This course is a combination of topics from functional analysis, real analysis, and complex analysis. The course starts with studying rates of growth of functions, infinite series and infinite products. Then metric and normed spaces are investigated. Measure theory is also within the scope of this course where students learn ?-algebra, measures, measurable functions, integrable functions, generation of measures (Lebesgue, Lebesgue-Stieltjes), differentiation, and functions of bounded variation. At the end, analytic functions, residues, and applications of residues are addressed.

This course introduces basic ideas and techniques of mathematical modeling: Modeling methodology and skills, model fitting, continuous and discrete dynamical systems, modeling with difference equations, modeling with systems of difference equations, modeling with differential equations, modeling with systems of differential equations: steady states and stability, integrability, diffusion equations, simulation random process, and dimensional analysis.

This course presents the finite element method as a numerical technique for solving problems which are described by PDEs. At the beginning of the course triangular discretization is considered to divide the domain into elements, and then interpolation functions are used to interpolate the fields over the elements. After that the assembly process of all element equations (that used for discretiztion) to the global algebraic system of equations is applied to convert the PDE into algebraic system of equations. Gaussian elimination method is considered as a direct method to solve resultant bounded system and iterative methods are used in the other cases.

This course covers the methodology and applications of time series analysis and forecasting. It reviews simple descriptive methods of time series: smoothing, decomposition and gives some fundamental concepts: stochastic process, dependency measures (autocorrelation, autocovariance), stationary process. It presents the probabilistic models: Autoregressive Integrated Moving Average (ARIMA) models and describes how to apply the Box-Jenkins modeling approach for building ARIMA models by time series data. After that this course deals with volatility models: Autoregressive Conditional Heteroscedasticity ARCH and the GARCH models. Finally multivariate time series models: Vector ARIMA Models, Vector Auto Regression (VAR), Granger causality, cointegration, and multivariate volatility models are studied. All these techniques are applied to actual data (primarily financial and economic time series) by using computer statistical packages.

Fuzzy Sets, Fuzzy Numbers, Fuzzy Arithmetic, Fuzzy Relations, Fuzzy Probability, ‎Fuzzy Equations, Fuzzy Functions, Fuzzy Differentiation, Fuzzy Integration, Fuzzy ‎Differential Equations.‎

Study of linear differential equations of a single variable of any order, Nonlinear first ordinary differential equations, Nonlinear second order differential equations and their solutions (graphical, exact). Applications of ordinary differential equations, Physical, Engineering, Mathematical, Chemical and Economic. The operators and its applications to solve the ordinary differential equations. Laplace transforms, introduction to systems of linear differential equations of any order, use of eigenvalues and eigenvectors in solving such systems.

This course presents formulation and solution techniques for optimization problems which can be modeled as linear, integer, and dynamic problems. The beginning of the course concentrates on model formulation and computations in linear programming. The simplex method and the generalized simplex algorithm are presented to solve the general linear programming problems. Cutting plane and B&B methods are considered in integer linear programming problems. Many dynamic programming problems with various computational methods are presented to investigate the mathematics behind using different methods. Deterministic inventory models in different situations are given. Transportation model is considered as a special class of linear programming. Many decision problems and real life applications are discussed throughout the course.

This course give an introduction to Stochastic Modeling, Probability Review, Conditional Probability and Conditional Expectation, Markov Chains in discrete time, The Poisson Process, Markov Processes in continuous time, Renewal This course aims to develop and analyse probability models and to predict the short and long term effects that randomness will have on the systems under consideration. The study of probability models for stochastic processes involves a broad range of mathematical and computational tools. This course will strike a balance between the mathematics and the applications

In this course we make a review of some linear algebra concept, eigenvalues and eigenvector ,sudy Caley Hemlton and Gorch Goren’s theorems, concical form ,polar and Cartesian decomposition ,solving system of linear first and second order D.E with there mathematical modeling, using matlap to solve System of O.D.E a n D.E.(or any subject in mathmaticalmodel approved by depertment)

Industrial Case Studies (likely to Change from Year to Year)

This course presents numerical methods for solving mathematical problems. It deals with the theory and application of numerical approximation techniques as well as their computer implementation. The course starts with studying Fundamentals(taylor series in one variable and two variable , vector matrix multiplication and norms ). Then Iterative Method for solving linear system(Jacobi, Gauss-seidel, SOR, and Conjugate Gradient Methods)are discussed. After that Direct Method for solving linear system (QR factorization , Cholesky factorization, Singular value decomposition, and LU factorization) are investigated. At the end , Newton’s Method for solving Non-linear system , and Solving first order Ordinary differential equation are addressed.

This course covers a wide range of topics that are most useful for a broad range of application areas. It starts studying the linear statistical models such as linear regression, analysis of covariance, factorial designs, and designed experiments. Then it turns to the generalized linear models such as binomial Data, Poisson and multinomial models. After that the random and mixed effects and non-Linear regression are discussed. This course also deals with exploratory multivariate analysis such as cluster analysis, factor analysis and classification analysis such as discriminant analysis and Neural Networks. In addition to other topics such as survival analysis, spatial experiments and spatial data analysis, resampling methods (bootstrap), Markov chain Monte Carlo, state-space models and Bayesian analysis.

Basic properties of vector spaces and linear transformations, algebra of polynomials, ‎characteristic values and diagonalizable operators, invariant subspaces and triangularly ‎operators. The primary decomposition theorem, cyclic decompositions and the ‎generalized Cayley-Hamilton theorem. Rational and Jordan forms, inner product ‎spaces, The spectral theorem, bilinear forms, symmetric and skew symmetric bilinear ‎forms.‎

"This course provides a mathematical background for general relativity. It is organized to ‎contain two parts, the first is a solid theory of differential geometry, whereas the other is ‎the applications of the manifold theory in general relativity.

Many natural phenomena have been successfully formulated as partial differential equations: common applications include Physics, Chemistry, Biology, Economics and population dynamics. This course will be primarily focused on the theory of partial differential equations such as Charpit"s Equations, Eikoral Equation, Systems of PDEs, Characteristics, Weak Solutions, Riemann"s Function, Maximum Principle, Comparison Methods, Green"s Functions.

Deterministic Finance, Cash Flow Analysis, Single-Point Uncertainty Finance, Portfolios of Stocks and Pricing Theory .

This course addresses the dynamic systems, the following concepts and how to find them: fixed points, functions of linear approximation and the conjugation of Libanov, the gradient system, knowledge of the periodic non-linear system of continuous and discrete time, knowledge of the linear and non-linear wave system with examples.

This course presents various computational methods used in mathematical modelling. The aim is for the students to investigate the mathematics behind various numerical processes and also the use of software for simulation and visualisation of outcomes. At the beginning of this course , we will study solution of first order ordinary differential equations by using different methods(Explicit and Implicit Euler,Modified Midpoints, Modified Euler, Runge Kutta ) with linear stability. Then centered difference and Finite Element methods for solving second order differential equations are discussed. After that Finite difference methods are considered for solving Partial differential equations. At the end , Some Applications of differential equations are addressed.

Gorsch Goren’s theorem, Schur’s theorem ,polar and Cartesian decomposition ,Matrix ‎inequality, Matrix norm with operation on it solving system of linear first and second ‎order D.E with there mathematical modeling using Matrices

Brownian Motion, Stochastic Calculus, Stochastic Models of Financial Markets, Pricing and Hedging Contingent Claims

This course covers various problems in mathematical modeling with an emphasis on industry. Topics includes neural information processing, biology to mathematical models, neural networks as associative memories, creating maps of the outside world and learning in multi-layer perceptrons. Industrial problems include Monte Carlo methods for a financial application, circadian rhythm analysis, atmospheric refraction correction, and the Fourier synthesis of ocean scenes. 

"‎-Spaces. ‎-Special Functions(Mittaq Leffler function, Wright Function)‎ ‎- Riemann Liouville fractional integrals and fractional Derivatives ‎with ‏their properties ‎- Caputo fractional Derivatives and its properties ‎-conformable fractional derivative and its properties ‎ ‎-Laplace transforms of fractional derivatives ‎- Methods of explicity solving fractional differential equations ‎- Applications of fractional derivatives "