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.

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 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

MA2025 - BRIDGE TO ADVANCED MATHEMATICS (4-1)

MA2025 is a first course in discrete mathematics for students of mathematics and computer science. Topics include propositional and predicate logic up to the deduction theorem, methods of mathematical proof, naive set theory, properties of functions, sequences and sums, mathematical induction, an introduction to divisibility and congruencies, and an introduction to enumerative combinatorics.
Prerequisites: None, although a review of algebra skills is recommended.

MA2043 - INTRODUCTION TO MATRIX AND LINEAR ALGEBRA (4-0)

The fundamental algebra of vectors and matrices including addition, scaling, and multiplication. Block operations with vectors and matrices. Algorithms for computing the LU (Gauss) factorization of an MxN 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. Introduction to eigenvalues and eigenvectors.
Prerequisites: Students should have mathematical background at the level generally expected of someone with a B.S. in Engineering, i.e. familiarity with Calculus and solid algebra skills. 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 (4-1)

MA3025 provides a rigorous foundation in logic and elementary discrete mathematics to students of mathematics and computer science. Topics from logic include modeling English propositions, propositional calculus, quantification, and elementary predicate calculus. Additional mathematical topics include elements of set theory, mathematical induction, relations and functions, and elements of number theory.
Prerequisite: MA1025 or MA2025

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)

This course provides students in the engineering and physical sciences curricula with an applications-oriented coverage of major topics of matrix and linear algebra. Matrix factorizations (LU, QR, Cholesky), the Singular Value Decomposition, eigenvalues and eigenvectors, the Schur form, subspace computations, structured matrices. Understanding of practical computational issues such as stability, conditioning, complexity, and the development of practical algorithms.
Prerequisites: MA2043 and EC1010

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: Sources and Analysis of Computational Error, Solution of Nonlinear Equations, Interpolation and Other Techniques for Approximating Functions, Numerical Integration and Differentiation, Numerical Solution of Initial and Boundary Value Problems in Ordinary Differential Equations, and Influences of Hardware and Software.
Prerequisites: MA1115, MA2121 and ability to program in MATLAB and MAPLE

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

Course designed to familiarize the student with some analytical techniques as well as 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. 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 the 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 MA3025 and a computer language

MA3301 - LINEAR PROGRAMMING (4-0)

Course taught by OR staff, same as OA3201.
See OA3201

MA3393 - TOPICS IN APPLIED MATHEMATICS (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.
Prerequisite: consent of instructor

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 - APPLIED MODERN ALGEBRA AND NUMBER THEORY (3-0)

This course is devoted to aspects of modern algebra and number theory that directly support applications, principally in communication. The algebraic emphasis is on ring and field theory, with special emphasis on the theory of finite fields, as well as those aspects of group theory that are important in the development of coding theory. Elements of number theory include congruences and factorization. Applications are drawn from topics of interest to DoN/DoD. These include error correcting codes and cryptography.
Prerequisite: MA3025

MA3607 - INTRODUCTION TO REAL ANALYSIS (4-0)

The objective of this course is for students to achieve a solid understanding of the basic concepts, analysis, and proofs in advanced calculus, including: limits, sequences, series, continuous functions, uniform convergence and uniform continuity, differentiation, and Riemann integration. This is a mathematics course in the pure sense. Proofs will be emphasized, and the student will learn how to reproduce, understand, create and enjoy mathematical proofs.
Prerequisite: MA1115

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

An introductory course on chaotic dynamics systems and fractals. Topics covered include: flows on the line, bifurcations, linear systems, phase plane, limit cycles, the Lorenz equations, fractals, and one-dimensional maps. Applications include population growth, laser threshold, the pendulum, relaxation oscillations, and synchronized chaos.
Prerequisites: MA1115 and MA2121

MA3677 - THEORY OF FUNCTIONS OF A COMPLEX VARIABLE (4-0)

Selected topics from the theory of functions of a complex variable; analytic functions, power series, Laurent series. Singularities of analytic functions; contour integration and residues; applications of residues to real integrals and Laplace transforms, zeros of analytic functions, 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: MA1116

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: 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

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.

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.
Prerequisite: consent of instructor

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 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 - COMPUTATIONAL LINEAR ALGEBRA (4-1)

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

MA4261 - DISTRIBUTED SCIENTIFIC COMPUTING (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.
See OA4201


MA4302 - DESIGN OF EXPERIMENTS (3-1)

Course taught by OR staff, same as OA4101.
See OA4101

MA4303 - REGRESSION ANALYSIS (4-0)

Course taught by OR staff, same as OA4102.
See OA4102

MA4304 - TIME SERIES ANALYSIS (4-0)

Course taught by OR staff, same as OA4308.
See OA4308

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)

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: MA3610

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

MA4362 - ASTRODYNAMICS (3-0)

Review of the two-body problem. The effects of a third point mass and a distributed mass.
Expansions of the disturbing potentials in series of Legendre functions. Variation of
parameter equations for osculating orbital elements. Perturbation and numerical solution
techniques. Statistical orbit determination. Codes used by the military to maintain the catalog of artificial satellites and space debris.
Prerequisite: SS2500 or equivalent.

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, MA3677

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.

MA4550 - COMBINATORIAL AND CRYPTOGRAPHIC PROPERTIES OF BOOLEAN FUNCTIONS (4-0)

The course will discuss the Fourier analysis of Boolean functions and the relevant combinatorics with an eye toward cryptography and coding theory. Particular topics will include avalanche features of Boolean functions, correlation immunity and resiliency, bentness, trade-offs among cryptographic criteria and real-life applications in the designs of stream and block ciphers. 
Prerequisites: MA3025

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

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: MA3607

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

Continuation of MA4635.
Prerequisite: MA4635

MA4675 - COMPLEX ANALYSIS (3-0)

A continuation of MA3677. Differential equations in the complex plane, transform methods, the Wiener-Hopf method, integral equations, discrete Fourier analysis.
Prerequisite: MA3677

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.
Prerequisite: consent of instructor

MO1901 - MATHEMATICS FOR ISSO (3-0)

A brief survey of selected calculus and post-calculus topics - single variable derivatives and integrals, infinite series and sequences, complex numbers, and Fourier series and transforms. (This course may not be taken for credit by students in an engineering or science degree program nor may it be used as a prerequisite for any other mathematics course.)
Prerequisites: MA1115

MO1903 - MATHEMATICS FOR ISSO SPACE SYSTEMS OPERATIONS SPECIALIZATION (3-0)

To be taken concurrently with MA1114. The course consists of a brief survey of the following topics: Complex numbers, Fourier series and transforms, and Ordinary Linear Differential Equations. (This course may not be taken for credit by students in an engineering or science degree program, nor may it be used as a prerequisite for any other mathematics course.) Taught at the rate of seven hours per week for five weeks.
Prerequisites: MA1113