2011-2013 Catalog (without addenda) 
    
    May 06, 2024  
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2011-2013 Catalog (without addenda) [ARCHIVED CATALOG]

Course Descriptions

A Brief Guide to Course Descriptions

Each program described in this catalog contains detailed descriptions of the courses offered within the program.

The first line gives the official course number for which students must register and the official course title. The letters indicate the discipline of the course and the first number of the official course numbers indicates the level of the course. The levels are as follows:

  • 1XXX - Freshman Level
  • 2XXX - Sophomore Level
  • 3XXX - Junior Level
  • 4XXX - Senior Level
  • 5XXX to 9XXX - Graduate level

Typically the last number of the course number indicates the number of credits. The breakdown of periods of the course is also listed.

The paragraph description briefly indicates the contents and coverage of the course. A detailed course syllabus may be available by request from the office of the offering department.

“Prerequisites” are courses (or their equivalents) that must be completed before registering for the described course. “Co-requisites” are courses taken concurrently with the described course.

The notation “Also listed…” indicates that the course is also given under the number shown. This means that two or more departments or programs sponsor the described course and that students may register under either number, usually the one representing the student’s major program. Classes are jointly delivered.
 

Mathematics
  

  • MA 4133 Time Series

    3 Credits
    This course examines properties of time series, regression methods, linear processes, moving average processes, autoregressive processes, ARIMA models, autocorrelation, nonstationarity, parameter estimation, forecasting, regression models, ARCH, GARCH models, applications.

    Prerequisite(s): MA 2222 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 4413 Applied Partial Differential Equations

    3 Credits
    This course looks at the heat equation, homogeneous and non-homogeneous boundary conditions, Green’s function, separation of variables, Fourier series and Fourier transform, Maximum principle, existence and uniqueness, Poisson integral formula, the wave equation. Shock waves, conservation laws.

    Prerequisite(s): MA 2132  and MA 3112 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 4423 Introductory Numerical Analysis

    3 Credits
    This course covers: Polynomial interpolation and approximation of functions. Divided differences. Least-squares data fitting, orthogonal polynomials. Numerical differentiation and integration. Solution of nonlinear equations. Gaussian elimination, pivoting, iterative refinement, conditioning of matrices. Numerical solution of ordinary differential equations.

    Prerequisite(s): MA 2132  and some experience in computer programming.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 4433 Complex Variables

    3 Credits
    This course covers: Functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theory. Power and Laurent series. Residue theory. Conformal mappings. Schwarz- Christoffel transformations.

    Prerequisite(s): MA 2132  and MA 3112 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 4613 Analysis I

    3 Credits
    This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

    Prerequisite(s): MA 2122  and MA 2132 .
    Note: This course is required for MA minors.

    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 4623 Analysis II

    3 Credits
    This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

    Prerequisite(s): MA 4613 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 4924 Project in Mathematics II

    4 Credits
    In this course, students read, study and investigate selected topics in mathematics. Students discuss and present problems.

    Prerequisite(s): Departmental adviser’s approval.
    Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 4993 Thesis for Bachelor of Science Degree

    3 Credits
    The course provides the framework for a Bachelor’s thesis. In the Bachelor’s thesis, a student reports on an independent investigation of a topic in Mathematics that demonstrates an in-depth knowledge of that area of Mathematics and proficiency in using its specific methods.

    Prerequisite(s): Departmental adviser’s approval.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 5313 Applied Mathematics in Engineering and Science I

    3 Credits
    This course covers: Use of matrix algebra techniques in applications. Vector spaces. Solutions of linear algebraic equations. Linear independence. Rank of matrix. Linear transformations. Orthogonality. Gram-Schmidt procedure. Orthogonal matrices. Eigenvalues and eigenvectors. Spectral decomposition. Similarity transformations. Pseudoinverses. Singular value decomposition. Jordan form. Condition numbers of matrices. Iterative methods for eigenvalues of symmetric matrices.

    Prerequisite(s): MA 2122  and MA 2132  or equivalent.
    Note: Not acceptable for graduate credit in the Department of Mathematics.

    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 5323 Applied Mathematics in Engineering and Science II

    3 Credits
    This course covers: Some common partial differential equations, boundary conditions, separation of variables. Wave equation, dif- fusion equation, Laplace equation. Axial symmetry and spherical symmetry. Adjoint operators and Sturm-Liouville problems. Expansions in orthogonal eigenfunctions. Method of Frobenius. Bessel functions. Integral representations. Asymptotic expansions. Legendre polynomials. Spherical harmonics. Spherical Bessel functions.

    Prerequisite(s): MA 5313 .
    Note: Not acceptable for graduate credit in the Department of Mathematics.

    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 5413 Stringology: Mathematics of String Comparisons in Computational Biology

    3 Credits
    The course addresses basic combinatorial problems of string manipulation, string matching, string editing, string distance computations, arising from areas of text processing, computational biology and genomics. Classical, modern and entirely new approaches to these problems are presented with all necessary mathematical and computer science backgrounds (including coding theory and symbolic manipulation). Emphasis is on practical and effective algorithm implementations.

    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6003 Elements of Discrete Mathematics

    3 Credits
    This course covers logic, sets and functions, algorithms, analysis of algorithms. Mathematical models, primitives of naïve set theory. Covered topics: Mathematical reasoning, methods of proof, mathematical induction, recursive definitions, recursive algorithms, Counting, the Pigeonhole principle, discrete probability, recurrence relations, generating functions, inclusion-exclusion. Introduction to graph theory, counting and algorithm analysis, relations, graphs, Boolean algebras, circuits. Turing Machines, algorithm complexity. Introduction to algebraic structures.

    Prerequisite(s): Adviser’s approval.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6013 Applied Matrix Theory I

    3 Credits
    This course covers the basics of linear algebra and matrix theory. Topics included: Vector Spaces, linear combinations, affine combinations, linear dependence, affine dependence, bases, dimension, isomorphism, subspaces, calculus of subspaces, dimension of subspaces, dual vector spaces and dual bases, direct sums of vector spaces, quotient spaces, bilinear forms, tensor products, permutations, cycles, parity, linear transformations, transformations as vectors, polynomials, inverses, matrices, matrices associated with linear transformations, invariance, reducibility, projections, adjoints, change of basis, similarity.

    Prerequisite(s): MA 2012  and MA 2122  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6023 Applied Matrix Theory II

    3 Credits
    linear algebra and matrix theory. Topics covered: Linear mappings, their range and null spaces, tensor product of transformations, determinants, eigenvalues, multiplicities, triangular form, nilpotence, Jordan form, inner products, inner product spaces, orthogonality, completeness Schwarz’s inequality, complete orthonormal sets, the projection theorem, linear functionals, selfadjoint transformations, polarization, positive transformations, isometries, change of orthonormal basis, characterization of spectra, the spectral theorem, normal transformations orthogonal transformations, functions of transformations, polar decomposition, commutativity. Applications for matrices and for differential equations.

    Prerequisite(s): MA 6013 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6103 Graph Theory

    3 Credits
    This course covers: Graphs and digraphs, subgraphs, paths, cycles, trees and forests. Contraction and minors. Vertex-connectivity and edge-connectivity. Structure of k-connected graphs. Menger’s theorem. Planar graphs, drawings and embeddings. Graph colorings: vertex-coloring, edge-coloring, listcoloring. Perfect graphs. Network flows, Ford- Fulkerson Theorem. Matching, Packing and Covering. Ramsey theory. Extremal graph theory, Szemeredi’s regularity lemma. Hamilton cycles. Random graphs. The probabilistic method. Tree-decompositions, treewidth. The graph minor theorem.

    Prerequisite(s): MA 6003  or adviser’s approval.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6123 Queueing Theory

    3 Credits
    This course covers: Steady-state solutions for single and multiple channels. Various arrival and service distributions and queuing disciplines. Transient solutions. Emphasis on theory, with solution techniques given for specific classes of queues.

    Prerequisite(s): MA 6003  or adviser’s approval.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6133 Elements of Number Theory

    3 Credits
    This course covers: Prime numbers, the fundamental theorem of arithmetic, linear Diophantine equations. Fermat’s Little Theorem, Wilson’s Theorem, Euler’s theorem. Linear congruences, Chinese Remainder Theorem, Euler phi function, Moebius inversion. Primitive roots and indices, quadratic congruences, Quadratic reciprocity law. Perfect numbers, sums of squares, Siegel’s theorem. The prime number theorem. Computational number theory, primality testing, Cryptography. Elliptic curves.

    Prerequisite(s): MA 6003  or adviser’s approval.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6143 Optimization: Linear and Nonlinear Programming

    3 Credits
    This course covers: Theory and application of linear programming techniques. Simplex and revised simplex algorithms. Duality theory, dual simplex method, post-optimality analysis. Degeneracy. Transportation and assignment problems. Quadratic programming, Kuhn-Tucker conditions. Wolfe’s method.

    Prerequisite(s): MA 6003  or adviser’s approval.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6213 Elements of Real Analysis I

    3 Credits
    This course and its sequel MA 6223  rigorously treat the basic concepts and results in real analysis. Course topics include limits of sequences, topological concepts of sets for real numbers, properties of continuous functions and differentiable functions. Important concepts and theorems include supremum and infimum, Bolzano-Weierstrass theorem, Cauchy sequences, open sets, closed sets, compact sets, topological characterization of continuity, intermediate value theorem, uniform continuity, mean value theorems and inverse function theorem.

    Prerequisite(s): MA 2122  or permission of adviser.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6223 Elements of Real Analysis II

    3 Credits
    This course continues MA 6213 . The topics are integration, series of real numbers, sequences and series of functions and Fourier series. Important concepts and theorems include Riemann and Riemann-Stieltjes integral, fundamental theorem of calculus, the mean value theorem of integrals, Dirichlet test, absolute and conditional convergence, uniform convergence, Weierstrass test, power series, orthogonal functions and Fourier series.

    Prerequisite(s): MA 6213 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6233 Theory of Ordinary Differential Equations I

    3 Credits
    This course covers: Ordinary differential equations. Existence and uniqueness theorems. Linear systems. Isolated singularities. Selfadjoint eigenvalue problems. Geometric theory of differential equations in the plane.

    Prerequisite(s): MA 6213  and MA 6223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6243 Theory of Ordinary Differential Equations II

    3 Credits
    This course covers: Ordinary differential equations. Existence and uniqueness theorems. Linear systems. Isolated singularities. Selfadjoint eigenvalue problems. Geometric theory of differential equations in the plane.

    Prerequisite(s): MA 6233 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6253 Theory of Partial Differential Equations I

    3 Credits
    This course covers: Partial differential equations. Cauchy-Kowalewski theorem. Firstorder differential equations, systems of differential equations in two variables, characteristics and classification, hyperbolic, parabolic and elliptic systems. Well-posedness.

    Prerequisite(s): MA 6213  and MA 6223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6263 Theory of Partial Differential Equations II

    3 Credits
    This course covers: Partial differential equations. Cauchy-Kowalewski theorem. Firstorder differential equations, systems of differential equations in two variables, characteristics and classification, hyperbolic, parabolic and elliptic systems. Well-posedness.

    Prerequisite(s): MA 6253 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6283 Mathematical Modeling in Biology

    3 Credits
    This course covers: Linear and nonlinear difference equations for population growth and propagation. Stability. Competitive systems. Growth of microorganisms. Steady states in chemostats. Predator-prey models. Populations of infectious diseases. Michaelis-Menten kinetics. Cooperative reactions. Hodgkin- Huxlley equations. Fitzhugh-Nagumo model of nerve impulses. Conservation equations. Convection and diffusion of species. Transport in axon. Slime molds. Aggregation. Morphogenesis.

    Prerequisite(s): MA 2122  and MA 2132 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6303 Elements of Complex Analysis

    3 Credits
    This course covers: Complex numbers, analytic functions, Cauchy’s theorem and consequences, isolated singularities, analytic continuation, open mapping theorem, infinite series and products, harmonic and subharmonic functions, maximum principle, fractional linear transformations, geometric and local properties of analytic functions, Weierstrass Theorem, normal families, residues, conformal mapping, Riemann mapping theorem, branch points, second order linear O.D.E.’s.

    Prerequisite(s): MA 2122  and MA 2132  or equivalent.
    Note: Not open to students who have taken MA 3112 or MA 4433.

    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6313 Applications of Complex Analysis

    3 Credits
    This course continues MA 6303 . Topics covered: Residues, complex integration, Laplace transforms, Harmonic functions and classical examples from thermodynamics, electricity and magnetism, fluid flow, The Schwarz-Christoffel transformation.

    Prerequisite(s): MA 6303 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6403 Elements of Geometry and Topology

    3 Credits
    This course covers: Differential geometry in the plane. Introduction to transformation groups. Space curves and ruled surfaces. Tensors and exterior forms. Manifolds and tensor fields. Theory of surfaces. Introduction to Riemannian geometry.

    Prerequisite(s): MA 2122  and MA 2132  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6513 Applied Statistics I (Data Analysis)

    3 Credits
    This course covers: Treatment of statistical methods and application to analysis of data, fitting of functions to data. Estimation of population parameters, t-tests, chi square tests, rank tests.

    Prerequisite(s): MA 1124  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6523 Regression-Analysis of Variance-Time Series Analysis

    3 Credits
    This course discusses models and computational schemes associated with correlation, regression coefficients, analysis of variance and time series models.

    Prerequisite(s): MA 4113  or MA 6513 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6583 Calculus of Variations

    3 Credits
    ers: Classical problems, such as geodesics, brachistochrones, isoperimetric problems. Euler equations. Geodesic coverings. Weierstrass condition. Hamilton-Jacobi equation. First and second variations. Transversality. Convex sets and functions. Duality. Existence theorems. Generalized curves. Control theory. Time-optimal problems. Optimal processes. Extension of elementary theory of maxima and minima. Euler equations, conditions of Weierstrass, Legendre and Jacobi; Mayer fields; Hamilton-Jacobi equations; transversality; conjugate and focal points. Applications to geodesics, minimal surfaces, isoperimetric problems, Hamilton’s principle, Fermat’s principle, brachistochrones.

    Prerequisite(s): MA 4623  or MA 6223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6653 Numerical Analysis

    3 Credits
    This course covers: Interpolation. Approximation of functions by polynomials. Fast Fourier transform. Numerical integration. Solution of nonlinear equations. Iterative improvement of solutions of linear equations. Eigenvalues of matrices. Numerical solution of ordinary differential equations.

    Prerequisite(s): MA 2122 , MA 2132  and some experience in computer programming.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6663 Numerical Solution of Partial Differential Equations

    3 Credits
    This course covers: Stability, consistency and convergence of finite-difference methods for initial-value problems. Explicit and implicit schemes. Alternating direction methods and fractional-step methods. Iterative solutions of finite-difference equations for elliptic boundary value problems. Finite elements. Integral equation methods. Nonlinear semigroups, conservation laws and level set methods.

    Prerequisite(s): MA 6013 , MA 6653  and some experience in computer programming.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6683 Partial Differential Equations of Mathematical Physics

    3 Credits
    This course covers: First and second order partial differential equations and systems of equations. Initial and boundary value problems. Fundamental solutions and Green’s functions. Theory of characteristics. Eigenvalue problems. Rayleigh-Ritz and Ritz-Galerkin methods. Approximate and asymptotic methods. Nonlinear equations. Applications.

    Prerequisite(s): MA 4623  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6813 Elements of Probability

    3 Credits
    This course covers: Probability of events, distribution of random variables, joint distribution, transformations.

    Prerequisite(s): MA 2122  and MA 3012  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6823 Stochastic Processes

    3 Credits
    This course covers: Normal and stationary processes, Wiener processes, Poisson and renewal processes, Markov processes.

    Prerequisite(s): MA 6813  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6833 Statistical Inference I

    3 Credits
    This course covers: Point and interval estimation of statistical parameters. Theory of statistical estimators. Fundamentals of statistical tests of hypotheses. Second semester: extended theory of hypothesis testing, including sequential tests. Nonparametric methods in statistics.

    Prerequisite(s): MA 6813  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6843 Statistical Inference II

    3 Credits
    This course covers: Point and interval estimation of statistical parameters. Theory of statistical estimators. Fundamentals of statistical tests of hypotheses. Second semester: extended theory of hypothesis testing, including sequential tests. Nonparametric methods in statistics.

    Prerequisite(s): MA 6833 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6853 Multivariate Analysis

    3 Credits
    This course covers: Multivariate normal distribution. Simple, partial and multiple correlation. Generalization of student’s ratio. Tests of significance of sets of means. Tests of general linear hypothesis. Some generalizations of analysis of variance.

    Prerequisite(s): MA 6843 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6863 Regression and Analysis of Variance

    3 Credits
    This course covers: Linear regression of one or more independent variables. Least square estimates regression coefficients. Gauss-Markov theorem. Confidence regions for and tests of hypotheses about regression coefficients. Tests of general linear hypothesis. Multiple classification in analysis of variance. Power of F-test. Alternative models: I and II, mixed models, analysis of covariance and components of variance.

    Prerequisite(s): MA 6843 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6873 Nonparametric Methods in Statistics

    3 Credits
    This course covers: Statistical methods not bound by assumption of known parametric form of the distribution of observations. Applications to engineering and scientific research in which observations are not ordered on a numerical scale. Order statistics, tolerance regions, permutation tests, goodness of fit tests, limiting distributions and largesample properties of tests.

    Prerequisite(s): MA 6813 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6913 Time Series Analysis I

    3 Credits
    In this course, students carefully study tractable models for statistical analysis of scalar time series. Models treated: (l) “error plus trend” models, (2) stationary stochastic process models with special emphasis on autoregressive models. Estimation, tests of hypotheses and multiple-decision procedures for these models. Spectral representation and filtering, estimation of spectral density.

    Prerequisite(s): MA 6813  and MA 6843 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 6923 Time Series Analysis II

    3 Credits
    In this course, students carefully study tractable models for statistical analysis of scalar time series. Models treated: (l) “error plus trend” models, (2) stationary stochastic process models with special emphasis on autoregressive models. Estimation, tests of hypotheses and multiple-decision procedures for these models. Spectral representation and filtering, estimation of spectral density.

    Prerequisite(s): MA 6913 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7013 Abstract Algebra

    3 Credits
    This course covers: Basic algebraic structures, groups, rings, fields, integral domains and modules. Field extensions and Galois theory.

    Prerequisite(s): MA 6013  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7033 Linear Algebra I

    3 Credits
    This course covers: Basic ideas of linear algebra: Fields, vector spaces, basis, dependence, independence, dimension. Relation to solving systems of linear equations and matrices. Homomorphisms, duality, inner products, adjoints and similarity.

    Prerequisite(s): MA 2012  and MA 2122  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7043 Linear Algebra II

    3 Credits
    This course continues MA 7033 . Topics covered: Basic concepts of linear algebra continuing with: Range, nullity, determinants and eigenvalues of matrices and linear homomorphisms, the polar decomposition and spectral properties of linear maps, orthogonality, adjointness and its applications.

    Prerequisite(s): MA 7033 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7213 Real and Complex Analysis I

    3 Credits
    This course provides rigorously and comprehensively treats real analysis. Topics covered: Outer measure, Lebesgue measure, Lebesgue integral, convergence theorems, functions of bounded variation, integration in measure spaces, the Radon- Nikodyn Theorem and Fubini’s theorm.

    Prerequisite(s): MA 6213  and MA 6223  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7223 Real and Complex Analysis II

    3 Credits
    This course continues MA 7213  and provides a rigorous and comprehensive treatment of complex analysis. Topics covered: Analytic and meromorphic functions, differentiation and integration, Cauchy’s theorem, Morera’s theorem, Power and Laurent series, residue theory, Rouche’s theorem, conformal mappings, the Riemann mapping theorem and Riemann surfaces.

    Prerequisite(s): MA 7213 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7313 Functional Analysis I

    3 Credits
    This course, together with its sequel MA 7323 , introduces the language and methods of functional analysis. It covers normed spaces, Hilbert spaces, bounded linear functionals, Hahn-Banach theorem, the dual space, bounded operators, Fredholm theory of compact operators, self-adjoint operators and applications to classical analysis.

    Prerequisite(s): MA 6013  and MA 7213 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7323 Functional Analysis II

    3 Credits
    This course, together with its sequel MA 7323, introduces the language and methods of functional analysis. It covers normed spaces, Hilbert spaces, bounded linear functionals, Hahn-Banach theorem, the dual space, bounded operators, Fredholm theory of compact operators, self-adjoint operators and applications to classical analysis.

    Prerequisite(s): MA 7313 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7333 Measure Theory I

    3 Credits
    This course presents a unified treatment of that part of measure theory that is most useful for its application in modern analysis. Topics covered: Sets and classes, measures and outer measures, measurable functions, integration, general set functions, product spaces, transformations, probability. The dominated convergence theorem, Riesz Representation Theorem, Vitali-Caratheodory theorem, etc. are covered in conjunction with many examples.

    Prerequisite(s): Graduate status.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7343 Measure Theory II

    3 Credits
    This course continues MA 7333  and presents a unified treatment of that part of measure theory that is most useful for applications in modern analysis. Topics covered: Fubini’s theorem, convolutions and distributions are applied to explicit examples. In this part, Baire’s theorem,the Banach-Steinhaus theorem, the Open Mapping theorem, the Hahn-Banach Theorem are derived with the properties of the Radon-Nikodym derivatives to naturally generalize calculus both differential and integral.

    Prerequisite(s): MA 7333 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7353 Fourier and Laplace Transforms

    3 Credits
    This course presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. Topics covered: Application of transform methods to partial differential equations of mathematical physics. Includes introduction to the Wiener- Hopf technique.

    Prerequisite(s): Graduate status or permission of adviser.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7403 Topology

    3 Credits
    This course covers: Topological spaces. Compactness, connectedness, continua, extension theorems and metrization theorems. Simplexes, simplicial topology and applications. Fixed point theorems. Graphs and networks. Homology and cohomology theory. Introduction to Morse theory.

    Prerequisite(s): MA 6213  and MA 6223  or equivalent.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7503 Manifolds and Lie Groups

    3 Credits
    This course covers: Elementary theory of manifolds. Tangent space, mappings, submanifolds, fields, fiber bundles, Lie groups, homogeneous spaces. Elements of the theory of connections, Riemannian geometry. Imbedded manifolds. Calculus of variations. Harmonic forms, complex manifolds and Morse theory.

    Prerequisite(s): MA 6213  and MA 6223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7543 Topological Methods in Analysis

    3 Credits
    This course covers: Aspects of topological methods and applications to existence theorems in analysis. Use of fixed-point theorems and topological degree to study properties of solutions to ordinary and partial differential equations. No previous courses in topology are required.

    Prerequisite(s): MA 4623  or MA 6223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7603 Topics in Algebra I

    3 Credits
    Course content varies. In spring of the year before the course offering, a detailed description is posted and mailed to all graduate mathematics students.

    Prerequisite(s): MA 7013 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7613 Topics in Algebra II

    3 Credits
    Course content varies. In spring of the year before the course offering, a detailed description is posted and mailed to all graduate mathematics students.

    Prerequisite(s): MA 7603 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7623 Topics in Linear Algebra I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7033  and MA 7043 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7633 Topics in Linear Algebra II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7623 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7643 Topics in Real Analysis I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6213  and MA 6223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7653 Topics in Real Analysis II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7643 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7663 Topics in Complex Analysis I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6303  and MA 6313 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7673 Topics in Complex Analysis II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7663 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7683 Topics in Geometry I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6403 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7693 Topics in Geometry II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7683 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7703 Topics in Topology I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6403 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7713 Topics in Topology II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7703 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7723 Topics in Applied Mathematics I

    3 Credits
    Course content varies.

    Prerequisite(s): Graduate status or permission of adviser.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7733 Topics in Applied Mathematics II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7723 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7743 Topics in Probability I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6813 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7753 Topics in Probability II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7743 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7763 Topics in Statistics I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6833  and MA 6843 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7773 Topics in Statistics II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7763 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7813 Probability

    3 Credits
    This course covers: Measure-theoretic foundations of probability. Expectations, distribution functions, characteristic functions. Modes of convergence of random variables and distribution functions. Laws of large numbers. The multidimensional central-limit theorems and related asymptotic expansions. Infinitely divisible distributions.

    Prerequisite(s): MA 7213 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7833 Stochastic Processes I

    3 Credits
    This course covers: Foundations of stochastic processes. Kolmogorov’s extension theorem. Properties of sample paths. Conditional expectation. Martingales. Classes of stochastic processes. Gaussian processes, Markov processes and others. Second order properties. Stationary processes. Applications.

    Prerequisite(s): MA 7813 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 7843 Stochastic Processes II

    3 Credits
    This course covers: Foundations of stochastic processes. Kolmogorov’s extension theorem. Properties of sample paths. Conditional expectation. Martingales. Classes of stochastic processes. Gaussian processes, Markov processes and others. Second order properties. Stationary processes. Applications.

    Prerequisite(s): MA 7833 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8003 Advanced Topics in Discrete Mathematics I

    3 Credits
    Course content varies. In spring of year before course offering, a detailed description is posted and mailed to all graduate mathematics students.

    Prerequisite(s): MA 6003 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8013 Advanced Topics in Discrete Mathematics II

    3 Credits
    Course content varies. In spring of year before course offering, a detailed description is posted and mailed to all graduate mathematics students.

    Prerequisite(s): MA 8003 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8023 Advanced Topics in Algebra I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7033  and MA 7043 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8033 Advanced Topics in Algebra II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 8023 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8043 Advanced Topics in Real Analysis I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6213  and MA 6223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8053 Advanced Topics in Real Analysis II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 8043 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8063 Advanced Topics in Linear Algebra I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6303  and MA 6313 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8073 Advanced Topics in Linear Algebra II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 8063 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8103 Advanced Topics in Complex Analysis I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7213  and MA 7223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8113 Advanced Topics in Complex Analysis II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7213  and MA 7223 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8123 Advanced Topics in Geometry I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6403 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8133 Advanced Topics in Geometry II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6403 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8143 Advanced Topics in Topology I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7403 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8153 Advanced Topics in Topology II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 7403 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8163 Advanced Topics in Applied Mathematics I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6003 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8173 Advanced Topics in Applied Mathematics II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6003 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8183 Advanced Topics in Probability I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6813 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8193 Advanced Topics in Probability II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6813 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8203 Advanced Topics in Statistics I

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6833  and MA 6843 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8213 Advanced Topics in Statistics II

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6833  and MA 6843 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8383 Advanced Topics in Differential Equations

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6233  and MA 6243 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 8583 Advanced Topics in Differential Geometry

    3 Credits
    Course content varies.

    Prerequisite(s): MA 6403 .
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
  

  • MA 9413 Reading in Mathematics I

    3 Credits
    In this course, reading is guided by faculty members and devoted mainly to scholarly papers.

    Prerequisite(s): Department’s permission.
    Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
 

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