MA - Mathematics


MA 101Intermediate AlgebraUNITS: 4 - Offered in Summer
Preparation for MA 103, MA 105, MA 107, MA 111, and MA 114. Reviews main topics from high school Algebra I and Algebra II emphasizing functions and problem solving. Other concepts and skills covered include algebraic operations, factoring, linear equations, graphs, exponents, radicals, complex numbers, quadratic equations, radical equations, inequalities, systems of equations, compound inequalities, absolute value in equations and inequalities. MA 101 may not be counted as credit toward meeting graduation. Credit for MA 101 is not allowed if student has prior credit in any other mathematical course.


MA 103Topics in Contemporary MathematicsUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: MA 101 or equivalent completed in high school
Primarily for students in Humanities and Social Sciences. Illustrations of contemporary uses of mathematics, varying from semester to semester, frequently including sets and logic, counting procedures, probability, modular arithmetic, and game theory.


MA 105Mathematics of FinanceUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: MA 101 or equivalent completed in high school
Simple and compound interest, annuities and their application to amortization and sinking fund problems, installment buying, calculation of premiums of life annuities and life insurance.


MA 107Precalculus IUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: C- or better in MA 101, or a 450 or better on the SAT Subject Test in Mathematics Level 2 or the NCSU Math Skills Test.
Algebra and basic trigonometry; polynomial, rational, exponential, logarithmic and trigonometric functions and their graphs. Credit for MA 107 does not count toward graduation for students in Engineering, College of Sciences, Bio and Ag Engineering (Science Program), Bio Sci (all options), Math Edu, Sci Edu, Textiles, and B.S. degrees in CHASS. Credit is not allowed for both MA 107 and MA 111


MA 108Precalculus IIUNITS: 3 - Offered in Spring Only
Prerequisite: C- or better in MA 107
Algebra, analytic geometry and trigonometry; inequalities, conic sections, complex numbers, sequences and series, solving triangles, polar coordinates, and applications.Credit for MA 108 does not count toward graduation for students in Engineering, College of Sciences, Design, Bio and Ag Engineering (Science Program), Bio Sci (all options), Math Edu, Sci Edu, Textiles, and B.S. degrees in CHASS. Credit is not allowed for both MA 108 and MA 111. Also, MA 108 should not be counted toward the GER mathematical sciences.


MA 111Precalculus Algebra and TrigonometryUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: C- or better in MA 101, or 480 or better on the SAT Subject Test in Mathematics Level 2 or the NCSU Math Skills Test.
Real numbers, functions and their graphs (special attention to polynomial, rational, exponential, logarithmic, and trigonometric functions), analytic trigonometry. Credit in MA 111 does not count toward graduation for students in Engr., College of Sciences., Design, Biological & Ag. Engr. (Science Program), Biological Sci.(all options),Math. Edu., Forestry, & Textiles. Credit is not allowed for both MA 111 and either MA 107 or MA 108.


MA 114Introduction to Finite Mathematics with ApplicationsUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: MA 101 or equivalent completed in high school.
Elementary matrix algebra including arithmetic operations, inverses, and systems of equations; introduction to linear programming including simplex method; sets and counting techniques, elementary probability including conditional probability; Markov chains; applications in the behavioral, managerial and biological sciences. Computer use for completion of assignments.


MA 116Introduction to Scientific Programming (Math)UNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 141, and either COS 100 or E 115; Corequisite: MA 241
Computer-based mathematical problem solving and simulation techniques using MATLAB. Emphasizes scientific programming constructs that utilize good practices in code development, including documentation and style. Covers user-defined functions, data abstractions, data visualization and appropriate use of pre-defined functions. Applications are from science and engineering. Prerequisites: MA 141 and either PMS 100 or E115. Corequisite: MA 241.


MA 121Elements of CalculusUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: MA 107 or 111 with a C- or better, or 480 on the SAT Subject Test in Mathematics Level 2 or the NCSU Math Skills Test, or 2 or better on an AP Calculus exam. Credit is not allowed for both MA 121 and MA 131 or MA 141.
For students who require only a single semester of calculus. Emphasis on concepts and applications of calculus, along with basic skills. Algebra review, functions, graphs, limits, derivatives, integrals, logarithmic and exponential functions, functions of several variables, applications in management, applications in biological and social sciences. Credit is not allowed in more than one of MA 121, 131, 141. MA 121 may not be substituted for MA 131 or MA 141 as a curricular requirement


MA 131Calculus for Life and Management Sciences AUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: C- or better in MA 107 or MA 111, or 520 or better on the SAT Subject Test in Mathematcs Level 2 or the NCSU Math Skills Test, or 2 or better on an AP Calculus exam. Credit is not allowed for both MA 131 and MA 121 or MA 141.
First order finite difference models; derivatives - limits, power rule, graphing, and optimization; exponential and logarithmic functions - growth and decay models; integrals - computation, area, total change; applications in life, management, and social sciences. Credit not allowed for more than one of MA 121, 131, and 141


MA 132Computational Mathematics for Life and Management SciencesUNITS: 1 - Offered in Fall Spring Summer
Prerequisite: C- or better in MA 121 or MA 131
Computational aspects of calculus for the life and management sciences; use of spreadsheets and a computer algebra system; applications to data models, differential equation models, and optimization.


MA 141Calculus IUNITS: 4 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: MA 111 or MA 108 with grade of C- or better, or 550 or better on the SAT Subject Test in Mathematics Level 2 or the NCSU Math Skills Test, or 2 or better on an AP Calculus exam. Credit is not allowed for both MA 141 and MA 121 or MA 131.
First of three semesters in a calculus sequence for science and engineering majors. Functions, graphs, limits, derivatives, rules of differentiation, definite integrals, fundamental theorem of calculus, applications of derivatives and integrals. Use of computation tools. Credit is not allowed for more than one of MA 141, 131, 121


MA 151Calculus for Elementary Education IUNITS: 3 - Offered in Fall Only, Mathematical Sciences
Prerequisite: C- or better in MA 107 or MA 111, or 520 or better on the SAT Subject Test in Mathematcs Level 2 or the NCSU Math Skills Test, or 2 or better on an AP Calculus exam. Credit is not allowed for both MA 131 and MA 121 or MA 141.
Calculus for Elementary Education I is the first semester of a two semester sequence of courses designed for the Elementary Education Program. Topics will include sequences, limit, and derivative. Also, topics related to teaching elementary mathematics will be discussed. Students cannot receive credit for more than one of MA 151, MA 121, MA 131, or MA 141. MA 151 is not an accepted prerequisite for MA 231 and MA 241. This course is restricted to Elementary Education majors only.


MA 152Calculus for Elementary Education IIUNITS: 3 - Offered in Spring Only, Mathematical Sciences
Prerequisite: MA 151
Calculus for Elementary Education II is the second semester of a two semester sequence of courses designed for the Elementary Education Program. Topics will include derivative, integrals, difference equations, and differential equations. Also, topics related to teaching elementary mathematics will be discussed. This course is restricted to Elementary Education majors only. Students cannot receive credit for both MA 152 and MA 121, MA 131, or MA 141. MA 152 is not an accepted prerequisite for MA 241.


MA 205Elements of Matrix ComputationsUNITS: 3 - Offered in Fall and Spring, Mathematical Sciences
Prerequisite: C- in MA 121, 131, or 141
Complex numbers and Euler's formula. Vectors in 2-D and 3-D, lines, planes, vector products and determinants. Vectors in n-D, matrices and matrix products. Algebraic systems, row operations, inverse matrices and LU factors. Least squares, undetermined systems and null and column spaces. Applications to linear systems of differential equations and/or to visualization and image filters. Emphasis is on by-hand computations, but it is to include applications and computing tools. Students cannot receive credit for more than one of MA 205, MA 305, or MA 405.


MA 225Foundations of Advanced MathematicsUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 241
Introduction to mathematical proof with focus on properties of the real number system. Elementary symbolic logic, mathematical induction, algebra of sets, relations, functions, countability. Algebraic and completeness properties of the reals.


MA 231Calculus for Life and Management Sciences BUNITS: 3 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: MA 131. Credit is not allowed for both MA 231 and MA 241.
Differential equations - population growth, flow processes, finance and investment models, systems; functions of several variables - partial derivatives, optimization, least squares, multiple integrals; Lagrange multiplier method - chain rule, gradient; Taylor polynomials and series; numerical methods. MA 121 is not an accepted prerequisite for MA 231.


MA 241Calculus IIUNITS: 4 - Offered in Fall Spring Summer, Mathematical Sciences
Prerequisite: MA 141 with grade of C- or better or AP Calculus credit. Credit is not allowed for both MA 241 and MA 231.
Second of three semesters in a calculus sequence for science and engineering majors. Techniques and applications of integration, elementary differential equations, sequences, series, power series, and Taylor's Theorem. Use of computational tools.


MA 242Calculus IIIUNITS: 4 - Offered in Fall Spring Summer
Prerequisite: MA 241 with grade of C- or better or AP Calculus credit, or Higher Level IB credit.
Third of three semesters in a calculus sequence for science and engineering majors. Vectors, vector algebra, and vector functions. Functions of several variables, partial derivatives, gradients, directional derivatives, maxima and mimima. Multiple integration. Line and surface integrals, Green's Theorem, Divergence Theorems, Stokes' Theorem, and applications. Use of computational tools.


MA 293Special Topics in MathematicsUNITS: 1-6 - Offered in Fall Spring Summer
Freshman-sophomore level experimental course offerings or directed individual study.


MA 302Numerical Applications to Differential EquationsUNITS: 1 - Offered in Fall and Spring
Prerequisite: MA 241
Numerical methods for approximating solutions for differential equations, with an emphasis on Runge-Kutta-Fehlberg methods with stepsize control. Applications to population, economic, orbital and mechanical models.


MA 303Linear AnalysisUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 241
Linear difference equations of first and second order, compound interest and amortization. Matrices and systems of linear equations, eigenvalues, diagonalization, systems of difference and differential equations, transform methods, population problems. Credit not allowed if credit has been obtained for MA 341 or MA 405


MA 305Introductory Linear Algebra and MatricesUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 241 or MA 231 with MA 132
The course is an elementary introduction to matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, Euclidean vector spaces, determinants, eigenvalues and eigenvectors, linear transformations, similarity, and applications such as numerical solutions of equations and computer graphics. Compares with MA 405 Introductory Linear Algebra, more emphasis is placed on methods and calculations,. Credit is not allowed for both MA 305 and MA 405.


MA 308College GeometryUNITS: 3
Prerequisite: MA 225
The axiomatic approach to mathematics. Congruences for triangles. Parallel postulate and consequences. Right triangles. Circles, tangents, chords. Area. Coordinate geometry. Lines and planes in space. Non-Euclidean geometries.


MA (MEA) 315Mathematics Methods in Atmospheric SciencesUNITS: 4 - Offered in Fall Only
Prerequisite: MA 116, MA 141, MA 241; Corequisite: MA 242
For sophomore meteorology and marine science students. A complement to MA 242 designed to prepare students for quantitative atmospheric applications. Topics include an introduction to vectors and vector calculus, atmospheric waves, phase and group velocity, perturbation analysis, fourier decomposition, matrix operations, chaos and predictability. For MY, MMY, and MRM majors only.


MA 325Introduction to Applied MathematicsUNITS: 3 - Offered in Spring Only
Prerequisite: (MA 231 or MA 242) and (MA 116 or CSC 112 or CSC 114 or CSC 116)
Introduces students with multivariable calculus to five different areas of applied mathematics. These areas will be five three-week modules, which lead to higher level courses in the application areas. Topics will vary, and examples of modules areheat and mass transfer, biology and population, probability and finance, acoustic models, cryptography as well as others.


MA (LOG) 335Symbolic LogicUNITS: 3 - Offered in Fall Only, Mathematical Sciences
Introduction to modern symbolic logic; the concept of proof, mathematical induction, recursion and the relationship between formal and informal theories (examples: group theory, Peano arithmetic). The Goedel Theorems and the mathematical study of logic.


MA 341Applied Differential Equations IUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 242 or (MA 132 and MA 231)
Differential equations and systems of differential equations. Methods for solving ordinary differential equations including Laplace transforms, phase plane analysis, and numerical methods. Matrix techniques for systems of linear ordinary differential equations. Credit is not allowed for both MA 301 and MA 341


MA 351Introduction to Discrete Mathematical ModelsUNITS: 3 - Offered in Fall Only
Prerequisite: MA 224, 225, 231 or 241
Basic concepts of discrete mathematics, including graph theory, Markov chains, game theory, with emphasis on applications; problems and models from areas such as traffic flow, genetics, population growth, economics, and ecosystem analysis.


MA 401Applied Differential Equations IIUNITS: 3 - Offered in Fall Spring Summer
Prequisite: MA 341; Credit not allowed for both MA 401 and MA 501
Wave, heat and Laplace equations. Solutions by separation of variables and expansion in Fourier Series or other appropriate orthogonal sets. Sturm-Liouville problems. Introduction to methods for solving some classical partial differential equations.Use of power series as a tool in solving ordinary differential equations. Credit for both MA 401 and MA 501 will not be given


MA 402Computational Mathematics: Models, Methods and AnalysisUNITS: 3 - Offered in Fall Only
Prerequisite: Programming proficiency (Matlab, C++, Java, Fortran, or other language) and PY 2** . Corequisite: MA 341
Introduction to high performance computing and numerical modeling. Matrix models and boundary value problems with an emphasis on heat and mass transfer. Assessments of all approximations in the computational engineering and science process.


MA 403Introduction to Modern AlgebraUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 225
Sets and mappings, equivalence relations, rings, integral domains, ordered integral domains, ring of integers. Other topics selected from fields, polynomial rings, real and complex numbers, groups, permutation groups, ideals, and quotient rings. Credit is not allowed for both MA 403 and MA 407


MA 405Introduction to Linear AlgebraUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 241 (MA 225 recommended); Corequisite: MA 341 is recommended
This course offiers a rigorous treatment of linear algebra, including systems of linear equations, matrices, determinants, abstract vector spaces, bases, linear independence, spanning sets, linear transformations, eigenvalues and eigenvectors, similarity, inner product spaces, orthogonality and orthogonal bases, factorization of matrices. Compared with MA 305 Introductory Linear Algebra, more emphasis is placed on theory and proofs. MA 225 is recommended as a prerequisite. Credit is not allowed for both MA 305 and MA 405


MA 407Introduction to Modern Algebra for Mathematics MajorsUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 225 and MA 405
Elementary number theory, equivalence relations, groups, homomorphisms, cosets, Cayley's Theorem, symmetric groups, rings, polynomial rings, quotient fields, principal ideal domains, Euclidean domains. Credit is not allowed for both MA 403 and MA 407


MA 408Foundations of Euclidean GeometryUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 225
An examination of Euclidean geometry from a modern perspective. The axiomatic approach with alternative possibilities explored using models.


MA 410Theory of NumbersUNITS: 3 - Offered in Spring Only
Prerequisite: One year of calculus
Arithmetic properties of integers. Congruences, arithmetic functions, diophantine equations. Other topics chosen from quadratic residues, the quadratic reciprocity Law of Gauss, primitive roots, and algebraic number fields.


MA (ST) 412Long-Term Actuarial ModelsUNITS: 3 - Offered in Fall Only
Prerequisite: MA 241 or MA 231, Corequisite: MA 421, BUS(ST) 350, ST 301, ST 305, ST 311, ST 361, ST 370, ST 371, ST 380 or equivalent
Long-term probability models for risk management systems. Theory and applications of compound interest, probability distributions of failure time random variables, present value models of future contingent cash flows, applications to insurance, health care, credit risk, environmental risk, consumer behavior and warranties.


MA (ST) 413Short-Term Actuarial ModelsUNITS: 3 - Offered in Spring Only
Prerequisite: MA 241 or MA 231, and one of MA 421, ST 301, ST 305, ST 370, ST 371, ST 380, ST 421.
Short-term probability models for risk management systems. Frequency distributions, loss distributions, the individual risk model, the collective risk model, stochastic process models of solvency requirements, applications to insurance and businessdecisions.


MA (CSC) 416Introduction to CombinatoricsUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: MA 225 or CSC 226
Basic principles of counting: addition and multiplication principles, generating functions, recursive methods, inclusion-exclusion, pigeonhole principle; basic concepts of graph theory: graphs, digraphs, connectedness, trees; additional topics from:Polya theory of counting, Ramsey theory; combinatorial optimization - matching and covering, minimum spanning trees, minimum distance, maximum flow; sieves; mobius inversion; partitions; Gaussian numbers and q-analogues; bijections and involutions; partially ordered sets.


MA 421Introduction to ProbabilityUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 242
Axioms of probability, conditional probability and independence, basic combinatorics, discrete and continuous random variables, joint densities and mass functions, expectation, central, limit theorem, simple stochastic processes.


MA 425Mathematical Analysis IUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 225 (MA 407 desirable)
Real number system, functions and limits, topology on the real line, continuity, differential and integral calculus for functions of one variable. Infinite series, uniform convergence. Credit is not allowed for both MA 425 and MA 511.


MA 426Mathematical Analysis IIUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 425 and 405
Calculus of several variables, topology in n-dimensions, limits, continuity, differentiability, implicit functions, integration. Credit is not allowed for both MA 426 and MA 512.


MA (CSC) 427Introduction to Numerical Analysis IUNITS: 3 - Offered in Fall Only
Prerequisite: MA 341 or 301 and programming language efficiency
Theory and practice of computational procedures including approximation of functions by interpolating polynomials, numerical differentiation and integration, and solution of ordinary differential equations including both initial value and boundary value problems. Computer applications and techniques.


MA (CSC) 428Introduction to Numerical Analysis IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA 405 or MA 305 and programming language proficiency.
Computational procedures including direct and iterative solution of linear and nonlinear equations, matrices and eigenvalue calculations, function approximation by least squares, smoothing functions, and minimax approximations.


MA 430Mathematical Models in the Physical SciencesUNITS: 3 - Offered in Fall Only
Prerequisite: MA 341 and MA 405
Application of mathematical techniques to topics in the physical sciences. Problems from such areas as conservative and dissipative dynamics, calculus of variations, control theory, and crystallography.


MA 432Mathematical Models in Life and Social SciencesUNITS: 3 - Offered in Spring Only
Prerequisite: MA 341, (MA 305 or MA 405), and programming proficiency; Corequisite: (MA 421 or ST 371)
Topics from differential and difference equations, probability, and matrix algebra applied to formulation and analysis of mathematical models in biological and social science (e.g., population growth).


MA 433History of MathematicsUNITS: 3
Prerequisite: One year of calculus
Development of mathematical thought and evolution of mathematical ideas examined in a historical setting. Biographical and historical content supplemented and reinforced by study of techniques and procedures used in earlier eras.


MA 437Applications of AlgebraUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 403 or 407, MA 405
Error correcting codes, cryptography, crystallography, enumeration techniques, exact solutions of linear equations, and block designs.


MA 440Game TheoryUNITS: 3 - Offered in Fall Only
Prerequisite: MA 231 or MA 242
Game Theory as a language for modeling situations involving conflict and cooperation in the social, behavioral, economic, and biological sciences. Backward induction; dominated strategies; Nash equilibria; games with incomplete information; repeated games; evolutionary dynamics.


MA 444Problem Solving Strategies for CompetitionsUNITS: 1 - Offered in Fall Only
Analyze the most common problem-solving techniques and illustrate their use by interesting examples from past Putnam and Virginia Tech math competitions. Problem solving methods are divided into groups and taught by professors of the math department. After the lecture, students practice writing the solutions for the assignment and have informal discussions in the next class.


MA 491Reading in Honors MathematicsUNITS: 1-6 - Offered in Fall and Spring
Prerequisite: Membership in honors program
A reading (independent study) course available as an elective for students participating in the mathematics honors program.


MA 493Special Topics in MathematicsUNITS: 1-6 - Offered in Fall and Spring
Directed individual study or experimental course offerings.


MA 494Major Paper in MathUNITS: 1 - Offered in Fall Spring Summer
Corequisite: MA class at the 400-level or above
Introduces students to one or more forms of writing used in scientific and research environments. Students are required to take a companion math course at the 400-level or above, and adapt writing assignment(s) to the topics in the companion course.Instruction covers all phases of the writing process (planning, drafting, revising, and critiquing other people's work). Emphasis is placed on organizing for needs of a variety of readers; concise, clear expression.


MA 499Independent Research in MathematicsUNITS: 1-6 - Offered in Fall Spring Summer
Study and research in mathematics. Topics for theoretical, modeling or computational investigation. Consent of Department Head. Honors Program should enroll in MA 491H. At most 6 hours total of MA 499 and 491H credit can be applied towards an undergraduate degree.


MA 501Advanced Mathematics for Engineers and Scientists IUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 341; credit not allowed for both MA 501 and MA 401
Survey of mathematical methods for engineers and scientists. Ordinary differential equations and Green's functions; partial differential equations and separation of variables; special functions, Fourier series. Applications to engineering and science. Not for credit by mathematics majors. Credit for this course and MA 401 is not allowed


MA 502Advanced Mathematics for Engineers and Scientists IIUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 341.
Determinants and matrices; line and surface integrals, integral theorems; complex integrals and residues; distribution functions of probability. Not for credit by mathematics majors. Any student receiving credit for MA 502 may receive credit for, atmost, one of the following: MA 405, MA 512, MA 513


MA (OR) 504Introduction to Mathematical ProgrammingUNITS: 3 - Offered in Fall Only
Prerequisite: MA 242, MA 405
Basic concepts of linear, nonlinear and dynamic programming theory. Not for majors in OR at Ph.D. level.


MA (ISE) (OR) 505Linear ProgrammingUNITS: 3 - Offered in Fall Only
Prerequisite: MA 405
Introduction including: applications to economics and engineering; the simplex and interior-point methods; parametric programming and post-optimality analysis; duality matrix games, linear systems solvability theory and linear systems duality theory; polyhedral sets and cones, including their convexity and separation properties and dual representations; equilibrium prices, Lagrange multipliers, subgradients and sensitivity analysis.


MA 507Analysis For Secondary TeachersUNITS: 3 - Offered in Fall and Summer, Offered Alternate Years
Prerequisite: Graduate standing
A course to update and broaden secondary teacher's capability and point-of-view with respect to topics in analysis. Historical development, logical refinement and applications of concepts such as limits, continuity, differentiation and integration. May be taken for graduate credit for certificate renewal by secondary school teachers. Credit towards graduate degree may be allowed only for students in mathematics education.


MA 508Geometry For Secondary TeachersUNITS: 3 - Offered in Spring and Summer, Offered Alternate Years
Prerequisite: Graduate standing
Topics in geometry of concern to secondary teachers in their work and provision for background and enrichment. Various approaches to study of geometry, including vector geometry, transformational geometry and axiomatics. Course may be taken for graduate credit and for certificate renewal by secondary school teachers. Credit towards a graduate degree may be allowed only for students in mathematics education.


MA 509Abstract Algebra For Secondary TeachersUNITS: 3 - Offered in Fall and Summer, Offered Alternate Years
Prerequisite: Graduate standing
From advanced viewpoint, an investigation of topics in algebra from high school curriculum. Theory of equations, polynomial rings, rational functions and elementary number theory. Course may be taken for graduate credit for certificate renewal by secondary school teachers. Credit towards a graduate degree may be allowed only for students in mathematics education.


MA 510Selected Topics In Mathematics For Secondary TeachersUNITS: 3 - Offered in Summer, Offered Alternate Years
Prerequisite: Graduate standing
Coverage of various topics in mathematics of concern to secondary teachers. Topics selected from areas such as mathematics of finance, probability, statistics, linear programming and theory of games, intuitive topology, recreational math, computers and applications of mathematics. Course may be taken for graduate credit for certification renewal by secondary school teachers. Credit towards a graduate degree may be allowed only for students in mathematics education.


MA 511Advanced Calculus IUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 341
Fundamental theorems on continuous functions; convergence theory of sequences, series and integrals; the Riemann integral. Credit for both MA 425 and MA 511 is not allowed


MA 512Advanced Calculus IIUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 341
General theorems of partial differentiation; implicit function theorems; vector calculus in 3-space; line and surface integrals; classical integral theorems. Credit will not be given for both MA 426 and MA 512.


MA 513Introduction To Complex VariablesUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: MA 242
Operations with complex numbers, derivatives, analytic functions, integrals, definitions and properties of elementary functions, multivalued functions, power series, residue theory and applications, conformal mapping.


MA 515Analysis IUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 426
Metric spaces: contraction mapping principle, Tietze extension theorem, Ascoli-Arzela lemma, Baire category theorem, Stone-Weierstrass theorem, LP spaces. Banach spaces: linear operators, Hahn-Banach theorem, open mapping and closed graph theorems. Hilbert spaces: projection theorem, Riesz representation theorem, Lax-Milgram theorem, complete orthonormal sets.


MA 518A First Course in Differential GeometryUNITS: 3 - Offered in Fall Only
Prerequisite: MA 405 and proficiency in multivariable calculus
Geometry of curves and surfaces in space; Arclength, torsion, and curvature of curves; Tangent spaces, shape operators, and curvatures of surfaces; metrics, covariant derivatives, geodesics, and holonomy. Applications in the physical sciences and/or projects using computer algebra.


MA 520Linear AlgebraUNITS: 3 - Offered in Fall Only
Prerequisite: MA 405
Vector spaces. Bases and dimension. Changes of basis. Linear transformations and their matrices. Linear functionals. Simultaneous triangularization and diagonalization. Rational and Jordan canonical forms. Bilinear forms.


MA 521Abstract Algebra IUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 405 and MA 407
Groups, normal subgroups, quotient groups, Cayley's theorem, Sylow's theorem. Rings, ideals and quotient rings, polynomial rings. Elements of field theory.


MA 522Computer AlgebraUNITS: 3 - Offered in Fall Only
Prerequisite: MA 407 or MA 521 and MA 405 or MA 520
Basic techniques and algorithms of computer algebra. Integer arithmetic, primality tests and factorization of integers, polynomial arithmetic, polynomial factorization, Groebner bases, integration in finite terms.


MA 523Linear Transformations and Matrix TheoryUNITS: 3 - Offered in Fall Only
Prerequisite: MA 405
Vector spaces, linear transformations and matrices, orthogonality, orthogonal transformations with emphasis on rotations and reflections, matrix norms, projectors, least squares, generalized inverses, definite matrices, singular values.


MA 524Combinatorics IUNITS: 3 - Offered in Fall Only
Prerequisite: MA 405 and MA 407
Enumerative combinatorics, including placements of balls in bins, the twelvefold way, inclusion/exclusion, sign-reversing involutions and lattice path enumeration. Partically ordered sets, lattices, distributive lattices, Moebius functions, and rational generating functions.


MA 526Algebraic GeometryUNITS: 3 - Offered in Fall Only
Prerequisite: MA 521
Abstract theory of solutions of systems of polynomial equations. Topics covered: ideals and affine varieties, the Nullstellensatz, irreducible varieties and primary decomposition, morphisms and rational maps, computational aspects including Groebner bases and elimination theory, projective varieties and homogeneous ideals, Grassmannians, graded modules, the Hilbert function, Bezout's theorem.


MA (E) (OR) 531Dynamic Systems and Multivariable Control IUNITS: 3 - Offered in Fall Only
Prerequisite: MA 341, MA 405
Introduction to modeling, analysis and control of linear discrete-time and continuous-time dynamical systems. State space representations and transfer methods. Controllability and observability. Realization. Applications to biological, chemical, economic, electrical, mechanical and sociological systems.


MA 532Ordinary Differential Equations IUNITS: 3 - Offered in Fall Only
Prerequisite: MA 341, 405, 425 or 511, Corequisite: MA 426 or 512
Existence and uniqueness theorems, systems of linear equations, fundamental matrices, matrix exponential, nonlinear systems, plane autonomous systems, stability theory.


MA 534Introduction To Partial Differential EquationsUNITS: 3 - Offered in Fall Only
Prerequisite: MA 425 or MA 511, MA 341, Corequisite: MA 426 or 512
Linear first order equations, method of characteristics. Classification of second order equations. Solution techniques for the heat equation, wave equation and Laplace's equation. Maximum principles. Green's functions and fundamental solutions.


MA 537Nonlinear Dynamics and ChaosUNITS: 3 - Offered in Spring Only
Prerequisite: MA 341 and MA 405
Usage of computer experiments for demonstration of nonlinear dynamics and chaos and motivation of mathematical definitions and concepts. Examples from finance and ecology as well as traditional science and engineering. Difference equations and iteration of functions as nonlinear dynamical systems. Fixed points, periodic points and general orbits. Bifurcations and transition to chaos. Symbolic dynamics, chaos, Sarkovskii's Theorem, Schwarzian derivative, Newton's method and fractals.


MA 540Uncertainty Quantification for Physical and Biological ModelsUNITS: 3 - Offered in Spring Only, Offered Alternate Even Years
Prerequisite: MA 341 and basic knowledge of probability, linear algebra, and scientific computation
Introduction to uncertainty quantification for physical and biological models. Parameter selection techniques, Bayesian model calibration, propagation of uncertainties, surrogate model construction, local and global sensitivity analysis.


MA 544Computer Experiments In Mathematical ProbabilityUNITS: 3 - Offered in Spring Only
Prerequisite: MA 421
Exposure of student to practice of performing mathematical experiments on computer, with emphasis on probability. Programming in an interactive language such as APL, MATLAB or Mathematica. Mathematical treatment of random number generation and application of these tools to mathematical topics in Monte Carlo method, limit theorems and stochastic processes for purpose of gaining mathematical insight.


MA (ST) 546Probability and Stochastic Processes IUNITS: 3 - Offered in Fall Only
Prerequisite: MA 421 and MA 425 or MA 511
Modern introduction to Probability Theory and Stochastic Processes. The choice of material is motivated by applications to problems such as queueing networks, filtering and financial mathematics. Topics include: review of discrete probability and continuous random variables, random walks, markov chains, martingales, stopping times, erodicity, conditional expectations, continuous-time Markov chains, laws of large numbers, central limit theorem and large deviations.


MA 547Financial MathematicsUNITS: 3 - Offered in Spring Only
Prerequisite: MA(ST) 546
Stochastic models of financial markets. No-arbitrage derivativepricing. From discrete to continuous time models. Brownian motion, stochastic calculus, Feynman-Kac formula and tools for European options and equivalent martingale measures. Black-Scholes formula. Hedging strategies and management of risk. Optimal stopping and American options. Term structure models and interest rate derivatives. Stochastic volatility models.


MA 551Introduction to TopologyUNITS: 3 - Offered in Fall Only
Prerequisite: MA 426
Set theory, topological spaces, metric spaces, continuous functions, separation, cardinality properties, product and quotient topologies, compactness, connectedness.


MA 555Introduction to Manifold TheoryUNITS: 3 - Offered in Spring Only
Prerequisite: MA 426 or MA 512
(See MA - Mathematics.)


MA 561Set Theory and Foundations Of MathematicsUNITS: 3 - Offered in Spring Only
Prerequisite: MA 407
Logic and axiomatic approach, the Zermelo-Fraenkel axioms and other systems, algebra of sets and order relations, equivalents of the Axiom of Choice, one-to-one correspondences, cardinal and ordinal numbers, the Continuum Hypothesis.


MA (CSC) (OR) 565Graph TheoryUNITS: 3 - Offered in Fall Only, Offered Alternate Even Years
Prerequisite: CSC 224 or MA 351.
Basic concepts of graph theory. Trees and forests. Vector spaces associated with a graph. Representation of graphs by binary matrices and list structures. Traversability. Connectivity. Matchings and assignment problems. Planar graphs. Colorability. Directed graphs. Applications of graph theory with emphasis on organizing problems in a form suitable for computer solution.


MA (BMA) 573Mathematical Modeling of Physical and Biological Processes IUNITS: 3 - Offered in Fall Only
Prerequisite: MA 341 and knowledge of high-level programming language.
Introduction to model development for physical and biological applications. Mathematical and statistical aspects of parameter estimation. Compartmental analysis and conservation laws, heat transfer, and population and disease models. Analytic and numerical solution techniques and experimental validation of models. Knowledge of high-level programming languages required.


MA (BMA) 574Mathematical Modeling of Physical and Biological Processes IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA/BMA 573
Model development, using Newtonian and Hamiltonian principles, for acoustic and fluid applications, and structural systems including membranes, rods, beams, and shells. Fundamental aspects of electromagnetic theory. Analytic and numerical solution techniques and experimental validation of models.


MA (CSC) 580Numerical Analysis IUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 405; MA 425 or MA 511; high-level computer language
Algorithm behavior and applicability. Effect of roundoff errors, systems of linear equations and direct methods, least squares via Givens and Householder transformations, stationary and Krylov iterative methods, the conjugate gradient and GMRES methods, convergence of method.


MA (CSC) 583Introduction to Parallel ComputingUNITS: 3 - Offered in Spring Only
Prerequisite: CSC 302 or MA 402 or MA/CSC 428 or MA/CSC 580
Introduction to basic parallel architectures, algorithms and programming paradigms; message passing collectives and communicators; parallel matrix products, domain decomposition with direct and iterative methods for linear systems; analysis of efficiency, complexity and errors; applications such as 2D heat and mass transfer.


MA 584Numerical Solution of Partial Differential Equations--Finite Difference MethodsUNITS: 3 - Offered in Fall Only
Prerequisite: MA 501; knowledge of a high level programming language
Survey of finite difference methods for partial differential equations including elliptic, parabolic and hyperbolic PDE's. Consideration of both linear and nonlinear problems. Theoretical foundations described; however, emphasis on algorithm design and implementation.


MA 587Numerical Solution of Partial Differential Equations--Finite Element MethodUNITS: 3 - Offered in Spring Only
Prerequisite: MA 501; knowledge of a high level programming language
Introduction to finite element method. Applications to both linear and nonlinear elliptic and parabolic partial differential equations. Theoretical foundations described; however, emphasis on algorithm design and implementation.


MA 591Special TopicsUNITS: 1-6 - Offered in Fall and Spring


MA 676Master's ProjectUNITS: 3 - Offered in Fall Spring Summer
Investigation of some topic in mathematics to a deeper and broader extent than typically done in a classroom situation. For the applied mathematics student the topic usually consists of a realistic application of mathematics to student's minor area.A written and oral report on the project required.


MA 685Master's Supervised TeachingUNITS: 1-3 - Offered in Fall Spring Summer
Prerequisite: Master's student
Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.


MA 688Non-Thesis Masters Continuous Registration - Half Time RegistrationUNITS: 1 - Offered in Fall Spring Summer
Prerequisite: Master's student
For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain half-time continuous registration to complete incomplete grades, projects, final master's exam, etc.


MA 689Non-Thesis Master Continuous Registration - Full Time RegistrationUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: Master's student
For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain full-time continuous registration to complete incomplete grades, projects, final master's exam, etc. Students may register for this course a maximum of one semester.


MA 690Master's ExaminationUNITS: 1-6 - Offered in Fall Spring Summer
Prerequisite: Master's student
For students in non thesis master's programs who have completed all other requirements of the degree except preparing for and taking the final master's exam.


MA 693Master's Supervised ResearchUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Master's student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.


MA 695Master's Thesis ResearchUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Master's student
Thesis Research


MA 696Summer Thesis ResearchUNITS: 1 - Offered in Summer
Prerequisite: Master's student
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.


MA 699Master's Thesis PreparationUNITS: 1-3 - Offered in Fall Spring Summer
Prerequisite: Master's student
For students who have completed all credit hour requirements and full-time enrollment for the master's degree and are writing and defending their thesis. Credits Arranged


MA (OR) (ST) 706Nonlinear ProgrammingUNITS: 3 - Offered in Spring Only
Prerequisite: OR(IE,MA) 505 and MA 425
An advanced mathematical treatment of analytical and algorithmic aspects of finite dimensional nonlinear programming. Including an examination of structure and effectiveness of computational methods for unconstrained and constrained minimization. Special attention directed toward current research and recent developments in the field.


MA (ISE) (OR) 708Integer ProgrammingUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: MA 405, OR (MA,IE) 505, Corequisite: Some familiarity with computers (e.g., CSC 112)
General integer programming problems and principal methods of solving them. Emphasis on intuitive presentation of ideas underlying various algorithms rather than detailed description of computer codes. Students have some "hands on" computing experience that should enable them to adapt ideas presented in course to integer programming problems they may encounter.


MA 715Analysis IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA 515
Integration: Legesgue measure and integration, Lebesgue-dominated convergence and monotone convergence theorems, Fubini's theorem, extension of the fundamental theorem of calculus. Banach spaces: Lp spaces, weak convergence, adjoint operators, compact linear operators, Fredholm-Fiesz Schauder theory and spectral theorem.


MA 716Advanced Functional AnalysisUNITS: 3 - Offered in Fall Only, Offered Alternate Years
Prerequisite: MA 715
Advanced topics in functional analysis such as linear topological spaces; Banach algebra, spectral theory and abstract measure theory and integration.


MA (OR) 719Vector Space Methods in System OptimizationUNITS: 3 - Offered in Fall Only
Prerequisite: MA 405, 511
Introduction to algebraic and function-analytic concepts used in system modeling and optimization: vector space, linear mappings, spectral decomposition, adjoints, orthogonal projection, quality, fixed points and differentials. Emphasis on geometricinsight. Topics include least square optimization of linear systems, minimum norm problems in Banach space, linearization in Hilbert space, iterative solution of system equations and optimization problems. Broad range of applications in operations research and system engineering including control theory, mathematical programming, econometrics, statistical estimation, circuit theory and numerical analysis.


MA 720Lie AlgebrasUNITS: 3 - Offered in Spring Only
Prerequisite: MA 520, MA 521
Definition of Lie algebras and examples. Nilpotent, solvable and semisimple Lie algebras. Engel's theorem, Lie's Theorem, Killing form and Cartan's criterion. Weyl's theorem on complete reducibility. Representations of s1(2,C). Root space decomposition of semisimple Lie algebras. Root system and Weyl group.


MA 721Abstract Algebra IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA 521
Field extensions, Galois theory, modules, tensor products, exterior products.


MA 722Computer Algebra IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA 522
Effective algorithms for symbolic matrices, commutative algebra, real and complex algebraic geometry, and differential and difference equations. The emphasis is on the algorithmic aspects.


MA 723Theory of Matrices and ApplicationsUNITS: 3 - Offered in Spring Only
Prerequisite: MA 520 or 523
Canonical forms, functions of matrices, variational methods, perturbation theory, numerical methods, nonnegative matrices, applications to differential equations, Markov chains.


MA 724Combinatorics IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA 524
Polytopes(V-polytopes and H-polytopes). Fourier-Motzkin elimination, Farkas Lemma, face numbers of polytopes, graphs of polytopes, linear programming for geometers, Balinski's Theorem, Steinitz' Theorem, Schlegel diagrams, polyhedral complexes, shellability, and face rings.


MA 725Lie Algebra Representation TheoryUNITS: 3 - Offered in Fall Only, Offered Alternate Odd Years
Prerequisite: MA 720
Semisimple Lie algebras, root systems, Weyl groups, Cartan matrices and Dynkin diagrams, universal enveloping algebras, Serre's Theorem, Kac-Moody algebras, highest weight representations of finite dimensional semisimple algebras and affine Lie algebras, Kac-Weyl character formula.


MA (E) (OR) 731Dynamic Systems and Multivariable Control IIUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: MA 531
Stability of equilibrium points for nonlinear systems. Liapunov functions. Unconstrained and constrained optimal control problems. Pontryagin's maximum principle and dynamic programming. Computation with gradient methods and Newton methods. Multidisciplinary applications.


MA 732Ordinary Differential Equations IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA 532, Corequisite: MA 515
Existence-uniqueness theory, periodic solutions, invariant manifolds, bifurcations, Fredholm's alternative.


MA 734Partial Differential EquationsUNITS: 3 - Offered in Spring Only
Prerequisite: MA 534, Corequisite: MA 515
Linear second order parabolic, elliptic and hyperbolic equations. Initial value problems and boundary value problems. Iterative and variational methods. Existence, uniqueness and regularity. Nonlinear equations and systems.


MA (ST) 746Introduction To Stochastic ProcessesUNITS: 3 - Offered in Spring Only
Prerequisite: MA 405 and MA(ST) 546 or ST 521
Markov chains and Markov processes, Poisson process, birth and death processes, queuing theory, renewal theory, stationary processes, Brownian motion.


MA (ST) 747Probability and Stochastic Processes IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA(ST) 546
Fundamental mathematical results of probabilistic measure theory needed for advanced applications in stochastic processes. Probability measures, sigma-algebras, random variables, Lebesgue integration, expectation and conditional expectations w.r.t.sigma algebras, characteristic functions, notions of convergence of sequences of random variables, weak convergence of measures, Gaussian systems, Poisson processes, mixing properties, discrete-time martingales, continuous-time markov chains.


MA (ST) 748Stochastic Differential EquationsUNITS: 3 - Offered in Fall Only
Prerequisite: MA(ST) 747
Theory of stochastic differential equations driven by Brownian motions. Current techniques in filtering and financial mathematics. Construction and properties of Brownian motion, wiener measure, Ito's integrals, martingale representation theorem, stochastic differential equations and diffusion processes, Girsanov's theorem, relation to partial differential equations, the Feynman-Kac formula.


MA 753Algebraic TopologyUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: MA 551
Homotopy, fundamental group, covering spaces, classification of surfaces, homology and cohomology.


MA 755Introduction To Riemannian GeometryUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: MA 555
Tensor algebra on vector spaces and tensor fields on manifolds; Koszul connections; parallel transport; torsion and curvature of connections; the Bianchi identities; metric tensor fields; metric and Levi-Civita connections; the Riemannian curvature,Ricci and Einstein tensors. Special topics: general relativity, embedding theory, integration on manifolds, the Gauss-Bonnet theorem, De Rahm cohomology.


MA (ISE) (OR) 766Network FlowsUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: OR(IE,MA) 505
Study of problems of flows in networks. These problems include the determination of shortest chain, maximal flow and minimal cost flow in networks. Relationship between network flows and linear programming developed as well as problems with nonlinear cost functions, multi-commodity flows and problem of network synthesis.


MA (BMA) (ST) 771Biomathematics IUNITS: 3 - Offered in Fall Only
Prerequisite: Advanced calculus, reasonable background in biology
Role of theory construction and model building in development of experimental science. Historical development of mathematical theories and models for growth of one-species populations (logistic and off-shoots), including considerations of age distributions (matrix models, Leslie and Lopez; continuous theory, renewal equation). Some of the more elementary theories on the growth of organisms (von Bertalanffy and others; allometric theories; cultures grown in a chemostat). Mathematical theories oftwo and more species systems (predator-prey, competition, symbosis; leading up to present-day research) and discussion of some similar models for chemical kinetics. Much emphasis on scrutiny of biological concepts as well as of mathematical structureof models in order to uncover both weak and strong points of models discussed. Mathematical treatment of differential equations in models stressing qualitative and graphical aspects, as well as certain aspects of discretization. Difference equation models.


MA (BMA) (ST) 772Biomathematics IIUNITS: 3 - Offered in Spring Only
Prerequisite: BMA 771, elementary probability theory
Continuation of topics of BMA 771. Some more advanced mathematical techniques concerning nonlinear differential equations of types encountered in BMA 771: several concepts of stability, asymptotic directions, Liapunov functions; different time-scales. Comparison of deterministic and stochastic models for several biological problems including birth and death processes. Discussion of various other applications of mathematics to biology, some recent research.


MA (BMA) (OR) (ST) 773Stochastic ModelingUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: BMA 772 or ST (MA) 746
Survey of modeling approaches and analysis methods for data from continuous state random processes. Emphasis on differential and difference equations with noisy input. Doob-Meyer decomposition of process into its signal and noise components. Examples from biological and physical sciences, and engineering. Student project.


MA (BMA) (OR) 774Partial Differential Equation Modeling in BiologyUNITS: 3 - Offered in Spring Only
Prerequisite: BMA 771 or MA/OR 731; BMA 772 or MA 401 or MA 501
Modeling with and analysis of partial differential equations as applied to real problems in biology. Review of diffusion and conservation laws. Waves and pattern formation. Chemotaxis and other forms of cell and organism movement. Introduction to solid and fluid mechanics/dynamics. Introductory numerical methods. Scaling. Perturbations, Asymptotics, Cartesian, polar and spherical geometries. Case studies.


MA 778Measure Theory and Advanced ProbabilityUNITS: 3 - Offered in Fall and Spring
Prerequisite: MA 426; ST 521 or MA(ST) 546
Modern measure and integration theory in abstract spaces. Probability measures, random variables, expectations. Distributions and characteristic functions. Modes of convergence. Independence, zero-one laws, laws of large numbers, three-series theorem. Central limit problem. Conditional expectations, martingales and martingale convergence theorems.


MA (ST) 779Advanced ProbabilityUNITS: 3 - Offered in Fall Only
Prerequisite: MA 425 and ST 521.
Sets and classes, sigma-fields and related structures, probability measures and extensions, random variables, expectation and integration, uniform integrability, inequalities, L_p-spaces, product spaces, independence, zero-one laws, convergence notions, characteristic functions, simplest limit theorems, absolute continuity, conditional expectation and conditional probabilities, martingales.


MA (CSC) 780Numerical Analysis IIUNITS: 3 - Offered in Spring Only
Prerequisite: MA 580
Approximation and interpolation, Fast Fourier Transform, numerical differentiation and integration, numerical solution of initial value problems for ordinary differential equations.


MA 784Nonlinear Equations and Unconstrained OptimizationUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: MA 580
Newton's method and Quasi-Newton methods for nonlinear equations and optimization problems, globally convergent extensions, methods for sparse problems, applications to differential equations, integral equations and general minimization problems. Methods appropriate for boundary value problems.


MA 785Numerical Solution of Ordinary Differential EquationsUNITS: 3 - Offered in Spring Only
Prerequisite: MA 511 or 512
Numerical methods for initial value problems including predictor-corrector, Runge-Kutta, hybrid and extrapolation methods; stiff systems; shooting methods for two-point boundary value problems; weak, absolute and relative stability results.


MA 788Numerical Nonlinear Partial Differential EquationsUNITS: 3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: MA 405 or 520 and MA 501 or 534; knowledge of a high level programming language
Nonlinear discrete equations; Newton and monotone methods for nonlinear equations; computational algorithms and applications; finite difference method-convergence, stability and error estimates; multiplicity of solutions and bifurcation; asymptotic behavior of solutions; and coupled systems of equations.


MA (ISE) (OR) 790Advanced Special Topics System OptimizationUNITS: 1-3 - Offered in Fall and Spring
Advanced topics in some phase of system optimization using traditional course format. Identification of various specific topics and prerequisites for each section from term to term.


MA 791Special Topics In Real AnalysisUNITS: 1-6 - Offered in Fall and Spring


MA 792Special Topics In AlgebraUNITS: 1-6 - Offered in Fall and Spring


MA 793Special Topics In Differential EquationsUNITS: 1-6


MA 795Special Topics In TopologyUNITS: 1-6


MA 796Special Topics In Combinatorial AnalysisUNITS: 1-6


MA 797Special Topics In Applied MathematicsUNITS: 1-6


MA 798Special Topics In Numerical AnalysisUNITS: 1-6


MA 810Special TopicsUNITS: 1-3 - Offered in Fall and Spring


MA (ISE) (OR) 812Special Topics in Mathematical ProgrammingUNITS: 1-3 - Offered in Spring Only, Offered Alternate Years
Prerequisite: IE(MA,OR) 505
Study of special advanced topics in area of mathematical programming. Discussion of new techniques and current research in this area. The faculty responsible for this course select areas to be covered during semester according to their preference and interest. This course not necessarily taught by an individual faculty member but can, on occasion, be joint effort of several faculty members from this university as well as visiting faculty from other institutions. To date, a course of Theory of Networks and another on Integer Programming offered under the umbrella of this course. Anticipation that these two topics will be repeated in future together with other topics.


MA (ISE) (OR) 816Advanced Special Topics Sys OptUNITS: 1-3 - Offered in Fall and Spring
Advanced topics in some phase of system optimization. Identification of various specific topics and prerequisite for each section from term to term.


MA 885Doctoral Supervised TeachingUNITS: 1-3 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.


MA 890Doctoral Preliminary ExaminationUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
For students who are preparing for and taking written and/or oral preliminary exams.


MA 893Doctoral Supervised ResearchUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.


MA 895Doctoral Dissertation ResearchUNITS: 1-9 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
Dissertation Research


MA 896Summer Dissertation ResearchUNITS: 1 - Offered in Summer
Prerequisite: Doctoral student
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.


MA 899Doctoral Dissertation PreparationUNITS: 1-3 - Offered in Fall Spring Summer
Prerequisite: Doctoral student
For students who have completed all credit hour requirements, full-time enrollment, preliminary examination, and residency requirements for the doctoral degree, and are writing and defending their dissertations.