SECOND YEAR
SAC 201:
Financial Mathematics I
Cash flow models for financial transactions, compound interest and discounting;
present values and accumulation of streams of payments, nominal and effective
rates of interest and discounts through standard compound functions; solving
equations of value for implied rate of interest; discounted cash flow techniques
in project appraisal; consumer credit; capital redemption contracts and annuity
certain.
SAC 202:
Fundamentals of Actuarial Mathematics II
The single decrement model and calculations based on it; the stationary
population model; present values and accumulations of stream of payments
based on a single decrement model; equation of value for payments based on a
single decrement model; annuity and assurance commutation functions and their
relationships; assurance and annuity contracts; product pricing, reserving,
surrender values, emergence of profit.
SAC 203:
Principles of Economics I
Economics as a science, the scope of economics. Introduction to
microeconomics. Demand and supply analysis; effect of controls on prices and
supply; elasticity of demand and supply, production factors, cost analysis.
Utility theory and consumer behaviour. Analysis of insurance problems in terms
of utility. Market forms and income distribution, general equilibrium theory.
The theory of firms.
SAC 204:
Principles of Operations Research
Survey of continuous optimisation problems; unconstrained optimisation
problems and methods of solution; introduction to constrained optimisation.
Linear Programming: formulation of LP problems, graphical solution of simple
LP's; the simplex algorithm, duality and economic interpretation; post
optimality/sensitivity analysis. Decision analysis: decisions under risk, decision
trees, decisions under uncertainty. Markov decision processes and dynamic
programming. Project scheduling; probability and cost considerations in project
scheduling; project control, critical path analysis. Integer programming.
Queuing models: types of queues, queues with combined arrivals and
departures; queues with priorities of service. Stochastic simulation: role of
random numbers; simulation experiments; Monte Carlo calculus.
SMA 201:
Advanced Calculus
Improper Integrals and their convergence; Mean value theorem of Integral
Calculus. Functions of Several variables and their applications. Center of masses
and moments of inertia. Differential and Integral calculus of functions of several
variables (Taylors theorem, Minimum and Maximum points). Lagrange's
Multipliers.
SMA 206:
Introduction to Analysis
The real number system, Completeness, Open and Closed intervals,
neighborhoods, interior points, limit points, countability, Sequences; Functions;
Limits of functions; Continuity; Concepts of differentiability and Integrability,
Riemann Integral.
SMA 208:
Ordinary Differential Equations I
First order equations and applications. Second order equations. Homogeneous
equations with constant coefficients. Equations with variable coefficients. Nonhomogeneous equations. Undetermined coefficients. Variations of parameters.
Inverse Differential operators. Applications.
SMA 209:
Elements of Algebra
Vector spaces over R. Vector subspaces. Linear independence. Matrices:
properties, operations, determinants, systems of linear equations. Eigenvalues
and eigenvectors. Quadratic forms. Orthogonal matrices. Matrix differentiation
and maximization problems.
STA 201:
Probability and Statistics I
Particular distributions: Bernoulli, binomial, Poisson, geometric, hyper
geometric, uniform, exponential and normal random variables and their
distributions. Bivariate frequency distributions. Joint probability tables and
marginal probabilities. Moments and moment generating function. Markov and
Chebychev inequalities. Special univariate distributions. Bivariate probability
distributions; joint marginal and conditional distributions; Independence ;
Bivariate expectation; Regression and Correlation; Calculation of regression and
correlation coefficients for bivariate data.
STA 202:
Introduction to Statistical Inference
Meaning of statistics, objectives of statistical investigation. Statistical decision
problems, basic concepts of inference. Role of normal distribution in statistics.
Random samples, use of random number tables. Inference about population
means: point and interval estimates, simple one sample and two sample tests.
Linear regression and correlation analysis. Analysis of variance. Analysis of
frequency data. Simple nonparametric tests.
STA 222:
Introduction to Time Series Analysis
An introduction to time series in time domain and spectral domain. Estimation
of trends and seasonal effects, autoregressive moving average models,
forecasting, indicators, harmonic analysis, spectra.
STA 224:
Computational Methods and Data Analysis II
Numerical solution of linear systems; numerical evaluation of eigenvalues and
eigenvectors. Numerical integration and differentiation. Data structures, arrays
and their implementation, strings; application and implementation of stacks,
queues, linked lists, trees and graphs: Survey application, questionnaire design;
data processing, data editing and correction; editing and imputation principles;
writing of edit specification, use of an edit specification, use of an edit package.
Tabulation, table design, writing of a table specification; use of a tabulation
package. Writing programs to implement numerical algorithms. Application of
numerical analysis software package such as NAG. Simulation: random and
pseudo random numbers; generation of uniform variates; outline of tests,
mention of physical devices for uniform generators; generation of variates from
standard distributions e.g. normal, exponential etc.