Mathematics 1

MATH 1613 Trigonometry (A) MATHEMATICS Prerequisites: MATH 1513 with grade of "C" or better or an acceptable placement score (see placement.okstate.edu). Courses Description: Trigonometric functions, solution of triangles and applications to physical sciences. Combined credit toward a degree for MATH 1483 Mathematical Functions and Their Uses (A) MATH 1513, MATH 1613 and MATH 1715 limited to six hours. Prerequisites: An acceptable placement score - see Credit hours: 3 placement.okstate.edu. Contact hours: Lecture: 3 Contact: 3 Description: Analysis of functions and their graphs from the viewpoint Levels: Undergraduate of rates of change. Linear, exponential, logarithmic and other functions. Schedule types: Lecture Applications to the natural sciences, agriculture, business and the social Department/School: Mathematics sciences. General Education and other Course Attributes: Analytical & Quant Credit hours: 3 Thought Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate MATH 1715 Precalculus (A) Schedule types: Lecture Prerequisites: An acceptable placement score (see http:// Department/School: Mathematics placement.okstate.edu). One year of high school geometry and two years General Education and other Course Attributes: Analytical & Quant of high school algebra recommended. Thought Description: Includes an integrated treatment of topics from College Algebra and Trigonometry. Combined credit toward a degree for MATH 1493 Applications of Modern Mathematics (A) MATH 1513, MATH 1613 and MATH 1715 limited to six hours. Satisfies Prerequisites: An acceptable placement score (see the six hour general education Analytical and Quantitative Thought placement.okstate.edu). requirement. Description: Introduction to contemporary applications of discrete Credit hours: 5 mathematics. Topics from management science, statistics, coding and Contact hours: Lecture: 5 Contact: 5 information theory, social choice and decision making, geometry and Levels: Undergraduate growth. Schedule types: Lecture Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 General Education and other Course Attributes: Analytical & Quant Levels: Undergraduate Thought Schedule types: Lecture Department/School: Mathematics MATH 1813 Preparation for Calculus (A) General Education and other Course Attributes: Analytical & Quant Prerequisites: MATH 1513 with grade of “C” or better or an acceptable Thought placement score (see placement.okstate.edu). Description: A conceptual approach to the algebra and trigonometry MATH 1513 College Algebra (A) needed for calculus. Trigonometry from the perspective of the unit Prerequisites: An acceptable placement score (see circle and right triangles, behavior of trigonometric functions, and placement.okstate.edu). Two years of high school algebra recommended. basic identities. Functions arising in calculus and the notion of an Description: Quadratic equations, functions and graphs, inequalities, inverse function, especially in the context of trigonometric, logarithmic, systems of equations, exponential and logarithmic functions, theory of and exponential functions. Rates of change and the limiting process. equations, sequences, permutations and combinations. Combined credit Combined credit toward a degree for MATH 1513, MATH 1613, and toward a degree for MATH 1513, MATH 1613 and MATH 1715 limited to MATH 1813 limited to six hours. May not be used for degree credit with six hours. MATH 1715. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics General Education and other Course Attributes: Analytical & Quant General Education and other Course Attributes: Analytical & Quant Thought Thought MATH 1583 Applied Geometry and Trigonometry (A) MATH 1910 Special Studies Prerequisites: A grade of "C" or better in one of MATH 1483 Prerequisites: Consent of instructor. or MATH 1513, or an acceptable placement score (see Description: Special subjects in mathematics. Offered for variable credit, placement.okstate.edu). 1-3 credit hours, maximum of 3 credit hours. Description: Geometry, trigonometry, and their applications to technology Credit hours: 1-3 and design. Not intended for calculus-bound students. Contact hours: Contact: 1-3 Other: 1-3 Credit hours: 3 Levels: Undergraduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Independent Study Levels: Undergraduate Department/School: Mathematics Schedule types: Lecture Department/School: Mathematics General Education and other Course Attributes: Analytical & Quant Thought 2 Mathematics

MATH 2103 Business Calculus (A) MATH 2153 Calculus II (A) Prerequisites: A grade of "C" or better in one of MATH 1483 or Prerequisites: MATH 2144 with grade of "C" or better. MATH 1513 or MATH 1715 or MATH 1813, or an acceptable placement Description: A continuation of MATH 2144, including techniques of score (see http://placement.okstate.edu). integration, series and their applications, parametric equations, and polar Description: An introduction to calculus in the context of applications to coordinates. Previously offered as MATH 2155, MATH 2163, and MATH business. Previously offered as MATH 2713. 2365. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 2 Contact: 3 Other: 1 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Levels: Undergraduate Schedule types: Discussion, Combined lecture & discussion, Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics General Education and other Course Attributes: Analytical & Quant General Education and other Course Attributes: Analytical & Quant Thought Thought MATH 2123 Calculus for Technology Programs I (A) MATH 2163 Calculus III Prerequisites: MATH 1613 with a grade of "C" or better, or MATH 1715 Prerequisites: MATH 2153 with grade of "C" or better. with a grade of "C" or better, or MATH 1813 with a grade of "C" or better, or Description: A continuation of MATH 2153, including differential and an acceptable placement score (see placement.okstate.edu). integral calculus of functions of several variables and an introduction to Description: First semester of a terminal sequence in calculus vector analysis. for students in the School of Technology. Functions and graphs, Credit hours: 3 differentiation and integration with applications. Previously offered as Contact hours: Lecture: 3 Contact: 3 MATH 2373. Levels: Undergraduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Undergraduate MATH 2233 Differential Equations Schedule types: Lecture Prerequisites: MATH 2153 with grade of "C" or better. Department/School: Mathematics Description: Methods of solution of ordinary differential equations with General Education and other Course Attributes: Analytical & Quant applications. First order equations, linear equations of higher order, series Thought solutions and Laplace transforms. Combined credit toward a degree for MATH 2133 Calculus for Technology Programs II (A) MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously Prerequisites: A grade of "C" or better in MATH 2123 or in MATH 2144. offered as MATH 2613. Description: Second semester of a terminal sequence in calculus Credit hours: 3 for students in the School of Technology. Calculus of trigonometric, Contact hours: Lecture: 3 Contact: 3 exponential and logarithmic functions and applications to physical Levels: Undergraduate problems. Previously offered as MATH 2383. Schedule types: Lecture Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 2890 Honors Experience in Math Levels: Undergraduate Prerequisites: Honors College participation and concurrent enrollment in Schedule types: Lecture a designated MATH course. Department/School: Mathematics Description: A supplemental Honors experience in mathematics to General Education and other Course Attributes: Analytical & Quant partner concurrently with designated MATH course(s). This course adds Thought a different intellectual dimension to the designated course(s). MATH 2144 Calculus I (A) Credit hours: 1 Prerequisites: MATH 1613 with grade of "C" or better, or MATH 1715 with Contact hours: Lecture: 1 Contact: 1 grade of "C" or better, or MATH 1813 with grade of "C" or better, or an Levels: Undergraduate acceptable placement score (see placement.okstate.edu). Schedule types: Lecture Description: An introduction to derivatives, integrals and their Department/School: Mathematics applications. Previously offered as MATH 2145 and MATH 2265. General Education and other Course Attributes: Honors Credit Credit hours: 4 MATH 2910 Special Studies Contact hours: Lecture: 4 Contact: 4 Prerequisites: Consent of instructor. Levels: Undergraduate Description: Special subjects in mathematics. Offered for variable credit. Schedule types: Lecture 1-3 credit hours, maximum of 6 credit hours. Department/School: Mathematics Credit hours: 1-3 General Education and other Course Attributes: Analytical & Quant Contact hours: Contact: 1-3 Other: 1-3 Thought Levels: Undergraduate Schedule types: Independent Study Department/School: Mathematics Mathematics 3

MATH 3013 Linear Algebra (A) MATH 3583 Introduction to Mathematical Modeling Prerequisites: MATH 2153 with a grade of "C" or better. Prerequisites: MATH 2153 and MATH 3013 with grades of "C" or better. Description: Algebra and geometry of finite-dimensional linear Description: A project-based introduction to the core methods used in spaces, linear transformations, algebra of matrices, eigenvalues mathematical modeling: model building, computation and simulation, and eigenvectors. Combined credit toward a degree for MATH 2233, model verification, interpretation, and refinement. Students conduct MATH 3013 and MATH 3263 limited to six hours. inquiries to create and analyze mathematical models to solve problems Credit hours: 3 in various scientific or business contexts, using approaches that may Contact hours: Lecture: 3 Contact: 3 include discrete or continuous models, dynamical systems, stochastic Levels: Undergraduate processes, empirical modeling, and others. Written reports and oral Schedule types: Lecture presentation of solutions required. May not be used for degree credit with Department/School: Mathematics MATH 4583. General Education and other Course Attributes: Analytical & Quant Credit hours: 3 Thought Contact hours: Lecture: 3 Contact: 3 MATH 3263 Linear Algebra and Differential Equations Levels: Undergraduate Prerequisites: MATH 2153 with a grade of "C" or better. Schedule types: Lecture Description: An integrated treatment of linear algebra and differential Department/School: Mathematics equations. Combined credit toward a degree for MATH 2233, MATH 3013, MATH 3603 Mathematical Structures for Early Childhood and Elementary and MATH 3263 limited to six hours. Previously offered as MATH 3623. Teachers Credit hours: 3 Prerequisites: MATH 1483 or MATH 1493 or MATH 1513. Contact hours: Lecture: 3 Contact: 3 Description: Foundations of mathematics and number concepts for Levels: Undergraduate prospective early childhood and elementary educators. Problem solving, Schedule types: Lecture logic, set theory, functions and relations, number systems, number theory, Department/School: Mathematics rational numbers, decimals and fractions, exponentation, probability, and MATH 3303 Advanced Perspectives on Functions and Modeling for applications. Class format may emphasize student investigation and Secondary Teachers discovery, discussion and presentation, and working with mathematical Prerequisites: MATH 2153 with grade of "C" or better, and a major in tools. Together with MATH 3403, it prepares students for SMED 3153 and MATH or science on the STCH option. SMED 4153 and/or HDFS 3223. Previously offered as MATH 3723. Description: A conceptually rigorous treatment of topics in secondary Credit hours: 3 mathematics including functions, rates of change, and modeling with Contact hours: Lecture: 3 Contact: 3 linear, exponential, logarithmic, and trigonometric functions. Emphasis on Levels: Undergraduate articulating ideas and developing pre-service teachers' ability to teach for Schedule types: Lecture understanding. Applies only towards the STCH option on the Math major; Department/School: Mathematics no credit towards the MATH minor. MATH 3613 Introduction to Abstract Algebra Credit hours: 3 Prerequisites: MATH 3013 with a grade of "C" or better. Contact hours: Lecture: 3 Contact: 3 Description: An introduction to mathematical reasoning including Levels: Undergraduate logical structure of statements, quantifiers, basic set theory and Schedule types: Lecture techniques of proof. Elementary number theory including divisors and Department/School: Mathematics prime factorization, the Euclidean algorithm, and modular arithmetic. MATH 3403 Geometric Structures for Early Childhood and Elementary Introduction to rings, integral domains, fields, and polynomial rings. Teachers Previously offered as MATH 3113. Prerequisites: MATH 1483 or MATH 1493 or MATH 1513. Credit hours: 3 Description: Foundations of geometry for prospective early childhood Contact hours: Lecture: 3 Contact: 3 and elementary educators. Linear and angular measure, polygons Levels: Undergraduate and polyhedra, similarity and congruence, geometric constructions, Schedule types: Lecture motion and transformations. Class format may emphasize student Department/School: Mathematics investigation and discovery, discussion and presentation, and working MATH 3890 Advanced Honors Experience in Mathematics with mathematical tools. This course, together with MATH 3603, prepares Prerequisites: Honors College participation and concurrent enrollment In students for SMED 3153 and SMED 4153 and/or HDFS 3223. Previously a designated MATH course. offered as MATH 3733. Description: A supplemental Honors experience in mathematics to Credit hours: 3 partner concurrently with designated upper-division MATH course(s). Contact hours: Lecture: 3 Contact: 3 This course adds a different intellectual dimension to the designated Levels: Undergraduate course(s). Schedule types: Lecture Credit hours: 1 Department/School: Mathematics Contact hours: Lecture: 1 Contact: 1 Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics General Education and other Course Attributes: Honors Credit 4 Mathematics

MATH 3910 Special Studies MATH 4023 Introduction to Analysis Prerequisites: Consent of instructor. Prerequisites: MATH 2153 and MATH 3613 with grades of "C" or better, or Description: Special subjects in mathematics. Offered for variable credit, consent of instructor. 1-3 credit hours, maximum of 3 credit hours. Description: An introduction to analysis of functions of one real variable Credit hours: 1-3 emphasizing the reading and writing of mathematical proof. Basic Contact hours: Contact: 1-3 Other: 1-3 logic, set theory, functions and relations, cardinality of sets. Structure Levels: Undergraduate of the real numbers, completeness, open and closed sets, compact Schedule types: Independent Study sets. Convergence of sequences bounded and monotone sequences, Department/School: Mathematics subsequences. Limits of functions, continuity. May not be used for MATH 3933 Research Methods degree credit with MATH 5073. Prerequisites: MATH 3013 with grade of "C" or better; MATH 3613 with Credit hours: 3 grade of "C" or better recommended. Contact hours: Lecture: 3 Contact: 3 Description: A project-based introduction to the core methods used in Levels: Undergraduate mathematical research: computation, pattern recognition, conjecture, Schedule types: Lecture proof, and generalization. Students conduct inquiries in various Department/School: Mathematics mathematical areas to be selected from number theory, combinatorics, MATH 4033 History of Mathematics game theory, and others. Calculation and computer experimentation will Prerequisites: MATH 2153 with a grade of "C" or better. be used to gather data and facilitate recognition of patterns. Written Description: Historical development of mathematical ideas and methods reports and oral presentation of solutions required. relating to concepts of number, geometry, algebra, and other areas, Credit hours: 3 from the time of the ancient Greeks through major developments in Contact hours: Lecture: 3 Contact: 3 the Renaissance and 17th and 18th centuries, with a brief survey of Levels: Undergraduate later developments. Includes contributions from diverse cultures and Schedule types: Lecture individuals, and influences from astronomy and physics. The emphasis Department/School: Mathematics in the course will be on replicating historical techniques and relating MATH 4003 Mathematical Logic and Computability them to contemporary practice. The course provides future secondary Prerequisites: MATH 3613 or PHIL 3003 or consent of instructor. and college teachers with a foundation for incorporating historical Description: The basic metatheorems of first order logic: soundness, perspectives in their lessons. May not be used for degree credit with completeness, compactness, Lowenheim-Skolem theorem, undecidability MATH 5033. of first order logic, Godel's incompleteness theorem. Enumerability, Credit hours: 3 diagonalization, formal systems, standard and nonstandard models, Contact hours: Lecture: 3 Contact: 3 Godel numberings, Turing machines, recursive functions, and evidence for Levels: Undergraduate Church's thesis. Same course as PHIL 4003. Schedule types: Lecture Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 4063 Advanced Linear Algebra Levels: Undergraduate Prerequisites: MATH 3013 and MATH 3613 with grades of “C” or better; Schedule types: Lecture grades of “B” or better recommended. Department/School: Mathematics Description: A rigorous treatment of vector spaces, linear MATH 4013 Calculus of Several Variables transformations, determinants, orthogonal and unitary transformations, Prerequisites: MATH 2163 and MATH 3013 with grades of "C" or better. canonical forms, bilinear and hermitian forms, and dual spaces. Honors Description: Differential and integral calculus of functions of several and regular sections are offered and meet with MATH 5023. May not be variables, vector analysis, Stokes’ Theorem, Green’s Theorem and used for degree credit with MATH 5023. applications. May not be used for degree credit with MATH 5063. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics Schedule types: Lecture Department/School: Mathematics MATH 4083 Intermediate Analysis Prerequisites: MATH 4023 with grade of “C” or better. Description: Continuation of MATH 4023. Review of limits and continuity. Properties of continuous functions, uniform continuity, the derivative, the Mean Value Theorem. The Riemann integral, the Fundamental Theorem of Calculus. Infinite series, power series, pointwise and uniform convergence of series of functions. May not be used for degree credit with MATH 5083. Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics Mathematics 5

MATH 4143 Advanced Calculus I MATH 4283 Complex Variables Prerequisites: MATH 2163, MATH 3013, and MATH 4023 with grades of Prerequisites: MATH 2163 with a grade of "C" or better. “C” or better; grades of “B” or better recommended. Description: Properties of complex numbers, analytic functions of a Description: A rigorous treatment of calculus for functions of one and complex variable, contour integrals, Cauchy's Integral Theorem, power several variables. Elementary topology of Euclidean and metric spaces, series and Laurent series, residues and poles, conformal mapping, and continuity and uniform continuity, differentiation and integration in applications. Previously offered as MATH 4673. May not be used for one variable. Honors and regular sections are offered and meet with degree credit with MATH 5273. MATH 5043. May not be used for degree credit with MATH 5043. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 4343 Introduction to Topology MATH 4153 Advanced Calculus II Prerequisites: MATH 4023 with a grade of "C" or better. Prerequisites: MATH 4143 with grade of “C” or better; grade of “B” or Description: Topological spaces, basic point-set topology, introduction to better recommended. surfaces and three-manifolds, introduction to knot theory, applications. Description: Continuation of MATH 4143. A rigorous treatment May not be used for degree credit with MATH 5343. of sequences and series of functions, uniform convergence, and Credit hours: 3 differentiation and integration of vector-valued functions. Honors and Contact hours: Lecture: 3 Contact: 3 regular sections are offered and meet with MATH 5053. May not be used Levels: Undergraduate for degree credit with MATH 5053. Schedule types: Lecture Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 4403 Geometry Levels: Undergraduate Prerequisites: MATH 3013 with a grade of "C" or better; MATH 3613 with Schedule types: Lecture a grade of "C" or better recommended. Department/School: Mathematics Description: An axiomatic development of Euclidean and non-Euclidean MATH 4233 Intermediate Differential Equations geometries. Previously offered as MATH 4043. Prerequisites: MATH 2233 and MATH 3013 with grades of "C" or better. Credit hours: 3 Description: Systems of differential equations, series solutions, special Contact hours: Lecture: 3 Contact: 3 functions, elementary partial differential equations, Sturm-Liouville Levels: Undergraduate problems, stability and applications. Previously offered as MATH 4653. Schedule types: Lecture May not be used for degree credit with MATH 5203. Department/School: Mathematics Credit hours: 3 MATH 4423 Geometry and Algorithms in Three-Dimensional Modeling Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 2163 and MATH 3013 and (CS 1103 or CS 1113 or Levels: Undergraduate ENGR 1412) with grades of "C" or better. Schedule types: Lecture Description: A project-based introduction to 3D computer-aided design Department/School: Mathematics tools from a mathematical perspective. Students will learn some MATH 4263 Introduction to Partial Differential Equations of the mathematical background behind computer representation Prerequisites: MATH 2163 and MATH 2233 and MATH 3013 with grades and manipulation of 3D geometry and will apply their knowledge, via of "C" or better. both graphical user and programming interfaces, to design and 3D- Description: Solution of the standard partial differential equations print models visualizing mathematical concepts. Written reports and (Laplace’s equation, transport equation, heat equation, wave equation) by oral presentation required. May not be used for degree credit with separation of variables and transform methods, including eigenfunction MATH 5423. expansions, Fourier and Laplace transform. Boundary value problems, Credit hours: 3 Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, Contact hours: Lecture: 3 Contact: 3 spherical harmonics. May not be used for degree credit with MATH 5263. Levels: Undergraduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics 6 Mathematics

MATH 4453 Mathematical Interest Theory MATH 4613 Abstract Algebra I Prerequisites: MATH 2153 and MATH 2233 with grades of "C" or better. Prerequisites: MATH 3613 with grade of “C” or better; grade of “B” or Description: Fundamental concepts of financial mathematics including better recommended. simple and compound interest, inflation, yield rates, and equations of Description: A rigorous treatment of group theory including subgroups value for annuities, stocks, bonds, and other financial instruments. and quotient groups, isomorphism and homomorphism, structure theory, Determining equivalent measures of interest, determining yield rates, group actions, and the Sylow theorems. Introduction to rings, ideals, and estimating rates of return, amortization. May not be used for degree homomorphisms. Honors and regular sections are offered and meet with credit with MATH 5453. MATH 5003. May not be used for degree credit with MATH 5003. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 4513 Numerical Analysis MATH 4623 Abstract Algebra II Prerequisites: MATH 2233 and MATH 3013 with grades of "C" or better Prerequisites: MATH 4613 with grade of “C” or better; grade of “B” or and knowledge of programming, or consent of instructor. better recommended. Description: Machine computing, algorithms, and analysis of errors Description: Continuation of MATH 4613. A rigorous treatment of ring applied to interpolation and approximation of functions solving equations theory including ideals, homomorphism, unique factorization domains, and systems of equations, discrete variable methods for integrals and principal ideal domains, modules and vector spaces. Field theory and differential equations. Same course as CS 4513. May not be used for Galois theory. Honors and regular sections are offered and meet with degree credit with MATH 5513. MATH 5013. May not be used for degree credit with MATH 5013. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 4553 Introduction to Optimization MATH 4663 Combinatorics Prerequisites: MATH 2163 and MATH 3013 with grades of "C " or better. Prerequisites: MATH 3013 with a grade of "C" or better. Description: A survey of optimization theory and methods for functions Description: Introduction to graph theory and network theory, counting of several variables. Unconstrained optimization, gradient methods. techniques, generating functions, recurrence relations, and difference Linear programming, simplex method, duality. Nonlinear constrained equations. Previously offered as MATH 4273. May not be used for degree optimization. May not be used for degree credit with MATH 5503. credit with MATH 5673. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 4590 Professional Practice in Mathematics MATH 4713 Number Theory Prerequisites: Declared major in mathematics and consent of instructor. Prerequisites: MATH 3613 with a grade of "C" or better. Description: Internship or practicum experience applying mathematical Description: Divisibility of integers, congruencies, quadratic residues, principles to solve problems encountered during employment or an distribution of primes, continued fractions and the theory of ideals. internship in business, industry, or government. Written and oral reports Previously offered as MATH 4243. May not be used for degree credit with may be required. Offered for variable credit, 1-3 credit hours, maximum of MATH 5713. 3 credit hours. Credit hours: 3 Credit hours: 1-3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Contact: 1-3 Other: 1-3 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Schedule types: Independent Study Department/School: Mathematics Department/School: Mathematics MATH 4603 Intermediate Abstract Algebra Prerequisites: MATH 3613 with grade of “C” or better. Description: Introduction to groups, subgroups, homomorphisms, quotient groups. Theory of field extensions and automorphisms, introduction to Galois theory. Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics Mathematics 7

MATH 4753 Introduction to Cryptography MATH 4973 Senior Project Prerequisites: MATH 3013 and (MATH 3613 or CS 3653) with grades of Prerequisites: Junior or senior standing, and consent of instructor. "C" or better. Description: A guided program of independent reading and inquiry under Description: Classical and modern techniques for transmitting and the direction of a faculty member, culminating in an oral presentation and managing information in the presence of eavesdroppers or adversaries written report. and the mathematical principles on which they are based. Symmetric and Credit hours: 3 asymmetric ciphers such as RSA and public key cryptography. Modular Contact hours: Contact: 3 Other: 3 arithmetic, the factoring problem, and the discrete logarithm problem. Levels: Undergraduate May not be used for degree credit with MATH 5753. Schedule types: Independent Study Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 4993 Senior Honors Thesis Levels: Undergraduate Prerequisites: Consent of instructor, senior standing, and Honors Schedule types: Lecture Program participation. Department/School: Mathematics Description: A guided reading and research program ending with an MATH 4813 Groups and Representations honors thesis under the direction of a faculty member, including a public Prerequisites: MATH 3013 and MATH 3613 with grades of "C" or better, or presentation. Required for graduation with departmental honors in consent of instructor. mathematics. Description: An introduction to groups, group actions, symmetry groups, Credit hours: 3 representations and characters. Further topics may include infinite Contact hours: Contact: 3 Other: 3 symmetry groups, applications to chemistry and physics, finite isometry Levels: Undergraduate groups and geometry. May not be used for degree credit with MATH 5803. Schedule types: Independent Study Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 General Education and other Course Attributes: Honors Credit Levels: Undergraduate MATH 5000 Master's Research and Thesis Schedule types: Lecture Prerequisites: Consent of advisory committee. Department/School: Mathematics Description: Directed reading and research culminating in the master's MATH 4900 Undergraduate Research report or master's thesis. Offered for variable credit, 1-6 credit hours, Prerequisites: Consent of instructor. maximum of 6 credit hours. Description: Directed readings and research in mathematics. Offered for Credit hours: 1-6 variable credit, 1-4 credit hours, maximum of 4 credit hours. Contact hours: Contact: 1-6 Other: 1-6 Credit hours: 1-4 Levels: Graduate Contact hours: Contact: 1-4 Other: 1-4 Schedule types: Independent Study Levels: Undergraduate Department/School: Mathematics Schedule types: Independent Study MATH 5003 Abstract Algebra I Department/School: Mathematics Prerequisites: MATH 3613 with grade of “C” or better; grade of “B” or MATH 4910 Special Studies better recommended. Prerequisites: Consent of instructor. Description: A rigorous treatment of group theory including subgroups Description: Special subjects in mathematics. Offered for variable credit, and quotient groups, isomorphism and homomorphism, structure theory, 1-3 credit hours, maximum of 9 credit hours. group actions, and the Sylow theorems. Introduction to rings, ideals, and Credit hours: 1-3 homomorphisms. Meets with MATH 4613. May not be used for degree Contact hours: Contact: 1-3 Other: 1-3 credit with MATH 4613. Levels: Undergraduate Credit hours: 3 Schedule types: Independent Study Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 4950 Problem Solving Seminar Schedule types: Lecture Prerequisites: MATH 2153 with a grade of "C" or better. Department/School: Mathematics Description: The general process of problem solving. Selected problem- MATH 5010 Seminar in Mathematics solving techniques. Applications to challenging problems from all areas Prerequisites: Consent of instructor. of mathematics. Offered for variable credit, 1-3 credit hours, maximum of Description: Topics in mathematics. Offered for variable credit, 1-3 credit 3 credit hours. hours, maximum of 12 credit hours. Credit hours: 1-3 Credit hours: 1-3 Contact hours: Lecture: 1-3 Contact: 1-3 Contact hours: Contact: 1-3 Other: 1-3 Levels: Undergraduate Levels: Graduate Schedule types: Lecture Schedule types: Independent Study Department/School: Mathematics Department/School: Mathematics 8 Mathematics

MATH 5013 Abstract Algebra II MATH 5053 Advanced Calculus II Prerequisites: A grade of “C” or better in one of MATH 4613 or Prerequisites: A grade of “C” or better in one of MATH 4143 or MATH 5003; grade of “B” or better recommended. MATH 5043; grade of “B” or better recommended. Description: Continuation of MATH 5003. A rigorous treatment of ring Description: Continuation of MATH 5043. A rigorous treatment theory including ideals, homomorphism, unique factorization domains, of sequences and series of functions, uniform convergence, and principal ideal domains, modules and vector spaces. Field theory and differentiation and integration of vector-valued functions. Meets with Galois theory. Meets with MATH 4623. May not be used for degree credit MATH 4153. May not be used for degree credit with MATH 4153. with MATH 4623. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 5063 Calculus of Several Variables MATH 5023 Advanced Linear Algebra Prerequisites: MATH 2163 and MATH 3013 with grades of "C" or better. Prerequisites: MATH 3013 and MATH 3613 with grades of “C” or better; Description: Differential and integral calculus of functions of several grades of “B” or better recommended. variables, vector analysis, Stokes’ Theorem, Green’s Theorem and Description: A rigorous treatment of vector spaces, linear applications. May not be used for degree credit with MATH 4013. transformations, determinants, orthogonal and unitary transformations, Credit hours: 3 canonical forms, bilinear and Hermitian forms, and dual spaces. Meets Contact hours: Lecture: 3 Contact: 3 with MATH 4063. May not be used for degree credit with MATH 4063. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 5073 Introduction to Analysis Schedule types: Lecture Prerequisites: MATH 2153 and MATH 3613 with grades of "C" or better, or Department/School: Mathematics consent of instructor. MATH 5033 History of Mathematics Description: An introduction to analysis of functions of one real variable Prerequisites: MATH 2153 with a grade of "C" or better. emphasizing the reading and writing of mathematical proof. Basic Description: Historical development of mathematical ideas and methods logic, set theory, functions and relations, cardinality of sets. Structure relating to concepts of number, geometry, algebra, and other areas, of the real numbers, completeness, open and closed sets, compact from the time of the ancient Greeks through major developments in sets. Convergence of sequences bounded and monotone sequences, the Renaissance and 17th and 18th centuries, with a brief survey of subsequences. Limits of functions, continuity. May not be used for later developments. Includes contributions from diverse cultures and degree credit with MATH 4023. individuals, and influences from astronomy and physics. The emphasis Credit hours: 3 in the course will be on replicating historical techniques and relating Contact hours: Lecture: 3 Contact: 3 them to contemporary practice. The course provides future secondary Levels: Graduate and college teachers with a foundation for incorporating historical Schedule types: Lecture perspectives in their lessons. May not be used for degree credit with Department/School: Mathematics MATH 4033. MATH 5083 Intermediate Analysis Credit hours: 3 Prerequisites: MATH 4023 with grade of “C” or better. Contact hours: Lecture: 3 Contact: 3 Description: Continuation of MATH 4023. Review of limits and continuity. Levels: Graduate Properties of continuous functions, uniform continuity, the derivative, Schedule types: Lecture the Mean Value Theorem. The Riemann integral, the Fundamental Department/School: Mathematics Theorem of Calculus. Infinite series, power series, pointwise and uniform MATH 5043 Advanced Calculus I convergence of series of functions. May not be used for degree credit Prerequisites: MATH 2163, MATH 3013, and MATH 4023 with grades of with MATH 4083. “C” or better; grades of “B” or better recommended. Credit hours: 3 Description: A rigorous treatment of calculus for functions of one and Contact hours: Lecture: 3 Contact: 3 several variables. Elementary topology of Euclidean and metric spaces, Levels: Graduate continuity and uniform continuity, differentiation and integration in one Schedule types: Lecture variable. Meets with MATH 4143. May not be used for degree credit with Department/School: Mathematics MATH 4143. Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics Mathematics 9

MATH 5133 Stochastic Processes MATH 5213 Fourier Analysis and Wavelets Prerequisites: MATH 2233, MATH 3013 and STAT 5123. Prerequisites: MATH 4013 or MATH 4023. Description: Definition of stochastic processes, probability structure, Description: Orthogonal series expansions, Fourier series and integrals mean and covariance function, the set of sample functions, stationary and boundary value problems. Haar wavelets and multiresolution processes and their spectral analysis, renewal processes, counting analysis. Applications. analysis, discrete and continuous Markov chains, birth and death Credit hours: 3 processes, exponential model, queuing theory. Same course as IEM 5133 Contact hours: Lecture: 3 Contact: 3 & STAT 5133. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 5233 Partial Differential Equations Schedule types: Lecture Prerequisites: MATH 4013, MATH 4143 and MATH 4233 or consent of Department/School: Mathematics instructor. MATH 5143 Real Analysis I Description: Representation formulas for solutions of transport equation, Prerequisites: MATH 4153 or MATH 5053. Laplace's equation, heat equation and wave equation, mean value Description: Measure theory, measurable functions, integration and theorems, maximum principle, Green's functions, characteristics, differentiation of functions. eigenvalue problems, separation of variables, transform methods, Credit hours: 3 variational methods, general theory of first order equations. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 5153 Real Analysis II Department/School: Mathematics Prerequisites: MATH 5143. MATH 5243 Ordinary Differential Equations Description: Differentiation with respect to measures. Aspects of Prerequisites: MATH 4143 or MATH 5043; MATH 4233; MATH 5023. point set topology: nets, locally compact spaces, product spaces. Description: Banach space, contraction mapping principle, existence Elementary functional analysis: Hahn-Banach, uniform boundedness, and uniqueness theorems, linear systems, higher-order linear equations, open mapping theorems, weak topologies, Hilbert spaces. Riesz boundary value and eigenvalue problems, stability and asymptotic representation theorems: duals of Lebesgue spaces and spaces of behavior, attractors, Gronwall's inequality, Liapunov method. continuous functions. Other topics may include: elements of Fourier Credit hours: 3 analysis, distribution theory, Stone-Weierstrass theorem. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 5253 Advanced Ordinary Differential Equations Department/School: Mathematics Prerequisites: MATH 5243. MATH 5193 Differentiable Manifolds Description: Selected topics in ordinary differential equations. Prerequisites: MATH 4153 or MATH 5053; recommended MATH 4343 or Credit hours: 3 MATH 5303. Contact hours: Lecture: 3 Contact: 3 Description: Differentiable manifolds and maps, tangent vectors, vector Levels: Graduate fields, integral curves, submanifolds, differential forms, and integration. Schedule types: Lecture Additional topics may be selected from: flows, Lie derivatives, the Department/School: Mathematics Frobenius theorem, structures defined by differential forms, vector MATH 5263 Introduction to Partial Differential Equations bundles and de Rham theory. Prerequisites: MATH 2163 and MATH 2233 and MATH 3013 with grades Credit hours: 3 of "C" or better. Contact hours: Lecture: 3 Contact: 3 Description: Solution of the standard partial differential equations Levels: Graduate (Laplace’s equation, transport equation, heat equation, wave equation) by Schedule types: Lecture separation of variables and transform methods, including eigenfunction Department/School: Mathematics expansions, Fourier and Laplace transform. Boundary value problems, MATH 5203 Intermediate Differential Equations Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, Prerequisites: MATH 2233 and MATH 3013 with grades of "C" or better. spherical harmonics. May not be used for degree credit with MATH 4263. Description: Systems of differential equations, series solutions, special Credit hours: 3 functions, elementary partial differential equations, Sturm-Liouville Contact hours: Lecture: 3 Contact: 3 problems, stability and applications. Previously offered as MATH 4653. Levels: Graduate May not be used for degree credit with MATH 4233. Schedule types: Lecture Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics 10 Mathematics

MATH 5273 Complex Variables MATH 5343 Introduction to Topology Prerequisites: MATH 2163 with a grade of "C" or better. Prerequisites: MATH 4023 with a grade of "C" or better. Description: Properties of complex numbers, analytic functions of a Description: Topological spaces, basic point-set topology, introduction to complex variable, contour integrals, Cauchy's Integral Theorem, power surfaces and three-manifolds, introduction to knot theory, applications. series and Laurent series, residues and poles, conformal mapping, and May not be used for degree credit with MATH 4343. applications. Previously offered as MATH 4673. May not be used for Credit hours: 3 degree credit with MATH 4283. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 5413 Differential Geometry Department/School: Mathematics Prerequisites: MATH 4013 or MATH 4143 or MATH 5043. MATH 5283 Complex Analysis I Description: Differential manifolds, vector fields, differential forms, Prerequisites: MATH 4153 or MATH 5053. connections, Riemannian metrics, geodesics, completeness, curvature, Description: Basic topology of the plane, functions of a complex variable, and related topics. analytic functions, transformations, infinite series, integration and Credit hours: 3 conformal mapping. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 5423 Geometry and Algorithms in Three-Dimensional Modeling Department/School: Mathematics Prerequisites: MATH 2163 and MATH 3013 and (CS 1113 or ENGR 1412) MATH 5293 Complex Analysis II with grades of "C" or better. Prerequisites: MATH 5283. Description: A project-based introduction to 3D computer-aided design Description: Riemann Mapping Theorem, meromorphic functions, analytic tools from a mathematical perspective. Students will learn some continuation, Dirichlet problem, and entire functions. of the mathematical background behind computer representation Credit hours: 3 and manipulation of 3D geometry and will apply their knowledge, via Contact hours: Lecture: 3 Contact: 3 both graphical user and programming interfaces, to design and 3D- Levels: Graduate print models visualizing mathematical concepts. Written reports and Schedule types: Lecture oral presentation required. May not be used for degree credit with Department/School: Mathematics MATH 4423. MATH 5303 General Topology Credit hours: 3 Prerequisites: MATH 4143 or MATH 5043 or consent of instructor. Contact hours: Lecture: 3 Contact: 3 Description: Basic properties of topological spaces and continuous Levels: Graduate functions, including connectedness, compactness, and separation and Schedule types: Lecture countability axioms. Metric, product, and quotient spaces, Urysohn Department/School: Mathematics lemma, and Tietze extension theorem. MATH 5453 Mathematical Interest Theory Credit hours: 3 Prerequisites: MATH 2153 and MATH 2233 with grades of "C" or better. Contact hours: Lecture: 3 Contact: 3 Description: Fundamental concepts of financial mathematics including Levels: Graduate simple and compound interest, inflation, yield rates, and equations of Schedule types: Lecture value for annuities, stocks, bonds, and other financial instruments. Department/School: Mathematics Determining equivalent measures of interest, determining yield rates, MATH 5313 Geometric Topology estimating rates of return, amortization. May not be used for degree Prerequisites: MATH 4613 or MATH 5003, MATH 5303. credit with MATH 4453. Description: Manifolds, complexes, the fundamental group, covering Credit hours: 3 spaces, combinatorial group theory, the Seifert-Van Kampen theorem, and Contact hours: Lecture: 3 Contact: 3 related topics. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate Schedule types: Lecture Department/School: Mathematics Mathematics 11

MATH 5473 Financial Calculus MATH 5553 Numerical Analysis for Linear Algebra Prerequisites: MATH 4143 or MATH 5043, STAT 4203 or consent of Prerequisites: MATH 3013, and MATH 4513 or CS 4513. instructor. Description: Advanced machine computing, algorithms, analysis of Description: Introduction to derivative pricing and market derivatives. rounding errors, condition, convergence, and stability applied to direct Introduction to the Ito-Doeblin calculus and martingales; the martingale and iterative solution of linear systems of equations, linear least squares properties of Brownian motion, the Black-Scholes-Merton theory as a problems, and algebraic eigenvalue problems, including LU and QR simple, special case of martingale pricing, market models of modern fixed factorization, conjugate gradients, QR algorithm, and Lanczos method. income pricing. Insurance, hedging, and options. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 5563 Finite Element Methods for Partial Differential Equations MATH 5503 Introduction to Optimization Prerequisites: MATH 4023; MATH 4263; and MATH 4513 or CS 4513 or Prerequisites: MATH 2163 and MATH 3013 with grades of "C " or better. equivalent. MATH 4143 or MATH 5043 preferred. Description: A survey of optimization theory and methods for functions Description: Theory and practice of finite element methods, including of several variables. Unconstrained optimization, gradient methods. elliptic boundary value problems, weak formulations, the Ritz-Galerkin Linear programming, simplex method, duality. Nonlinear constrained method, conforming and non-conforming finite elements, error estimates, optimization. May not be used for degree credit with MATH 4553. and numerical experiments. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 5513 Numerical Analysis MATH 5580 Case Studies in Applied Mathematics Prerequisites: MATH 2233 and MATH 3013 with grades of "C" or better Prerequisites: MATH 2233, MATH 4013, and knowledge of computer and knowledge of programming, or consent of instructor. programming. Description: Machine computing, algorithms, and analysis of errors Description: Selected mathematical problems from industry. Independent applied to interpolation and approximation of functions solving equations problem-solving, oral presentation of solutions, and technical report and systems of equations, discrete variable methods for integrals writing. Seminar-style format. Offered for variable credit, 1-3 credit hours, and differential equations. May not be used for degree credit with maximum of 6 credit hours. MATH 4513. (MATH 5513 was used to denote Numerical Analysis I prior Credit hours: 1-3 to 1992.) Contact hours: Contact: 1-3 Other: 1-3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Independent Study Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 5593 Methods of Applied Mathematics Department/School: Mathematics Prerequisites: MATH 2233, MATH 4013, and knowledge of computer MATH 5543 Numerical Analysis for Differential Equations programming. Prerequisites: MATH 4233, MATH 4513 or CS 4513. Description: Continuous and discrete techniques in modern applied Description: Advanced machine computing, algorithms, analysis of mathematics. Positive definite matrices, eigenvalues and dynamical truncation and rounding errors, convergence and stability applied to systems, discrete and continuous equilibrium equations, least squares discrete variables, finite elements, and spectral methods in ordinary and estimation and the Kalman filter, potential flow, calculus of variations, partial differential equations. network flows, and combinatorics. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 5613 Algebra I Prerequisites: MATH 4613 or MATH 5003. Description: A rigorous treatment of classical results in group theory, ring theory, and field theory. Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics 12 Mathematics

MATH 5623 Algebra II MATH 5903 Seminar and Practicum in the Teaching of College Prerequisites: MATH 5613. Mathematics Description: A rigorous treatment of classical results in module theory, Prerequisites: Graduate standing in mathematics or consent of multilinear algebra, and representation theory. instructor. Credit hours: 3 Description: Foundations of college mathematics teaching, including Contact hours: Lecture: 3 Contact: 3 lecturing, grading and exam preparation. Adapting classroom activities Levels: Graduate to better serve different types of learners. Current trends in mathematics Schedule types: Lecture education such as calculus reform, cooperative learning, and technology Department/School: Mathematics in the classroom. Previously offered as MATH 5902. MATH 5673 Combinatorics Credit hours: 3 Prerequisites: MATH 3013 with a grade of "C" or better. Contact hours: Lecture: 3 Contact: 3 Description: Introduction to graph theory and network theory, counting Levels: Graduate techniques, generating functions, recurrence relations, and difference Schedule types: Lecture equations. May not be used for degree credit with MATH 4663. Department/School: Mathematics Credit hours: 3 MATH 5913 Introduction to Research in Mathematics Education Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 3613 or MATH 4023 or equivalent. Levels: Graduate Description: Examination and critique of research in mathematics Schedule types: Lecture education. A comparative study of research design, analysis, and Department/School: Mathematics reporting of both qualitative and quantitative research. MATH 5713 Number Theory Credit hours: 3 Prerequisites: MATH 3613 with a grade of "C" or better. Contact hours: Lecture: 3 Contact: 3 Description: Divisibility of integers, congruencies, quadratic residues, Levels: Graduate distribution of primes, continued fractions and the theory of ideals. May Schedule types: Lecture not be used for degree credit with MATH 4713. Department/School: Mathematics Credit hours: 3 MATH 6000 Doctoral Research and Dissertation Contact hours: Lecture: 3 Contact: 3 Prerequisites: Consent of advisory committee. Levels: Graduate Description: Directed reading and research culminating in the PhD or EdD Schedule types: Lecture thesis. Offered for variable credit, 1-9 credit hours, maximum of 24 credit Department/School: Mathematics hours. MATH 5753 Introduction to Cryptography Credit hours: 1-9 Prerequisites: MATH 3013 and (MATH 3613 or CS 3653) with grades of Contact hours: Contact: 1-9 Other: 1-9 "C" or better. Levels: Graduate Description: Classical and modern techniques for transmitting and Schedule types: Independent Study managing information in the presence of eavesdroppers or adversaries Department/School: Mathematics and the mathematical principles on which they are based. Symmetric and MATH 6010 Advanced Seminar in Mathematics asymmetric ciphers such as RSA and public key cryptography. Modular Prerequisites: Consent of instructor and student's advisory committee. arithmetic, the factoring problem, and the discrete logarithm problem. Description: Directed reading on advanced topics in mathematics. May not be used for degree credit with MATH 4753. Offered for variable credit, 1-3 credit hours, maximum of 12 credit hours. Credit hours: 3 Credit hours: 1-3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Contact: 1-3 Other: 1-3 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Independent Study Department/School: Mathematics Department/School: Mathematics MATH 5803 Groups and Representations MATH 6090 Doctoral Research Project Prerequisites: MATH 3013 and MATH 3613 with grades of "C" or better, or Prerequisites: Consent of advisory committee. consent of instructor. Description: Directed reading and research culminating in preliminary Description: An introduction to groups, group actions, symmetry groups, doctoral research project. Offered for variable credit, 1-6 credit hours, representations and characters. Further topics may include infinite maximum of 6 credit hours. symmetry groups, applications to chemistry and physics, finite isometry Credit hours: 1-6 groups and geometry. May not be used for degree credit with MATH 4813. Contact hours: Contact: 1-6 Other: 1-6 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Independent Study Levels: Graduate Department/School: Mathematics Schedule types: Lecture Department/School: Mathematics Mathematics 13

MATH 6143 Functional Analysis I MATH 6290 Topics in Analysis Prerequisites: MATH 4613 or MATH 5003 or MATH 5023, MATH 5153, Prerequisites: Consent of instructor. MATH 5303. Description: Advanced topics in analysis. Offered for variable credit, 1-3 Description: Theory of topological vector spaces including metrizability, credit hours, maximum of 9 credit hours. consequences of completeness, Banach spaces, weak topologies, and Credit hours: 1-3 convexity. Contact hours: Contact: 1-3 Other: 1-3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Independent Study Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 6323 Algebraic Topology I Department/School: Mathematics Prerequisites: MATH 5313. MATH 6213 Harmonic Analysis Description: Chain complexes, homology and cohomology groups, Prerequisites: MATH 5153, MATH 5283. the Eilenberg-Steenrod axioms, Mayer-Vietoris sequences, universal Description: Classical results giving connections among the size of a coefficient theorems, the Eilenberg-Zilber theorem and Kunneth formulas, harmonic or analytic function on a complex domain, the existence and cup and cap products, and duality in manifolds. smoothness of its boundary values, and behavior of the Fourier series; Credit hours: 3 selected extensions, related topics and applications. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 6390 Topics in Topology Department/School: Mathematics Prerequisites: Consent of instructor. MATH 6233 Advanced Partial Differential Equations Description: Advanced topics in topology. Offered for variable credit, 1-3 Prerequisites: MATH 5233 or consent of instructor. credit hours, maximum of 9 credit hours. Description: Schwarz class, tempered distributions, basic linear Credit hours: 1-3 functional analysis, Holder spaces, Sobolev spaces, spaces involving Contact hours: Contact: 1-3 Other: 1-3 time, Sobolev inequalities, existence and regularity theory of second-order Levels: Graduate elliptic, parabolic, and hyperbolic equations, semigroup theory. Schedule types: Independent Study Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 6433 Algebraic Geometry Levels: Graduate Prerequisites: MATH 5623. Schedule types: Lecture Description: Affine and projective varieties, dimension, algebraic curves, Department/School: Mathematics divisors and Riemann-Roch theorem for curves. MATH 6263 Potential Theory Credit hours: 3 Prerequisites: MATH 5153 and MATH 5283. Contact hours: Lecture: 3 Contact: 3 Description: Subharmonic and superharmonic functions, potentials, Levels: Graduate energy problems (including problems with external fields), equilibrium Schedule types: Lecture measures, capacities, Dirichlet problems, regularity, Green functions, Department/School: Mathematics harmonic measures, conformal mappings, and applications. MATH 6453 Complex Geometry Credit hours: 3 Prerequisites: MATH 5283. Contact hours: Lecture: 3 Contact: 3 Description: Complex manifolds, analytic sheaves, differential forms, Levels: Graduate Dolbeault cohomology, Hodge theory, line bundles, divisors, Kodaira Schedule types: Lecture embedding, and vanishing. Department/School: Mathematics Credit hours: 3 MATH 6283 Several Complex Variables Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 5283. Levels: Graduate Description: Elements of function theory of several complex variables, Schedule types: Lecture including extension phenomena, domains of holomorphy, notions of Department/School: Mathematics convexity, holomorphic maps, and complex analytic varieties. MATH 6490 Topics in Geometry Credit hours: 3 Prerequisites: Consent of instructor. Contact hours: Lecture: 3 Contact: 3 Description: Advanced topics in geometry. Offered for variable credit, 1-3 Levels: Graduate credit hours, maximum of 9 credit hours. Schedule types: Lecture Credit hours: 1-3 Department/School: Mathematics Contact hours: Contact: 1-3 Other: 1-3 Levels: Graduate Schedule types: Independent Study Department/School: Mathematics 14 Mathematics

MATH 6513 Theoretical Numerical Analysis MATH 6723 Algebraic Number Theory Prerequisites: MATH 5153, MATH 5543 or CS 5543, and MATH 5553 or Prerequisites: MATH 5013 or MATH 5623. CS 5553. Description: Number fields, ideal theory, units, decomposition of primes, Description: An advanced theoretical treatment based on function spaces quadratic and cyclotomic fields, introduction to local fields. and operator theory of algorithms for machine computing and analysis of Credit hours: 3 errors. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Graduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Graduate Department/School: Mathematics Schedule types: Lecture MATH 6790 Topics in Number Theory Department/School: Mathematics Prerequisites: Consent of instructor. MATH 6590 Topics in Applied Mathematics Description: Advanced topics in number theory. Offered for variable credit, Prerequisites: Consent of instructor. 1-3 credit hours, maximum of 9 credit hours. Description: Advanced topics in applied mathematics. Offered for variable Credit hours: 1-3 credit, 1-3 credit hours, maximum of 9 credit hours. Contact hours: Contact: 1-3 Other: 1-3 Credit hours: 1-3 Levels: Graduate Contact hours: Contact: 1-3 Other: 1-3 Schedule types: Independent Study Levels: Graduate Department/School: Mathematics Schedule types: Independent Study MATH 6813 Lie Groups and Representations Department/School: Mathematics Prerequisites: MATH 4153 or MATH 5053, MATH 4613 or MATH 5003, MATH 6613 Commutative Algebra MATH 5303. Prerequisites: MATH 5623. Description: Differentiable manifolds, vector fields, Lie groups, Description: Commutative rings, exactness properties of modules, tensor exponential map, homogeneous spaces, representations of compact Lie products, integral dependence, chain conditions, completions, filtrations, groups, and maximal tori. local rings, dimension theory, and flatness. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 6823 Lie Algebras MATH 6623 Homological Algebra Prerequisites: MATH 5013 and MATH 5023. Prerequisites: MATH 5623. Description: Matrix groups, Lie algebras, root systems, structure Description: Closed and projective classes, resolution and derived of semisimple Lie algebras, universal enveloping algebra, and functors, adjoint theorem, construction of projective classes in the representations of lie algebras. categories of groups, rings and modules; categories, Abelian categories. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Lecture Department/School: Mathematics Department/School: Mathematics MATH 6890 Topics in Representation Theory MATH 6690 Topics in Algebra Prerequisites: Consent of instructor. Prerequisites: Consent of instructor. Description: Advanced topics in representation theory. Offered for Description: Advanced topics in algebra. Offered for variable credit, 1-3 variable credit, 1-3 credit hours, maximum of 9 credit hours. credit hours, maximum of 9 credit hours. Credit hours: 1-3 Credit hours: 1-3 Contact hours: Contact: 1-3 Other: 1-3 Contact hours: Contact: 1-3 Other: 1-3 Levels: Graduate Levels: Graduate Schedule types: Independent Study Schedule types: Independent Study Department/School: Mathematics Department/School: Mathematics MATH 6923 Research in Undergraduate Mathematics Education MATH 6713 Analytic Number Theory Prerequisites: MATH 5913. Prerequisites: MATH 4283 or MATH 5283. Description: Continuation of MATH 5913 with an emphasis on design Description: Arithmetic functions, Zeta and L functions, distribution of of research in undergraduate mathematics education. Development of primes and introduction to modular forms. research questions, review of the literature, data collection and analysis, Credit hours: 3 development and evaluation of research proposals, reporting research Contact hours: Lecture: 3 Contact: 3 results. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate Schedule types: Lecture Department/School: Mathematics Mathematics 15

MATH 6990 Topics in Collegiate Mathematics Education Prerequisites: Consent of instructor. Description: Advanced topics in collegiate mathematics education. Offered for variable credit, 1-3 credit hours, maximum of 9 credit hours. Credit hours: 1-3 Contact hours: Contact: 1-3 Other: 1-3 Levels: Graduate Schedule types: Independent Study Department/School: Mathematics