Course descriptions for Applied Mathematics

MAR125 - INTRODUCTION TO FINITE MATHEMATICS (3-0)

(NO CREDIT) Meets last 6 weeks of quarter.

An introduction to the elements of set theory and mathematical reasoning. Topics covered include; symbolic logic (propositional calculus, truth tables, predicates, and quantifiers); methods of proof (direct and indirect proof, mathematical induction, case analysis and counter examples); sets and set operations; relations and functions.

MA0810 - THESIS RESEARCH (0-8)

Every student conducting thesis research will enroll in this course.

MA1000 - COLLEGE ALGEBRA (2-0)

Real number system, complex numbers, exponents and radicals, algebraic expressions and operations, linear and quadratic equations, inequalities, functions and graphs, polynomials and their zeros, rational functions, exponential and logarrithmic functions, systems of equations, matrices.

MA1010 - ALGEBRA AND TRIGONOMETRY (4-0)

Real number system, complex numbers, exponents and radicals, algebraic expressions and operations, linear and quadratic equations, inequalities, functions and graphs, polynomials and their zeros, rational functions, exponential and logarrithmic functions, systems of equations, matrices, trigonometry and unit circles, trigonometric identities and functions.

MA1025 - FINITE MATHEMATICS FOR OPERATIONS RESEARCH (4-0)

An introductory course in logic and elementary discrete mathematics to be taken by students in Operations Research and Mathematics in their refresher quarter. Considerable emphasis is placed on propositional and predicate logic and on techniques of proof in mathematics. Mathematical topics include sets, functions, and relations. Coverage of combinatorics includes an introduction to permutations, combinations, the pigeon-hole principle, and the principle of inclusion/exclusion. No previous experience with this material is assumed.

MA1113 - SINGLE VARIABLE CALCULUS I (4-0)

Review of analytic geometry and trigonometry, functions of one variable, limits, derivatives, continuity and differentiability; differentiation of algebraic, trigonometric, logarithmic and exponential functions with applications to maxima and minima, rates, differentials; product rule, quotient rule, chain rule; anti-derivatives, integrals and the fundamental theorem of calculus; definite integrals, areas. Taught at the rate of nine hours per week for five weeks.
Prerequisite: Precalculus mathematics.

MA1114 - SINGLE VARIABLE CALCULUS II with Matrix Algebra (4-0)

Topics in Calculus include applications of integration, special techniques of integration, infinite series, convergence tests, and Taylor series. Matrix algebra topics covered are: the fundamental algebra of matrices including addition, multiplication of matrices, multiplication of a matrix by a constant and a column (vector) by a matrix; elementary matrices and inverses, together with the properties of these operations; solutions to mxn systems of linear algebraic equations using Gaussian elimination and the LU decomposition (without pivoting); determinants, properties of determinants; and a brief introduction to the arithmetic of complex numbers and DeMoivre’s theorem. Taught at the rate of nine hours per week for five weeks.
Prerequisite: MA1113

MA1115 - Multivariable Calculus (4-0)

Vector algebra and calculus, directional derivative, gradient, polar coordinates and parametric equations, functions of several independent variables, limits, continuity, partial derivatives, chain rule, maxima and minima, double and triple integrals, cylindrical and spherical coordinate systems. Taught at the rate of nine hours per week for five weeks.
Prerequisite: MA1114.

MA1116 - VECTOR CALCULUS (3-0)

The calculus of vector fields; directional derivative, gradient, divergence, curl; potential fields; Green’s, Stokes’, and the divergence integral theorems. Applications in engineering and physics. Taught at the rate of seven hours per week for five weeks
Prerequisites: MA1115

MA2043 - Introduction to Matrix and Linear Algebra (4-0)

The fundamental algebra of vectors and matrices including addition, scaling, and multiplication will be covered, including block operations with vectors and matrices. Other topics covered by the course include: algorithms for computing the LU (Gauss) factorization of an NxM matrix with pivoting; matrix representation of systems of linear equations and their solution via the LU factorization; basic properties of determinants; matrix inverses; linear transformations and change of basis; the four fundamental subspaces and the fundamental theorem of linear algebra; and eigenvalues/eigenvectors of matrices.
Prerequisites: EC1010 (May be taken concurrently.)

MA2121 - DIFFERENTIAL EQUATIONS (4-0)

Ordinary differential equations: linear and nonlinear (first order) equations, homogeneous and non-homogeneous equations, linear independence of solutions, power series solutions, systems of differential equations, Laplace transforms. Applications include radioactive decay, elementary mechanics, mechanical and electrical oscillators, forced oscillations and resonance.
Prerequisites: MA1114,

MA2300 - MATHEMATICS FOR MANAGEMENT (5-0)

Mathematical basis for modern managerial tools and techniques. Elements of functions and algebra; differential calculus of single- and multi- variable functions; integration (antidifferentiation) of single-variable functions. Applications of the derivative to rates of change, curve sketching, and optimization, including the method of Lagrange multipliers.
Prerequisite: College algebra.

MA3001 - INCREMENTED DIRECTED STUDY (1-0)

Provides the opportunity for a student who is enrolled in a 3000 level mathematics course to pursue the course material and its applications in greater depth by directed study to the extent of one additional hour beyond the normal course credit.
Prerequisites: Enrollment in a 3000 level mathematics course.

MA3025 - LOGIC AND DISCRETE MATHEMATICS (5-1)

MA3025 is designed to provide a rigorous foundation in logic and elementary discrete mathematics to students of mathematics and computer science. The emphasis is on logic and its application; the remaining mathematical topics are approached as a sequence of extensions to the predicate calculus. Topics from logic include textual substitution, Boolean expressions, modeling English propositions, propositional calculus, quantification, and elementary predicate calculus. Additional mathematical topics include elements of set theory, induction, relations and functions, and elements of number theory.
Prerequisite: MAR125.

MA3026 - DISCRETE MATHEMATICS WITH APPLICATIONS (5-0)

Graphs, trees, matchings and network flows. Introduction to combinatorial problems and counting techniques. Recurrence relations. Combinatorial circuits and introduction to finite state machines.
Prerequisite: MAR125.

MA3030 - INTRODUCTION TO COMBINATORICS AND ITS APPLICATIONS (4-1)

MA3030 is designed to provide a thorough grounding in elementary combinatorics and its applications to computer science and discrete probability theory to students of computer science who concurrently take MA3025 Logic, Sets, and Functions. Topics from combinatorics include fundamental counting rules, binomial and multinomial theorems, the pigeonhole and inclusion/exclusion principles, and homogeneous and nonhomogeneous recurrence relations. Elementary discrete probability is covered, up to the expectation of a discrete random variable. Coverage of predicate calculus is centered on the resolution principle and its applications. Also included is a brief introduction to algebraic structures.
Corequisite: MA3025.

MA3042 - LINEAR ALGEBRA (4-0)

Finite-dimensional vector spaces, linear dependence, basis and dimension, change of basis. Linear transformations and similarity. Scalar product, inner product spaces. Orthogonal subspaces and least squares. LU (with pivoting), Cholesky, and QR factorizations. Eigenvalues/eigenvectors, diagonalization. Hermitian matrices, quadratic forms, definite matrices. Vector and matrix norms, orthogonal transformations, condition numbers
Prerequisites: MA1115 taken concurrently, MA1114.

MA3046 - MATRIX ANALYSIS (4-1)

Linear algebra from a constructive point of view, important for applications. Gauss and Cholesky factorizations. Orthogonalization, linear least squares problems and the fundamental theorem of linear algebra. Hermitian eigenproblems and singular value decompositions. General eigenproblems. Structured and inverse problems from signal analysis and control.
Prerequisites: MA1043, familiarity with MATLAB.

MA3110 - INTERMEDIATE ANALYSIS (4-0)

Multi-variable calculus integrated with linear algebra. Functions of several variables, continuous transformations, Jacobians, chain rule, implicit function theorem, inverse function theorem, extreme, optimization and Lagrange multiplier technique, difference equations, and convex sets & functions. Applications in Operations Research
Prerequisites: MA1115, MA3042.

MA3132 - PARTIAL DIFFERENTIAL EQUATIONS AND INTEGRAL TRANSFORMS (4-0)

Solution of boundary value problems by separation of variables; Sturm-Liouville problems; Fourier and Bessel series solutions, Fourier transforms; classification of second-order equations; applications, method of characteristics. Applications to engineering and physical science. Satisfies the ESR in differential equations for the Applied Mathematics program
Prerequisite: MA2121 and MA1116.

MA3139 - FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS (4-0)

Fourier series; solution of the one and two-dimensional wave equations, D’Alembert’s solution, frequency and time domain interpretations; Fourier integral transforms and applications to ordinary and partial differential equations and linear systems; Convolution theorems. Course covers basic material essential for signal processing, filtering, transmission, waveguides, and other related problems. Applications include spectral analysis of electronic signals, e.g. radar or sonar. Designed for UW and EW/IW students
Prerequisites: MA1116, and MA2121.

MA3185 - TENSOR ANALYSIS (3-0)

Definition and algebra of tensors. Dyadic representation in Cartesian and general components. Calculus of tensor fields in curvilinear coordinates. Derivation and application of the basic equations of heat conduction, rigid body mechanics, elasticity, fluid mechanics, electromagnetism, Newtonian and Einsteinian orbital mechanics.
Prerequisite: MA1116.

MA3232 - NUMERICAL ANALYSIS (4-0)

Provides the basic numerical tools for understanding more advanced numerical methods. Topics for the course include: Source and Analysis of Computational Error, Solution of Nonlinear Equations, Interpolation, Numerical Integration and Differentiation, and Numerical Solution of Ordinary Differential Equations and Boundary Value Problems.
Prerequisites: MA2121, MA2043 and ability to program in a high level language such as Fortran, C, or Matlab. Credit cannot be obtained for both MA3232 and MA3243.

MA3243 - NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (4-1)

Course designed to familiarize the student with classical finite difference techniques in the numerical solution of partial differential equations. In addition to learning some of the applicable algorithms, the student will be required to do some programming in FORTRAN. Topics covered include: Implicit, Explicit, and Semi-Implicit Methods in the solution of Elliptic and Parabolic PDE's, Iterative Methods for solving Elliptic PDE's (SOR, Gauss- Seidel, Jacobi), the Lax-Wendroff and Explicit methods in the solution of 1st and 2nd order Hyperbolic PDE's.
Prerequisites: MA3132 and ability to program in a high level language such as Fortran, C, or Matlab.

MA3261 - BASIC PARALLEL COMPUTATION (3-0)

The course has two goals: First to introduce some fundamental issues: shared vs. distributed memory, connection topologies, communication algorithms, speedup, efficiency, storage requirements, granularity, pipelining, problem scaling, useful paradigms for algorithm development. Second, to develop working proficiency by designing, implementing and evaluating the performance of several parallel algorithms. These include, but are not limited to numerical quadrature, matrix computations, sorting, network analysis, and dynamic programming.
Prerequisites: MA1115 or MA3026 and a computer language.

MA3301 - LINEAR PROGRAMMING (4-0)

Course taught by OR staff, same as OA3201.

Theory of optimization of linear functions subject to linear constraints The simplex algorithm, duality, sensitivity analyses, parametric linear programming. Applications to resource allocation, manpower planning, transportation and communications, network models, ship scheduling, etc. Introduction to computer-based linear programming systems.
Prerequisites: MA3042, MA3110 and OA3200.

MA3393 - TOPICS IN APPLIED MATHEMATICS (V-0)

Variable hours 1-0 to 4-0.

A selection of topics in applied mathematics. The course content varies and the credit varies. This course is intended to reflect study for the beginning graduate student in an area for which no formal course is taught. Credit for this course may be granted more than one time to an individual student.

MA3400 - MATHEMATICAL MODELING PROCESSES (4-0)

Practice model construction while demonstrating the utility and universality of mathematics. Topics include modeling using graphical analysis, the model building process, modeling using proportionality, analysis of data, modeling using dimensional analysis, dynamical models, optimization of models and simulation. Models investigated include the nuclear arms race, drag force on a submarine, optimization of inventory levels, and fuel consumption.
Prerequisite: MA1115.

MA3560 - MODERN APPLIED ALGEBRA (3-0)

The techniques and tools of abstract algebra. The emphasis is on group theory: classification, subgroups, conjugates, isomorphism, direct products, homeomorphism, and factor groups. The course concludes with a brief look at the theory of rings and field, especially finite fields. Applications may vary, but typically are drawn from topics of interest to DoN/DoD. These include error correcting codes, reliable and secure communications and cryptography. Satisfies the algebra ESR.
Prerequisite: MA3042.

MA3605 - FUNDAMENTALS OF ANALYSIS I (3-0)

The real number system and the usual topology of the real line; properties of continuous functions; differentiation. Functions of bounded variation and theory of Riemann-Stieltjes integration, convergence theorems for sequence and series of functions. Satisfies the analysis ESR for the applied mathematics program.
Prerequisite: MA3110.

MA3606 - FUNDAMENTALS OF ANALYSIS II (3-0)

Continuation of MA3605.
Prerequisite: MA3605.

MA3610 - TOPOLOGY, FRACTALS, AND CHAOTIC DYNAMICS (3-0)

An introductory course on fractals and chaotic dynamics utilizing techniques and ideas of metric space topology. Topics covered include: metric and topological spaces, completeness, the Hausdorff metric on the "space of fractals", affine transformations, iterated function systems, computer generation of fractals, dynamical systems, shift maps on code spaces, characterizations of chaotic dynamics, fractal dimension. Applications include feedback in predator-prey models, light emissions by cluster groups, photosynthesis, and electrical circuits.
Prerequisites: MA1115 and MA2121.

MA3675 - THEORY OF FUNCTIONS OF A COMPLEX VARIABLE I (3-0)

Selected topics from the theory of functions of a complex variable; complex functions, power series, Laurent series. Singularities of complex functions; contour integration and residues; zeros of analytic functions, factors of and infinite product representation for analytic functions; maximum modulus theorems for analytic and harmonic functions; conformal mapping. Applications include interference effects in optics and problems from heat flow and fluid flow.
Prerequisite: MA1115.

MA3676 - THEORY OF FUNCTIONS OF A COMPLEX VARIABLE II (3-0)

Continuation of MA3675.
Prerequisite: MA3675.

MA3730 - THEORY OF NUMERICAL COMPUTATION (3-0)

Analysis of computational methods used for the solution of problems from the areas of algebraic equations, polynomial approximation, numerical differentiation and integration, and numerical solutions of ordinary differential equations.
Prerequisites: MA3042, MA2121.

MA4026 - COMBINATORIAL MATHEMATICS (4-0)

Advanced techniques in enumerative combinatorics and an introduction to combinatorial structures. Topics include generating functions, recurrence relations, elements of Ramsey theory, theorems of Burnside and Polya, and balanced incomplete block designs. Application areas with DoD/DoN relevance range from mathematics to computer science and operations research, including applications in probability, game theory, network design, coding theory, and experimental design.
Prerequisite: MA3025.

MA4027 - GRAPH THEORY AND APPLICATIONS (4-0)

Advanced topics in the theory of graphs and digraphs. Topics include graph coloring, Eulerian and Hamiltonian graphs, perfect graphs, matching and covering, tournaments, and networks. Application areas with DoD/DoN relevance range from mathematics to computer science and operations research, including applications to coding theory, searching and sorting, resource allocation, and network design.
Prerequisite: MA3025 .

MA4101 - INCREMENTED DIRECTED STUDY (1-0)

Provides the opportunity for the student enrolled in a 4000 level mathematics course to pursue the subject under faculty supervision to greater depth. One extra credit is assigned beyond the normal course credit.
Prerequisites: Enrollment in a 4000 level math course.

MA4103 - THESIS TOPICS SEMINAR (3-0)

Explores in depth discrete dynamical systems and the thesis topics of students enrolled in the applied mathematics degree program. Fulfills the ESR to provide students with the experience of organizing and presenting applied mathematical ideas to students and faculty, including a classroom environment.
Graded on a Pass/Fail basis only.

MA4230 - NUMERICAL FUNCTIONAL ANALYSIS (3-0)

Linear functionals, Riesz representation theorem, Hilbert spaces, Sobolev spaces, interpolation and approximation in Hilbert spaces, nonlinear operators, Newton's method.
Prerequisites: MA3232, MA4635.

MA4237 - ADVANCED TOPICS IN NUMERICAL ANALYSIS (V-0)

Variable credit usually 4-0.

The subject matter will vary according to the abilities and interest of those enrolled. Applications of the subject matter to DoD/DoN are discussed.

MA4242 - NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3-1)

Adams formulas, Runge-Kutta formulas, extrapolation methods, implicit formulas for stiff equations; convergence and stability, error estimation and control, order and stepsize selection, applications.
Prerequisite: MA3232.

MA4243 - NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (3-1)

Finite difference methods for parabolic, elliptic, and hyperbolic equations, multi-grid methods; convergence and stability, error estimation and control, numerical solution of finite difference equations, applications.
Prerequisites: MA3232, MA3132, MA4230 suggested.

MA4245 - MATHEMATICAL FOUNDATIONS OF FINITE ELEMENTS (3-1)

Variational formulation of boundary value problems, finite element and boundary element approximations, types of elements, stability, eigenvalue problems.
Prerequisites: MA3232, MA3132.

MA4248 - MATRIX COMPUTATIONS (3-1)

Development of algorithms for matrix computations. Rounding errors and introduction to stability analysis. Stable algorithms for solving systems of linear equations, linear least squares problems and eigenproblems. Iterative methods for linear systems. Structured problems from applications in various disciplines.
Prerequisites: MA3046, advanced matlab programming.

MA4251 - APPLIED APPROXIMATION THEORY (3-1)

Univariate and tensor product spline approximation, interpolation in Hilbert spaces, scattered data approximation, applications.
Prerequisites: MA3232, MA4230.

MA4261 - PARALLEL SCIENTIFIC COMPUTATION (3-2)

General principles of parallel computing, parallel techniques and algorithms, solution of systems of linear equations, eigenvalues and singular value decomposition, domain decomposition and application (e.g., satellite orbit determination and shallow water fluid flow).
Prerequisites: MA3042 or MA3046, MA3132, and MA3232.

MA4301 - NONLINEAR PROGRAMMING (4-0)

Course taught by OR staff, same as OA4201.

Introduction to modern optimization techniques, Karesh-Kuhn- Tucker necessary and sufficient conditions for optimality, quadratic and separable programming, basic gradient search algorithms and penalty function methods. Applications to weapons assignment, force structuring, parameter estimation for nonlinear or constrained regression, personnel assignment and resource allocation.
Prerequisites: OA3201 and MA3110.

MA4302 - DESIGN OF EXPERIMENTS (3-1)

Course taught by OR staff, same as OA4101.

Theory and application of the general linear hypothesis model. Analysis of variance and analysis of covariance. Planning experiments, traditional and hybrid experimental designs. Use of standard computer packages for analysis of experimental data.
Prerequisite: OA3103 or equivalent.

MA4303 - REGRESSION ANALYSIS (4-0)

Course taught by OR staff, same as OA4102.

Construction, analysis and testing of regression models. An in-depth study of regression and its application in operations research, economics and the social sciences.
Prerequisites: OA3102, OA3103 and OA3104.

MA4304 - TIME SERIES ANALYSIS (4-0)

Course taught by OR staff, same as OA4308.

Second order stationary processes. Harmonic analysis of correlation functions. Filters and spectral windows. Ergodic properties. Problems of inference in time series analysis. Box-Jenkins techniques. Introduction to the analysis of multivariate processes.
Prerequisites: OA3301 and OA3104.

MA4311 - CALCULUS OF VARIATIONS (3-0)

Euler equation, Weierstrass condition, Legendre condition, numerical procedures for determining solutions, gradient method, Newton method, Transversality condition, Rayleigh Ritz method, conjugate points. Concepts are related to geometric principles whenever possible.
Prerequisites: MA2121 (programming experience desirable).

MA4312 - TOPICS IN CALCULUS OF VARIATIONS (3-0)

Topics covering extensions of concepts presented in MA4311.
Prerequisites: MA4311 and computer programming.

MA4321 - STABILITY, BIFURCATION AND CHAOS (3-0)

Differential equations and dynamical systems, equilibrium of autonomous systems, stability, Liapunov's method, examples of chaos, local bifurcations of vector fields and maps, chaotic dynamical systems.
Prerequisite: MA4620.

MA4322 - PRINCIPLES AND TECHNIQUES OF APPLIED MATHEMATICS I (3-0)

Linear operators, generalized functions and Hilbert spaces; solutions of partial differential equations by Green's functions and eigenfunctions; variational techniques; Fredholm and Volterra integral equations; asymptotic methods and perturbations. Applications to wave propagation, optimization, fluid dynamics, and numerical methods.
Prerequisites: MA3132 and MA3042. MA3232 strongly recommended.

MA4323 - PRINCIPLES AND TECHNIQUES OF APPLIED MATHEMATICS II (3-0)

Continuation of MA4322.
Prerequisite: MA4322.

MA4332 - PARTIAL DIFFERENTIAL EQUATIONS (3-0)

Diffusion, wave and Laplace equations. Classification of second order equations, discontinuities and signal propagation, transform methods, Green's functions, first order equations and characteristics.
Prerequisite: MA3132.

MA4335 - LINEAR AND NONLINEAR WAVES (3-0)

Analysis of the two main classes of wave motion, hyperbolic waves and linear dispersive waves. Topics covered include: kinematic waves, shock waves, shock structure and shock fitting, Burger's equation, the wave equation, linear dispersive waves, wave patterns and water waves.
Prerequisite: MA3132.

MA4340 - ADVANCED MATHEMATICAL MODELING (3-0)

A course intended to bring advanced mathematical methods to bear on the modeling and study of physical problems. Topics to be discussed include: simple dynamic models, the phase plane, stable and unstable motion, wave motion, bifurcation, catastrophe and chaos.
Prerequisites: MA3400, MA3132.

MA4362 - ORBITAL MECHANICS (3-0)

Review of the two-body problem. The effects of a third point mass and a distributed mass. Expansion of the disturbing potential in series of Legendre functions. Variation of parameter equations for osculating orbital elements. Perturbation and numerical solution techniques. Codes used by the military to predict orbits of artificial satellites and space debris.
Prerequisite: PH2511.

MA4370 - THEORY OF PLATES AND SHELLS (3-0)

Theory of the mathematical theory of thin plates and shells. Analytical and numerical solution techniques. Applications to structures used by the military.
Prerequisite: MA3132

MA4372 - INTEGRAL TRANSFORMS (3-0)

The Laplace, Fourier and Hankel transforms and their inversions; Asymptotic behavior. Applications to problems in engineering and physics.
Prerequisites: MA3132, MA3675.

MA4377 - ASYMPTOTIC AND PERTURBATION METHODS I (3-0)

Advanced course in the application of approximate methods to the study of integrals and differential equations arising in physical problems. Topics covered include: asymptotic sequences and expansions, integrals of a real variable, contour integrals, limit process expansions applied to ordinary differential equations, multiple variable expansion procedures and applications to partial differential equations.
Prerequisite: MA3132.

MA4378 - ASYMPTOTIC AND PERTURBATION METHODS II (3-0)

Advanced course in the application of approximate methods to the study of integrals and differential equations arising in physical problems. Topics covered include: asymptotic sequences and expansions, integrals of a real variable, contour integrals, limit process expansions applied to ordinary differential equations, multiple variable expansion procedures and applications to partial differential equations.
Prerequisite: MA4377.

MA4391 - ANALYTICAL METHODS FOR FLUID DYNAMICS (4-0)

The basic fluid dynamic equations will be derived, and a variety of analytical methods will be applied to problems in viscous flow, potential flow, boundary layers, and turbulence. Applications in aeronautics will be discussed.
Prerequisites: MA3132 or MA3139.

MA4392 - NUMERICAL METHODS FOR FLUID DYNAMICS (4-0)

Numerical methods exclusively will be applied to fluid dynamics problems in viscous flow, potential flow, boundary layers, and turbulence. Applications in aeronautics will be discussed.
Prerequisites: MA4391 and MA3232.

MA4393 - TOPICS IN APPLIED MATHEMATICS (3-0)

A selection of topics in applied mathematics. The course content varies but applications of interest to the DoN/DoD will be discussed. Credit may be granted for taking this course more than once.

MA4560 - CODING AND INFORMATION THEORY (4-0)

Mathematical analysis of the codes used over communication channels is made. Techniques developed for efficient, reliable and secure communication are stressed. Effects of noise on information transmission are analyzed and techniques to combat their effects are developed. Linear codes, finite fields, single and multiple error-correcting codes are discussed. Codes have numerous applications for communication in the military, and these will be addressed.
Prerequisite: MA3560.

MA4565 - ADVANCED MODERN ALGEBRA (3-0)

A continuation of MA3560. Rings, ring homomorphism, integral domains and euclidean domains. Unique factorization rings, polynomial rings. Modules and ideals. Noetherian rings, Field extension and Galois theory
Prerequisite: MA3560.

MA4570 - CRYPTOGRAPHY (4-0)

The methods of secret communication are addressed. Some simple cryptosystems are described and classical techniques of substitution and transposition are considered. The public-key cryptosystems, RSA, Discrete Logarithm and other schemes are introduced. Applications of cryptography and cryptanalysis.
Prerequisite: MA3560.

MA4593 - TOPICS IN ALGEBRA (3-0)

A selection of topics in algebra. Content of the course varies. Credit for taking the course more than once is allowed. Students may select a topic of interest to the DON/DOD, so the course can support the MER's in a variety of curricula.
Prerequisite: MA3560.

MA4595 - MATHEMATICAL FOUNDATIONS OF FAST SIGNAL PROCESSING ALGORITHMS (3-0)

Advanced transform algorithms for signal processing. Generalized Cooley-Tukey, Rader prime factor, and Winograd FFT algorithms. Polynomial rings, the Chinese Remainder theorem for polynomials, quotient fields, and reduced multiplication convolution algorithms. Application to hardware and software design for signal processing systems
Prerequisites: EC3400 or equivalent, and MA3042.

MA4620 - THEORY OF ORDINARY DIFFERENTIAL EQUATIONS (3-0)

Introduction to the modern theory of ordinary differential equations. Systems of equations. Theoretical and constructive methods of solutions.
Prerequisites: MA2121 and MA3042.

MA4635 - FUNCTIONS OF REAL VARIABLES I (3-0)

Semi-continuous functions, absolutely continuous functions, functions of bounded variation; classical Lebesgue measure and integration theory, convergence theorems and Lp spaces. Abstract measure and integration theory, signed measures, Radon-Nikodym theorem; Lebesgue decomposition and product measure; Daniell integrals and integral representation of linear unctionals.
Prerequisite: MA3606.

MA4636 - FUNCTIONS OF REAL VARIABLES II (3-0)

Continuation of MA4635.
Prerequisite: MA4635.

MA4675 - COMPLEX ANALYSIS (3-0)

A continuation of MA3675, MA3676. Differential equations in the complex plane, transform methods, the Wiener-Hopf method, integral equations, discrete Fourier analysis.
Prerequisite: MA3675, MA3676.

MA4693 - TOPICS IN ANALYSIS (3-0)

A selection of topics in analysis. Content of the course varies. Students will be allowed credit for taking the course more than once.
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