GENERAL INFORMATION COURSE DESCRIPTIONS COURSE SCHEDULE REGISTRATION
ACTIVITIES CAREER OPPORTUNITIES COURSE BIBLIOGRAPHY
       
UNDERGRADUATE PROGRAM


 

 

 Department of Mathematics and Statistics
P.O. . 20537, 1678 Nicosia
‘elephone : + 357 22 892600
Fax : + 357 22 892601

 


Course Descriptions
: Part 1 | Part 2


MAS 254 NONPARAMETRIC STATISTICS
(Prerequisite: MAS 251 )
Order statistics and their distributions. Sign test, rank test, Wilcoxon and Mann-Whitney tests. Spearman's rank correlation coefficient and tests. Confidence intervals. Contingency tables, Kolmogorov and goodness-of-fit tests. Tests for independence and homogeneity. Lilliefors test for normality.

MAS 255 SAMPLING THEORY (Prerequisite: MAS 250 )
Survey design. Simple random sampling, stratified, systematic, cluster and multi-stage sampling. Mean and variance estimation, ratio estimators, regression estimators. Determination of optimum sample size. Sampling errors.

MAS 256 TIME SERIES (Prerequisite: MAS 251 )
Stationary time series, moment estimation. ARMA and ARIMA processes. Maximum likelihood estimation, least squares estimators, Yule-Walker estimators. Prediction of stationary processes. Introduction to model selection.

MAS 257 DECISION THEORY (Prerequisite: MAS 251 )
Elements of decision theory, subjective probability and utility, Bayes Rules, admissibility of decision rules and completeness, minimax rules, invariant decision problems.

MAS 258 STATISTICAL DATA ANALYSIS(Prerequisites: MAS 251, MAS 253 )
Exploratory statistics. Linear models and applications. Analysis of variance, classification analysis, data structure analysis, exploratory methods. Fitting of curves and surfaces. Nonlinear models, robust methods, experimental design methods. Statistical computing methods and software. Biometric, econometric and other applications.

MAS 259 MULTIVARIATE ANALYSIS (Prerequisite: MAS 251 )
Multivariate Normal distribution, estimation of the mean vector and the covariance matrix, maximum likelihood estimation. Correlation coefficient, partial correlation coefficient and their distribution. T2- statistic and its distribution, T2- tests. Distribution of the sample covariance matrix, Wishart distribution, Cochran's theorem, generalized variance, inverted Wishart distribution. Principal components, canonical correlations, cluster and discriminant analysis. Introduction to multivariate analysis of variance: parameter estimation and tests.

MAS 260 DESIGN OF EXPERIMENTS (Prerequisite: MAS 251 )
Principles and applications of experimental design, completely randomized designs, complete block designs, nested, split plot designs, latin squares, factorial, balanced and partially balanced incomplete block designs, multiple comparison, analysis of variance, analysis of covariance, fractional replications, designs for the exploration of response surfaces.

MAS 271 NUMERICAL ANALYSIS II (Prerequisite: MAS 171 )
Numerical Linear Algebra. Iterative methods for the solution of linear systems. Computation of eigenvalues and eigenvectors. Polynomial interpolation, Gaussian quadrature, Spline functions.

MAS 272 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
(Prerequisites: MAS 203, MAS 271 )
Numerical solution of ordinary differential equations: Linear multistep methods-theory and applications, Runge-Kutta methods, First order systems and the problem of stiffness. Two-point Boundary Value Problems.

MAS 273 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (PDE'S)
(Prerequisites: MAS 272, MAS 204 )
Hyperbolic equations of first and second order, the method of characteristics, finite difference methods, finite element method. Parabolic equations, numerical solution of the heat equation in one and two space variables. Elliptic equations, finite difference schemes for the numerical solution of Laplace and Poisson problems.

MAS 274 APPROXIMATION THEORY (Prerequisites: MAS 201 )
Introduction to metric spaces, normed linear spaces and inner product spaces. Best approximation in normed linear spaces and inner product spaces. Uniform approximation. Polynomial approximation. Jackson type inequalities, theorems of Stone-Weierstrass, Lipschitz spaces. Interpolatory cubic splines.

MAS 281 APPLIED MATHEMATICAL ANALYSIS (Prerequisite: MAS 203 )
Calculus of Variations. Fourier and Laplace transforms. Special functions, Integral equations, Asymptotic Analysis.

MAS 282 CLASSICAL MECHANICS (Prerequisite: MAS 181 )
Newton's Laws. Central Forces. Moving Coordinate Systems. Systems of Particles. Motion of Rigid Bodies. Language's Equations. Hamiltonian Theory.

MAS 283 MATHEMATICAL PHYSICS I
Basic notions and coordinate systems. Vector and tensor calculus. Surface theory and integral theorems. Conservation laws and Navier-Stokes equations. Elements of partial differential equations and methods of solution. Flow problems with analytical solution. Potential flow problems. Waves and hydrodynamic stability.

MAS 299 INDEPENDENT STUDY
An independent study with sufficient elements of initiative and novelty under the guidance of a faculty member.

DESCRIPTION OF SERVICE COURSES

MAS 001 MATHEMATICS I
Real functions of one variable. Continuity. Differentiation and applications. Riemann integration. Fundamental theorems of Calculus. Mean-Value Theorem. Logarithmic and exponential functions.

MAS 002 MATHEMATICS II (Prerequisite: MAS 001 )
Integration techniques. Improper integrals. Sequences and infinite series of real numbers and real functions. Ordinary differential equations. Partial derivatives. Introduction to Linear algebra (matrices, determinants, linear systems, vector spaces).

MAS 003 BASIC MATHEMATICS
Sequences, Functions (continuity, limits). Differentiation and applications. Integration and applications. Logarithmic and Exponential functions. Matrices, Linear Systems.

MAS 004 INTRODUCTORY MATHEMATICS I
Sequences, Series, Vectors. Differentiation of functions of one variable and applications. Integration of functions of one variable and applications.

MAS 005 INTRODUCTORY MATHEMATICS II (Prerequisite: MAS 004 )
Matrices, Vector spaces, Determinants, Matrix Diagonalization, Eigenvalues, Eigenvectors, Hamilton Theorem. Functions of several variables, Vector functions.

MAS 051 STATISTICAL METHODS
Descriptive statistics, probability, Binomial distribution, Normal distribution, correlation, regression analysis, sampling, confidence intervals, hypothesis testing. Introduction to analysis of variance.

MAS 055 INTRODUCTION TO PROBABILITY AND STATISTICS
Probability. Random variables. Probability density function. Distributions. Independence. Expectation. Moment generating functions. Convergence of random variables. Central limit theorem. Point estimation (sufficiency, completeness), confidence intervals, Exponential familes of distributions. Statistical hypotheses, X2 tests. Simple linear regression, analysis of variance, nonparametric statistics.

MAS 061 STATISTICAL ANALYSIS I
Descriptive statistics, probability models. Random variables, expected value, sampling, Central Limit Theorem. Estimation, confidence intervals, hypothesis testing. Introduction to regression analysis.

MAS 062 STATISTICAL ANALYSIS II (Prerequisite: MAS 061 )
Regression analysis. Analysis of qualitative data. X2 tests. Analysis of variance. Nonparametrics. Time Series. Decision Theory.

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