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, area in 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

The course provides a rigorous foundation in the principles of probability and mathematical statistics underlying statistical inference in the field of economics and business. Special emphasis is given to the study of parametric families of distributions, univariate as well as multivariate, and to basic asymptotics for sample averages.

The concept of set and its notations, classification of sets, ordered pairs, Cartesian product, product set, function on mapping, mappings, graph of function, function as sets of ordered pairs, relations, partition of asset ,equivalence class, composite mapping and its inverse, mathematical logic, number system.

Three-dimensional coordinate systems; 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; 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.

Three-dimensional coordinate systems; 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; 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.

Transcendental functions: Exponential and Logarithmic functions,   The hyperbolic functions, The inverse function of the trigonometric and hyperbolic functions, Technique, Integration by parts; Trigonometric substitutions partial fraction, Quadratic expressions The conic sections, Plane curves and polar coordinates: parametric equations, Area in polar coordinates, surface of revolution, Indeterminate   forms and improper integrals.

the primary objective of the course is to introduce to Fourier series, beta and gamma functions, the definition of the Laplace transform, calculating inverse Laplace transforms, Legendre and associated Legendre functions, eigenvalues, and Eigenfunctions, strum- Liouville boundary value problems, series solutions near regular singular points (Bessel functions).

Welcome to geometry! As you know from previous schooling, geometry is all around you. I hope this year you will learn about and appreciate the beauty of it. We will study the properties of many geometric figures and develop your abstract and logical thinking through deductive and inductive reasoning techniques. I expect you to put forth your best effort, enjoy the journey of learning, and have a great year!

Introduction to Partial Differential Equations(PDEs), Classification of PDEs; some physical models: the heat equation, the wave equation, and Laplace's equations; separation of variables for linear homogeneous PDEs; Eigenfunction expansions, Fourier transforms: properties and some applications; Laplace transform, Duhamel’s Principle, the heat equation for a finite rod, the wave equation for finite string, D’ Alembert solution, second order equations and classification into canonical forms (parabolic, elliptic, and hyperbolic), the method of characteristics, The Laplace equation in Cartesian & polar coordinates.

This course covers the foundations of main topics in real analysis variables such as; Real Numbers, Metric spaces, Sequences, Continuity and compactness, Riemann Integration.

The objective of this course is to introduce the fundamental ideas of the functions of complex variables and developing a clear understanding of the fundamental concepts of Complex Analysis such as analytic functions, complex integrals and a range of skills which will allow students to work effectively with the concepts.

Discrete Distribution and continuous Distribution moment, moment Generating Function, Expectation and variance using M.g.f probability density function for two random variables, Expectation, Cumulative distribution function for two random variables, conditional Expectation, conditional variance, M .g .f for two random variables Expectation,  distributions of functions of random variables (distribution function method, moment generating function method, and the Jacobian transformation method); limiting distributions.

Error Analysis, Numerical solutions of linear algebraic equations (Direct and Iterative methods such as Jacobi, Gauss – Seidel, SOR methods), Numerical solutions of non – linear equations, Interpolation, Approximation, Difference equations, Special Types of Matrices, Norms of vectors and Matrices, Eigenvalues and Eigenvectors.

This course is a three credit hours course. It is a compulsory course for the students in the department of Mathematics. It is a core course used to build a strong theoretical background that enable students to deep understanding of Statistical concepts and techniques. Topics include point estimation including method of moments, maximum likelihood estimation, uniform minimum variance estimation, and properties of the associated estimators; hypothesis testing including uniformly most powerful, likelihood ratio tests. Application to normal distribution(s), Chi-Square test for independence

Central limit Theorem , Estimation Theory, Point Estimation – Confidence Interval, Testing Hypothesis Theory, X²  – test, Test of variance Type1, ANOVA Type 2 , Non parametric Tests, Sign test, Rank sign test (Wilcoxon),  Sum of Rank Test (Man- Whitney test), Rank sum test Kruskal- Wallis test, Test of Randomness.

Group theory, basic structure of groups, subgroups and cyclic subgroups, normal subgroups, quotients groups, homomorphism, automorphisms, Cayley's Theorem, permutation groups, Sylow's Theorem. External and internal direct products.  Cosets and Lagrange's Theorem.

The evolution of some concepts, facts and mathematical algorithms in arithmetic, algebra, triangles, planar geometry, analytical geometry and calculus across ancient, Egyptian, Babylonian, Greek, Indian, Chinese, Islamic and European civilizations, the development of some intuitions and open problems and attempts to solve them

Topological spaces, Open sets, Closed sets, Closure, Interior, Exterior, Boundary, Isolated points, Subspace Base, Subbase, Continuous functions, Open functions, Closed function, Homeomorphism,  spaces, Product of finite number of spaces.

Forming a mathematical model for  Linear programming problems, solving the  Linear programming  by graphical method, simplex method and big M, Duality (definition of the dual problem, interpretations, the duality theorem, the complementary slackness theorem, dual simplex algorithm 

Solving the transportation problems, finding the optimal solution by using stepping stone method

First order partial differential equations (linear, semi linear, and quasilinear), Cauchy problem, the Characteristic method, Lagrange method, nonlinear equations of first order the characteristic method, Charpit’s method, Classification of second order equations. Hadamard conditions, Cauchy – Kowalevski theorem, the potential theory.

Uniform continuity, Sequence of functions: Convergence and uniform convergence, Approximation theorem (stone, weierstrass theorems), Series of function: Absolute and uniform convergence, Cauchy criterion, Weierstrass M-test, Dirichlet test, Abel test. Differentiation in , Chain Rule and Mean value theorem.

Series, Residues and Poles: Evaluation of improper real integrals, Improper integral involving sins

and cosines, Definite integrals involving sines and cosines, Integration through a Branch cut,

Logarithmic residues and Rouche s theorem, Mapping by elementary functions, Conformal

mappings and transformations of Harmonic functions.

Properties of solutions of n –th order linear systems , The existence and uniquence theorem , Continuous dependence on initial conditions , Phase plane for autonomous linear systems and their critical points , Stability of linear and almost linear systems .

The course is intended to allow students to be exposed to some foundational ideas in number theory without

the technical baggage often associated with a more advanced courses. The course provides students an

opportunity to develop an appreciation of pure mathematics while engaged in the study of number theoretic

results. The course is also designed to provide students an opportunity to work with conjectures, proofs, and

analyzing mathematics

This course discusses the following subjects:

Central limit Theorem , Estimation Theory, Point Estimation – Confidence Interval, Testing Hypothesis Theory, X² – test(for independence and goodness of fit), Test of variance analysis of variance, Non parametric Tests, Sign test, Rank sign test (Wilcoxon),  Sum of Rank Test (Man- Whitney test), Rank sum test Kruskal- Wallis test, Test of Randomness.

Rings, integral domains and fields, Some non – Commutative example, Ideals and quotient rings, Prime and maximal ideals, The field of quotient of an integral domain, Ring of polynomials, Division algorithm, Homomorphism, Principal ideal domain and unique factorization domains, Euclidean domains and the ring of Gaussian integers, Field extensions: Algebraic elements and their irreducible polynomials.

The algebraic eigenvalue problems, Numerical integration and differentiation, Numerical solution’s of ODE’s and PDE’s

Solution problems for two random variable, Solution for inventory problems, Mathematical Analysis for inventory problems, Mathematical Analysis using PERT, Queuing Theory problems, Markov chains, mathematical Analysis for Queuing Theory, Death and Birth problems .

A study should be done by the student in any of the mathematical subject under the supervision of the instructor

_{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 ; logarithmic and exponential functions and their derivatives and integrals; limits (the indeterminate forms); some techniques of integration.}

This course aims to introduce students of economics and administrative sciences to the basic concepts and principles of mathematics and to prepare them to deal with the various courses that involve quantitative analysis in the various disciplines in the college. It includes an introduction to functions (linear and quadratic functions), solving systems of linear equations, matrices, and introduction to programming. Linearity, derivation and integration, with a focus on economic applications in each of the previous topics

This course includes the study of Systems of Linear Equations. Solve the system of linear equations by using (Gaussian and Gauss-Jordan elimination). Matrices; their operations and their algebraic properties, Inverse of a matrix and its properties, methods for finding the inverse; solve the system of linear equations by using inverse of a matrix. Determinants with minors and cofactors; solve the system of linear equations by Crammers rule. Vector Spaces, subspaces, linear independence, basis, dimension, Eigenvalues and eigenvectors and their applications.