematical modelling mathematical
structure of the primal; Equivalent linear programmes, simplex
and revised simplex techniques, dual linear programmes; Complimentary
slackness, matrix theoretic, the duality theorem; Networks.
Computations involving computers and software; Sensitivity analysis. |
| |
|
|
|
| Examination: |
One
2-hour written paper
Two in-course tests
|
70%
30% |
| |
|
|
|
| M32C |
TOPICS
IN OPERATIONS RESEARCH |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M21A
Note: Cannot be credited with EC337 or
its equivalent |
| |
|
|
|
| Syllabus: |
Theory of inventory, replacement, sequencing, queuing theory,
decision theory and theory of games, simulation, discussion
and use of computer software. |
| |
|
|
|
| Examination: |
One
2-hour written paper
|
|
| |
|
|
|
| M32Q |
SOLUTIONS
OF ORDINARY DIFFERENTIAL EQUATIONS |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M21A,
M21B and M20B |
| |
|
|
|
| Syllabus: |
First order equations
Separable and homogeneous types, pfaffin forms in 2 variables,
Bernoulli and Riccati types. Existence and uniqueness theorem
for the initial problem.
Higher order equations
Theory of the Wronskian and linear independence of solutions
of higher order linear equations. The Euler equation.
First order linear systems
Matrix formulation of first order systems for both normal and
defective matrices. Funamental matrices, matrix valued functions
and computation.
The
Laplace Transform
Theory of the Laplace Transform and its use in the solution
of differential equations. |
| |
|
|
|
| Examination: |
One
2-hour written paper
Course work
|
85%
15 % |
| |
|
|
|
| M33Q |
ELEMENTARY
NUMBER THEORY |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M20A,
M20B and M21A |
| |
|
|
|
| Syllabus: |
Prime numbers; Unique Factorization in zand k[x]; Arithmetic
functions, m, d, w and lattice points; Congruence; Chinese remainder
theorem; Quadratic reciprocity law; Algebraic numbers and algebraic
integers; Transcendental numbers; Finite fields; Diophantine
equations; Distribution of prime numbers; Chybeshev Theorem;
The Riemann-Zeta Function. |
| |
|
|
|
| Examination: |
One
2-hour written paper
Two in-course tests
|
70%
30% |
| |
|
|
|
| M33R |
COMPLEX
ANALYSIS |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M21A |
| |
|
|
|
| Syllabus: |
Differentiablity, analyticity; contour integrals, Cauchy's Theorem
and its consequences; Taylor series, Laurent series; residue
calculus. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M34Q |
LIFE
CONTINGENCIES |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M25A,
M25B and M27B |
| |
|
|
|
| Syllabus: |
Multiple life functions, multiple decrement model; Insurance
models including expenses; Nonforfeiture, benefits and dividends;
valuation theory for pension plans. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M34R |
RISK
THEORY |
| |
(4
Credits) |
Semester
I |
Level
III |
| |
|
|
|
| Pre-requisite: |
M21A,
M21B, M25A and M25B |
| |
|
|
|
| Syllabus: |
Review of earlier statistical work; Individual risk theory;
Other frequency distributors; Mixed distributions; Stoploss
insurance; Ruin theory. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
80%
20% |
| |
|
|
|
| M35R |
PRINCIPLES
OF ASSET/LIABILITY MANAGEMENT FOR ACTUARIAL SCIENCE |
| |
(4
Credits) |
Semester
II |
Level
III |
| |
|
|
|
| Pre-requisite: |
M27A,
MS28D and MS38H |
| |
|
|
|
| Syllabus: |
Review of Macroeconomics; Characteristics of the various types
of investments used to fund financial security programmes; Traditional
techniques of financial analysis used in selecting and managing
investment portfolios.
The course builds on the material in courses MS28D and MS38H,
introducing further tools and techniques of asset/liability
management, general product design , as well as issues of pricing
and valuation and asset management. |
| |
|
|
|
| Examination: |
One
2-hour written paper
Course work (or in-course test)
|
80%
20% |
| |
|
|
|
| M36Q |
METRIC
SPACES AND TOPOLOGY |
| |
(4
Credits) |
Semester
II |
Level
III |
| |
|
|
|
| Pre-requisite: |
M21A
and M20B |
| |
|
|
|
| Syllabus: |
Metric spaces, examples; Continuity; Completeness; Topological
spaces; Hausdorfness; Connectedness. |
| |
|
|
|
| Examination: |
One
2-hour written paper
One in-course test
|
72%
28% |
| |
|
|
|
|
|
