North Carolina State University at Raleigh · Courses
MA
174 courses with the subject MA, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MA 101Intermediate Algebra ()4
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.
3 or MA 105 or Mathematics of Finance 3 or MA 114 or Introduction to Finite Mathematics 3 with Applications 3 Select one: 3 3 MA 305 Introductory Linear Algebra and Matrices 3 or MA 405 or Introduction to Linear Algebra 3 Science Elective (p. 485) 3 Mathematics Elective 3 3 EDP 304 Educational Psychology 3 3 ECI 309 Teaching in the Middle Years 3 3 GEP Interdisciplinary Perspectives (p. 103) 3 3 Hours 18 3 Third Year 3 Fall Semester 4 Mathematics Elective 3 4 ELP 344 School and Society 3 3 ED 311 Classroom Assessment Principles and 2
MA 105(Before registering for these courses students should check
4 to make sure they have met the necessary prerequisites and that 3 credit restrictions do not apply— e.g. credit is not allowed for both ARE 201 and either EC 201 or EC 205). 3 ACC 200 Introduction to Managerial Accounting 3 3 ACC 210 Concepts of Financial Reporting 3 3 ACC 220 Introduction to Managerial Accounting 3 3 ACC 230 Individual Income Taxation 3
The study of real numbers, functions and their graphs with an emphasis on absolute value, polynomial, piecewise, rational, exponential, and logarithmic functions. Note that this course does not count towards graduation for all programs: please check with your program. Restriction: Credit is not allowed for both MA 107 and MA 111.
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. Typically offered in Spring only
The study of real numbers, functions and their graphs with an emphasis on absolute value, polynomial, piecewise, rational, exponential, logarithmic, and trigonometric functions. Credit is not allowed for both MA 111 and either MA 107 or MA 108. Note that this course does not count towards graduation for all programs: please check with your program.
MA 116Introduction to Scientific Programming (Math) (3
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. Typically offered in Fall and Spring
MA 141, and either COS 100 or E 115; Corequisite: MA 241
MA 121Elements of Calculus ()3
For students who require only a single semester of calculus. Emphasis on concepts and applications of calculus, along with basic skills. Algebr review, functions, graphs, limits, derivatives, integrals, logarithmic an exponential functions, functions of several variables, applications in business and management. math placement exam. Credit is not allowed in more than one of MA 121, 131, 141.
C- or better in MA 107 or MA 111, or qualifying score on
MA 131Calculus for Life and Management Sciences A (3
hours) 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. math placement exam. Credit is not allowed in more than one of MA 121, MA 131, or MA 141.
C- or better in MA 107 or MA 111, or qualifying score on
MA 132Computational 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. Typically offered in Fall and Spring
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. math placement exam. Credit is not allowed in more than one of MA 121, MA 131, or MA 141.
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. Typically offered in Fall, Spring, and Summer
MA 231Calculus for Life and Management Sciences B (3
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. and MA 241.
MA 131 or MA 141; Credit is not allowed for both MA 231
MA 241Calculus II ()4
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. Credit is not allowed for both MA 241 and MA 231.
MA 141 with grade of C- or better or AP Calculus credit.
MA 242Calculus III ()4
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. Higher Level IB credit. Typically offered in Fall, Spring, and Summer
MA 241 with grade of C- or better or AP Calculus credit, or
MA 302Numerical Applications to Differential Equations (1
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. Typically offered in Fall and Spring
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 Typically offered in Fall and Spring
MA 306 provides the essential matrix theory background required for the proof-oriented MA 405. This course is specifically designed for students who have not completed MA 305 but wish to take MA 405. Topics include systems of linear equations, row reduction, linear independence and spanning in Euclidean spaces, determinants, and eigenvalues and eigenvectors of matrices. This course can be taken alongside MA 405. Students cannot receive credit for both MA 305 and MA 306. Typically offered in Fall and Spring MA 315/MEA 315 Mathematics Methods in Atmospheric Sciences (2 credit hours) A complement to MA 241 designed to prepare students for quantitative atmospheric applications. Topics include an introduction to vectors and vector calculus, numerical differentiation, gradients and derivatives, advection, Lagrangian versus Eulerian perspectives, representation of Earth apparent and fundamental forces. For Meteorology and Marine Science majors and Meteorology minors only. Others may enroll with permission of the instructor. 17MYM Typically offered in Fall only
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. or CSC 116) Typically offered in Spring only
(MA 231 or MA 242) and (MA 116 or CSC 112 or CSC 114
MA 326Mathematical Foundations of Data Science I (3
hours) The course covers foundational mathematical concepts fundamental to data science and data-driven mathematical modeling. The course includes the following topics: introductory probability and vector calculus, theory for classification algorithms, linear and parametric classifiers, unsupervised and clustering methods, decision trees and ensemble methods. The focus is on applying mathematical concepts to data science methods. The course includes an introduction to Python, but some familiarity with programming is strongly recommended. Basic programming proficiency (Python preferred). Typically offered in Fall and Spring
MA 331Differential Equations for the Life Sciences ()3
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.
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 f both MA 301 and MA 341 Typically offered in Fall, Spring, and Summer
MA 351Introduction to Discrete Mathematical Models (3
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. Typically offered in Fall only
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 Typically offered in Fall, Spring, and Summer
MA 341; Credit not allowed for both MA 401 and MA 501
MA 402Mathematics of Scientific Computing ()3
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
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 Typically offered in Fall only
MA 404Mathematical Foundations of Data Science II (3
hours) The course covers foundational mathematical concepts fundamental to data science. It builds upon the basic concepts in MA 326 and develops theory for a range of central data science techniques. The course includes the following topics: Optimization algorithms, neural networks, graph-based models and generative learning. These algorithms will be explored computationally using Python and practical data sets. Typically offered in Fall only
An examination of Euclidean geometry from a modern perspective. The axiomatic approach with alternative possibilities explored using models. Typically offered in Fall and Spring
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. 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. 301, ST 305, ST 311, ST 361, ST 370, ST 371, ST 380 or equivalent Typically offered in Fall and Summer 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. 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. 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. Typically offered in Spring only This course is offered alternate years Graduate Catalog 1329
One year of calculus MA 241 or MA 231, Corequisite: MA 421, BUS(ST) 350, ST MA 241 or MA 231, and one of MA 421, ST 301, ST 305, (CSC 226 AND CSC 333) OR MA 225 Grade of C or better in either MA 225 or CSC 226
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. Typically offered in Fall, Spring, and Summer
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. Typically offered in Fall and Spring
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. 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. 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. 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 MA 580 MA 432 Mathematical Models in Life Sciences 3 MA 583 MA 437 Applications of Algebra 3 MA 584 MA 440 3 MA 444 Problem Solving Strategies for Competitions 1 MA 587
MA 430Mathematical Models in the Physical Sciences (3
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. Typically offered in Fall only
Topics from differential and difference equations, and matrix algebra applied to formulation and analysis of mathematical models in biological science (e.g., population growth or disease models). Programming proficiency and some experience with basic statistics is recommended. Typically offered in Spring only
Error correcting codes, cryptography, crystallography, enumeration techniques, exact solutions of linear equations, and block designs. Typically offered in Fall and Spring
MA 444Problem Solving Strategies for Competitions (1
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
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. Typically offered in Fall only
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. Typically offered in Spring only MA 467/MA 567/ECE 567/CSC 467/CSC 567/ECE 467 Introduction to Quantum Algorithms (3 credit hours) The course will develop some well-known algorithms in quantum computing. Learning about quantum algorithms requires background in linear algebra and quantum gates, and many of our algorithmic insights will come from a signal processing angle. Therefore, we will review linear algebra, signal processing, and quantum gates. (Some students will not have all the background, in which case they should be willing to work somewhat harder during the first half of the course as we review these concepts. Specifically, students are expected to have encountered Fourier transforms in past coursework, but a review will be provided for those less familiar with the topic.) Armed with this background, we will study several quantum algorithms based on the quantum Hadamard and Fourier transforms, which connect to signal processing. Grover's unstructured quantum search algorithm will also be covered. Restriction: Much of the background will be covered during the first half of the course. Students who are unsure about their linear algebra and signal processing background can consult with the instructor Typically offered in Spring only
A reading (independent study) course available as an elective for students participating in the mathematics honors program. Typically offered in Fall and Spring
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
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 Typically offered in Fall and Spring
Operations with complex numbers, derivatives, analytic functions, integrals, definitions and properties of elementary functions, multivalued functions, power series, residue theory and applications, conformal mapping. Typically offered in Fall and Spring
The course is an introduction to measure theory and Lebesgue integration. The topics covered include Sigma algebras and measurable sets, measures, measurable functions, Lebesgue integration, Lebesgue n spaces, and product measures. Typically offered in Fall only
This course covers topics in classical complex analysis with more emphasis on rigor, abstraction, and connections to other parts of mathematics. The topics include properties of holomorphic functions, the Cauchy integral formula, the Cauchy residue theorem, classification of singularities, the Hadamard factorization theorem, and conformal mappings and the Riemann mapping theorem. Typically offered in Fall only
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. Typically offered in Fall and Spring
Groups, quotient groups, group actions, Sylow's Theorems. Rings, ideals and quotient rings, factorization, principal ideal domains. Fields, field extensions, Galois theory. Typically offered in Fall only
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. Typically offered in Fall only
Existence and uniqueness theorems, systems of linear equations, fundamental matrices, matrix exponential, nonlinear systems, plane autonomous systems, stability theory. Typically offered in Fall only
MA 341, 405, 425 or 511, Corequisite: MA 426 or 512
MA 534Introduction To Partial Differential Equations (3
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. Typically offered in Fall only
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. Typically offered in Spring only
Applied Harmonic Analysis studies the theory and modern extensions of Fourier analysis, with an emphasis on its role in data representation and analysis across diverse fields such as engineering, medicine, and finance. Applications include signal and image processing, data denoising and compression, and image reconstruction. Topics include Fourier series, the Fourier transform, the discrete and fast Fourier transforms (DFT/FFT), interpolation and sampling theory, wavelet analysis, and the discrete wavelet transform with applications. The course emphasizes the mathematical foundations underlying these methods, as well as the derivation and implementation of practical algorithms. Differential Equations (MA 341 or MA 401) is desired. The students are expected to have programming experience in MATLAB. Typically offered in Spring only
MA 542Convex Optimization Methods in Data Science (3
hours) Convex optimization methods and their applications in various areas of data science including, but not limited to, signal and image processing, inverse problems, statistical data analysis, machine learning and classification. Basic theory, algorithm design and concrete applications. Some notions of elementary convex analysis are an asset but are neither required nor assumed known. Typically offered in Spring only
3 MA 551 Introduction to Topology 3 3 MA 555 Introduction to Manifold Theory 3 3 MA 561 Set Theory and Foundations Of Mathematics 3 3 MA 565 Graph Theory 3 3 MA 573 Mathematical Modeling of Physical and Biological 3 3 Processes I 3 MA 574 Mathematical Modeling of Physical and Biological 3 3 Processes II
Set theory, topological spaces, metric spaces, continuous functions, separation, cardinality properties, product and quotient topologies, compactness, connectedness. Typically offered in Fall only
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, exterio calculus, and integration on manifolds. Typically offered in Spring only MA 560/CSC 560 Numerical Analysis I (3 credit hours) This course provides a rigorous introduction to fundamentals of numerical analysis, with emphasis on discrete approximations and their properties: Errors in numerical computations, approximation and interpolation, root finding, numerical quadratures, introduction to numerical solution of ordinary differential equations. programming experience is helpful but not essential Typically offered in Fall only
Review and discussion of scientific articles, progress reports on research and special problems of interest to mathematicians. P: Graduate Standing Typically offered in Fall and Spring
Independent study of an advanced mathematics topic under the direction of mathematics faculty member on tutorial basis. Requires a faculty sponsor and departmental approval. R: Graduate Standing Typically offered in Fall and Spring
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. Typically offered in Fall, Spring, and Summer
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. Typically offered in Fall and Spring
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. l Prerequisite: Master's student Typically offered in Fall and Spring
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. Typically offered in Summer only
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. Typically offered in Spring only
This course covers: Module theory including the structure theory of modules over a PID and primary decomposition; Tensor, exterior, and symmetric algebras; introductory homological algebra including: complexes, derived functors, Ext and Tor; and the representation theory of groups. Further topics will be covered as time permits. Typically offered in Spring only
Effective algorithms for symbolic matrices, commutative algebra, real and complex algebraic geometry, and differential and difference equations. The emphasis is on the algorithmic aspects. Typically offered in Spring only
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. Typically offered in Spring only
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. Typically offered in Fall only This course is offered alternate odd years
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. Typically offered in Spring 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. Multidisciplinary applications. Typically offered in Spring only This course is offered alternate years
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. Typically offered in Spring only MA 747/ST 747 Probability and Stochastic Processes II (3 credit hours) Advanced development of stochastic processes. Conditional expectation, filtrations of sigma-algebras, stopping times. Martingales, associated convergence theorems and inequalities, martingale decomposition, optional stopping. Markov chains including random walks, recurrence versus transience, asymptotic behavior. General Markov processes and the related semigroup operators. Construction and properties of Brownian motion, Donsker's invariance principle. Other potential topics include stationary processes, Birkhoff's ergodic theorem, branching processes, Poisson processes. 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. Typically offered in Fall only
Data Science and AI Select one of the following courses OR/CSC/ECE Introduction to Computer Performance Modeling 579 OR/CE 537 Computer Methods and Applications
Properties of cohomology, homotopy groups, fiber bundles, characteristic classes, and homological algebra. Additional topics may include spectra, spectral sequences, K-theory, group cohomology, and connections with smooth manifold topology. Typically offered in Fall only This course is offered alternate odd years
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. Typically offered in Spring only This course is offered alternate years 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. Typically offered in Spring only This course is offered alternate years 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. Typically offered in Fall only MA 772/ST 772/BMA 772 Biomathematics II: Stochastic Models in Biology (3 credit hours) Theory of stochastic processes and its application to contemporary problems in biology. Discrete- and continuous-time Markov chains, branching processes, birth-and-death processes, diffusion approximations, and elementary stochastic differential equations. Survey of applications in areas such as population genetics, infectious disease dynamics, neurobiology, and community ecology. Typically offered in Spring only
MA 776Mathematical Methods in the Physical Sciences II
MA(NE) 777 Exact and Approximate Solutions in Particle Transport The MA(ST) 778, 779 Measure Theory and Advanced Probability MA(CSC) 780 Numerical Analysis II
MA 788Numerical Nonlinear Partial Differential Equations
MAIE,OR) 790 Advanced Special Topics in System Optimization (The subject matter in the following special topics courses varies f advance by the department.)
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 repeate in future together with other topics. Typically offered in Spring only This course is offered alternate years 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
Independent study of an advanced mathematics topic under the direction of mathematics faculty member on tutorial basis. Requires a faculty sponsor and departmental approval. R: Graduate Standing Typically offered in Fall and Spring
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. Typically offered in Fall and Spring
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. Typically offered in Summer only
