List of Courses
* All credit hours are based on the current term, this may vary for previous terms.
MATH105  Calculus I 
(3 credit hours) 
Elementary functions, limits, continuity, limits involving infinity, tangent lines, derivative of elementary functions, differentiation rules, chain rule, implicit differentiation, linear approximation, l'Hospital rule. Graph sketching (extrema, intervals of monotonicity, concavity), optimization. Antiderivatives, definite integrals, Fundamental Theorem of Calculus, integration by substitution, area between curves, improper integrals.

Prerequisite: 
 (MATU1332) or (MTSU1305) or (MATU1435X) or (MATU1435 + BNCHFORMIN.SCOREOF5.0 + ENGU1304) or (ENGU1305)

Corequisite: 

Semester: 
Fall Spring 
Go To Index 
MATH110  Calculus II 
(3 credit hours) 
Integration techniques (by parts, by use of trigonometry, by partial fractions), volume and area of solids of revolution, arc length. Parametric curves: velocity vector, enclosed area, arc length. Curves in polar coordinates: enclosed area, conic sections. Sequences, series, convergence tests, alternating series, absolute convergence, power series, Taylor series, Fourier series.

Prerequisite: 
 MATH105

Corequisite: 

Semester: 
All 
Go To Index 
MATH1110  Calculus I for Engineering 
(3 credit hours) 
Differential calculus of functions of one variable: functions of one variable, techniques of differentiation, derivatives of trigonometric, exponential, and logarithmic functions, chain rule, implicit differentiation, maximum and minimum values, increasing, decreasing and concave functions, inverse trigonometric functions, hyperbolic functions, some engineering applications. Integral calculus of functions of one variable: definite and indefinite integrals, techniques of integration (integration by substitution, integration by trigonometric substitutions, integration by parts, integration by partial fractions), applications of definite integrals in geometry, some engineering applications.

Prerequisite: 
 (MATU1332) or (MATU1435) or (MATU1435X + BNCHFORMIN.SCOREOF5.0 + ENGU1305) or (ENGU1304X) or (ENGU1304)

Corequisite: 

Semester: 
All 
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MATH1120  Calculus II for Engineering 
(3 credit hours) 
Differential calculus of functions of several variables: vectors, vector valued functions, functions of several variables, partial derivatives, chain rule, gradient and directional derivatives, extrema of functions of several variables. Quadratic surfaces. Vector fields and line integrals, double integrals in Cartesian and polar coordinates, triple integrals in Cartesian, cylindrical and spherical coordinates.

Prerequisite: 
 MATH1110
 ENGU1304 or ENGU1304X or ENGU1305

Corequisite: 

Semester: 
Fall Spring 
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MATH115  Calculus for Business&Economic 
(3 credit hours) 
This course introduces the concepts of differential and integral calculus useful to students in business, economics. Among the topics studied are: curve sketching for some functions relevant to business and economics applications, derivatives and techniques of differentiation, exponential growth, antiderivatives and methods of integration, definite and indefinite integrals with applications. The course also covers topics on partial derivatives and matrices, in addition to many applications in Business and Economics.

Prerequisite: 
 MATU1312 or MATU1332 or MTSU1305 or MATU1305 or MATU1425
 ENGU1304 or ENGU1305 or BNCHFORMIN.SCOREOF5.0

Corequisite: 

Semester: 
All 
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MATH120  Contemporary Appl. of Math 
(3 credit hours) 
Problem solving, fair divisions, Mathematics of Apportionment, Euler circuits, network, scheduling methods, population growth, symmetry, fractal geometry.

Prerequisite: 
 ENGU1304 or ENGU1305 or ENGU1304X or BNCHFORMIN.SCOREOF5.0

Corequisite: 

Semester: 
All 
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MATH140  Linear Algebra I 
(3 credit hours) 
Systems of linear equations, matrices and determinants. Vector spaces, inner product spaces. Matrix representations of linear operators. Eigenvalues, eigenvectors, and CayleyHamilton Theorem.

Prerequisite: 
 (MATU1435X) or (MATU1435 + BNCHFORMIN.SCOREOF5.0)

Corequisite: 

Semester: 
Fall Spring 
Go To Index 
MATH210  Calculus III 
(3 credit hours) 
Euclidean space: dot product, cross product, lines, planes, surfaces. Parametric curves in space. Functions of several variables: limits, continuity, partial derivatives, tangent plane, linear approximation, chain rule, gradient, directional derivative, extrema, Lagrange multipliers. Double integrals, applications (area, volume, center of mass), change to polar coordinates. Triple integrals, change to cylindrical and spherical coordinates. Vector fields, line integrals, conservative fields, Green's theorem.

Prerequisite: 
 MATH110
 MATH140

Corequisite: 

Semester: 
Fall Spring 
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MATH215  Introduction to Analysis 
(3 credit hours) 
Sets, functions, cardinality, countable and uncountable sets, methods of proofs, mathematical induction. Completeness of the line, supremum and infimum, Cantor's nested intervals theorem. Sequences, limits and their properties, monotone sequences, BolzanoWeierstrass Theorem, Cauchy criterion, properly divergent sequences. Series, absolute and conditional convergence, tests of convergence.

Prerequisite: 
 MATH110
 MATH140

Corequisite: 

Semester: 
Fall Spring 
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MATH2210  Differ. Equations & Eng. Appl. 
(3 credit hours) 
Ordinary differential equations: first order differential equations: separable; homogenous, linear, Bernoulli, exactintegrating factors. Second order linear differential equations: homogenous equations with constant coefficients; undetermined coefficients method; variation of parameters method; Euler's Equation; Nonhomogenous equations; higher order linear equations; systems of differential equations. Laplace transforms: basic properties; solving initial value problems using Laplace; solving integral equations; solving systems of differential equations. Engineering applications.

Prerequisite: 
 MATH1120

Corequisite: 

Semester: 
Fall Spring 
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MATH2220  Linear Algebra & Eng. Appl. 
(3 credit hours) 
Linear algebra: matrices; determinants; system of linear equations; eigenvalues and eigenvectors; diagonalization. Some engineering applications. Complex analysis: complex numbers; complex variables; differentiation of complex functions; complex integration; conformal mappings.

Prerequisite: 
 MATH1120

Corequisite: 

Semester: 
All 
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MATH245  Set Theory and Logic 
(3 credit hours) 
Compound and simple propositions, truth table, quantifiers, propositional calculus, methods of proofs. Sets and operations on sets. Cartesian products, relations, equivalence relation, order relation. Functions, images of sets and cardinality.

Prerequisite: 
 MATH140 or MATH1120

Corequisite: 

Semester: 
Fall Spring 
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MATH246  Number Theory 
(3 credit hours) 
Divisibility, Euclidean algorithm, prime numbers, the Fundamental Theorem of Arithmetic, the Sieve of Eratosthenes. Congruences, Diaphontine equations, Chinese Remainder Theorem. Fermat?s theorem, Wilson?s theorem, Euler?s theorem, The Legendre symbol and Quadratic Reciprocity.

Prerequisite: 
 MATH245 or MATH215 or MATH215

Corequisite: 

Semester: 
Fall Spring 
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MATH260  Foundation of Geometry 
(3 credit hours) 
Euclid's postulates and plane geometry. VonNeumann postulates. The parallel postulate. Affine geometry and geometry on the sphere. Projective and hyperbolic geometries. KleinBeltrami and Poincare models of the plane. Pappus and Desargues theorems. Transformations: automorphisms, motions, similarities, and congruence.

Prerequisite: 
 (MATH140 + MATH110) or (MATH1120) or (MATH1120)

Corequisite: 

Semester: 
Fall Spring 
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MATH275  Ordinary Differential Eqn. 
(3 credit hours) 
First order differential equations: examples, separable equations, homogeneous and exact equations, integrating factor and Bernoulli's equation, linear equations, initial value problems. Higher order differential equations: linear equations, linear independence and Wronskian matrices, existence and uniqueness of solutions. Particular solutions: the method of undetermined coefficients, the method of variation of parameters. Laplace transforms and initial value problems. Series solution of differential equations. System of equations and their matrix form.

Prerequisite: 
 MATH110
 MATH140

Corequisite: 

Semester: 
Fall Spring 
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MATH305  Mathematics For Teachers I 
(3 credit hours) 
Introduction to mathematical logic, sets, operation on sets, the set of natural numbers, the set of integers, the set of rational numbers, graphical representation of numbers, decimal representation of numbers, other bases, divisibility, solution of arithmetic problems, applications.

Prerequisite: 
 MATU1332 or MATU1312 or MTSU1305 or MTAU1305 or MATU1415X or MATU1415

Corequisite: 

Semester: 
Fall Spring 
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MATH310  Real Analysis 
(3 credit hours) 
Functions, limits of functions, limits involving infinity, continuity, uniform continuity, Extreme Value Theorem, Intermediate Value Theorem, monotone and inverse functions. Differentiation, Mean Value theorem, L'Hospital's rule, Taylor's theorem. Riemann integral, the Fundamental Theorem of Calculus

Prerequisite: 
 MATH215 or MATH245 or MATH215

Corequisite: 

Semester: 
Fall Spring 
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MATH315  Complex Analysis I 
(3 credit hours) 
Complex numbers: properties and representations. Complex functions: limits, continuity, and the derivative. Analytic functions: Cauchy  Riemann equations, harmonic functions, elementary analytic functions. Integration in the complex plane: complex line integrals, Cauchy integral theorem, Morera's theorem, Cauchy integral formula; Maximum principle. Liouville's theorem and the fundamental theorem of algebra.

Prerequisite: 
 MATH210 or MATH215 or MATH215

Corequisite: 

Semester: 
All 
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MATH320  Numerical Analysis I 
(3 credit hours) 
Error analysis: solutions of nonlinear equations in one variable, bisection, fixed point, and false position methods, Newton and secant methods; Solution of a system of linear equations: Gaussian elimination method, Cholesky factorization method. Iterative methods: Interpolation: Lagrange, divided differences, forward, backward, and central methods. Numerical differentiation, two, three and five point formulas. Numerical integration, trapezoidal, Simpson?s rules and composite quadrature.

Prerequisite: 
 MATH210

Corequisite: 

Semester: 
Fall Spring 
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MATH321  Linear Programming 
(3 credit hours) 
The general Linear Programming Problem. The Simplex method. The revised Simplex method. Computer implementations. Duality. Parametric linear programming. Interior point methods. Applications including: transportation problem, inventory problems, blending problems and game theory.

Prerequisite: 
 MATH210

Corequisite: 

Semester: 
All 
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MATH335  Mathematics For Teachers II 
(3 credit hours) 
Geometrical figures in plane and space and their properties. Areas and volumes of geometrical figures; unitary and nonunitary linear transformations and their properties. Ratio, proportion, percentage and their practical applications. The geometric problem: construction and solutions methods.

Prerequisite: 
 MATH305 or MATH3052

Corequisite: 

Semester: 
Fall Spring 
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MATH340  Abstract Algebra 
(3 credit hours) 
Groups: examples, subgroups, cyclic subgroups; cosets and Lagrange's theorem; Cyclic groups and permutation groups. Normal subgroups, quotient groups; homomorphisms and isomorphisms; Direct products of groups. Rings: examples, sub rings, ideals, quotient rings, integral domains, Fields. Ring homomorphisms and isomorphisms.

Prerequisite: 
 MATH245 or MATH215 or MATH215

Corequisite: 

Semester: 
Fall Spring 
Go To Index 
MATH341  Linear Algebra II 
(3 credit hours) 
Linear Transformations: Isomorphisms of vector spaces, representation by matrices, and change of basis. Eigenvalues and eigenvectors: diagonalization and triangularization of linear operators. Inner product spaces: Orthogonalization and Rieze representation theorem. Selfadjoint operators: the Spectral theorem, Bilinear and quadratic forms.

Prerequisite: 
 MATH245 or MATH215

Corequisite: 

Semester: 
Fall Spring 
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MATH342  Graph Theory 
(3 credit hours) 
Definition of a graph. Examples, paths and cycles: Eulerian and Hamiltonian graphs. Application to ?shortest path? and ?Chinese postman? problems, trees, applications, including ?enumeration of molecules? planar graphs, graphs on other surfaces, dual graphs. Coloring maps edges, vertices. Digraphs, Markov chains, Hall?s marriage theorem and applications. Network flows.

Prerequisite: 
 MATH245 or MATH215

Corequisite: 

Semester: 
Spring 
Go To Index 
MATH344  Int.to Cryptograp.&Coding Theo 
(3 credit hours) 
This course introduces students to the principals and practices which are required for secure communication: cryptography and cryptanalysis, including authentication and digital signatures. Mathematical tools and algorithms are used to build and analyze secure cryptographic systems. Basic notions of coding theory will be also covered.

Prerequisite: 
 MATH215

Corequisite: 

Semester: 
Spring 
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MATH372  Partial Differential Equ 
(3 credit hours) 
Definitions and concepts: General and particular solutions. Elimination of arbitrary constants and functions. First order equations the method of characteristics. Second order equations: classifications hyperbolic, elliptic, parabolic, the normal form. Boundary value problems: the heat equation, the wave equation, Laplace equation, methods of solutions: separation of variables, the Fourier and Laplace transforms.

Prerequisite: 
 MATH275
 MATH210

Corequisite: 

Semester: 
Fall Spring 
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MATH374  Dynmical Systems and Appl. 
(3 credit hours) 
One dimensional discrete dynamical systems. Steady states, stability, periodic points. Chaos. Lyapunov exponents. Symbolic dynamics. 2dimensional systems. Mandelbort set. Fractals. Applications in ecology population growth, Predatorprey and competition models. Applications in medicine fractal structure of the lung, heart rat variability.

Prerequisite: 
 MATH210
 MATH275

Corequisite: 

Semester: 
Spring 
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MATH391  Financial Mathematics 
(3 credit hours) 
Introduction to the concepts of financial markets and products. Financial derivatives, options, futures and forwards. Pricing, hedging and no arbitrage concepts. The Binomial model. Introduction to stochastic calculus, Stochastic processes, Markov property, martingales. Brownian motion, stochastic integration, stochastic differential equations, Ito's Lemma. Black and Scholes formula, delta hedging. Numerical Methods for finance, Finite Difference Methods, Monte Carlo simulation. Optional topics: Value at Risk, Greeks, Implied volatility, implementation of pricing formulas in VBA for Excel, interest rate models, exotic options, path dependent options, Asian options.

Prerequisite: 
 MATH320
 STAT230

Corequisite: 

Semester: 
Fall 
Go To Index 
MATH413  Complex Analysis II 
(3 credit hours) 
Sequences and series of complex numbers, Power series, Taylor and Laurent expansions, differentiation and integration of power series, application of the Cauchy theorem: Residue theorem, evaluation of improper real integrals, conformal mappings, mapping by elementary functions.

Prerequisite: 
 MATH315

Corequisite: 

Semester: 
Fall 
Go To Index 
MATH422  Numerical Analysis II 
(3 credit hours) 
Approximation theory: Orthogonal and Chebyschev polynomials, rational and trigonometric polynomials, multiple integrals, initial value problems: Taylor?s methods, multistep and RungeKutta methods, boundary value problems: shooting, finite difference and RayleighRitz methods.

Prerequisite: 
 MATH320

Corequisite: 

Semester: 
Spring 
Go To Index 
MATH462  Introduction To Topology 
(3 credit hours) 
Topological spaces, Bases and subbases, subspaces, finite product spaces, continuous maps, homomorphisms, Hausdorff spaces, metric spaces, compactness and connectedness, separation axioms.

Prerequisite: 
 MATH310

Corequisite: 

Semester: 
Spring 
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MATH470  Mathematical Modeling 
(3 credit hours) 
The modeling process, dimensional analysis, model fitting techniques, discrete models difference equations, logistic equation. Continuous models using derivatives for example: predatorprey, population, harvesting, models. Discussion of stability, phase plane. Applications using Mathematica.

Prerequisite: 
 MATH500_{1}
 MATH495_{1}

Corequisite: 

Semester: 
Fall Spring 
Go To Index 
MATH471  Control Theory & Applications 
(3 credit hours) 
Introduction and motivation. Problem formulation. Systems models: linear and nonlinear systems. Optimal control problems arising from different fields. Calculus of variation with application to system modeling. Limitation of calculus of variation leading to modern control theory. Time optimal control, attainable state, reachable sets, and BangBang principle. Pontryagin minimum principle and transversality conditions. Linear quadratic control problems. Optimal linear state feedback control. Applications: 3axis attitude control of communication satellites, road building and fisheries problems, geosynchronous satellites, speed controls of electric motors.

Prerequisite: 
 MATH275

Corequisite: 

Semester: 
Fall 
Go To Index 
MATH491  Selected Topics In Pure Math 
(3 credit hours) 
Selected topics in pure mathematics proposed by the instructor are offered upon the consent of the department.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH492  Selected Topics In Applied Mat 
(3 credit hours) 
Selected topics in applied mathematics proposed by the instructor are offered upon the consent of the department. Prerequisite: departmental consent

Prerequisite: 

Corequisite: 

Semester: 
Spring 
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MATH495  Research Project 
(3 credit hours) 
Students are supervised during their formulation of research proposals. Instructors direct their students in carrying out different tasks leading to the execution of the projects. Students are required to give presentations regarding their achievements, and the written final reports are submitted for evaluation.

Prerequisite: 
 MATH500_{1}
 MATH470_{1}

Corequisite: 

Semester: 
Fall Spring 
Go To Index 
MATH500  Internship 
(6 credit hours) 
The Internship training program is coordinated by both the department, academic supervisor and the faculty training committee. The program is continuously monitored and reviewed by a field supervisor staff member at one of the institutions, establishments, or work sites in the United Arab Emirates.

Prerequisite: 
 MATH470_{1}
 MATH495_{1}

Corequisite: 

Semester: 
Fall Spring 
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MATH510  Real Analysis 
(3 credit hours) 
Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the RiemannStieltjes integral, sequences and series of functions, uniform convergence, the StoneWeirestrass theorem, equicontiuity, the ArzelaAscoli theorem.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH513  Calculus on Manifold 
(3 credit hours) 

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH515  Functions of Complex Variables 
(3 credit hours) 
Numbers and complex valued function of one complex variables, differentiation, and contour integration, Cauchy?s Theorem, Taylor and Laurent series, residues, conformal mapping, applications.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH516  C*Algebras 
(3 credit hours) 
Introductions to Banach and Hilbert spaces, Bounded operators on Hilbert spaces. Introduction to C*algebras: definition and examples, projections and unitary groups. Types of C*algebras, Finite and approximately finite dimensional algebras (AFalgebras), the Bratteli diagrams for AFalgebras. The von Neumann algebras and Factors. Irrational rotation algebras and Cuntz algebras. Dimension groups. Basics of Ktheory, classifications of C*algebras using the Ktheory and the unitary groups.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH520  Numerical Analysis 
(3 credit hours) 
Error analysis. Solutions of linear systems: LU factorization and Gaussian elimination, QR factorization, condition numbers and numerical stability, computational cost. Least squares problems: the singular value decomposition (SVD), QR algorithm, numerical stability. Eigenvalue problems: Jordan canonical form and conditioning, Schur factorization, the power method, QR algorithm for eigenvalues. Iterative Methods: construction of Krylov subspace, the conjugate gradient and GMRES methods for linear systems, the Arnoldi and Lanczos method for eigenvalue problems.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH522  Numerical Methods in Differ Eq 
(3 credit hours) 
Theory and implementation of numerical methods for initial and boundary value problems in ordinary differential equations. Onestep, linear multistep, Runge Kutta, and extrapolation methods; convergence, stability, error estimates, and practical implementation, Study and analysis of shooting, finite difference and projection methods for boundary value problems for ordinary differential equations. Theory and implementation of numerical methods for boundary value problems in partial differential equations (elliptic, parabolic, and hyperbolic). Finite difference and finite element methods: convergence, stability, and error estimates. Projection methods and fundamentals of variational methods. RitzGalerkin and weighted residual methods.

Prerequisite: 
 MATH520

Corequisite: 

Semester: 
Fall Spring 
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MATH540  Algebra I 
(3 credit hours) 
Group theory: definitions, subgroups, permutation groups, cyclic groups, quotient groups, homomorphism, the isomorphism and the correspondence theorems. Ring theory: definitions, rings homomorphism, ideals, quotient rings, fraction fields, polynomial rings, Euclidean domain, and unique factorization domain. Field theory: algebraic field, extensions.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH541  Number Theory 
(3 credit hours) 
Basics of number theory: divisibility, unique factorization, congruence arithmetic, Chinese remainder theorem, integers modulo n, Finite fields, Fermat's little theorem, and Wilson's theorem. Introduction to Algebraic number theory: the Pell equation, the Gaussian integers, Quadratic integers, and the Four square theorem. Quadratic reciprocity and quadratic congruence with composite modules.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH561  General Topology 
(3 credit hours) 
Fundamentals of point set topology: topological spaces, neighborhoods of points, basis, subbases, and weight of spaces. Continuous maps and homeomorphisms, closed and open mappings, quotient mappings. Metric and normal spaces, accountability and separation axioms. Product spaces and quotient spaces. Compactness and connectedness of spaces and properties. Complete metric space and function spaces.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH570  Theory of Partial Differen.Eq. 
(3 credit hours) 
The theory of initial value and boundary value problems for hyperbolic, parabolic, and elliptic partial differential equations, with emphasis on nonlinear equations. More general types of equations and systems of equations. Sequence begins fall.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH572  Theory of Ordinary Diffe Equat 
(3 credit hours) 
Initial Value Problem: Existence and Uniqueness of Solutions; Continuation of Solutions; Continuous and Differential Dependence of Solutions. Linear Systems: Linear Homogeneous And Nonhomogeneous Systems with Constant and Variable Coefficients; Structure of Solutions of Systems with Constant and Periodic Coefficients; Higher Order Linear Differential Equations; Sturmian Theory, Stability: Lyapunov Stability and Instability. Lyapunov Functions; Lyapunov's Second Method; Quasilinear Systems; Linearization; Stability of an Equilibrium and Stable Manifold Theorem for Nonautonomous Differential Equations.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH573  Dynamical Systems&Chaos Theory 
(3 credit hours) 
Discrete time dynamical systems. Continuous time dynamical systems. Invariant manifolds, homoclinic orbits, global bifurcations. Hamiltonian systems, completely integrable systems, KAM theory. Different mechanisms for chaotic dynamics, symbolic dynamics, Applications in physics, biology and economics.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH598  Selected Topics 
(3 credit hours) 
Selected reading and indepth discussions of current and emerging issues in the field. May be repeated for credit to a maximum of 3 credit hours.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH599  Independent Study 
(3 credit hours) 
Topics to be assigned and approved by Advisory Committee and the Program Committee. May be repeated for credit to a maximum of 3 credit hours.

Prerequisite: 

Corequisite: 

Semester: 
Fall Spring 
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MATH611  Several Complex Variables 
(3 credit hours) 
Power series holomorphic functions, representation by integrals, extension of functions holomorhpically to convex domain. Local theory of analytic sets (Weierstrass preparation theorem and consequences). Functions and sets in the projective space P (theorems of Weierstrass and Chow and extensions).

Prerequisite: 

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Semester: 
Fall Spring 
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MATH612  Measure Theory 
(3 credit hours) 
Metric space topology, continuity, convergence, equicontinuity, compactness, bounded variation, Helly selection theorem, Riemann?Stieltjes integral, Lebesque measure, abstract measure space, Lpspaces, Holder and Minkowski inequalities, RieszFischer theorem.

Prerequisite: 
 MATH510

Corequisite: 

Semester: 
Fall Spring 
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MATH616  Functional Analysis 
(3 credit hours) 
Fundamentals of functional analysis, Banach space, HahnBanach theorem, principle of uniform boundedness. Closed graph and open mapping theorem, applications, Hilbert spaces, orthonormal sets, spectral theorem for Hermitian operators and for compact operators.

Prerequisite: 
 MATH510

Corequisite: 

Semester: 
Fall Spring 
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MATH622  Finite Element Methods 
(3 credit hours) 
Numerical methods for partial differential equations, Finite difference methods for elliptic equations, stability and error estimates of finite difference methods. Finite difference methods for heat equations. Preliminaries of finite element methods, Variational formulation, existence and uniqueness, Cea’s theorem, Construction of finite element spaces, Barycentric coordinates, Polynomial approximation theory, BrambleHilbert Theorem, transformation formula.

Prerequisite: 

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Semester: 
Fall Spring 
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MATH633  Seminar I 
(1 credit hours) 
Students taking this course are expected to participate actively and regularly to the departmental seminars, in which they are required to present at least one talk of their choice or may be related to any material suggested by their advisor.

Prerequisite: 

Corequisite: 

Semester: 
All 
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MATH634  Seminar II 
(1 credit hours) 
This course is a continuation of Math. 633. Students are expected to participate in the departmental seminar and present at least one talk. The topic of their talk(s) must be related to their thesis.

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Semester: 
Fall Spring 
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MATH640  Algebra II 
(3 credit hours) 

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Semester: 
Fall Spring 
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MATH662  Algebraic Topology 
(3 credit hours) 
Fundamental group and covering spaces, simplicial and singular homology theory with applications, cohomology theory, duality theorem. Homotopy theory, fibration, relations between homotopy and homology, obstruction theory, and topic from spectral sequences, cohomology operations, and characteristic classes.

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Semester: 
Fall Spring 
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MATH670  Adv. Partial Differential Equ. 
(3 credit hours) 
Boundary Value Problems, the Mollifier theorem, basic facts about Hilbert space, FourierSobolev spaces, advanced properties of Sobolev spaces, Hspace duality, weak formulation of elliptic boundary value problems, spectral properties of elliptic operators, evolution equations, Parabolic and Hyperbolic equations, linear operators, Introduction to simegroups, the HilleYosida theorem, the LumerPhilips theorem, Alternative development of S/G’s, summary of Sg results, analytic semigroups, nonlinear boundary value problems.

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Semester: 
Fall Spring 
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MATH675  The Mathematics of Finance 
(3 credit hours) 
Introduction to the Mathematics’ of financial models. Hedging, pricing by arbitrage. Discrete and continuous stochastic models. Martingales. Brownian motion, stochastic calculus. BlackScholes model, adaptations to dividend paying equities, currencies and couponpaying bonds, interest rate market, foreign exchange models.

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Semester: 
Fall Spring 
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MATH695  Independent Studies 
(3 credit hours) 
Graduate students will study topics related to their Ph.D. thesis independently. The selection of these topics will be with the consent of advisor.

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Semester: 
Fall Spring 
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MATH701  Applied Numerical Methods 
(2 credit hours) 
Error Analysis, solving nonlinear equations in one variable Bisection method, fixed point method, Newton?s method solving linear system of equations Gaussian elimination method, Choleski?s method interpolation Lagrange interpolation, Newton?s interpolation, Numerical differentiation and integration.

Prerequisite: 

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Semester: 
Fall Spring 
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MATH702  Applied Num. & Stat. Methods 
(3 credit hours) 
Initial and boundary value problems for ordinary differential equations. Formulation and numerical solution of parabolic, elliptic, and hyperbolic PDE?s using finite difference discretizations. Probability distributions, modeling random samples and parameter estimation, Inferences on underlying mean, variance, and proportion, Linear and multiple regressions, confidence intervals, Statistical analysis of field data. Applications in Electrical Engineering.

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Corequisite: 

Semester: 
Fall Spring 
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