| | Theory of point estimation: unbiasedness, equivariance, resampling: bootstrap and Jackknife estimates, large sample theory, asymptotic optimality, theory of testing statistical hypotheses, the decision problem, uniformly most powerful tests, unbiasedness, invariance, minimax principles.
| Ph. D. | | | Kolmogorrov's axioms, random variables, distributions, expected values, conditional probability, independence, Borel-Cantelli lemma, characteristic functions and inversion formula, convergence concepts, laws of large numbers, central limit theorems.
| M. Sc. | | | Mathematica package is used in a computer Lab to illustrate selected mathematical concepts, explore some mathematical facts, build algorithms for problem solving cases, do numerical and analytical computations, do simulation studies and plot graphs. The selected topics can cover a wide range of mathematical topics such as geometry, calculus, linear algebra, linear programming, differential equations, probability, statistics, number theory, Fourier and Laplace transforms. The course starts with training on using the package and ends with writing Mathematica programs to solve some specific Mathematical problems.
| B. Sc. 4th year | | | Functional equations, classification of information measures, survey of well known measures, required properties of information measures, axiomatic approach to characterizations of entropies, extensions of entropies to the continuous case, relationship measures, sufficient partitions and efficiency, maximum-entropy models, Akaiki information criterion and model selection, Kullback-Leibler divergence and testing statistical models, Applications to censoring schemes.
| Ph. D. | | | Markov chains, transition probability, classification of states, branching and queueing chains, stationary distributions of Markov chain, Markov pure jump processes; second order processes, mean and covariance functions, Gaussian Process and Wiener process.
| B. Sc. 3rd year | | | Functions: domain, operations on functions, graphs of functions; trigonometric functions; limits: meaning of a limit, computational techniques, limits at infinity, infinite limits ;continuity; limits and continuity of trigonometric functions; the derivative: techniques of differentiation, derivatives of trigonometric functions; the chain rule; implicit differentiation; differentials; Roll’s Theorem; the mean value theorem; the extended mean value theorem; L’Hopital’s rule; increasing and decreasing functions; concavity; maximum and minimum values of a function; graphs of functions including rational functions (asymptotes) and functions with vertical tangents (cusps); antiderivatives; the indefinite integral; the definite integral; the fundamental theorem of calculus ; the area under a curve; the area between two curves; transcendental functions: inverse functions, logarithmic and exponential functions; derivatives and integrals; limits (the indeterminate forms); hyperbolic functions and their inverses; inverse trigonometric functions; some techniques of integration.
| B. Sc. 1st year | | | Techniques of integration: integration by substitution; integration by parts, integrating powers of trigonometric functions, trigonometric substitutions, integrating rational functions, partial fractions, rationalization, miscellaneous substitution; improper integrals; application of definite integral: volumes, length of a plane curve, area of a surface of revolution polar coordinates and parametric equations: polar coordinates, graphs in polar coordinates , conics in polar coordinates, area in Polar coordinates; parametric equations; tangent lines and arc length in parametric curves and polar coordinates; infinite series: sequences, infinite series, convergence tests, absolute convergence, conditional convergence; alternating series; power series: Taylor and Maclurine series, differentiation and integration of power series: topics in analytic geometry : the parabola, the ellipse, the hyperbola; second degree equations: rotation of axes.
| B. Sc. 1st year | | | Describing statistical data by tables, graphs and numerical measures, Chebychev’s inequality and the empirical rule, counting methods, combinations, permutations, elements of probability and random variables, the binomial, the Poisson, and the normal distributions, sampling distributions, elements of testing hypotheses, statistical inference about one and two populations parameters.
| B. Sc. 1st year | | | Logic and proofs; quantifiers; rules of inference mathematical proofs, sets: set operations, extended set operations and indexed families of sets; relations; Cartesian products and relations; equivalence relations; partitions; functions; onto functions, one-to-one functions; induced set functions; cardinality; equipotence of sets; finite and infinite sets; countable sets, topology of R.
| B. Sc. 2nd year | | | Ordinary differential equations, linear differential equations of second and higher order, systems of differential equations, phase plane, stability, series solutions of differential equations, orthogonal functions, Laplace transforms, linear systems of equations, matrices and determinants.
| B. Sc. 2nd year | | | Three dimensional space and vectors rectangular coordinates in 3-space; spheres, cylindrical surfaces; quadric surfaces; vectors: dot product, projections, cross product, parametric equations of lines. planes in 3-spaces; vector -valued functions: calculus of vector valued functions, change of parameters, arc length, unit tangent and normal vectors, curvature, functions of two or more variable: domain, limits, and continuity; partial derivatives; differentiability; total differentials; the chain rule; the gradient; directional derivatives; tangent planes; normal lines maxima and minima of functions of two variables; Lagrange multipliers; multiple integrals: double integral, double integrals in polar coordinates; triple integrals; triple integrals in cylindrical and spherical coordinates; change of variables in multiple integrals; Jacobian .
| B. Sc. 2nd year | | | Equations: linear, quadratic, cubic; functions: linear, polynomials, rational, exponential, logarithmic, multivariable functions; differentiation: derivative , rules of derivation, partial derivative, extrema of one variable functions, and two variable functions; integration: definite, rules of integration, by substitution, by parts, by partial fractions, improper integral, applications; matrices: algebra of matrices, element2ary operations, Echelon form and solution of system of linear equations, determinants and Cramer’s rule and solutions of system of linear equations, applications to economics.
| B. Sc. 1st year | | | Organizing and summarizing data, sampling methods and statistical distributions (binomial, Poisson, normal, χ2 ,t and f), sampling methods and distributions, estimation and hypotheses about means, proportions and variances based on large and small samples, analysis of variance (one-way, two-way, factorial designs, Latin square), regression analysis (simple and multiple), Chi-square tests, correlation coefficient and nonparametric methods.
| M. Sc. | | | Mathematical & Statistical techniques in compound interest, discounted cash flow, valuation of cash flows of insurance contracts, analysis and valuation of annuities, bonds, loans and other securities. Yield curves and immunization. Stochastic interest rate models. Actuarial applications.
| B. Sc. 2nd year | | | Types of data; vital statistics; plots; measures of location and variation; probability; binomial; Poisson distributions; normal, chi-square, t, and F distributions; sampling distributions; tests about means and proportions (one ans two samples); simple linear regression;correlation; ANOVA; chi-square tests of independence; sign and rank tests; probit analysis.
| B. Sc. 3rd year | | | Simple and multiple regression, correlation coefficient, the analysis of variance of one and two-factor experiments, the Latin squares, Chi square test for homogeneity, independent, and goodness of fit, non-parametric statistics that includes the sign test, Wilcoxon rank sum test, W. lcoxon signed rank test, and the Mann-Whiteny test, Spearman correlation coefficient.
| B. Sc. 3rd year | | | Revision of probability distributions, queueing theory, reliability theory, quality control and acceptance sampling, information theory and coding.
| B. Sc. 3rd year | | | Distributions of random variables; conditional probability and stochastic independence; some special distributions (discrete and continuous distributions); univariate, bivariate and multivariate distributions; distributions of functions of random variables (distribution function method, moment generating function method, and the Jacobian transformation method); limiting distributions.
| B. Sc. 3rd year | | | Estimation: point estimation, confidence interval; statistical test: UMP test; likelihood ratio tests, chi-square tests, SPRT; non -parametric methods; Sufficient statistics and its properties; complete statistics exponential family; Fisher Information and the Rao-Cramer inequality.
| B. Sc. 4th year | | | Descriptive techniques; types of variations: trend, cycle and seasonal fluctuations, autocorrelation; probability models for time series; stationary processes; autocorrelation function; estimation in time domain; fitting an autoregressive process; fitting a moving average process; forecasting; box and Jenkin`s methods; stationary processes in the frequency domain; spectral analysis.
| B. Sc. 4th year | | | Methods and concepts of information; information measures: Hartley entropy; Wiener concept of information, Shannon entropy, Boltzmann entropy; A-entropy, Renyi entropy; Entropy generating function; required properties of an entropy measure; Coding theory: constructions of codes; capacity of a channel; properties of codes; Fisher information; Tukey information; Kullback-Leibler divergence; Akaiki information criterion; statistical applications: beta-I-equivalent distributions, sample efficiency; normal approximations, beta-sufficient partitions, characterizations of random variables, model selection, Bayesian information, improvement measure, normed information rate, information correlation, chi-square test, most influential part of data.
| B. Sc. 4th year | | | Loss functions, discrete frequency-severity insurance model under independence, limited fluctuation credibility approach, Buhlmann’s approach, Buhlmann-Straub model, credibility and Bayesian inference, frequency-severity insurance model with continuous severity component, credibility and least squares, Morris-Van Slyke estimation, empirical Bayes parameter estimation, Decision Theory.
| B. Sc. 4th year | | | Mathematical and Statistical techniques in compound interest,
discounted cash flow, valuation of cash flows of insurance
contracts, analysis and valuation of annuities, bonds, loans and
other securities. Yield curves and immunization. Stochastic
interest rate models. Actuarial applications. | B. Sc. 2nd year | | | Systematic sampling, simple random sampling, stratified
sampling, cluster sampling, multistage sampling, questionnaire
building, ratio and regression estimation. | B. Sc. 3rd year | | | Student is supposed to write a graduation project in actuarial sciences, after introducing him to different problems and issues in actuarial studies. The course also enables the student to write reports about actuarial problems, to draw conclusions, and to prepare recommendations concerning them.
| B. Sc. 4th year | | | Distribution free statistics, counting and ranking statistics, one-sample and two sample U-statistics, power function and nonparametric alternatives, Pitman asymptotic relative efficiency, Noether’s theorem, confidence intervals and bounds, Hodges-Lehman location estimators and their asymptotic properties, linear rank statistics and distribution properties, two-sample location and scale problems, other important problems.
| M. Sc. | | | Univariate and multivariate distribution theory, sufficient statistics, minimal sufficient statistics, completeness, methods of point estimation and properties of point estimators, confidence, intervals, testing hypotheses, Neman-Pearson lemma, randomized tests, uniformly most powerful test, likelihood ratio tests, mimimax methods.
| M. Sc. | | | Topics to be chosen from various fields of mathematics. Prediction Analysis : Bayesian and non-Bayesian predictive distributions, prediction intervals using various methods, statistics, and distributions | Ph. D. | | | Coherent systems, reliability of coherent systems, classes of distributions of importance in reliability theory IFR, IFRA, NBU, NBUE, DMRL, and their dual classes, shock models, stress-strength models, preservation of life distribution classes under reliability operations, multivariate exponential distributions, maintenance policies, replace-ment models, some inference problems in reliability theory, limit distributions of coherent system life.
| Ph. D. | | | | M. Sc. | | | | M. Sc. | | | Evolution of some mathematical concepts, facts and algorithms in arithmetic, algebra, trigonometry, Euclidean geometry, analytic geometry , calculus and Analysis through early civilizations, Egyptians, Babylonians, Greeks, Indians, Chinese, Muslims and Europeans, evolution of solutions of some conjectures and open problems. | B. Sc. 2012-2013 |
|
