This course introduces the students with the concepts of applied computing through case studies from: machine learning, data mining, artificial intelligence, computer vision computer graphics, image processing, computer animation, and information retrieval. A detailed exposition of relevant computing concepts will be given to the students with the hands-on introduction to a working system that embodies these concepts. Students will use these systems to perform design and problem-solving tasks, thereby reinforcing the abstract concepts presented.

Fractals, Chaos, Macroscopic Scale Models and Partial Deferential Equations Root-Locus Analysis Control Systems Design by the Root-Locus Method, Control Systems Design by the Root-Locus Method.

This course establishes a link between Riemannian geometry and semi-Riemannian one. It presents an overview to surfaces and curves in Euclidean spaces, then defines the concept of a Riemannian manifold generalizing it to semi-Riemannian manifolds. Its goal to study gravitation and to make a comparison between Newtonian's concept of gravity and the general concept of general relativity. Thus, we need to explore the concepts of Minkwiski spaces and Lorantzian geometry and its corresponding semi-linear algebra. At the end, we give brief descriptions of most important spacetime models especially the GRW model. If time permits, we give a brief discussion for black holes.

Laplace and saddle point methods, asymptotic analysis of integrals and differential equations, special functions, Sturm-Liouville theory, perturbation theory.

Introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature with a computer. Focusing mostly on geometry and on its applications to the design and representation of polynomial curves and surfaces and splines.

Different modeling approaches to various biological and physiological phenomena (e.g., population and cell growth, spread of disease, epidemiology, biological fluid dynamics, nutrient transport, biochemical reactions, tumor growth, genetics).

Non-linear elements and networks, finite (Boolean) problems, network capacity, learning theory, learning algorithms, learning complexity.

Matrices and their eigenvalues determinants and traces. Spectral theory. The Jordan normal form. Matrix factorizations. Matrix polynomials and matrix functions. Norms. Scalar products. Singular values. Normal matrices. Quadratic and Hermitian forms. The Least Squares method and pseudo inverses. Non-negative matrices, positive definite and semidefinite Matrices, Numerical range and spectral radius application of matrix analysis

Basic concepts of measure theory, probability theory, random variables, expectation, and independence, the weak and strong laws of large numbers, the central and Poisson limit theorem, conditional expectations, stochastic integration and differential equations.

Metric Spaces, Banach Spaces, Hilbert Spaces, Banach Fixed Point Theorem, Applications of Banach Fixed Point Theorem to Linear Equations, Applications of Banach Fixed Point Theorem to Differential Equations, Applications of Banach Fixed Point Theorem to Integral Equations, Approximation in Normed Spaces, Approximation in Hilbert Space, Mapping by Elementary Complex Functions, Conformal Mappings, Applications of Conformal Mappings.

Approximation theory. Numerical Methods the matrix eigenvalue problems: power method and its variants, Householder method, the QR algorithm. Numerical solutions to ordinary and partial differential equations.

Vector spaces, linear transformations, bases, direct sums, eigenvalues and generalized eigenvectors, Jordan canonical form, inner product spaces, adjoint, Hermitian and unitary operators, singular value decomposition, tensor products, outer product and finite groups, with applications in, for example, differential equations, signal analysis, inverse problems, linear regression, image compression, Markov chains or graph theory.

Pressure, hydrostatics, and buoyancy; open systems and control volume analysis; mass conservation and momentum conservation for moving fluids; viscous fluid flows, flow through pipes; dimensional analysis; boundary layers, and lift and drag on objects. Students will work to formulate the models necessary to study, analyze, and design fluid systems through the application of these concepts, and to develop the problem-solving skills essential to good engineering practice of fluid mechanics in practical applications.

Finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems will be introduced. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments.

Counting techniques, binomial coefficients, generating functions, partitions, the inclusion-exclusion principle and partition theory.

Nonlinear Optimization Methods. Multivariable Optimization. Modeling Decision Making with Multi-Attribute Decision Modeling with Game Theory.

Groups as symmetries and transformations of space, compact Lie groups and their representations, connections between orthogonal polynomials, classical transcendental functions and group representations, finite groups and their applications in coding theory, structural properties of linear systems of equations relevant to their numerical solution, eigenvalues and the spectral theory of matrices, solving systems of polynomial equations.