Mathematics (MA)

MA 101  Intermediate Algebra  (4 credit hours)  

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.

Typically offered in Summer only

MA 103/MA 103A  Topics in Contemporary Mathematics  (3 credit hours)  

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.

Prerequisite: MA 101 or equivalent completed in high school

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 103A/MA 103  Topics in Contemporary Mathematics  (3 credit hours)  

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.

Prerequisite: MA 101 or equivalent completed in high school

GEP Mathematical Sciences

Typically offered in Fall and Spring

MA 105  Mathematics of Finance  (3 credit hours)  

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.

Prerequisite: MA 101 or equivalent completed in high school

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 107  Precalculus I  (3 credit hours)  

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

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.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 108  Precalculus II  (3 credit hours)  

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.

Prerequisite: C- or better in MA 107

Typically offered in Spring only

MA 111  Precalculus Algebra and Trigonometry  (3 credit hours)  

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.

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.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 114  Introduction to Finite Mathematics with Applications  (3 credit hours)  

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.

Prerequisite: MA 101 or equivalent completed in high school.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 116  Introduction to Scientific Programming (Math)  (3 credit hours)  

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.

Prerequisite: MA 141, and either COS 100 or E 115; Corequisite: MA 241

Typically offered in Fall and Spring

MA 121  Elements of Calculus  (3 credit hours)  

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

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.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 131  Calculus for Life and Management Sciences A  (3 credit hours)  

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

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.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 132  Computational Mathematics for Life and Management Sciences  (1 credit hours)  

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.

Prerequisite: C- or better in MA 121 or MA 131

Typically offered in Fall, Spring, and Summer

MA 141  Calculus I  (4 credit hours)  

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

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.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 151  Calculus for Elementary Education I  (3 credit hours)  

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.

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.

GEP Mathematical Sciences

Typically offered in Spring only

MA 152  Calculus for Elementary Education II  (3 credit hours)  

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.

Prerequisite: MA 151

GEP Mathematical Sciences

Typically offered in Fall only

MA 205  Elements of Matrix Computations  (3 credit hours)  

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.

Prerequisite: C- in MA 121, 131, or 141

GEP Mathematical Sciences

Typically offered in Fall and Spring

MA 225  Foundations of Advanced Mathematics  (3 credit hours)  

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.

Prerequisite: MA 241

Typically offered in Fall, Spring, and Summer

MA 231  Calculus for Life and Management Sciences B  (3 credit hours)  

Functions of several variables - partial derivatives, optimization, least squares, Lagrange multiplier method; differential equations - population growth, finance and investment models, systems, numerical methods; MA 121 is not an accepted prerequisite for MA 231.

Prerequisite: MA 131 or MA 141; Credit is not allowed for both MA 231 and MA 241.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 241  Calculus II  (4 credit hours)  

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.

Prerequisite: MA 141 with grade of C- or better or AP Calculus credit. Credit is not allowed for both MA 241 and MA 231.

GEP Mathematical Sciences

Typically offered in Fall, Spring, and Summer

MA 242  Calculus III  (4 credit hours)  

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.

Prerequisite: MA 241 with grade of C- or better or AP Calculus credit, or Higher Level IB credit.

Typically offered in Fall, Spring, and Summer

MA 302  Numerical Applications to Differential Equations  (1 credit hours)  

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.

Prerequisite: MA 241

Typically offered in Fall and Spring

MA 303  Linear Analysis  (3 credit hours)  

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

Prerequisite: MA 241

Typically offered in Fall and Spring

MA 305  Introductory Linear Algebra and Matrices  (3 credit hours)  

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.

Prerequisite: MA 241 or MA 231 with MA 132

Typically offered in Fall, Spring, and Summer

MA 315/MEA 315  Mathematics Methods in Atmospheric Sciences  (4 credit hours)  

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.

Prerequisite: MEA 217 or MA 116 or CSC 113; Corequisite: MA 242

Typically offered in Spring only

MA 325  Introduction to Applied Mathematics  (3 credit hours)  

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.

Prerequisite: (MA 231 or MA 242) and (MA 116 or CSC 112 or CSC 114 or CSC 116)

Typically offered in Spring only

MA 331  Differential Equations for the Life Sciences  (3 credit hours)  

This course provides students with an understanding of how mathematics and life sciences can stimulate and enrich each other. The course topics include first order differential equations, separable equations, second order systems, vector and matrix systems, eigenvectors/eigenvalues, graphical and qualitative methods. The methods are motivated with examples from the biological sciences (growth models, kinetics and compartmental models, epidemic models, predator-prey, etc). Computational modeling will be carried out using SimBiology, a MATLAB toolbox based graphical user interface, which which automates and simplifies the process of modeling biological systems. Credit cannot be given for both MA 341 and MA 331.

P: MA 231 or MA 241; X: Credit cannot be given for both MA 341 and MA 331

Typically offered in Fall only

MA 335/LOG 335  Symbolic Logic  (3 credit hours)  

Intermediate level introduction to modern symbolic logic focusing on standard first-order logic; topics include proofs, interpretations, applications and basic metalogical results.

Prerequisite: LOG 201 or MA 225 or CSC 226

GEP Mathematical Sciences

Typically offered in Fall only

MA 341  Applied Differential Equations I  (3 credit hours)  

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

Prerequisite: MA 242 or (MA 132 and MA 231)

Typically offered in Fall, Spring, and Summer

MA 351  Introduction to Discrete Mathematical Models  (3 credit hours)  

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.

Prerequisite: MA 224, 225, 231 or 241

Typically offered in Fall only

MA 401  Applied Differential Equations II  (3 credit hours)  

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

Prerequisite: MA 341; Credit not allowed for both MA 401 and MA 501

Typically offered in Fall, Spring, and Summer

MA 402  Mathematics of Scientific Computing  (3 credit hours)  

This course will provide an overview of methods to solve quantitative problems and analyze data. The tools to be introduced are mathematical in nature and have links to Algebra, Analysis, Geometry, Graph Theory, Probability and Topology. Students will acquire an appreciation of (I) the fundamental role played by mathematics in countless applications and (II) the exciting challenges in mathematical research that lie ahead in the analysis of large data and uncertainties. Students will work on a project for each unit. While this is not a programming class, the students will do some programming through their projects.

P: (MA 341 or MA 405) and programming proficiency (MATLAB, C++, Java, Fortran, or other language)

Typically offered in Fall and Spring

MA 403  Introduction to Modern Algebra  (3 credit hours)  

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

Prerequisite: MA 225

Typically offered in Fall and Spring

MA 405  Introduction to Linear Algebra  (3 credit hours)  

This course offers 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

Prerequisite: MA 241 (MA 225 recommended); Corequisite: MA 341 is recommended

Typically offered in Fall, Spring, and Summer

MA 407  Introduction to Modern Algebra for Mathematics Majors  (3 credit hours)  

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

Prerequisite: MA 225 and MA 405

Typically offered in Fall and Spring

MA 408  Foundations of Euclidean Geometry  (3 credit hours)  

An examination of Euclidean geometry from a modern perspective. The axiomatic approach with alternative possibilities explored using models.

Prerequisite: MA 225

Typically offered in Fall and Spring

MA 410  Theory of Numbers  (3 credit hours)  

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.

Prerequisite: One year of calculus

Typically offered in Spring only

MA 412/ST 412  Long-Term Actuarial Models  (3 credit hours)  

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.

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

Typically offered in Fall only

MA 413/ST 413  Short-Term Actuarial Models  (3 credit hours)  

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.

Prerequisite: MA 241 or MA 231, and one of MA 421, ST 301, ST 305, ST 370, ST 371, ST 380, ST 421.

Typically offered in Summer only

MA 414/MA 514/CSC 414/CSC 514  Foundations of Cryptography  (3 credit hours)  

Cryptography is the study of mathematical techniques for securing digital information, systems and distributed computation against adversarial attacks. In this class you will learn the concepts and the algorithms behind the most used cryptographic protocols: you will learn how to formally define security properties and how to formally prove/disprove that a cryptographic protocol achieves a certain security property. You will also discover that cryptography has a much broader range of applications. It solves absolutely paradoxical problems such as proving knowledge of a secret without ever revealing the secret (zero-knowledge proof), or computing the output of a function without ever knowing the input of the function (secure computation). Finally, we will look closely at one of the recent popular application of cryptography: the blockchain technology. Additionally, graduate students will study some of the topics in greater depth.

Prerequisite: (CSC 226 AND CSC 333) OR MA 225

Typically offered in Fall only

MA 416/CSC 416  Introduction to Combinatorics  (3 credit hours)  

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.

Prerequisite: Grade of C or better in either MA 225 or CSC 226

Typically offered in Spring only

MA 421  Introduction to Probability  (3 credit hours)  

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.

Prerequisite: MA 242

Typically offered in Fall, Spring, and Summer

MA 425  Mathematical Analysis I  (3 credit hours)  

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.

Prerequisite: MA 225 (MA 407 desirable)

Typically offered in Fall and Spring

MA 426  Mathematical Analysis II  (3 credit hours)  

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.

Prerequisite: MA 425 and 405

Typically offered in Fall and Spring

MA 427/CSC 427  Introduction to Numerical Analysis I  (3 credit hours)  

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.

Prerequisite: (MA 341 or MA 301) and ( CSC 111 or CSC 112 or CSC 113 or CSC 114 or CSC 116 or MA 116 or PY 251 or ST 114 or ECE 209)

Typically offered in Fall only

MA 428/CSC 428  Introduction to Numerical Analysis II  (3 credit hours)  

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.

Prerequisite: (MA 305 or MA 405) and (CSC 111 or CSC 112 or CSC 113 or CSC 114 or CSC 116 or MA 116 or PY 251 or ST 114 or ECE 209)

Typically offered in Spring only

MA 430  Mathematical Models in the Physical Sciences  (3 credit hours)  

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.

Prerequisite: MA 341 and MA 405

Typically offered in Fall only

MA 432  Mathematical Models in Life and Social Sciences  (3 credit hours)  

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).

Prerequisite: MA 341, (MA 305 or MA 405), and programming proficiency; Corequisite: (MA 421 or ST 371)

Typically offered in Spring only

MA 437  Applications of Algebra  (3 credit hours)  

Error correcting codes, cryptography, crystallography, enumeration techniques, exact solutions of linear equations, and block designs.

Prerequisite: MA 403 or 407, MA 405

Typically offered in Fall and Spring

MA 440  Game Theory  (3 credit hours)  

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.

Prerequisite: MA 231 or MA 242

Typically offered in Fall only

MA 444  Problem Solving Strategies for Competitions  (1 credit hours)  

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.

Typically offered in Fall only

MA 450  Methods of Applied Mathematics I  (3 credit hours)  

Mathematical methods covered include dimensional analysis, asymptotics, continuum modeling and traffic flow analysis. These topics are discussed in the context of applications and real data. This course is independent of MA 451 Methods of Applied Mathematics II.

Prerequisite: MA 341

Typically offered in Fall only

MA 451  Methods of Applied Mathematics II  (3 credit hours)  

The mathematical methods of this course give insight into physical continuum processes such as fluid flow and the deformation of solid elastic materials. Techniques include the modeling and formulation of equations of motion, the use of Lagrangian and Eulerian variables; further topics are: examples of incompressible fluid flow, calculus of variations and applications to optimal control problems. This course is independent of MA 450 Methods of Applied Mathematics I.

Prerequisite: MA 341

Typically offered in Spring only

MA 491  Reading in Honors Mathematics  (1-6 credit hours)  

A reading (independent study) course available as an elective for students participating in the mathematics honors program.

Prerequisite: Membership in honors program

Typically offered in Fall and Spring

MA 493  Special Topics in Mathematics  (1-6 credit hours)  

Directed individual study or experimental course offerings.

Typically offered in Fall and Spring

MA 494  Major Paper in Math  (1 credit hours)  

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.

Corequisite: MA class at the 400-level or above

Typically offered in Fall and Spring

MA 499  Independent Research in Mathematics  (1-6 credit hours)  

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. Individualized/Independent Study and Research courses require a Course Agreement for Students Enrolled in Non-Standard Courses be completed by the student and faculty member prior to registration by the department.

Typically offered in Fall, Spring, and Summer

MA 501  Advanced Mathematics for Engineers and Scientists I  (3 credit hours)  

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

Prerequisite: MA 341; credit not allowed for both MA 501 and MA 401

Typically offered in Fall, Spring, and Summer

MA 502  Advanced Mathematics for Engineers and Scientists II  (3 credit hours)  

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

Prerequisite: MA 341.

Typically offered in Fall, Spring, and Summer

MA 504/OR 504  Introduction to Mathematical Programming  (3 credit hours)  

Basic concepts of linear, nonlinear and dynamic programming theory. Not for majors in OR at Ph.D. level.

Prerequisite: MA 242, MA 405

Typically offered in Fall only

MA 505/OR 505/ISE 505  Linear Programming  (3 credit hours)  

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.

Prerequisite: MA 405

Typically offered in Fall only

MA 507  Survey of Real Analysis  (3 credit hours)  

A broad overview of topics in analysis. Historical development, logical refinement and applications of concepts such as limits, continuity, differentiation and integration. May not be taken for graduate credit by Master's or Ph.D. students in Mathematics or Applied Mathematics.

Prerequisite: Graduate standing

Typically offered in Fall, Spring, and Summer

MA 508  Geometry For Secondary Teachers  (3 credit hours)  

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.

Prerequisite: Graduate standing

Typically offered in Spring and Summer

MA 509  Survey of Abstract Algebra  (3 credit hours)  

A broad overview of topics in abstract algebra. Theory of equations, polynomial rings, rational functions and elementary number theory. May not be taken for graduate credit by Master's or Ph.D. students in Mathematics or Applied Mathematics.

Prerequisite: Graduate standing

Typically offered in Fall, Spring, and Summer

MA 510  Selected Topics In Mathematics For Secondary Teachers  (1-6 credit hours)  

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.

Prerequisite: Graduate standing

Typically offered in Spring and Summer

MA 511  Advanced Calculus I  (3 credit hours)  

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

Prerequisite: MA 341

Typically offered in Fall, Spring, and Summer

MA 512  Advanced Calculus II  (3 credit hours)  

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.

Prerequisite: MA 341

Typically offered in Fall, Spring, and Summer

MA 513  Introduction To Complex Variables  (3 credit hours)  

Operations with complex numbers, derivatives, analytic functions, integrals, definitions and properties of elementary functions, multivalued functions, power series, residue theory and applications, conformal mapping.

Prerequisite: MA 242

Typically offered in Fall and Spring

MA 514/CSC 414/CSC 514/MA 414  Foundations of Cryptography  (3 credit hours)  

Cryptography is the study of mathematical techniques for securing digital information, systems and distributed computation against adversarial attacks. In this class you will learn the concepts and the algorithms behind the most used cryptographic protocols: you will learn how to formally define security properties and how to formally prove/disprove that a cryptographic protocol achieves a certain security property. You will also discover that cryptography has a much broader range of applications. It solves absolutely paradoxical problems such as proving knowledge of a secret without ever revealing the secret (zero-knowledge proof), or computing the output of a function without ever knowing the input of the function (secure computation). Finally, we will look closely at one of the recent popular application of cryptography: the blockchain technology. Additionally, graduate students will study some of the topics in greater depth.

Prerequisite: (CSC 226 AND CSC 333) OR MA 225

Typically offered in Fall only

MA 515  Analysis I  (3 credit hours)  

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.

Prerequisite: MA 426

Typically offered in Fall and Spring

MA 518  Geometry of Curves and Surfaces  (3 credit hours)  

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.

Prerequisite: MA 242 and MA 405

Typically offered in Spring only

MA 520  Linear Algebra  (3 credit hours)  

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.

Prerequisite: MA 405

Typically offered in Fall and Spring

MA 521  Abstract Algebra I  (3 credit hours)  

Groups, quotient groups, group actions, Sylow's Theorems. Rings, ideals and quotient rings, factorization, principal ideal domains. Fields, field extensions, Galois theory.

Prerequisite: MA 405 and MA 407

Typically offered in Fall only

MA 522  Computer Algebra  (3 credit hours)  

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.

Prerequisite: MA 407 or MA 521 and MA 405 or MA 520

Typically offered in Fall only

MA 523  Linear Transformations and Matrix Theory  (3 credit hours)  

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.

Prerequisite: MA 405

Typically offered in Fall and Spring

MA 524  Combinatorics I  (3 credit hours)  

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.

Prerequisite: MA 405 and MA 407

Typically offered in Fall only

MA 526  Algebraic Geometry  (3 credit hours)  

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.

Prerequisite: MA 521

Typically offered in Fall only

MA 528/ECG 528/MBA 528/FIM 528  Options and Derivatives Pricing  (3 credit hours)  

The course covers (i) structure and operation of derivative markets, (ii) valuation of derivatives, (iii) hedging of derivatives, and (iv) applications of derivatives in areas of risk management and financial engineering. Models and pricing techniques include Black-Scholes model, binomial trees, Monte-Carlo simulation. Specific topics include simple no-arbitrage pricing relations for futures/forward contracts; put-call parity relationship; delta, gamma, and vega hedging; implied volatility and statistical properties; dynamic hedging strategies; interest-rate risk, pricing of fixed-income product; credit risk, pricing of defaultable securities.

Prerequisites: MA 341 and MA 405 and MA 421

Typically offered in Fall only

MA 531/E 531/OR 531  Dynamic Systems and Multivariable Control I  (3 credit hours)  

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.

Prerequisite: MA 341, MA 405

Typically offered in Fall only

MA 532  Ordinary Differential Equations I  (3 credit hours)  

Existence and uniqueness theorems, systems of linear equations, fundamental matrices, matrix exponential, nonlinear systems, plane autonomous systems, stability theory.

Prerequisite: MA 341, 405, 425 or 511, Corequisite: MA 426 or 512

Typically offered in Fall only

MA 534  Introduction To Partial Differential Equations  (3 credit hours)  

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.

Prerequisite: MA 425 or MA 511, MA 341, Corequisite: MA 426 or 512

Typically offered in Fall only

MA 537  Nonlinear Dynamics and Chaos  (3 credit hours)  

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.

Prerequisite: MA 341 and MA 405

Typically offered in Spring only

MA 540  Uncertainty Quantification for Physical and Biological Models  (3 credit hours)  

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.

Prerequisite: MA 341 and basic knowledge of probability, linear algebra, and scientific computation

Typically offered in Spring only

MA 544  Computer Experiments In Mathematical Probability  (3 credit hours)  

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.

Prerequisite: MA 421

Typically offered in Spring only

MA 546/ST 546  Probability and Stochastic Processes I  (3 credit hours)  

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.

Prerequisite: MA 421 and MA 425 or MA 511

Typically offered in Fall only

MA 547  Financial Mathematics  (3 credit hours)  

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.

Prerequisite: MA(ST) 546

Typically offered in Spring only

MA 548/FIM 548  Monte Carlo Methods for Financial Math  (3 credit hours)  

Monte Carlo (MC) methods for accurate option pricing, hedging and risk management. Modeling using stochastic asset models (e.g. geometric Brownian motion) and parameter estimation. Stochastic models, including use of random number generators, random paths and discretization methods (e.g. Euler-Maruyama method), and variance reduction. Implementation using Matlab. Incorporation of the latest developments regarding MC methods and their uses in Finance.

Prerequisites: (MA 421 or ST 421), MA 341, and MA 405

Typically offered in Spring only

MA 549/FIM 549  Financial Risk Analysis  (3 credit hours)  

This course focuses on mathematical methods to analyze and manage risks associated with financial derivatives. Topics covered include aggregate loss distributions, extreme value theory, default probabilities, Value-at-Risk and expected shortfall, coherent risk measures, correlation and copula, applications of principle component analysis and Monte Carlo simulations in financial risk management, how to use stochastic differential equations to price financial risk derivatives, and how to back-test and stress-test models.

Prerequisites: MA 405 and (MA 421 or ST 421) and (MA/ST 412 or MA/ST 413)

Typically offered in Spring only

MA 551  Introduction to Topology  (3 credit hours)  

Set theory, topological spaces, metric spaces, continuous functions, separation, cardinality properties, product and quotient topologies, compactness, connectedness.

Prerequisite: MA 426

Typically offered in Fall only

MA 555  Introduction to Manifold Theory  (3 credit hours)  

An introduction to smooth manifolds. Topics include: topological and smooth manifolds, smooth maps and differentials, vector fields and flows, Lie derivatives, vector bundles, tensors, differential forms, exterior calculus, and integration on manifolds.

Prerequisite: MA 405 and MA 426

Typically offered in Fall only

MA 561  Set Theory and Foundations Of Mathematics  (3 credit hours)  

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.

Prerequisite: MA 407

Typically offered in Spring only

MA 565/OR 565/CSC 565  Graph Theory  (3 credit hours)  

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. Dire

Prerequisite: CSC 226 or MA 351.

Typically offered in Spring only

MA 573/BMA 573  Mathematical Modeling of Physical and Biological Processes I  (3 credit hours)  

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.

Prerequisite: MA 341 and knowledge of high-level programming language.

Typically offered in Fall only

MA 574/BMA 574  Mathematical Modeling of Physical and Biological Processes II  (3 credit hours)  

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.

Prerequisite: MA/BMA 573

Typically offered in Spring only

MA 580/CSC 580  Numerical Analysis I  (3 credit hours)  

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.

Prerequisite: MA 405; MA 425 or MA 511; high-level computer language

Typically offered in Fall and Spring

MA 583/CSC 583  Introduction to Parallel Computing  (3 credit hours)  

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.

Prerequisite: CSC 302 or MA 402 or MA/CSC 428 or MA/CSC 580

Typically offered in Spring only

MA 584  Numerical Solution of Partial Differential Equations--Finite Difference Methods  (3 credit hours)  

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.

Prerequisite: MA 501; knowledge of a high level programming language

Typically offered in Fall only

MA 587  Numerical Solution of Partial Differential Equations--Finite Element Method  (3 credit hours)  

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.

Prerequisite: MA 501; knowledge of a high level programming language

Typically offered in Spring only

MA 591  Special Topics  (1-6 credit hours)  

Typically offered in Fall and Spring

MA 676  Master's Project  (3 credit hours)  

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 wr

Typically offered in Fall, Spring, and Summer

MA 685  Master's Supervised Teaching  (1-3 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Fall and Spring

MA 689  Non-Thesis Master Continuous Registration - Full Time Registration  (3 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

MA 690  Master's Examination  (1-9 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Fall and Spring

MA 693  Master's Supervised Research  (1-9 credit hours)  

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

MA 695  Master's Thesis Research  (1-9 credit hours)  

Thesis Research

Prerequisite: Master's student

Typically offered in Fall and Spring

MA 696  Summer Thesis Research  (1 credit hours)  

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.

Prerequisite: Master's student

Typically offered in Summer only

MA 699  Master's Thesis Preparation  (1-9 credit hours)  

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

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

MA 706/OR 706/ST 706  Nonlinear Programming  (3 credit hours)  

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. Specia

Prerequisite: OR(IE,MA) 505 and MA 425

Typically offered in Spring only

MA 708/OR 708/ISE 708  Integer Programming  (3 credit hours)  

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 experienc

Prerequisite: MA 405, OR (MA,IE) 505, Corequisite: Some familiarity with computers (e.g., CSC 112)

Typically offered in Spring only

MA 715  Analysis II  (3 credit hours)  

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.

Prerequisite: MA 515

Typically offered in Spring only

MA 716  Advanced Functional Analysis  (3 credit hours)  

Advanced topics in functional analysis such as linear topological spaces; Banach algebra, spectral theory and abstract measure theory and integration.

Prerequisite: MA 715

Typically offered in Fall only

MA 719/OR 719  Vector Space Methods in System Optimization  (3 credit hours)  

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.

Prerequisite: MA 405, 511

Typically offered in Fall only

MA 720  Lie Algebras  (3 credit hours)  

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.

Prerequisite: MA 520

Typically offered in Spring only

MA 721  Abstract Algebra II  (3 credit hours)  

Field extensions, Galois theory, modules, tensor products, exterior products.

Prerequisite: MA 521

Typically offered in Spring only

MA 722  Computer Algebra II  (3 credit hours)  

Effective algorithms for symbolic matrices, commutative algebra, real and complex algebraic geometry, and differential and difference equations. The emphasis is on the algorithmic aspects.

Prerequisite: MA 522

Typically offered in Spring only

MA 723  Theory of Matrices and Applications  (3 credit hours)  

Canonical forms, functions of matrices, variational methods, perturbation theory, numerical methods, nonnegative matrices, applications to differential equations, Markov chains.

Prerequisite: MA 520 or 523

Typically offered in Spring only

MA 724  Combinatorics II  (3 credit hours)  

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.

Prerequisite: MA 524

Typically offered in Spring only

MA 725  Lie Algebra Representation Theory  (3 credit hours)  

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.

Prerequisite: MA 720

Typically offered in Fall only

MA 731/OR 731/E 731  Dynamic Systems and Multivariable Control II  (3 credit hours)  

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. Multidiscipl

Prerequisite: OR(E,MA) 531

Typically offered in Spring only

MA 732  Ordinary Differential Equations II  (3 credit hours)  

Existence-uniqueness theory, periodic solutions, invariant manifolds, bifurcations, Fredholm's alternative.

Prerequisite: MA 532, Corequisite: MA 515

Typically offered in Spring only

MA 734  Partial Differential Equations  (3 credit hours)  

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.

Prerequisite: MA 534, Corequisite: MA 515

Typically offered in Spring only

MA 746/ST 746  Introduction To Stochastic Processes  (3 credit hours)  

Markov chains and Markov processes, Poisson process, birth and death processes, queuing theory, renewal theory, stationary processes, Brownian motion.

Prerequisite: MA 405 and MA(ST) 546 or ST 521

Typically offered in Spring only

MA 747/ST 747  Probability and Stochastic Processes II  (3 credit hours)  

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.

Prerequisite: MA(ST) 546

Typically offered in Spring only

MA 748/ST 748  Stochastic Differential Equations  (3 credit hours)  

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.

Prerequisite: MA(ST) 747

Typically offered in Fall only

MA 753  Algebraic Topology  (3 credit hours)  

Homotopy, fundamental group, covering spaces, classification of surfaces, homology and cohomology.

Prerequisite: MA 551 or MA 555

Typically offered in Spring only

MA 755  Introduction to Riemannian Geometry  (3 credit hours)  

An introduction to smooth manifolds with metric. Topics include: Riemannian metric and generalizations, connections, covariant derivatives, parallel translation, Riemannian (or Levi-Civita) connection, geodesics and distance, curvature tensor, Bianchi identities, Ricci and scalar curvatures, isometric embeddings, Riemannian submanifolds, hypersurfaces, Gauss Bonnet Theorem; applications and connections to other fields.

Prerequisite: MA 555

Typically offered in Spring only

MA 766/OR 766/ISE 766  Network Flows  (3 credit hours)  

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.

Prerequisite: OR(IE,MA) 505

Typically offered in Spring only

MA 771/ST 771/BMA 771  Biomathematics I  (3 credit hours)  

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.

Prerequisite: Advanced calculus, reasonable background in biology

Typically offered in Fall only

MA 772/ST 772/BMA 772  Biomathematics II  (3 credit hours)  

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.

Prerequisite: BMA 771, elementary probability theory

Typically offered in Spring only

MA 773/OR 773/ST 773/BMA 773  Stochastic Modeling  (3 credit hours)  

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.

Prerequisite: BMA 772 or ST (MA) 746

Typically offered in Spring only

MA 774/BMA 774/OR 774  Partial Differential Equation Modeling in Biology  (3 credit hours)  

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.

Prerequisite: BMA 771 or MA/OR 731; BMA 772 or MA 401 or MA 501

Typically offered in Spring only

MA 780/CSC 780  Numerical Analysis II  (3 credit hours)  

Approximation and interpolation, Fast Fourier Transform, numerical differentiation and integration, numerical solution of initial value problems for ordinary differential equations.

Prerequisite: MA 580

Typically offered in Spring only

MA 784  Nonlinear Equations and Unconstrained Optimization  (3 credit hours)  

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.

Prerequisite: MA 580

Typically offered in Spring only

MA 785  Numerical Solution of Ordinary Differential Equations  (3 credit hours)  

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.

Prerequisite: MA 511 or 512

Typically offered in Spring only

MA 788  Numerical Nonlinear Partial Differential Equations  (3 credit hours)  

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.

Prerequisite: MA 405 or 520 and MA 501 or 534; knowledge of a high level programming language

Typically offered in Spring only

MA 790/ISE 790  Advanced Special Topics System Optimization  (1-6 credit hours)  

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.

Typically offered in Fall and Spring

MA 791  Special Topics In Real Analysis  (1-6 credit hours)  

Typically offered in Fall and Spring

MA 792  Special Topics In Algebra  (1-6 credit hours)  

Typically offered in Fall and Spring

MA 793  Special Topics In Differential Equations  (1-6 credit hours)  
MA 796  Special Topics In Combinatorial Analysis  (1-6 credit hours)  
MA 797  Special Topics In Applied Mathematics  (1-6 credit hours)  
MA 798  Special Topics In Numerical Analysis  (1-6 credit hours)  
MA 810  Special Topics  (1-6 credit hours)  

Typically offered in Fall and Spring

MA 812/ISE 812  Special Topics in Mathematical Programming  (1-6 credit hours)  

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.

Prerequisite: IE(MA,OR) 505

Typically offered in Spring only

MA 816/ISE 816  Advanced Special Topics Sys Opt  (1-6 credit hours)  

Advanced topics in some phase of system optimization. Identification of various specific topics and prerequisite for each section from term to term.

Typically offered in Fall and Spring

MA 885  Doctoral Supervised Teaching  (1-3 credit hours)  

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.

Prerequisite: Doctoral student

Typically offered in Fall and Spring

MA 890  Doctoral Preliminary Examination  (1-9 credit hours)  

For students who are preparing for and taking written and/or oral preliminary exams.

Prerequisite: Doctoral student

Typically offered in Fall and Spring

MA 893  Doctoral Supervised Research  (1-9 credit hours)  

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Doctoral student

Typically offered in Fall, Spring, and Summer

MA 895  Doctoral Dissertation Research  (1-9 credit hours)  

Dissertation Research

Prerequisite: Doctoral student

Typically offered in Fall and Spring

MA 896  Summer Dissertation Research  (1 credit hours)  

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.

Prerequisite: Doctoral student

Typically offered in Summer only

MA 899  Doctoral Dissertation Preparation  (1-9 credit hours)  

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.

Prerequisite: Doctoral student

Typically offered in Fall, Spring, and Summer