MATH 1483
(A)Mathematical Functions and Their Uses
Prerequisite(s): Intermediate algebra or placement into 1513. Analysis of functions and their graphs from the viewpoint of rates of change. Linear, exponential, logarithmic and other functions. Applications to the natural sciences, agriculture, business and the social sciences.

MATH 1493
(A)Applications of Modern Mathematics
Prerequisite(s): Intermediate algebra or placement into 1513. Introduction to contemporary applications of discrete mathematics. Topics from management science, statistics, coding and information theory, social choice and decision making, geometry and growth.

MATH 1513
(A)College Algebra
Prerequisite(s): Two years of high school algebra or intermediate algebra. Quadratic equations, functions and graphs, inequalities, systems of equations, exponential and logarithmic functions, theory of equations, sequences, permutations and combinations. No credit for those with prior credit in 1715 or any mathematics course for which 1513 is a prerequisite.

MATH 1613
(A)Trigonometry
Prerequisite(s): 1513 or equivalent, or concurrent enrollment. Trigonometric functions, logarithms, solution of triangles and applications to physical sciences. No credit for those with prior credit in 1715 or any course for which 1613 is a prerequisite.

MATH 1715
(A)College Algebra and Trigonometry
Prerequisite(s): One unit of high school plane geometry, and intermediate algebra or high school equivalent. An integrated course in college algebra and trigonometry. Combined credit for 1513, 1613, and 1715 limited to six hours. No credit for those with prior credit in any course for which 1613 is a prerequisite. Satisfies the six hour general education Analytical and Quantitative Thought area requirement.

MATH 2103
(A)Elementary Calculus
Prerequisite(s): 1513. An introduction to differential and integral calculus. For students of business and social sciences.

MATH 2123
(A)Calculus for Technology Programs I
Prerequisite(s): 1715 or 1513 and 1613. First semester of a terminal sequence in calculus for students in the School of Technology. Functions and graphs, differentiation and integration with applications.

MATH 2133
(A)Calculus for Technology Programs II
Prerequisite(s): 2123. Second semester of a terminal sequence in calculus for students in the School of Technology. Calculus of trigonometric, exponential and logarithmic functions and applications to physical problems.

MATH 2144
(A)Calculus I
Prerequisite(s): 1715, or 1513 and 1613. An introduction to derivatives, integrals and their applications.

MATH 2153
(A)Calculus II
Prerequisite(s): 2144. A continuation of 2144, including series and their applications, elementary geometry of three dimensions and introductory calculus of vector functions.

MATH 2163
Calculus III
Prerequisite(s): 2153. A continuation of 2153, including differential and integral calculus of functions of several variables and an introduction to vector analysis.

MATH 2233
Differential Equations
Prerequisite(s): 2153. Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms.

MATH 2910
Special Studies
1-3 credits, max 6. Prerequisite(s): Consent of instructor. Special subjects in mathematics.

MATH 3013*
Linear Algebra
Prerequisite(s): 2153. Algebra and geometry of finite-dimensional linear spaces, linear transformations, algebra of matrices, eigenvalues and eigenvectors.

MATH 3263*
Linear Algebra and Differential Equations
Prerequisite(s): 2153. An integrated treatment of linear algebra and differential equations. No credit for those with credit in 2233 or 3013.

MATH 3403
Geometric Structures
Prerequisite(s): 1483, 1493 or 1513. Fundamentals of plane geometry, geometric motion (translation, rotations, reflections), polyhedra, applications to measurements.

MATH 3603
Mathematical Structures
Prerequisite(s): 1483, 1493 or 1513. Foundations of numbers (set theory, numeration, and the real number system), number theory, algebraic systems, functions and applications and probability.

MATH 3613*
Introduction to Modern Algebra
Prerequisite(s): 3013. Introduction to set theory and logic; elementary properties of rings, integral domains, fields and groups.

MATH 4003*
Mathematical Logic and Computability
Prerequisite(s): 3613 or PHIL 3000 or 3003 or consent of instructor. The basic metatheorems of first order logic: soundness, completeness, compactness, Lowenheim-Skolem theorem, undecidability of first order logic, Godel's incompleteness theorem. Enumerability, diagonalization, formal systems, standard and nonstandard models, Godel numberings, Turing machines, recursive functions, and evidence for Church's thesis. (Same course as PHIL 4003*)

MATH 4013*
Calculus of Several Variables
Prerequisite(s): 2163 and 3013. Differential and integral calculus of functions of several variables, vector analysis, Stokes' Theorem, Green's Theorem and applications.

MATH 4023*
Introduction to Modern Analysis
Prerequisite(s): 2163 and 3613 or consent of instructor. An introduction to the theorems and proofs of one-variable calculus. Properties of the real numbers, sequences and series of constants and functions, limits, continuity, differentiation and integration.

MATH 4033*
History of Mathematics
Prerequisite(s): 2153. Early development of mathematics as a science, contributions of Greek mathematics, mathematical advancements of the 17th and 18th centuries, and the mathematics of the 19th and 20th centuries. The emphasis in the course will be on replicating the setting and techniques of the times to understand the nature of a discovery and its relationship to contemporary thought.

MATH 4143
Advanced Calculus I
Prerequisite(s): 3013 and 4023. A rigorous treatment of calculus of one and several variables. Elementary topology of Euclidean spaces, continuity and uniform continuity, differentiation and integration. No credit for students with credit in 5043. (Same course as MATH 5043*)

MATH 4153*
Advanced Calculus II
Prerequisite(s): 4143. Continuation of 4143. A rigorous treatment of sequences and series of functions, uniform convergence, differentiation and integration of vector-valued functions, and differential forms. No credit for students with credit in 5053. (Same course as MATH 5053*)

MATH 4233*
Intermediate Differential Equations
Prerequisite(s): 2233, 3013. Systems of differential equations, series, solutions, special functions, elementary partial differential equations, Sturm-Liouville problems, stability and applications.

MATH 4263*
Introduction to Partial Differential Equations
Prerequisite(s): 2163, 2233, 3013. Solution of the standard partial differential equations (Laplace's equation, transport equation, heat equation, wave equation) by separation of variables and transform methods, including eigenfunction expansions, Fourier and Laplace transform. Boundary value problems, Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, spherical harmonics.

MATH 4283*
Complex Variables
Prerequisite(s): 4013. Analytic functions, power series, residues and poles, conformal mapping and applications.

MATH 4403*
Geometry
Prerequisite(s): 3013, recommended 3613. An axiomatic development of Euclidean and non-Euclidean geometries.

MATH 4453*
Mathematical Interest Theory
Prerequisite(s): 2153. Fundamental concepts of financial mathematics, including simple and compound interest, inflation, yield rates, and equations of value for annuities, stocks, bonds, and other financial instruments. Determining equivalent measures of interest, determining yield rates, estimating rates of return, amortization.

MATH 4513*
Numerical Mathematics: Analysis
Prerequisite(s): 2233, 3013, knowledge of programming or consent of instructor. Machine computing, algorithms, and analysis of errors applied to interpolation and approximation of functions solving equations and systems of equations, discrete variable methods for integrals and differential equations. (Same course as CS 4513*)

MATH 4553*
Linear and Nonlinear Programming
Prerequisite(s): 2163, 3013. Linear programming, simplex methods, duality, sensitivity analysis, integer programming and nonlinear programming.

MATH 4583*
Introduction to Mathematical Modeling
Prerequisite(s): 3013. Techniques of problem solving and mathematical models presented by examples and case studies of applications of mathematics in industrial settings. Oral and written presentation of solutions.

MATH 4613
Modern Algebra I
Prerequisite(s): 3613. An introduction to the theory of groups and vector spaces. Meets with 5003*. No credit for students with credit in 5003.

MATH 4623
Modern Algebra II
Prerequisite(s): 4613. Continuation of 4613. An introduction to the theory of rings, linear transformation and fields. Meets with 5013*. No credit for students with credit in 5013.

MATH 4663*
Combinatorial Mathematics
Prerequisite(s): 3013. Counting techniques, generating functions, difference equations and recurrence relations, introduction to graph and network theory.

MATH 4713*
Number Theory
Prerequisite(s): 3613. Divisibility of integers, congruencies, quadratic residues, distribution of primes, continued fractions and the theory of ideals.

MATH 4813*
Groups and Representations
Prerequisite(s): 3013 and either 3613 or consent of instructor. An introduction to groups, group actions, symmetry groups, representations and characters. Further topics may include infinite symmetry groups, applications to chemistry and physics, and finite isometry groups and geometry.

MATH 4900
Undergraduate Research
1-4 credits, max 4. Prerequisite(s): Consent of instructor. Directed readings and research in mathematics.

MATH 4910*
Special Studies
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Special subjects in mathematics.

MATH 4950
Problem Solving Seminar
1-3 credits, max 3. Prerequisite(s): 2233, 3013. The general process of problem solving. Selected problem-solving techniques. Applications to challenging problems from all areas of mathematics.

MATH 4993
Senior Honors Thesis
Prerequisite(s): Senior standing and Honors Program participation. A guided reading and research program ending with an honors thesis under the direction of a faculty member, including a public presentation. Required for graduation with departmental honors in mathematics.

MATH 5000*
Research and Thesis
1-6 credits, max 6. Prerequisite(s): Consent of advisory committee. Directed reading and research culminating in the master's report or master's thesis.

MATH 5003*
Modern Algebra I
Prerequisite(s): 3613. An introduction to the theory of groups and vector spaces. Meets with 4613. No credit for students with credit in 4613.

MATH 5010*
Seminar in Mathematics
1-3 credits, max 12. Prerequisite(s): Consent of instructor. Topics in mathematics.

MATH 5013*
Modern Algebra II
Prerequisite(s): 4613 or 5003. Continuation of 5003. An introduction to the theory of rings, linear transformations and fields. Meets with 4623. No credit for students with credit in 4623.

MATH 5023*
Advanced Linear Algebra
Prerequisite(s): 3013. A rigorous treatment of vector spaces, linear transformations, determinants, orthogonal and unitary transformations, canonical forms, bilinear and hermitian forms, and dual spaces.

MATH 5043*
Advanced Calculus I
Prerequisite(s): 3013 and 4023. A rigorous treatment of calculus of one and several variables. Elementary topology of Euclidean spaces, continuity and uniform continuity, differentiation and integration. Meets with 4143. No credit for students with credit in 4143.

MATH 5053*
Advanced Calculus II
Prerequisite(s): 4143 or 5043. Continuation of 5043. A rigorous treatment of sequences and series of functions, uniform convergence, differentiation and integration of vector-valued functions and differential forms. Meets with 4153*. No credit for students with credit in 4153. (Same course as MATH 4153*)

MATH 5133*
Stochastic Processes
Prerequisite(s): 2233, 3013 and STAT 5123. Definition of stochastic processes, probability structure, mean and covariance function, the set of sample functions, stationary processes and their spectral analysis, renewal processes, counting analysis, discrete and continuous Markov chains, birth and death processes, exponential model, queuing theory. (Same course as IEM 5133* & STAT 5133*)

MATH 5143*
Real Analysis I
Prerequisite(s): 4153 or 5053. Measure theory, measurable functions, integration and differentiation with respect to measures.

MATH 5153*
Real Analysis II
Prerequisite(s): 5143. Aspects of point set topology: nets, locally compact spaces, product spaces, Stone-Weierstrass theorem. Elementary functional analysis: Hahn-Banach, uniform boundedness, and open mapping theorems, Hilbert spaces. Riesz representation theorems: duals of Lebesgue spaces and spaces of continuous functions.

MATH 5213*
Fourier Analysis and Wavelets
Prerequisite(s): 4013 or 4023. Orthogonal series expansions, Fourier series and integrals and boundary value problems. Haar wavelets and multiresolution analysis. Applications.

MATH 5233*
Partial Differential Equations
Prerequisite(s): 4013, 4143 and 4233 or consent of instructor. Representation formulas for solutions of transport equation, Laplace’s equation, heat equation and wave equation, mean value theorems, maximum principle, Green’s functions, characteristics, eigenvalue problems, separation of variables, transform methods, variational methods, general theory of first order equations.

MATH 5243*
Ordinary Differential Equations
Prerequisite(s): 4143 or 5043; 4233; 5023. Banach space, contraction mapping principle, existence and uniqueness theorems, linear systems, higher-order linear equations, boundary value and eigenvalue problems, stability and asymptotic behavior, attractors, Gronwall’s inequality, Liapunov method.

MATH 5253*
Advanced Ordinary Differential Equations
Prerequisite(s): 5243. Selected topics in ordinary differential equations.

MATH 5283*
Complex Analysis I
Prerequisite(s): 4143 or 5043. Basic topology of the plane, functions of a complex variable, analytic functions, transformations, infinite series, integration and conformal mapping.

MATH 5293*
Complex Analysis II
Prerequisite(s): 5283. Riemann Mapping Theorem, meromorphic functions, analytic continuation, Dirichlet problem, and entire functions.

MATH 5303*
General Topology
Prerequisite(s): 4143 or 5043 or consent of instructor. Basic properties of topological spaces and continuous functions, including connectedness, compactness, and separation and countability axioms. Metric, product, and quotient spaces, Urysohn lemma, and Tietze extension theorem.

MATH 5313*
Geometric Topology
Prerequisite(s): 4613 or 5003, 5303. Manifolds, complexes, the fundamental group, covering spaces, combinatorial group theory, the Seifert-Van Kampen theorem, and related topics.

MATH 5413*
Differential Geometry
Prerequisite(s): 4013 or 4143 or 5043. Differential manifolds, vector fields, differential forms, connections, Riemannian metrics, geodesics, completeness, curvature, and related topics.

MATH 5543*
Numerical Analysis for Differential Equations
Prerequisite(s): 4233, 4513 or CS 4513. Advanced machine computing, algorithms, analysis of truncation and rounding errors, convergence and stability applied to discrete variables, finite elements, and spectral methods in ordinary and partial differential equations.

MATH 5553*
Numerical Analysis for Linear Algebra
Prerequisite(s): 3013, and 4513 or CS 4513. Advanced machine computing, algorithms, analysis of rounding errors, condition, convergence, and stability applied to direct and iterative solution of linear systems of equations, linear least squares problems, and algebraic eigenvalue problems, including LU and QR factorization, conjugate gradients, QR algorithm, and Lanczos method.

MATH 5580*
Case Studies in Applied Mathematics
1-3 credits, max 6. Prerequisite(s): 2233, 4013, and knowledge of computer programming. Selected mathematical problems from industry. Independent problem-solving, oral presentation of solutions, and technical report writing. Seminar-style format.

MATH 5593*
Methods of Applied Mathematics
Prerequisite(s): 2233, 4013, and knowledge of computer programming. Continuous and discrete techniques in modern applied mathematics. Positive definite matrices, eigenvalues and dynamical systems, discrete and continuous equilibrium equations, least squares estimation and the Kalman filter, potential flow, calculus of variations, network flows, and combinatorics.

MATH 5613*
Algebra I
Prerequisite(s): 4613 or 5003. A rigorous treatment of classical results in group theory and ring theory.

MATH 5623*
Algebra II
Prerequisite(s): 5613. A rigorous treatment of classical results in module theory and field theory.

MATH 5902*
Seminar and Practicum in the Teaching of College Mathematics
Prerequisite(s): Graduate standing in mathematics or consent of instructor. Foundations of college mathematics teaching, including lecturing, grading and exam preparation. Adapting classroom activities to better serve different types of learners. Current trends in mathematics education such as calculus reform, cooperative learning, and technology in the classroom.

MATH 6000*
Research and Thesis
1-9 credits, max 24. Prerequisite(s): Consent of advisory committee. Directed reading and research culminating in the PhD or EdD thesis.

MATH 6010*
Advanced Seminar in Mathematics
1-3 credits, max 12. Prerequisite(s): Consent of instructor and student's advisory committee. Directed reading on advanced topics in mathematics.

MATH 6143*
Functional Analysis I
Prerequisite(s): 4613 or 5003 or 5023, 5153, 5303. Theory of topological vector spaces including metrizability, consequences of completeness, Banach spaces, weak topologies, and convexity.

MATH 6213*
Harmonic Analysis
Prerequisite(s): 5153, 5283. Classical results giving connections among the size of a harmonic or analytic function on a complex domain, the existence and smoothness of its boundary values, and behavior of the Fourier series; selected extensions, related topics and applications.

MATH 6233*
Advanced Partial Differential Equations
Prerequisite(s): 5233 or consent of instructor. Schwarz class, tempered distributions, basic linear functional analysis, Holder spaces, Sobolev spaces, spaces involving time, Sobolev inequalities, existence and regularity theory of second-order elliptic, parabolic, and hyperbolic equations, semigroup theory.

MATH 6283*
Several Complex Variables
Prerequisite(s): 5293. Elements of function theory of several complex variables, including extension phenomena, domains of holomorphy, notions of convexity, holomorphic maps, and complex analytic varieties.

MATH 6290*
Topics in Analysis
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Advanced topics in analysis.

MATH 6323*
Algebraic Topology I
Prerequisite(s): 5313. Chain complexes, homology and cohomology groups, the Eilenberg-Steenrod axioms, Mayer-Vietoris sequences, universal coefficient theorems, the Eilenberg-Zilber theorem and Kunneth formulas, cup and cap products, and duality in manifolds.

MATH 6390*
Topics in Topology
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Advanced topics in topology.

MATH 6433*
Algebraic Geometry
Prerequisite(s): 5623. Affine and projective varieties, dimension, algebraic curves, divisors and Riemann-Roch theorem for curves.

MATH 6453*
Complex Geometry
Prerequisite(s): 5283. Complex manifolds, analytic sheaves, differential forms, Dolbeault cohomology, Hodge theory, line bundles, divisors, Kodaira embedding, and vanishing.

MATH 6490*
Topics in Geometry
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Advanced topics in geometry.

MATH 6513*
Theoretical Numerical Analysis
Prerequisite(s): 5153, 5543 or CS 5543, and 5553 or CS 5553. An advanced theoretical treatment based on function spaces and operator theory of algorithms for machine computing and analysis of errors.

MATH 6590*
Topics in Applied Mathematics
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Advanced topics in applied mathematics.

MATH 6613*
Commutative Algebra
Prerequisite(s): 5623. Commutative rings, exactness properties of modules, tensor products, integral dependence, chain conditions, completions, filtrations, local rings, dimension theory, and flatness.

MATH 6623*
Homological Algebra
Prerequisite(s): 5623. Closed and projective classes, resolution and derived functors, adjoint theorem, construction of projective classes in the categories of groups, rings and modules; categories, Abelian categories.

MATH 6690*
Topics in Algebra
1-3 credits, max 9. Prerequisite: consent of instructor. Advanced topics in algebra.

MATH 6713*
Analytic Number Theory
Prerequisite(s): 4283 or 5283. Arithmetic functions, Zeta and L functions, distribution of primes and introduction to modular forms.

MATH 6723*
Algebraic Number Theory
Prerequisite(s): 5013 or 5623. Number fields, ideal theory, units, decomposition of primes, quadratic and cyclotomic fields, introduction to local fields.

MATH 6790*
Topics in Number Theory
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Advanced topics in number theory.

MATH 6813*
Lie Groups and Representations
Prerequisite(s): 4153 or 5053, 4613 or 5003, 5303. Differentiable manifolds, vector fields, Lie groups, exponential map, homogeneous spaces, representations of compact Lie groups, and maximal tori.

MATH 6823*
Lie Algebras
Prerequisite(s): 5013 and 5023. Matrix groups, Lie algebras, root systems, structure of semisimple Lie algebras, universal enveloping algebra, and representations of lie algebras.

MATH 6890*
Topics in Representation Theory
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Advanced topics in representation theory.

MATH 6990*
Topics in Collegiate Mathematics Education
1-3 credits, max 9. Prerequisite(s): Consent of instructor. Advanced topics in collegiate mathematics education.

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