25-811. Abstract Algebra

The student should understand the theory of groups, rings and fields.

 

25-821. Scientific Computation I

The student should become familiar with matrix analysis and matrix computation.

 

25-822. Scientific Computation II

The student should become familiar with numerical approximations such as finite element methods in computational electromagnetism.

 

25-833. Stochastic Processes

The student should become familiar with the theory and applications of Stochastic processes.

 

25-851. Ordinary Differential Equations

The purpose of this course is to present techniques of solving ordinary differential equations. The students should become familiar with Boundary Value Problems, Systems of Ordinary Differential Equations, Phase Diagrams and Stability.

 

25-857. Integral Equations

The student should become familiar with the theory and applications of Integral Equations.

 

25-861. Real Analysis

To provide the students with the background in those parts of modern mathematics which have their roots in the classical theory of functions of a real variable. These include the classical theory of functions of a real variable itself, measure and integration, point-set topology, and the theory of normed linear space. 

 

25-871. Complex Analysis

Upon successful completion of this course, the student will be familiar with Complex Analysis and various applications of Complex Analysis physical and engineering disciplines.

 

25-863. Functional Analysis

To provide students theories of Metric Spaces, Hilbert Spaces and Banach Spaces.

 

25-853. Partial Differential Equations

This course is designed to acquaint students to Classifications of Partial Differential Equations, Methods of Solution for the Wave Equation, Laplace's Equation, and the Heat Equation.

 

25-867.   Numerical Analysis

The student should become familiar with advanced techniques for solving numerically large problems in Linear Algebra. In particular, students should become familiar with the effects of ill conditioning, and of ways in which special information about matrices, such as sparsity can be used. An important part of all of this is the consideration of error from various sources and ways of controlling its accumulation.

 

25-883. Wavelet Analysis

The student should become familiar with Wavelets and their applications in signal and image processing.

 

25-887. Image Processing

The student should become familiar with Image Enhancement, Image Restoration, Wavelets and Multiresolution Processing, Image Compression, Morphological Image Processing, Image Segmentation, Representation and Description, and Object Recognition.

 

25-875. Inverse Problems

The student should become familiar with Ill-posed problems, regularization methods, Tikhonov regularization, the discrepancy principle, and the regularization by discretization.

 

25-885. Computational Geometry

The student should become familiar with communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on a sphere, derandomization, convex hulls and Voronoi diagrams, linear programming, geometric sampling and VC-dimension theory, minimum spanning trees, circuit complexity, and multidimensional searching.

 

25-845. Theory of Solitons                           

The aim of the course is to introduce the basic concepts of the mathematical aspects of Soliton Theory. This will include the derivation and the introduction to the Korteweg-de Vries equation; the travelling wave solution, Inverse Scattering Transform; N-soliton solution; Lax pair; Integrals of Motion; Hirota’s bilinear method; Backlund Transform; AKNS (Ablowitz, Kaup, Newell and Segur) scheme; Zakharov-Shabat scheme; Painleve transcedents; Painleve conjecture; perturbation of solitons; adiabatic parameter dynamics; Topological solitons, kinks and anti-kinks, breathers, phonons, skyrimions; Chiral solitons.

 

25-852. Pattern Recognition            

Pattern recognition is integral part of image processing, video surveillance and data mining, which are research areas at Delaware State University. Potential junior researchers in applied mathematics and/or applied optics field need this course to become familiar with techniques that can be subsequently used for identifying interesting phenomena in observed data and/or for design and implementation of stand-alone real-time applications for military and homeland security.

 

25-787. Digital Signal Processing                

The goal of this course is to provide the student with the mathematical tools and techniques for analyzing, modeling, and implementing digital signal processing systems. This course also provides the relevant background knowledge to students of applied mathematics and theoretical physics who need the signal processing tools for the analysis of data obtained during research in their fields.

 

25-850. Mathematical Theory of Algorithms

Main purpose of the course is to provide students with systematic overview about techniques for analysis and design of algorithms and to familiarize the students with notions related to computational complexity, intractability and approximation algorithms. This way, the students will become more capable of designing efficient algorithms for specific tasks in applied mathematics, included but not limited to computational geometry, image processing, video surveillance analysis, data mining, etc.

 

25-854. Numerical Methods for Partial Differential Equations

Numerical methods for Partial Differential Equations (PDEs) are a part of the problem solving skills that are expected to be mastered by most of the university graduates working in a quantitative field. The same fundamental concepts of convection, diffusion, dispersion and non-linearity are used to simulate applications in physics, economics, biology, engineering and social sciences. Quantitative answers for the real world can generally be obtained only from computations. The goal of this course is to provide a basic foundation in numerical methods for PDEs include finite difference method and finite element method.

 

25-843. Advanced Statistics                         

Main purpose of the course is to provide students with systematic overview of advanced statistical techniques that can be useful in their research and future careers. The statistical techniques are applicable in various fields including video surveillance analysis, data mining, natural resources, finance, etc.

 

25-835. Advanced Perturbation Theory    

The aim of the course is to lay an introduction to the perturbation theory to solve ordinary differential equations, partial differential equations as well as integral equations. Topics that will be covered in this course are Regular perturbations; Error Estimates; Periodic solutions and Lindstedt Series, Harmonic Resonance, Duffing’s equation, Multiple Scales, Struble’s Method, Averaging, Krylov-Bogoliubov Method of Averaging, Krylov-Bogoliubov-Mitropoloski generalized method of Averaging; Forced Duffing and Van der Pol’s equations, Wentzel–Kramer–Brillouin–Jeffreys (WKBJ) Approximation, Fredholm’s Alternative, Latta’s method of composite expansion; Matched Asymptotic Expansion. The emphasis in this course is on the adaptation of these mathematical methods and techniques to their swift and effective application in solving advanced problems in applied mathematics and theoretical physics.

 

26-652. Classical Mechanics

Lagrangian formulation, the Kepler problem, Rutherford scattering, rotating coordinate systems, rigid body motion, small oscillations, stability problems, and Hamiltonian formulation.

 

26-655. Computational Methods

Designed to familiarize students with the use of computers in pursuing theoretical research. Numerical analysis techniques and computational methods employed in the study of physical models will be studied.

 

26-661. Solid State Physics

An introductory study of the structure and physical properties of crystalline solids. Included are topics in crystal structure, lattice vibrations, thermal properties of solids, x-ray diffraction, free electron theory and energy based theory.

 

26-665. Statistical Mechanics

Laws of thermodynamics, Boltzmann and quantum statistical distributions, with applications to properties of gases, specific heats of solids, paramagnetism, black body radiation and Bose-Einstein condensation.

 

26-667. Mathematical Methods IV

An advanced treatment of mathematical topics including operators, matrix mathematics, complex variables and eigenvalue problems.

 

26-671-672. Advanced Electromagnetic Theory

Treatment of boundary value problems of electrostatics and magnetostatics, electromagnetic radiation, radiating systems, wave guides, resonating systems and multipole fields.

 

26-675-676. Quantum Mechanics

collision and scattering problems, classification of atomic states and introduction A study of the Schrödinger wave equation, operators and matrices, perturbation theory, to field quantization.

  

Back to Dept Home

 

Back to College Homepage