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
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.
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
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.
259 MULTIVARIATE ANALYSIS (Prerequisite: MAS
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.
260 DESIGN OF EXPERIMENTS (Prerequisite: MAS
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.
271 NUMERICAL ANALYSIS II (Prerequisite: MAS
Numerical Linear Algebra. Iterative methods for the
solution of linear systems. Computation of eigenvalues
and eigenvectors. Polynomial interpolation, Gaussian
quadrature, Spline functions.
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.
273 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
(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.
274 APPROXIMATION THEORY (Prerequisites: MAS
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
281 APPLIED MATHEMATICAL ANALYSIS (Prerequisite:
MAS 203 )
Calculus of Variations. Fourier and Laplace transforms.
Special functions, Integral equations, Asymptotic Analysis.
282 CLASSICAL MECHANICS (Prerequisite: MAS
Newton's Laws. Central Forces. Moving Coordinate Systems.
Systems of Particles. Motion of Rigid Bodies. Language's
Equations. Hamiltonian Theory.
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.
299 INDEPENDENT STUDY
An independent study with sufficient elements of initiative
and novelty under the guidance of a faculty member.
OF SERVICE COURSES
001 MATHEMATICS I
Real functions of one variable. Continuity. Differentiation
and applications. Riemann integration. Fundamental theorems
of Calculus. Mean-Value Theorem. Logarithmic and exponential
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).
003 BASIC MATHEMATICS
Sequences, Functions (continuity, limits). Differentiation
and applications. Integration and applications. Logarithmic
and Exponential functions. Matrices, Linear Systems.
004 INTRODUCTORY MATHEMATICS I
Sequences, Series, Vectors. Differentiation of functions
of one variable and applications. Integration of functions
of one variable and applications.
005 INTRODUCTORY MATHEMATICS II (Prerequisite:
MAS 004 )
Matrices, Vector spaces, Determinants, Matrix Diagonalization,
Eigenvalues, Eigenvectors, Hamilton Theorem. Functions
of several variables, Vector functions.
051 STATISTICAL METHODS
Descriptive statistics, probability, Binomial distribution,
Normal distribution, correlation, regression analysis,
sampling, confidence intervals, hypothesis testing.
Introduction to analysis of variance.
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.
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.
062 STATISTICAL ANALYSIS II (Prerequisite:
MAS 061 )
Regression analysis. Analysis of qualitative data. X2
tests. Analysis of variance. Nonparametrics. Time Series.