Master in Mathematics

·               Providing students with modern and highly efficient education in mathematics, consistent with the highest global standards.

·               Enhancing students’ abilities in abstract and critical thinking, solving problems logically, and constructing and writing proofs in an organized manner.

·               Enabling students to enjoy mathematical sciences and learn about their importance and necessity in life.

·               Enlightening students about the significance of scientific research in developing their local communities and humanity in general.

Bachelor’s with Good GPA, English score 5.5 IELTS or equivalent.

103711 Real Analysis
Prerequisite: None
Topics: Sigma algebras, outer measures, measures, Lebesgue measure, measurable sets, measurable functions, Lebesgue integration, Lp-spaces, differentiation of monotone functions, functions of bounded variation, basics of normed spaces.
Credit Hours: 3

103712 Functional Analysis
Prerequisite: 103711
Topics: Normed spaces, basics of Banach and Hilbert spaces, linear operators on Hilbert and Banach spaces, dual spaces, Riesz Representation Theorem, sequence spaces and their duals, examples of bounded linear operators, closed unit ball, closed convex sets, extreme and exposed points, closed operators, closed graph theorem, and basic functional analysis theorems.
Credit Hours: 3

103713 Complex Analysis
Prerequisite: None
Topics: Complex numbers review, analytic and harmonic functions, maximum modulus principle, open mapping theorem, conformal mapping, cross ratio, stereographic projections, linear fractional transformations, complex integrals, zeros of holomorphic functions, power and Laurent series, singularities, residue theorem, applications of residues, Schwartz Lemma, Rouche’s theorem, reflection principle, Dirichlet problem, mean value property, Poisson formula, and normal families.
Credit Hours: 3

103721 Matrix Analysis
Prerequisite: None
Topics: Hilbert space geometry, Riesz representation theorem, orthonormal bases, isomorphic Hilbert spaces, operators on Hilbert spaces, similarity and canonical forms, diagonalization, eigenvalue location, special matrix classes, unitary equivalence, Schur’s theorem, spectral theorem, singular value decomposition, polar decomposition, generalized inverses, least-squares solutions, determinant and trace inequalities, min-max principle, vector and matrix norms, spectral and numerical radius, unitarily invariant norms, Lowner ordering, Hadamard product, and applications.
Credit Hours: 3

103722 Theory of Inequalities
Prerequisite: None
Topics: Classical inequalities (convex functions, Jensen, Young, Holder, Minkowski), inequalities related to Cauchy-Schwarz, Kantorovich inequality, classical and weighted means, bounds for zeros of polynomials, matrix inequalities, noncommutative inequalities, and miscellaneous recent bounds.
Credit Hours: 3

103731 Mathematical Statistics
Prerequisite: None
Topics: Univariate and multivariate distributions, sufficient and minimal sufficient statistics, completeness, point estimation and its properties, confidence intervals, hypothesis testing, Neyman-Pearson lemma, randomized tests, uniformly most powerful tests, likelihood ratio tests, minimax methods.
Credit Hours: 3

103732 Probability Theory
Prerequisite: None
Topics: Events and classes, algebra of sets, fields, σ-fields, random variables, Borel-Cantelli lemma, expectations, Jensen’s, Chebyshev’s, Holder-Minkowski inequalities, moment-generating functions, convergence of random variables, characteristic functions, laws of large numbers, Kolmogorov’s inequality, central-limit theorem.
Credit Hours: 3

103733 Nonparametric Statistics
Prerequisite: None
Topics: Theory and computational tools for nonparametric tests (sign test, Wilcoxon signed-rank, Wilcoxon rank-sum), nonparametric point and interval estimation, Kruskal-Wallis and Friedman tests, multiple comparisons, dispersion and independence, nonparametric density estimation.
Credit Hours: 3

103734 Linear Statistical Models
Prerequisite: None
Topics: Normal equations, least squares estimation, generalized matrix inverse, invariant and estimable linear parametric functions, multidimensional normal distribution, noncentral Chi-square distribution, linear and quadratic form distributions, independence and orthogonality, full and less than full rank models, ANOVA for linear models, variance components, mixed models, Gauss-Markov and BLUE estimators.
Credit Hours: 3

103735 Data Analysis by R-Programming
Prerequisite: None
Topics: Introduction to R and R Studio, data structures, control structures, functions and operators, databases (import/export, preprocessing), data visualization, descriptive and multivariate statistics, and statistical inference using R.
Credit Hours: 3

103741 Algebra (1)
Prerequisite: None
Topics: Isomorphism theorems of groups, group automorphisms, finite direct products, finitely generated groups, group actions, Sylow theorems, rings and ideals, prime and maximal ideals, polynomial rings and irreducibility tests, unique factorization domains, Euclidean domains.
Credit Hours: 3

103742 Algebra (2)
Prerequisite: 103741
Topics: R-modules, products and sums, exact and split exact sequences, simple and semisimple modules, essential and small submodules, endomorphism rings, projective and injective modules, regular rings, radical and socle, Noetherian and Artinian R-modules, field extensions, algebraic elements, splitting fields.
Credit Hours: 3

103761 Topology
Prerequisite: None
Topics: Topological spaces, continuous functions, separation axioms, countability axioms, separable spaces, connected and locally connected spaces, pathwise connected spaces, compact spaces, Heine-Borel theorem, countably compact spaces, Bolzano-Weierstrass property, metrizable spaces.
Credit Hours: 3

103771 Advanced Ordinary Differential Equations
Prerequisite: None
Topics: Qualitative theory of ODE solutions, existence, uniqueness, continuous dependence, linear equations, constant coefficient systems, phase plane analysis, nonlinear ODEs, stability analysis.
Credit Hours: 3

103772 Advanced Partial Differential Equations
Prerequisite: None
Topics: Classification, boundary and initial conditions, PDEs in mathematical physics, characteristics, Green’s functions, variational principles.
Credit Hours: 3

103781 Special Studies in Mathematics
Prerequisite: None
Topics: Selected topics from various fields of mathematics.
Credit Hours: 3