Comprehensive Exam Track: Total Credit Hours Required to Finish the Degree ( 36 Credit Hours ) as Follows
Specialization Requirements
Students must pass all of the following courses
|
Course Number |
Course Name |
Weekly Hours |
Cr. Hrs. |
Prerequisite |
||
|---|---|---|---|---|---|---|
|
Theoretical |
Practical |
|||||
| 151026000 | ADVANCED RESEARCH METHODS | The course prepares students for conducting scientific research and development of their thesis work. It provides content on the logic of inquiry and the necessity for an empirical approach to practice. It also addresses the process of formulating appropriate research questions, objectives, and hypotheses, techniques for reviewing literature, approaches for testing relationships and patterns among variables, methods of data collection and analysis, methods for assessing and improving the validity and reliability of data and measurements, and the ethics of scientific research. Some practical experience on various novel topics in Applied Mathematics can be employed for satisfying the mentioned goals. | 3 | - | 3 |
- |
| 151026030 | ADVANCED ORDINARY DIFFERENTIAL EQUATIONS | Existence and uniqueness of solutions for nth order linear differential equations, existence and uniqueness for systems of differential equations, dependence of solution on function and initial conditions, phase-plane and autonomous systems, Sturm-Liouville boundary value problems and orthogonal functions. | 3 | - | 3 |
- |
| 151026040 | ADVANCED PARTIAL DIFFERENTIAL EQUATIONS | First order equations, theory of characteristics and classifications, Cauchy problem of higher order equations, wave equation, heat equation, Laplace equation, Green's functions. | 3 | - | 3 |
- |
| 151026130 | REAL ANALYSIS | Algebra of sets, the Cantor-Bernstein theorem, Borel sets, measurable sets, Lebesgue measure, measurable functions, the Riemann and the Lebesgue integrals, differentiation and integration, general measure and integration theory. | 3 | - | 3 |
- |
| 151026150 | FUNCTIONAL ANALYSIS | Review of topological spaces, metric spaces, linear Spaces, the Hahn-Banach theorem, normed linear spaces, Hilbert spaces, the Inverse, adjoint and self-adjoint operators, spectrum and resolvent, compact operators. | 3 | - | 3 |
151026130 REAL ANALYSIS Algebra of sets, the Cantor-Bernstein theorem, Borel sets, measurable sets, Lebesgue measure, measurable functions, the Riemann and the Lebesgue integrals, differentiation and integration, general measure and integration theory. |
| 151026310 | NUMERICAL ANALYSIS | Numerical methods for ordinary differential equations and partial differential equations, matrix eigenvalue problems, numerical integration. | 3 | - | 3 |
- |
| 151026810 | MATHEMATICAL STATISTICS | Review of probability distributions and transformations of random variables, sufficient and minimal sufficient statistics, completeness, point estimation, Cramer-Rao inequality, minimum variance unbiased estimates, moments, maximum likelihood and least square estimation methods, test of hypotheses, Neyman-Pearson lemma, randomized tests, uniformly most powerful tests, confidence intervals, order statistics. | 3 | - | 3 |
- |
| 151026830 | OPERATIONS RESEARCH | Decision theory and games, inventory models, queuing theory and some optimization techniques. | 3 | - | 3 |
- |
| 151026950 | SEMINAR | An advanced study in an applied mathematics topic. The student must submit by the end of the course a thesis-style report and present it. | 3 | - | 3 |
- |
Students must pass ( 9 ) credit hours from any of the following courses
|
Course Number |
Course Name |
Weekly Hours |
Cr. Hrs. |
Prerequisite |
||
|---|---|---|---|---|---|---|
|
Theoretical |
Practical |
|||||
| 151026120 | COMPLEX ANALYSIS | Analytic functions, power series, Conformal mappings, zeros and poles, calculus of residues, the argument principle, definite integrals, harmonic functions, the mean value property, Poisson’s formula, Schwarz’s theorem, the reflection principle, Weierstrass’ theorem, Taylor and Laurent Series, partial fractions, infinite products | 3 | - | 3 |
- |
| 151026210 | TOPICS IN MODELING | In this course,the students study advanced topics in the filed of Modeling. | 3 | - | 3 |
- |
| 151026410 | APPLIED LINEAR ALGEBRA | Iterative methods for systems of equations, inner product spaces, least squares, projections, minimal polynomial, Jordan canonical form, LU, QR, Cholesky, and LDL factorizations. | 3 | - | 3 |
- |
| 151026710 | TOPICS IN APPLIED MATHEMATICS | In this course,the students study advanced topics in the applied field of Mathematics. | 3 | - | 3 |
- |
| 151026730 | INTEGRAL EQUATIONS | Classification of integral equation, classification of kernels, Fredholm integral equation, Volterra integral equation, Fredholm Alternative theorem, Applications to Ordinary differential equations, Green’s Function approach, Singular integral equations, Laplace Transform Method approach. | 3 | - | 3 |
- |
| 151026740 | MATHEMATICAL PHYSICS | Coordinate systems, complex variables and applications, infinite series and their uses in differential equations, multiple integrals, Fourier series, Green's functions, calculus of variations, partial differential equations in physics, special functions, distributions, Monte Carlo simulation methods, tensors. | 3 | - | 3 |
- |
| 151026760 | GRAPH THEORY AND COMBINATORICS WITH APPLICATIONS | Connected and disconnected graphs, trees, graph planarity, Hamiltonian circuits and Euler tours, coloring, matching, graph algorithms (flow, optimization, etc), recurrence relations, generating functions, inclusion-exclusion principle, Ramsey theory, applications in telecommunications, networks, parallel processing and multiprocessors. | 3 | - | 3 |
- |
| 151026780 | INTRODUCTION TO WAVELETS | Heisenberg Uncertainty Principle and the Shannon Sampling Theorem Haar Wavelet, Haar Basis, Definition of a Wavelet Inversion Formula, Plancherel’s Formula, Discrete Wavelet Transform, Continuous Wavelet Transform, Fast Wavelet Transform Multiresolution analysis, wavelets in higher dimensions, orthonormal waveletswith compact support, applications in differential equations, signal processing, computergraphics and medical imaging, computer vision, and quantum mechanics. | 3 | - | 3 |
- |
| 151026840 | TOPICS IN OPERATIONS RESEARCH | In this course,the students study advanced topics in the field of Operations Research. | 3 | - | 3 |
- |
| 151026860 | TOPICS IN APPLIED STATISTICS | In this course,the students study advanced topiccs in the field of Applied Statistics. | 3 | - | 3 |
- |
| 151026870 | APPLIED PROBABILITY | Stochastic Processes, Markov Chains, Markov Processes, Renewal Theory, Brownian Motion | 3 | - | 3 |
- |
| 151026910 | OPTIMIZATION | Classical optimization theory, Newton-type, and conjugate gradient methods for unconstrained optimization, Karush-Kuhn-Tucker conditions for optimality. nonlinear programming, integer programming, optimality conditions, saddle points, dual problems, anticycling, penalties, decomposition, minimax theorems, convex functions, introduction to calculus of variations. | 3 | - | 3 |
- |
Thesis\Treatise Track: Total Credit Hours Required to Finish the Degree ( 36 Credit Hours ) as Follows
Specialization Requirements
Students must pass all of the following courses plus ( 6 ) credit hours for the Thesis
|
Course Number |
Course Name |
Weekly Hours |
Cr. Hrs. |
Prerequisite |
||
|---|---|---|---|---|---|---|
|
Theoretical |
Practical |
|||||
| 151026000 | ADVANCED RESEARCH METHODS | The course prepares students for conducting scientific research and development of their thesis work. It provides content on the logic of inquiry and the necessity for an empirical approach to practice. It also addresses the process of formulating appropriate research questions, objectives, and hypotheses, techniques for reviewing literature, approaches for testing relationships and patterns among variables, methods of data collection and analysis, methods for assessing and improving the validity and reliability of data and measurements, and the ethics of scientific research. Some practical experience on various novel topics in Applied Mathematics can be employed for satisfying the mentioned goals. | 3 | - | 3 |
- |
| 151026030 | ADVANCED ORDINARY DIFFERENTIAL EQUATIONS | Existence and uniqueness of solutions for nth order linear differential equations, existence and uniqueness for systems of differential equations, dependence of solution on function and initial conditions, phase-plane and autonomous systems, Sturm-Liouville boundary value problems and orthogonal functions. | 3 | - | 3 |
- |
| 151026040 | ADVANCED PARTIAL DIFFERENTIAL EQUATIONS | First order equations, theory of characteristics and classifications, Cauchy problem of higher order equations, wave equation, heat equation, Laplace equation, Green's functions. | 3 | - | 3 |
- |
| 151026130 | REAL ANALYSIS | Algebra of sets, the Cantor-Bernstein theorem, Borel sets, measurable sets, Lebesgue measure, measurable functions, the Riemann and the Lebesgue integrals, differentiation and integration, general measure and integration theory. | 3 | - | 3 |
- |
| 151026150 | FUNCTIONAL ANALYSIS | Review of topological spaces, metric spaces, linear Spaces, the Hahn-Banach theorem, normed linear spaces, Hilbert spaces, the Inverse, adjoint and self-adjoint operators, spectrum and resolvent, compact operators. | 3 | - | 3 |
151026130 REAL ANALYSIS Algebra of sets, the Cantor-Bernstein theorem, Borel sets, measurable sets, Lebesgue measure, measurable functions, the Riemann and the Lebesgue integrals, differentiation and integration, general measure and integration theory. |
| 151026310 | NUMERICAL ANALYSIS | Numerical methods for ordinary differential equations and partial differential equations, matrix eigenvalue problems, numerical integration. | 3 | - | 3 |
- |
| 151026810 | MATHEMATICAL STATISTICS | Review of probability distributions and transformations of random variables, sufficient and minimal sufficient statistics, completeness, point estimation, Cramer-Rao inequality, minimum variance unbiased estimates, moments, maximum likelihood and least square estimation methods, test of hypotheses, Neyman-Pearson lemma, randomized tests, uniformly most powerful tests, confidence intervals, order statistics. | 3 | - | 3 |
- |
| 151026830 | OPERATIONS RESEARCH | Decision theory and games, inventory models, queuing theory and some optimization techniques. | 3 | - | 3 |
- |
Students must pass ( 6 ) credit hours from any of the following courses
|
Course Number |
Course Name |
Weekly Hours |
Cr. Hrs. |
Prerequisite |
||
|---|---|---|---|---|---|---|
|
Theoretical |
Practical |
|||||
| 151026120 | COMPLEX ANALYSIS | Analytic functions, power series, Conformal mappings, zeros and poles, calculus of residues, the argument principle, definite integrals, harmonic functions, the mean value property, Poisson’s formula, Schwarz’s theorem, the reflection principle, Weierstrass’ theorem, Taylor and Laurent Series, partial fractions, infinite products | 3 | - | 3 |
- |
| 151026210 | TOPICS IN MODELING | In this course,the students study advanced topics in the filed of Modeling. | 3 | - | 3 |
- |
| 151026410 | APPLIED LINEAR ALGEBRA | Iterative methods for systems of equations, inner product spaces, least squares, projections, minimal polynomial, Jordan canonical form, LU, QR, Cholesky, and LDL factorizations. | 3 | - | 3 |
- |
| 151026710 | TOPICS IN APPLIED MATHEMATICS | In this course,the students study advanced topics in the applied field of Mathematics. | 3 | - | 3 |
- |
| 151026730 | INTEGRAL EQUATIONS | Classification of integral equation, classification of kernels, Fredholm integral equation, Volterra integral equation, Fredholm Alternative theorem, Applications to Ordinary differential equations, Green’s Function approach, Singular integral equations, Laplace Transform Method approach. | 3 | - | 3 |
- |
| 151026740 | MATHEMATICAL PHYSICS | Coordinate systems, complex variables and applications, infinite series and their uses in differential equations, multiple integrals, Fourier series, Green's functions, calculus of variations, partial differential equations in physics, special functions, distributions, Monte Carlo simulation methods, tensors. | 3 | - | 3 |
- |
| 151026760 | GRAPH THEORY AND COMBINATORICS WITH APPLICATIONS | Connected and disconnected graphs, trees, graph planarity, Hamiltonian circuits and Euler tours, coloring, matching, graph algorithms (flow, optimization, etc), recurrence relations, generating functions, inclusion-exclusion principle, Ramsey theory, applications in telecommunications, networks, parallel processing and multiprocessors. | 3 | - | 3 |
- |
| 151026780 | INTRODUCTION TO WAVELETS | Heisenberg Uncertainty Principle and the Shannon Sampling Theorem Haar Wavelet, Haar Basis, Definition of a Wavelet Inversion Formula, Plancherel’s Formula, Discrete Wavelet Transform, Continuous Wavelet Transform, Fast Wavelet Transform Multiresolution analysis, wavelets in higher dimensions, orthonormal waveletswith compact support, applications in differential equations, signal processing, computergraphics and medical imaging, computer vision, and quantum mechanics. | 3 | - | 3 |
- |
| 151026840 | TOPICS IN OPERATIONS RESEARCH | In this course,the students study advanced topics in the field of Operations Research. | 3 | - | 3 |
- |
| 151026860 | TOPICS IN APPLIED STATISTICS | In this course,the students study advanced topiccs in the field of Applied Statistics. | 3 | - | 3 |
- |
| 151026870 | APPLIED PROBABILITY | Stochastic Processes, Markov Chains, Markov Processes, Renewal Theory, Brownian Motion | 3 | - | 3 |
- |
| 151026910 | OPTIMIZATION | Classical optimization theory, Newton-type, and conjugate gradient methods for unconstrained optimization, Karush-Kuhn-Tucker conditions for optimality. nonlinear programming, integer programming, optimality conditions, saddle points, dual problems, anticycling, penalties, decomposition, minimax theorems, convex functions, introduction to calculus of variations. | 3 | - | 3 |
- |
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