WSU Graduate Courses - Mathematics/MTH

MTH 503 DIFFERENTIAL EQUATIONS II (Credits: 3)

Examples of systems of differential equations, complex and repeated eigenvalues, solutions of systems, matrix exponential, qualitative behavior of first-order equations, planar systems and stability, almost linear systems, and energy methods.

PREREQUISITE: MTH 233, MTH 253.

MTH 516 NUMERICAL METHODS FOR DIGITAL COMPUTERS (Credits: 4)

Introduction to numerical methods used in the sciences. Includes methods of interpolation, data smoothing, functional approximation, integration, solutions of systems of equations, and solutions of ordinary differential equations. 3 hours lecture, 2 hours lab

PREREQUISITE: MTH 231, EITHER MTH 253 OR 255, AND ONE OF
CS 142, CS 220, CS 241, EGR 153.

MTH 516 NUMERICAL METHODS FOR DIGITAL COMPUTERS LABORATORY (Credits: )

MTH 517 NUMERICAL METHODS FOR DIGITAL COMPUTERS (Credits: 4)

An introduction to numerical methods used in the sciences.Includes methods of interpolation, data smoothing, functional approximation, integration, solutions of systems of equations, and solutions of ordinary differential equations.

PREREQUISITE: MTH 233, MTH 316, AND EITHER MTH 253 OR
MTH 355.

MTH 517 NUMERICAL METHODS FOR DIGITAL COMPUTERS LABORATORY (Credits: )

MTH 532 COMPLEX VARIABLES (Credits: 3)

Topics discussed include power series expansion, the formula of Cauchy, residues, conformal mappings, and elementary functions in the complex domain.

PREREQUISITE: MTH 232.

MTH 533 PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS (Credits: 3)

Partial differential equations, boundary value problems, eigenfunctions, Fourier series, and applications

PREREQUISITE: MTH 232 AND MTH 233.

MTH 581 ELEMENTARY NUMBER THEORY (Credits: 3)

Divisibility properties of integers, prime numbers, congruences, the Chinese remainder theorem, quadratic reciprocity law, Mobius inversion formula, Euler f-function, other number-theoretic functions.

MTH 599 SELECTED TOPICS (Credits: 1 TO 5)

Selected topics in mathematics. May be taken for letter grade or pass/unsatisfactory.

PREREQUISITE: PRE REQUISITES MTH 232, 253, AND 233 OR MTH 235
OR EQUIVALENT.

MTH 603 ADVANCED ENGINEERING MATHEMATICS I (Credits: 4)

Ordinary differential equations, linear algebra, systems and qualitative theory of ordinary differential equations, numerical methods, Fourier series and integrals, Fourier and Laplace transforms, partial differential equations, vector spaces.

PREREQUISITE: MTH 233.

MTH 604 ADVANCED ENGINEERING MATHEMATICS II (Credits: 4)

Linear transformations, applications and properties of matrices, vector calculus, calculus of variations, functions of a complex variable, series, residues, poles, stability, conformal mapping.

PREREQUISITE: MTH 603.

MTH 606 MATHEMATICAL MODELING (Credits: 3)

Structure and properties of mathematical models. Size effects, dimensional analysis, graphical methods, comparative statics, stability, optimization techniques, probabilistic models, and Monte Carlo simulation.

PREREQUISITE: MTH 233 AND MTH 253 OR MTH 355, OR PERMISSION
OF INSTRUCTOR.

MTH 607 OPTIMIZATION TECHNIQUES (Credits: 3)

Concepts of minima and maxima; linear programming; simplex method, sensitivity, and duality; transportation and assignment problems; and dynamic programming.

PREREQUISITE: MTH 233, AND EITHER MTH 253 OR 255.

MTH 610 THEORETICAL FOUNDATIONS OF COMPUTING (Credits: 4)

Turing machines; m-recursive functions; equivalence of computing paradigms; Church-Turing thesis; undecidability; intractability. 3 hours lecture, 2 hours lab.

PREREQUISITE: CS 666.

MTH 610 FOUNDATIONS OF COMPUTING LABORATORY (Credits: )

Turing machines; m-recursive functions; equivalence of computing paradigms; Church-Turing thesis; undecidability; intractability. 3 hours lecture, 2 hours lab.

MTH 614 INTRODUCTION TO MATHEMATICAL SOFTWARE (Credits: 3)

Solving scientific problems using computational software packages MATLAB and MATHEMATICA, including procedural and functional programming.

PREREQUISITE: MTH 233 AND MTH 253, OR INSTRUCTOR PERMISSION.

MTH 615 INTRODUCTION TO SCIENTIFIC COMPUTATION (Credits: 4)

In a hands-on multidisciplinary setting, the student will use modern computational techniques to simulate phenomena, running and modifying existing programs.

PREREQUISITE: A YEAR OF PHYSICS, MTH 314/614 OR MTH 416/616
OR MTH 717; MTH 306/606 OR COURSES IN PROBABILITY
AND STATISTICS; OR PERMISSION OF INSTRUCTOR.

MTH 616 MATRIX COMPUTATIONS (Credits: 4)

Survey of numerical methods in linear algebra emphasizing practice with high-level computer tools. Topics include Gaussian elimination, LU decomposition, numerical eigenvalue problems, QR factorization, least squares, singular value decompositions, and iterative methods.

PREREQUISITE: MTH 253 OR 355; CS 142 OR 241.

MTH 619 CRYPTOGRAPHY AND DATA SECURITY (Credits: 3)

Introduces the mathematical principles of data security. Various developments in cryptography discussed, including public-key encryption, digital signatures, data encryption standard (DES), and key safeguarding schemes.

PREREQUISITE: MTH 253 OR 255.

MTH 623 ADVANCED LOGIC (Credits: 3 TO 4)

(Offered jointly with the Department of Philosophy.)This course treats logic as an object rather than a subject.Although it contains extensions to higher order logic, its main concern will be with the use of logic and with the limitations of logical systems.

PREREQUISITE: PHL 123 AND 323, OR ONE OF THESE TOGETHER WITH
ONE MATH COURSE BEYOND CALCULUS, OR CONSENT OF
INSTRUCTOR.

MTH 631 REAL VARIABLES I (Credits: 3)

Functions, sequences, limits, continuity, differentiability, integration, and mean-value theorems.

PREREQUISITE: MTH 232 OR EQUIVALENT.

MTH 632 REAL VARIABLES II (Credits: 3)

Infinite series, uniform convergence, Taylor series, improper integrals, special functions, and Fourier series.

PREREQUISITE: MTH 631.

MTH 633 REAL VARIABLES III (Credits: 3)

Theory of functions of several variables and vector-valued functions.

PREREQUISITE: MTH 632.

MTH 634 INTRODUCTION TO COMPLEX ANALYSIS (Credits: 5)

Complex arithmetic, differentiation (analytic functions, the Cauchy-Riemann equations), elementary functions and their mapping properties, integration (Cauchy's theorem, Cauchy integral Formula), Taylor and Laurent series, poles, residues, the residue theorem.

PREREQUISITE: MTH 232 IS REQUIRED. (MTH 431 IS RECOMMENDED).

MTH 650 DESCRETE ALGEBRAIC STRUCTURES (Credits: 3)

Introduces several abstract algebraic structures and their models that are used in computer science. Examples include semigroups, finite-state machines, and groups and cod.

PREREQUISITE: MTH 253 OR 255 OR EQUIVALENT.

MTH 651 INTRODUCTION TO MODERN ALGEBRA I (Credits: 3)

Introduction to abstract algebraic structures including groups, rings, integral domains, and fields.

PREREQUISITE: MTH 231.

MTH 652 INTRODUCTION TO MODERN ALGEBRA II (Credits: 3)

Introduction to abstract algebraic structures including groups, rings, integral domains, and fields.

PREREQUISITE: MTH 651.

MTH 655 ADVANCED LINEAR ALGEBRA (Credits: 3)

Vector spaces and subspaces, basis and dimension, linear transformations and matrices, eigenvalues and eigenvectors, inner product spaces.

PREREQUISITE: MTH 255 OR PERMISSION OF INSTRUCTOR.

MTH 656 CODING THEORY (Credits: 3)

Introduction to the essentials of error-correcting codes, the study of methods for efficient and accurate transfer of information. Topics covered include basic concepts, perfect and related codes, cyclic codes,
and BCH codes.

PREREQUISITE: MTH 253 OR MTH 355 (OR EQUIVALENT).

MTH 657 COMBINATORICS (Credits: 3)

Topics from permutations, combinatorics, generating functions, recurrence relations, and Polya-s theory of counting

PREREQUISITE: MTH 231 AND AT LEAST JUNIOR STANDING.

MTH 658 APPLIED GRAPH THEORY (Credits: 3)

Introduction to methods, results, and algorithms from graph theory. Emphasis on graphs as mathematical models applicable to organizational and industrial situations.

PREREQUISITE: MTH 231, AND EITHER CS 142 OR 241.

MTH 659 COMBINATORIAL TOOLS FOR COMPUTER SCIENCE (Credits: 3)

Introduction to some of the mathematical tools needed for an understanding of computer programming. Topics covered are summations, elementary number theory, combinatorial identities, generating functions, and asymptotics.

MTH 671 GEOMETRY (Credits: 3)

Topics in the foundation of Euclidean geometry, introduction to non-Euclidean and other geometries.

PREREQUISITE: MTH 231.

MTH 672 PROJECTIVE GEOMETRY (Credits: 3)

Projective and affine planes and spaces. Change of coordinates. Projective transformations. Conics.

PREREQUISITE: MTH 231.

MTH 675 DIFFERENTIAL GEOMETRY (Credits: 4)

Calculus on Euclidean space, Frame fields, calculus on a surface, shape operators, and geometry of surfaces in Euclidean 3 space.

PREREQUISITE: MTH 232.

MTH 680 METHODS OF APPLIED MATHEMATICS: GEOMETRIC METHODS (Credits: 3)

Basic mathematical tools for the description of physical systems in three dimensions. Vector and tensor analysis, curvilinear coordinate systems, calculus of variations, Lagrangian mechanics, Lagrange multipliers.

PREREQUISITE: MTH 232, AND EITHER MTH 253 OR 255.

MTH 681 METHODS OF APPLIED MATHEMATICS: DIFFERENTIAL EQUATIONS (Credits: 3)

Solution methods for ordinary differential equations commonly arising in physics and engineering. Systems of equations, stability theory, Liapunov's methods, autonomous systems, existence and uniqueness of solutions, Poincare phase plane.

PREREQUISITE: MTH 233; MTH 355 OR 480.

MTH 682 METHODS OF APPLIED MATHEMATICS: INTEGRAL METHODS (Credits: 3)

Use of integral transforms in the solution of differential and integral equations. Fourier series, Fourier and Laplace transforms distributions, integral equations, Greens functions, Sturm-Liouville theory, perturbation methods and asymptotics, orthogonal functions, special functions.

PREREQUISITE: MTH 332 OR 434; MTH 355 OR 480.

MTH 688 INDEPENDENT READING (Credits: 1 TO 5)

Titles vary.

MTH 699 SELECTED TOPICS (Credits: 1 TO 5)

Selected topics in mathematics.

MTH 700 PRINCIPLES OF INSTRUCTION IN MATHEMATICS (Credits: 3)

Survey of available instructional materials and discussion of educational theory and techniques leading to more effective instruction.

MTH 716 NUMERICAL ANALYSIS I: APPLIED LINEAR ALGEBRA (Credits: 4)

Topics chosen with emphasis on computational linear algebra. Systems of linear equations and Gaussian elimination; computation of eigenvalues and eigenvectors; matrix exponential; norm and condition number; and iterative methods.

PREREQUISITE: MTH 355 AND CS 142 (OR KNOWLEDGE OF A HIGH
LEVEL LANGUAGE) OR PERMISSION OF INSTRUCTOR.

MTH 717 NUMERICAL ANALYSIS II: FINITE DIFFERENCE METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (Credits: 4)

Finite difference methods for partial differential equations; analysis of stability and convergence

PREREQUISITE: MTH 333, 431, 716 OR PERMISSION OF INSTRUCTOR.

MTH 718 NUMERICAL ANALYSIS III: FINITE ELEMENT METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (Credits: 4)

Finite element methods for elliptic boundary value problems, analysis of errors, approximation by finite element spaces, effects of curved boundaries, numerical integration, and finite element methods for parabolic problems.

PREREQUISITE: MTH 333, 431, 716 OR PERMISSION OF INSTRUCTOR.

MTH 725 COMPUTATIONAL LOGIC (Credits: 4)

Introduces predicate logic as an inference system, emphasizing refutation procedures, problem reduction, and resolution. A basis for studying logic programming and artificial intelligence.

PREREQUISITE: CS 400 OR EQUIVALENT AND DEPARTMENTAL
PERMISSION.

MTH 730 PRINCIPLES OF ANALYSIS (Credits: 4)

Metric spaces: convergence, completeness, compactness, Ascoli-Arzela theorem. Stone-Weierstrass theorem. Banach spaces. Dual of Lp, of C[a,b].

PREREQUISITE: MTH 633.

MTH 731 REAL ANALYSIS I (Credits: 4)

Lebesque measure and integration on the real line. Convergence theorems, differentiation of integrals, functions of bounded variation, and absolute continuity.

PREREQUISITE: MTH 730.

MTH 732 REAL ANALYSIS II (Credits: 4)

LP spaces and their bounded linear functionals. Banach spaces, Hahn-Banach theorem, and closed-graph theorem. Hilbert space, Riesz representation theorem, orthonormal bases, and general measure spaces.

PREREQUISITE: MTH 731 OR EQUIVALENT.

MTH 733 REAL ANALYSIS III (Credits: 4)

Outer measure, measure, integration, general convergence theorems, Radon-Nikodym theorem, product measure, and Fubini's theorem.

PREREQUISITE: MTH 732 OR EQUIVALENT.

MTH 751 ALGEBRA I (Credits: 4)

Group theory-isomorphism theorems, Jordan-Holder theorem, permutation groups, Sylow theorems, finitely generated Abelian groups, and free groups.

PREREQUISITE: MTH 355, MTH 452 OR EQUIVALENT.

MTH 752 ALGEBRA II (Credits: 4)

Ring theory-polynomial rings, unique factorization, radicals, and Wedderburn-Artin structure theory.

PREREQUISITE: MTH 751.

MTH 753 ALGEBRA III (Credits: 4)

Field theory-simple extensions, Galois theory, solvability by radicals, cyclotomy, finite fields, and Wedderburn's theorem.

PREREQUISITE: MTH 752.

MTH 777 APPLIED ANALYSIS I (Credits: 4)

Function spaces, differential and integral equations, fixed point theorems, Hilbert spaces, compact operators, eigenvalues, eigenfunction expansions, and Sturm-Liouville problems.

PREREQUISITE: MTH 730.

MTH 778 APPLIED ANALYSIS II (Credits: 4)

Inverse operators, fixed-point theorems, compactness, variational methods, and functional analysis of numerical methods.

PREREQUISITE: MTH 777.

MTH 792 SPECIAL PROBLEMS (Credits: 1 TO 5)

Titles vary.

MTH 799 SELECTED TOPICS (Credits: 1 TO 5)

Selected topics in mathematics.

MTH 899 GRADUATE RESEARCH (Credits: 1 TO 18)

Titles vary.