# Course Contents

DEPARTMENT OF MATHEMATICS
DESCRIPTION OF COURSES

MAT 113 Calculus I    (3,2,4)
Real numbers.Functions,limit and derivative of a single variable function. Discussion of basic theorems of differential calculus.Intermediate value,extreme value,and the mean value theorems ,applications.Graph sketching and problems of extrema.Integration.Applications of definite integrals.

MAT 114 Calculus II   (3,2,4)
Transcendental functions.Techniques of integration.Infinite sequences and series.Vectors and geometry of space.Partial derivatives.Multiple integrals.

MAT 221 Linear Algebra I   (3,0,3)
Matrices and systems of linear equations.Determinants. Vector spaces.Linear dependence,bases,dimension.Linear transformations,kernel,range.

MAT 222 Linear Algebra II  (3,0,3)
Characteristic and minimal polynomials of an operator.eigenvalues.Inner product spaces,norm and orthogonality.Bilinear and quadratic forms.

MAT 233 Calculus  III   (2,2,3)
Functions of several variables:limit,continuity,partial derivatives,the chain rule,directional derivatives.Extreme values,Lagrange multipliers.Double and triple integrals with applications.The line integral.

Topology of R,R2 and R3 .Functions of several variables,limit and continuity,partial derivatives.The mean value,implicite and inverse function theorems..

MAT 261 Introduction to Probability Theory  (3,0,3)
Events and probability.Combinatorial problems.Independence and conditional probability.Random variables and distribution functions.Moments and characteristic functions.Law of large numbers.

MAT 262 Mathematical Statistics  (3,0,3)
Probability and distributions Multivariate distributions. Special distributions.Distribution functions of random variables.

MAT 311 Abstract Algebra  I (3,0,3)

Groups, subgroups, finite groups, cyclic groups, permutation groups. Isomorphisms, cosets and Lagrange’s Theorem. External Direct Products. Normal Subgroups and factor groups. Group homomorphisms. Fundamental Theorem of Finite Abelian Groups.

MAT 312 Abstract Algebra  II (3,0,3)

Rings, subrings, integral domains, ideals, factor rings, homomorphisms of rings, polynomial rings, factorization of polynomials, principal ideal domains, field extensions, finite fields, geometric constructions, Galois Theory, cyclotomic extensions, Sylow Theory.

MAT 351 General  Topology  (3, 0, 3)
Topological spaces;basis,subspaces.Closed sets,limit points.Hausdorff spaces.Connectedness and compactness.Homeomorphism.Seperation axioms.

MAT 352 Differential Geometry
Curves in 3-space.Frenet formulae.Theory of surfaces.Vector fields.First fundamental form.Gauss map.

MAT 371 Differential Equations  (3,0,3)
First order equations and various applications.Higher order linear differential equations.The Laplace transform:solution of initial value problems.Systems of linear differential equations.

MAT 372 Partial Differential Equations (3,0,3)
First order equations;linear,quasilinear and nonlinear equations.Classification of second order linear partial differential equations.The Cauchy problem for the wave equation.Dirichlet and Neumann problems for the Laplace equation.

MAT381 Actuarial Mathematics I (3,0,3)

 Interest.Simple and Compound Interest.Present Value and Discount.Interest Applications. Time Weighted Rate of Return.Annuities.Continuous Annuities.Varying annnuities.Amortization.Sinking Funds and Yields Rates.Bond Amortization.Bond Amortization Schedulesi

MAT382 Actuarial Mathematics II (3,0,3)

 Life Tables and Populations Problems .Stationary Population and Life Expectations.Life Annuities.Commutation Functions.Life Insurance.Insurance Payable at the Moment of Death.Benefit Reserves.Reserves for Contingent Payments Models.Multi Life Theory.Last Survival. Models.Multiple Decrements.Pension Theory and Applications.

MAT 432  Real Analysis  (3,0,3)
Classes of sets.Consruction of measures.Integration.The Riemann integral. Lebesgue integral.

MAT 441  Complex Analysis I (3,0,3)
Complex numbers.Analytic functions.Cauchy-Riemann equations.Power series.Elementary functions.The line integral. Cauchy theorem. Cauchy integral formula.Taylor, Maclaurin series.Residue theorem.Improper integrals.

MAT461 Functional Analysis I (3,0,3)
Metric Spaces, Topological Spaces, Banach Spaces, Hilbert Spaces, completeness, bounded
operators, sums and quotients of Banach Spaces, spaces of continuous and differentiable
functions, orthonormal bases, the Projection Theorem, the Riesz Lemma, operators defined via forms, orthogonal sums and tensor products, compact operators, the Spectral Theorem for Compact Symmetric Operators,

MAT462 Functional Analysis II (3,0,3)
The Baire Category Theorem, The Hahn-Banach Theorem, Weak Convergence, Canonical Forms of Compact Operators,  Hilbert-Schmidt Operators, Fredholm Theory, Banach Algebras, The C -algebra of Operators, The Spectral Theorem, Spectral Measures, The Stone-Weierstraß Theorem.