Mathematics 1

MATHEMATICS Courses MATH 1483 Mathematical Functions and Their Uses (A) Math is the language of science and a vital part of both cutting-edge Prerequisites: An acceptable placement score - see research and daily life. Contemporary mathematics investigates such placement.okstate.edu. basic concepts as space and number and also the formulation and Description: Analysis of functions and their graphs from the viewpoint analysis of mathematical models arising from applications. Mathematics of rates of change. Linear, exponential, logarithmic and other functions. has always had close relationships to the physical sciences and Applications to the natural sciences, agriculture, business and the social engineering. As the biological, social, and management sciences have sciences. become increasingly quantitative, the mathematical sciences have Credit hours: 3 moved in new directions to support these fields. Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Mathematicians teach in high schools and colleges, do research and Schedule types: Lecture teach at universities, and apply mathematics in business, industry, Department/School: Mathematics and government. Outside of education, mathematicians usually work General Education and other Course Attributes: Analytical & Quant in research and analytical positions, although they have become Thought increasingly involved in management. Firms in the aerospace, MATH 1493 Applications of Modern Mathematics (A) communications, computer, defense, electronics, energy, finance, and Prerequisites: An acceptable placement score (see insurance industries employ many mathematicians. In such employment, placement.okstate.edu). a mathematician typically serves either in a consulting capacity, giving Description: Introduction to contemporary applications of discrete advice on mathematical problems to engineers and scientists, or as a mathematics. Topics from management science, statistics, coding and member of a research team composed of specialists in several fields. information theory, social choice and decision making, geometry and Among the qualities that he or she should possess are breadth of growth. interests and outlook, the ability to think abstractly, and a keen interest in Credit hours: 3 problem-solving. Contact hours: Lecture: 3 Contact: 3 An undergraduate specializing in mathematics will often begin with Levels: Undergraduate calculus or sometimes with college algebra or preparation for calculus. Schedule types: Lecture All math majors take courses in differential equations, linear algebra, Department/School: Mathematics abstract algebra, and analysis. The student’s interests and future plans General Education and other Course Attributes: Analytical & Quant determine the remainder of the field of concentration. Students are Thought encouraged to acquire proficiency in computer programming and to take MATH 1513 College Algebra (A) substantial work in related fields in which they have a special interest. Prerequisites: An acceptable placement score (see placement.okstate.edu). Two years of high school algebra recommended. Undergraduate degree tracks are available to prepare students for: Description: Quadratic equations, functions and graphs, inequalities, 1. employment in industry, business or government; systems of equations, exponential and logarithmic functions, theory of equations, sequences, permutations and combinations. Combined credit 2. secondary school mathematics teaching; and, toward a degree for MATH 1513, MATH 1613 and MATH 1715 limited to 3. graduate study in mathematics. six hours. Credit hours: 3 Students choosing secondary school teaching complete all requirements Contact hours: Lecture: 3 Contact: 3 for state certification as part of this program. Levels: Undergraduate Many of the more challenging positions in mathematics require study Schedule types: Lecture beyond a bachelor's degree. For example, university teaching requires a Department/School: Mathematics PhD, while teaching in a community college requires at least a master's General Education and other Course Attributes: Analytical & Quant degree and possibly a doctorate. Approximately 25 percent of the Thought students receiving a bachelor's degree in mathematics go on to graduate MATH 1583 Applied Geometry and Trigonometry (A) work. Prerequisites: A grade of "C" or better in one of MATH 1483 or MATH 1513, or an acceptable placement score (see placement.okstate.edu). Description: Geometry, trigonometry, and their applications to technology and design. Not intended for calculus-bound students. Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics General Education and other Course Attributes: Analytical & Quant Thought 2 Mathematics

MATH 1613 Trigonometry (A) MATH 2103 Business Calculus (A) Prerequisites: MATH 1513 with grade of "C" or better or an acceptable Prerequisites: A grade of "C" or better in one of MATH 1483 or placement score (see placement.okstate.edu). MATH 1513 or MATH 1715 or MATH 1813, or an acceptable placement Description: Trigonometric functions, solution of triangles and score (see http://placement.okstate.edu). applications to physical sciences. Combined credit toward a degree for Description: An introduction to calculus in the context of applications to MATH 1513, MATH 1613 and MATH 1715 limited to six hours. business. Previously offered as MATH 2713. Credit hours: 3 Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 2 Contact: 3 Other: 1 Levels: Undergraduate Levels: Undergraduate Schedule types: Lecture Schedule types: Discussion, Combined lecture & discussion, 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 1715 Precalculus (A) MATH 2123 Calculus for Technology Programs I (A) Prerequisites: An acceptable placement score (see http:// Prerequisites: MATH 1613 with a grade of "C" or better, or MATH 1715 placement.okstate.edu). One year of high school geometry and two years with a grade of "C" or better, or MATH 1813 with a grade of "C" or better, or of high school algebra recommended. an acceptable placement score (see placement.okstate.edu). Description: Includes an integrated treatment of topics from College Description: First semester of a terminal sequence in calculus Algebra and Trigonometry. Combined credit toward a degree for for students in the School of Technology. Functions and graphs, MATH 1513, MATH 1613 and MATH 1715 limited to six hours. Satisfies differentiation and integration with applications. Previously offered as the six hour general education Analytical and Quantitative Thought MATH 2373. requirement. Credit hours: 3 Credit hours: 5 Contact hours: Lecture: 3 Contact: 3 Contact hours: Lecture: 5 Contact: 5 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 2133 Calculus for Technology Programs II (A) MATH 1813 Preparation for Calculus (A) Prerequisites: A grade of "C" or better in MATH 2123 or in MATH 2144. Prerequisites: MATH 1513 with grade of “C” or better or an acceptable Description: Second semester of a terminal sequence in calculus placement score (see placement.okstate.edu). for students in the School of Technology. Calculus of trigonometric, Description: A conceptual approach to the algebra and trigonometry exponential and logarithmic functions and applications to physical needed for calculus. Trigonometry from the perspective of the unit problems. Previously offered as MATH 2383. circle and right triangles, behavior of trigonometric functions, and Credit hours: 3 basic identities. Functions arising in calculus and the notion of an Contact hours: Lecture: 3 Contact: 3 inverse function, especially in the context of trigonometric, logarithmic, Levels: Undergraduate and exponential functions. Rates of change and the limiting process. Schedule types: Lecture Combined credit toward a degree for MATH 1513, MATH 1613, and Department/School: Mathematics MATH 1813 limited to six hours. May not be used for degree credit with General Education and other Course Attributes: Analytical & Quant MATH 1715. Thought Credit hours: 3 MATH 2144 Calculus I (A) Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 1613 with grade of "C" or better, or MATH 1715 with Levels: Undergraduate grade of "C" or better, or MATH 1813 with grade of "C" or better, or an Schedule types: Lecture acceptable placement score (see placement.okstate.edu). Department/School: Mathematics Description: An introduction to derivatives, integrals and their General Education and other Course Attributes: Analytical & Quant applications. Previously offered as MATH 2145 and MATH 2265. Thought Credit hours: 4 MATH 1910 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 3 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 2153 Calculus II (A) MATH 3013 Linear Algebra (A) Prerequisites: MATH 2144 with grade of "C" or better. Prerequisites: MATH 2153 with a grade of "C" or better. Description: A continuation of MATH 2144, including techniques of Description: Algebra and geometry of finite-dimensional linear integration, series and their applications, parametric equations, and polar spaces, linear transformations, algebra of matrices, eigenvalues coordinates. Previously offered as MATH 2155, MATH 2163, and MATH and eigenvectors. Combined credit toward a degree for MATH 2233, 2365. MATH 3013 and MATH 3263 limited to six hours. 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 2163 Calculus III MATH 3263 Linear Algebra and Differential Equations Prerequisites: MATH 2153 with grade of "C" or better. Prerequisites: MATH 2153 with a grade of "C" or better. Description: A continuation of MATH 2153, including differential and Description: An integrated treatment of linear algebra and differential integral calculus of functions of several variables and an introduction to equations. Combined credit toward a degree for MATH 2233, MATH 3013, vector analysis. and MATH 3263 limited to six hours. Previously offered as MATH 3623. 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 2233 Differential Equations MATH 3303 Advanced Perspectives on Functions and Modeling for Prerequisites: MATH 2153 with grade of "C" or better. Secondary Teachers Description: Methods of solution of ordinary differential equations with Prerequisites: MATH 2153 with grade of "C" or better, and a major in applications. First order equations, linear equations of higher order, series MATH or science on the STCH option. solutions and Laplace transforms. Combined credit toward a degree for Description: A conceptually rigorous treatment of topics in secondary MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously mathematics including functions, rates of change, and modeling with offered as MATH 2613. linear, exponential, logarithmic, and trigonometric functions. Emphasis on Credit hours: 3 articulating ideas and developing pre-service teachers' ability to teach for Contact hours: Lecture: 3 Contact: 3 understanding. Applies only towards the STCH option on the Math major; Levels: Undergraduate no credit towards the MATH minor. 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 MATH 3403 Geometric Structures for Early Childhood and Elementary partner concurrently with designated MATH course(s). This course adds Teachers a different intellectual dimension to the designated course(s). Prerequisites: MATH 1483 or MATH 1493 or MATH 1513. Credit hours: 1 Description: Foundations of geometry for prospective early childhood Contact hours: Lecture: 1 Contact: 1 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 General Education and other Course Attributes: Honors Credit with mathematical tools. This course, together with MATH 3603, prepares MATH 2910 Special Studies students for SMED 3153 and SMED 4153 and/or HDFS 3223. Previously Prerequisites: Consent of instructor. offered as MATH 3733. Description: Special subjects in mathematics. Offered for variable credit. Credit hours: 3 1-3 credit hours, maximum of 6 credit hours. Contact hours: Lecture: 3 Contact: 3 Credit hours: 1-3 Levels: Undergraduate Contact hours: Contact: 1-3 Other: 1-3 Schedule types: Lecture Levels: Undergraduate Department/School: Mathematics Schedule types: Independent Study Department/School: Mathematics 4 Mathematics

MATH 3583 Introduction to Mathematical Modeling MATH 3910 Special Studies Prerequisites: MATH 2153 and MATH 3013 with grades of "C" or better. Prerequisites: Consent of instructor. Description: A project-based introduction to the core methods used in Description: Special subjects in mathematics. Offered for variable credit, mathematical modeling: model building, computation and simulation, 1-3 credit hours, maximum of 3 credit hours. model verification, interpretation, and refinement. Students conduct Credit hours: 1-3 inquiries to create and analyze mathematical models to solve problems Contact hours: Contact: 1-3 Other: 1-3 in various scientific or business contexts, using approaches that may Levels: Undergraduate include discrete or continuous models, dynamical systems, stochastic Schedule types: Independent Study processes, empirical modeling, and others. Written reports and oral Department/School: Mathematics presentation of solutions required. May not be used for degree credit with MATH 3933 Research Methods MATH 4583. 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 3603 Mathematical Structures for Early Childhood and Elementary game theory, and others. Calculation and computer experimentation will Teachers be used to gather data and facilitate recognition of patterns. Written Prerequisites: MATH 1483 or MATH 1493 or MATH 1513. reports and oral presentation of solutions required. Description: Foundations of mathematics and number concepts for Credit hours: 3 prospective early childhood and elementary educators. Problem solving, Contact hours: Lecture: 3 Contact: 3 logic, set theory, functions and relations, number systems, number theory, Levels: Undergraduate rational numbers, decimals and fractions, exponentation, probability, and Schedule types: Lecture applications. Class format may emphasize student investigation and Department/School: Mathematics discovery, discussion and presentation, and working with mathematical MATH 4003 Mathematical Logic and Computability tools. Together with MATH 3403, it prepares students for SMED 3153 and Prerequisites: MATH 3613 or PHIL 3003 or consent of instructor. SMED 4153 and/or HDFS 3223. Previously offered as MATH 3723. Description: The basic metatheorems of first order logic: soundness, Credit hours: 3 completeness, compactness, Lowenheim-Skolem theorem, undecidability Contact hours: Lecture: 3 Contact: 3 of first order logic, Godel's incompleteness theorem. Enumerability, Levels: Undergraduate diagonalization, formal systems, standard and nonstandard models, Schedule types: Lecture Godel numberings, Turing machines, recursive functions, and evidence for Department/School: Mathematics Church's thesis. Same course as PHIL 4003. 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 4013 Calculus of Several Variables Introduction to rings, integral domains, fields, and polynomial rings. Prerequisites: MATH 2163 and MATH 3013 with grades of "C" or better. Previously offered as MATH 3113. Description: Differential and integral calculus of functions of several Credit hours: 3 variables, vector analysis, Stokes’ Theorem, Green’s Theorem and Contact hours: Lecture: 3 Contact: 3 applications. May not be used for degree credit with MATH 5063. Levels: Undergraduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Undergraduate MATH 3890 Advanced Honors Experience in Mathematics Schedule types: Lecture Prerequisites: Honors College participation and concurrent enrollment In Department/School: Mathematics a designated MATH course. Description: A supplemental Honors experience in mathematics to partner concurrently with designated upper-division MATH course(s). This course adds a different intellectual dimension to the designated course(s). Credit hours: 1 Contact hours: Lecture: 1 Contact: 1 Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics General Education and other Course Attributes: Honors Credit Mathematics 5

MATH 4023 Introduction to Analysis MATH 4143 Advanced Calculus I Prerequisites: MATH 2153 and MATH 3613 with grades of "C" or better, or Prerequisites: MATH 2163, MATH 3013, and MATH 4023 with grades of consent of instructor. “C” or better; grades of “B” or better recommended. Description: An introduction to analysis of functions of one real variable Description: A rigorous treatment of calculus for functions of one and emphasizing the reading and writing of mathematical proof. Basic several variables. Elementary topology of Euclidean and metric spaces, logic, set theory, functions and relations, cardinality of sets. Structure continuity and uniform continuity, differentiation and integration in of the real numbers, completeness, open and closed sets, compact one variable. Honors and regular sections are offered and meet with sets. Convergence of sequences bounded and monotone sequences, MATH 5043. May not be used for degree credit with MATH 5043. subsequences. Limits of functions, continuity. May not be used for Credit hours: 3 degree credit with MATH 5073. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Undergraduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Undergraduate Department/School: Mathematics Schedule types: Lecture MATH 4153 Advanced Calculus II Department/School: Mathematics Prerequisites: MATH 4143 with grade of “C” or better; grade of “B” or MATH 4033 History of Mathematics better recommended. Prerequisites: MATH 2153 with a grade of "C" or better. Description: Continuation of MATH 4143. A rigorous treatment Description: Historical development of mathematical ideas and methods of sequences and series of functions, uniform convergence, and relating to concepts of number, geometry, algebra, and other areas, differentiation and integration of vector-valued functions. Honors and from the time of the ancient Greeks through major developments in regular sections are offered and meet with MATH 5053. May not be used the Renaissance and 17th and 18th centuries, with a brief survey of for degree credit with MATH 5053. later developments. Includes contributions from diverse cultures and Credit hours: 3 individuals, and influences from astronomy and physics. The emphasis Contact hours: Lecture: 3 Contact: 3 in the course will be on replicating historical techniques and relating Levels: Undergraduate them to contemporary practice. The course provides future secondary Schedule types: Lecture and college teachers with a foundation for incorporating historical Department/School: Mathematics perspectives in their lessons. May not be used for degree credit with MATH 4233 Intermediate Differential Equations MATH 5033. 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 4063 Advanced Linear Algebra Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 3013 and MATH 3613 with grades of “C” or better; Levels: Undergraduate grades of “B” or better recommended. Schedule types: Lecture Description: A rigorous treatment of vector spaces, linear Department/School: Mathematics transformations, determinants, orthogonal and unitary transformations, MATH 4263 Introduction to Partial Differential Equations canonical forms, bilinear and hermitian forms, and dual spaces. Honors Prerequisites: MATH 2163 and MATH 2233 and MATH 3013 with grades and regular sections are offered and meet with MATH 5023. May not be of "C" or better. used for degree credit with MATH 5023. Description: Solution of the standard partial differential equations Credit hours: 3 (Laplace’s equation, transport equation, heat equation, wave equation) by Contact hours: Lecture: 3 Contact: 3 separation of variables and transform methods, including eigenfunction Levels: Undergraduate expansions, Fourier and Laplace transform. Boundary value problems, Schedule types: Lecture Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, Department/School: Mathematics spherical harmonics. May not be used for degree credit with MATH 5263. MATH 4083 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: Undergraduate 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 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 6 Mathematics

MATH 4283 Complex Variables MATH 4453 Mathematical Interest Theory Prerequisites: MATH 2163 with a grade of "C" or better. Prerequisites: MATH 2153 and MATH 2233 with grades of "C" or better. Description: Properties of complex numbers, analytic functions of a Description: Fundamental concepts of financial mathematics including complex variable, contour integrals, Cauchy's Integral Theorem, power simple and compound interest, inflation, yield rates, and equations of series and Laurent series, residues and poles, conformal mapping, and value for annuities, stocks, bonds, and other financial instruments. applications. Previously offered as MATH 4673. May not be used for Determining equivalent measures of interest, determining yield rates, degree credit with MATH 5273. estimating rates of return, amortization. May not be used for degree Credit hours: 3 credit with MATH 5453. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Undergraduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Undergraduate Department/School: Mathematics Schedule types: Lecture MATH 4343 Introduction to Topology Department/School: Mathematics Prerequisites: MATH 4023 with a grade of "C" or better. MATH 4513 Numerical Analysis Description: Topological spaces, basic point-set topology, introduction to Prerequisites: MATH 2233 and MATH 3013 with grades of "C" or better surfaces and three-manifolds, introduction to knot theory, applications. and knowledge of programming, or consent of instructor. May not be used for degree credit with MATH 5343. Description: Machine computing, algorithms, and analysis of errors Credit hours: 3 applied to interpolation and approximation of functions solving equations Contact hours: Lecture: 3 Contact: 3 and systems of equations, discrete variable methods for integrals and Levels: Undergraduate differential equations. Same course as CS 4513. May not be used for Schedule types: Lecture degree credit with MATH 5513. Department/School: Mathematics Credit hours: 3 MATH 4403 Geometry Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 3013 with a grade of "C" or better; MATH 3613 with Levels: Undergraduate a grade of "C" or better recommended. Schedule types: Lecture Description: An axiomatic development of Euclidean and non-Euclidean Department/School: Mathematics geometries. Previously offered as MATH 4043. MATH 4553 Introduction to Optimization Credit hours: 3 Prerequisites: MATH 2163 and MATH 3013 with grades of "C " or better. Contact hours: Lecture: 3 Contact: 3 Description: A survey of optimization theory and methods for functions Levels: Undergraduate of several variables. Unconstrained optimization, gradient methods. Schedule types: Lecture Linear programming, simplex method, duality. Nonlinear constrained Department/School: Mathematics optimization. May not be used for degree credit with MATH 5503. MATH 4423 Geometry and Algorithms in Three-Dimensional Modeling Credit hours: 3 Prerequisites: MATH 2163 and MATH 3013 and (CS 1103 or CS 1113 or Contact hours: Lecture: 3 Contact: 3 ENGR 1412) with grades of "C" or better. Levels: Undergraduate Description: A project-based introduction to 3D computer-aided design Schedule types: Lecture tools from a mathematical perspective. Students will learn some Department/School: Mathematics of the mathematical background behind computer representation MATH 4590 Professional Practice in Mathematics and manipulation of 3D geometry and will apply their knowledge, via Prerequisites: Declared major in mathematics and consent of instructor. both graphical user and programming interfaces, to design and 3D- Description: Internship or practicum experience applying mathematical print models visualizing mathematical concepts. Written reports and principles to solve problems encountered during employment or an oral presentation required. May not be used for degree credit with internship in business, industry, or government. Written and oral reports MATH 5423. may be required. Offered for variable credit, 1-3 credit hours, maximum of Credit hours: 3 3 credit hours. Contact hours: Lecture: 3 Contact: 3 Credit hours: 1-3 Levels: Undergraduate Contact hours: Contact: 1-3 Other: 1-3 Schedule types: Lecture Levels: Undergraduate Department/School: Mathematics Schedule types: Independent Study 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 4613 Abstract Algebra I MATH 4753 Introduction to Cryptography Prerequisites: MATH 3613 with grade of “C” or better; grade of “B” or Prerequisites: MATH 3013 and (MATH 3613 or CS 3653) with grades of better recommended. "C" or better. Description: A rigorous treatment of group theory including subgroups Description: Classical and modern techniques for transmitting and and quotient groups, isomorphism and homomorphism, structure theory, managing information in the presence of eavesdroppers or adversaries group actions, and the Sylow theorems. Introduction to rings, ideals, and and the mathematical principles on which they are based. Symmetric and homomorphisms. Honors and regular sections are offered and meet with asymmetric ciphers such as RSA and public key cryptography. Modular MATH 5003. May not be used for degree credit with MATH 5003. arithmetic, the factoring problem, and the discrete logarithm problem. Credit hours: 3 May not be used for degree credit with MATH 5753. Contact hours: Lecture: 3 Contact: 3 Credit hours: 3 Levels: Undergraduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Lecture Levels: Undergraduate Department/School: Mathematics Schedule types: Lecture MATH 4623 Abstract Algebra II Department/School: Mathematics Prerequisites: MATH 4613 with grade of “C” or better; grade of “B” or MATH 4813 Groups and Representations better recommended. Prerequisites: MATH 3013 and MATH 3613 with grades of "C" or better, or Description: Continuation of MATH 4613. A rigorous treatment of ring consent of instructor. theory including ideals, homomorphism, unique factorization domains, Description: An introduction to groups, group actions, symmetry groups, principal ideal domains, modules and vector spaces. Field theory and representations and characters. Further topics may include infinite Galois theory. Honors and regular sections are offered and meet with symmetry groups, applications to chemistry and physics, finite isometry MATH 5013. May not be used for degree credit with MATH 5013. groups and geometry. May not be used for degree credit with MATH 5803. 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 4663 Combinatorics MATH 4900 Undergraduate Research Prerequisites: MATH 3013 with a grade of "C" or better. Prerequisites: Consent of instructor. Description: Introduction to graph theory and network theory, counting Description: Directed readings and research in mathematics. Offered for techniques, generating functions, recurrence relations, and difference variable credit, 1-4 credit hours, maximum of 4 credit hours. equations. Previously offered as MATH 4273. May not be used for degree Credit hours: 1-4 credit with MATH 5673. Contact hours: Contact: 1-4 Other: 1-4 Credit hours: 3 Levels: Undergraduate Contact hours: Lecture: 3 Contact: 3 Schedule types: Independent Study Levels: Undergraduate Department/School: Mathematics Schedule types: Lecture MATH 4910 Special Studies Department/School: Mathematics Prerequisites: Consent of instructor. MATH 4713 Number Theory Description: Special subjects in mathematics. Offered for variable credit, Prerequisites: MATH 3613 with a grade of "C" or better. 1-3 credit hours, maximum of 9 credit hours. Description: Divisibility of integers, congruencies, quadratic residues, Credit hours: 1-3 distribution of primes, continued fractions and the theory of ideals. Contact hours: Contact: 1-3 Other: 1-3 Previously offered as MATH 4243. May not be used for degree credit with Levels: Undergraduate MATH 5713. Schedule types: Independent Study Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 4950 Problem Solving Seminar Levels: Undergraduate Prerequisites: MATH 2153 with a grade of "C" or better. Schedule types: Lecture Description: The general process of problem solving. Selected problem- Department/School: Mathematics solving techniques. Applications to challenging problems from all areas of mathematics. Offered for variable credit, 1-3 credit hours, maximum of 3 credit hours. Credit hours: 1-3 Contact hours: Lecture: 1-3 Contact: 1-3 Levels: Undergraduate Schedule types: Lecture Department/School: Mathematics 8 Mathematics

MATH 4973 Senior Project MATH 5013 Abstract Algebra II Prerequisites: Junior or senior standing, and consent of instructor. Prerequisites: A grade of “C” or better in one of MATH 4613 or Description: A guided program of independent reading and inquiry under MATH 5003; grade of “B” or better recommended. the direction of a faculty member, culminating in an oral presentation and Description: Continuation of MATH 5003. A rigorous treatment of ring written report. theory including ideals, homomorphism, unique factorization domains, Credit hours: 3 principal ideal domains, modules and vector spaces. Field theory and Contact hours: Contact: 3 Other: 3 Galois theory. Meets with MATH 4623. May not be used for degree credit Levels: Undergraduate with MATH 4623. Schedule types: Independent Study Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 4993 Senior Honors Thesis Levels: Graduate 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 5023 Advanced Linear Algebra honors thesis under the direction of a faculty member, including a public Prerequisites: MATH 3013 and MATH 3613 with grades of “C” or better; presentation. Required for graduation with departmental honors in grades of “B” or better recommended. mathematics. Description: A rigorous treatment of vector spaces, linear Credit hours: 3 transformations, determinants, orthogonal and unitary transformations, Contact hours: Contact: 3 Other: 3 canonical forms, bilinear and Hermitian forms, and dual spaces. Meets Levels: Undergraduate with MATH 4063. May not be used for degree credit with MATH 4063. 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: Graduate 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 5033 History of Mathematics report or master's thesis. Offered for variable credit, 1-6 credit hours, Prerequisites: MATH 2153 with a grade of "C" or better. maximum of 6 credit hours. Description: Historical development of mathematical ideas and methods Credit hours: 1-6 relating to concepts of number, geometry, algebra, and other areas, Contact hours: Contact: 1-6 Other: 1-6 from the time of the ancient Greeks through major developments in Levels: Graduate the Renaissance and 17th and 18th centuries, with a brief survey of Schedule types: Independent Study later developments. Includes contributions from diverse cultures and Department/School: Mathematics individuals, and influences from astronomy and physics. The emphasis MATH 5003 Abstract Algebra I in the course will be on replicating historical techniques and relating Prerequisites: MATH 3613 with grade of “C” or better; grade of “B” or them to contemporary practice. The course provides future secondary better recommended. and college teachers with a foundation for incorporating historical Description: A rigorous treatment of group theory including subgroups perspectives in their lessons. May not be used for degree credit with and quotient groups, isomorphism and homomorphism, structure theory, MATH 4033. group actions, and the Sylow theorems. Introduction to rings, ideals, and Credit hours: 3 homomorphisms. Meets with MATH 4613. May not be used for degree Contact hours: Lecture: 3 Contact: 3 credit with MATH 4613. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 5043 Advanced Calculus I Schedule types: Lecture Prerequisites: MATH 2163, MATH 3013, and MATH 4023 with grades of Department/School: Mathematics “C” or better; grades of “B” or better recommended. MATH 5010 Seminar in Mathematics Description: A rigorous treatment of calculus for functions of one and Prerequisites: Consent of instructor. several variables. Elementary topology of Euclidean and metric spaces, Description: Topics in mathematics. Offered for variable credit, 1-3 credit continuity and uniform continuity, differentiation and integration in one hours, maximum of 12 credit hours. variable. Meets with MATH 4143. May not be used for degree credit with Credit hours: 1-3 MATH 4143. 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 Department/School: Mathematics Mathematics 9

MATH 5053 Advanced Calculus II MATH 5133 Stochastic Processes Prerequisites: A grade of “C” or better in one of MATH 4143 or Prerequisites: MATH 2233, MATH 3013 and STAT 5123. MATH 5043; grade of “B” or better recommended. Description: Definition of stochastic processes, probability structure, Description: Continuation of MATH 5043. A rigorous treatment mean and covariance function, the set of sample functions, stationary of sequences and series of functions, uniform convergence, and processes and their spectral analysis, renewal processes, counting differentiation and integration of vector-valued functions. Meets with analysis, discrete and continuous Markov chains, birth and death MATH 4153. May not be used for degree credit with MATH 4153. processes, exponential model, queuing theory. Same course as IEM 5133 Credit hours: 3 & STAT 5133. 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 5063 Calculus of Several Variables Department/School: Mathematics Prerequisites: MATH 2163 and MATH 3013 with grades of "C" or better. MATH 5143 Real Analysis I Description: Differential and integral calculus of functions of several Prerequisites: MATH 4153 or MATH 5053. variables, vector analysis, Stokes’ Theorem, Green’s Theorem and Description: Measure theory, measurable functions, integration and applications. May not be used for degree credit with MATH 4013. differentiation of functions. 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 5073 Introduction to Analysis MATH 5153 Real Analysis II Prerequisites: MATH 2153 and MATH 3613 with grades of "C" or better, or Prerequisites: MATH 5143. consent of instructor. Description: Differentiation with respect to measures. Aspects of Description: An introduction to analysis of functions of one real variable point set topology: nets, locally compact spaces, product spaces. emphasizing the reading and writing of mathematical proof. Basic Elementary functional analysis: Hahn-Banach, uniform boundedness, logic, set theory, functions and relations, cardinality of sets. Structure open mapping theorems, weak topologies, Hilbert spaces. Riesz of the real numbers, completeness, open and closed sets, compact representation theorems: duals of Lebesgue spaces and spaces of sets. Convergence of sequences bounded and monotone sequences, continuous functions. Other topics may include: elements of Fourier subsequences. Limits of functions, continuity. May not be used for analysis, distribution theory, Stone-Weierstrass theorem. degree credit with MATH 4023. 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 5193 Differentiable Manifolds MATH 5083 Intermediate Analysis Prerequisites: MATH 4153 or MATH 5053; recommended MATH 4343 or Prerequisites: MATH 4023 with grade of “C” or better. MATH 5303. Description: Continuation of MATH 4023. Review of limits and continuity. Description: Differentiable manifolds and maps, tangent vectors, vector Properties of continuous functions, uniform continuity, the derivative, fields, integral curves, submanifolds, differential forms, and integration. the Mean Value Theorem. The Riemann integral, the Fundamental Additional topics may be selected from: flows, Lie derivatives, the Theorem of Calculus. Infinite series, power series, pointwise and uniform Frobenius theorem, structures defined by differential forms, vector convergence of series of functions. May not be used for degree credit bundles and de Rham theory. with MATH 4083. 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 5203 Intermediate Differential Equations Prerequisites: MATH 2233 and MATH 3013 with grades of "C" or better. Description: Systems of differential equations, series solutions, special functions, elementary partial differential equations, Sturm-Liouville problems, stability and applications. Previously offered as MATH 4653. May not be used for degree credit with MATH 4233. Credit hours: 3 Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics 10 Mathematics

MATH 5213 Fourier Analysis and Wavelets MATH 5273 Complex Variables Prerequisites: MATH 4013 or MATH 4023. Prerequisites: MATH 2163 with a grade of "C" or better. Description: Orthogonal series expansions, Fourier series and integrals Description: Properties of complex numbers, analytic functions of a and boundary value problems. Haar wavelets and multiresolution complex variable, contour integrals, Cauchy's Integral Theorem, power analysis. Applications. series and Laurent series, residues and poles, conformal mapping, and Credit hours: 3 applications. Previously offered as MATH 4673. May not be used for Contact hours: Lecture: 3 Contact: 3 degree credit with MATH 4283. 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 5283 Complex 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: Basic topology of the plane, functions of a complex variable, theorems, maximum principle, Green's functions, characteristics, analytic functions, transformations, infinite series, integration and eigenvalue problems, separation of variables, transform methods, conformal mapping. variational methods, general theory of first order equations. 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 5293 Complex Analysis II MATH 5243 Ordinary Differential Equations Prerequisites: MATH 5283. Prerequisites: MATH 4143 or MATH 5043; MATH 4233; MATH 5023. Description: Riemann Mapping Theorem, meromorphic functions, analytic Description: Banach space, contraction mapping principle, existence continuation, Dirichlet problem, and entire functions. and uniqueness theorems, linear systems, higher-order linear equations, Credit hours: 3 boundary value and eigenvalue problems, stability and asymptotic Contact hours: Lecture: 3 Contact: 3 behavior, attractors, Gronwall's inequality, Liapunov method. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 5303 General Topology Schedule types: Lecture Prerequisites: MATH 4143 or MATH 5043 or consent of instructor. Department/School: Mathematics Description: Basic properties of topological spaces and continuous MATH 5253 Advanced Ordinary Differential Equations functions, including connectedness, compactness, and separation and Prerequisites: MATH 5243. countability axioms. Metric, product, and quotient spaces, Urysohn Description: Selected topics in ordinary differential equations. lemma, and Tietze extension theorem. 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 5263 Introduction to Partial Differential Equations MATH 5313 Geometric Topology Prerequisites: MATH 2163 and MATH 2233 and MATH 3013 with grades Prerequisites: MATH 4613 or MATH 5003, MATH 5303. of "C" or better. Description: Manifolds, complexes, the fundamental group, covering Description: Solution of the standard partial differential equations spaces, combinatorial group theory, the Seifert-Van Kampen theorem, and (Laplace’s equation, transport equation, heat equation, wave equation) by related topics. separation of variables and transform methods, including eigenfunction Credit hours: 3 expansions, Fourier and Laplace transform. Boundary value problems, Contact hours: Lecture: 3 Contact: 3 Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, Levels: Graduate spherical harmonics. May not be used for degree credit with MATH 4263. Schedule types: Lecture Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics Mathematics 11

MATH 5343 Introduction to Topology MATH 5473 Financial Calculus Prerequisites: MATH 4023 with a grade of "C" or better. Prerequisites: MATH 4143 or MATH 5043, STAT 4203 or consent of Description: Topological spaces, basic point-set topology, introduction to instructor. surfaces and three-manifolds, introduction to knot theory, applications. Description: Introduction to derivative pricing and market derivatives. May not be used for degree credit with MATH 4343. Introduction to the Ito-Doeblin calculus and martingales; the martingale Credit hours: 3 properties of Brownian motion, the Black-Scholes-Merton theory as a Contact hours: Lecture: 3 Contact: 3 simple, special case of martingale pricing, market models of modern fixed Levels: Graduate income pricing. Insurance, hedging, and options. Schedule types: Lecture Credit hours: 3 Department/School: Mathematics Contact hours: Lecture: 3 Contact: 3 MATH 5413 Differential Geometry Levels: Graduate Prerequisites: MATH 4013 or MATH 4143 or MATH 5043. Schedule types: Lecture Description: Differential manifolds, vector fields, differential forms, Department/School: Mathematics connections, Riemannian metrics, geodesics, completeness, curvature, MATH 5503 Introduction to Optimization and related topics. Prerequisites: MATH 2163 and MATH 3013 with grades of "C " or better. Credit hours: 3 Description: A survey of optimization theory and methods for functions Contact hours: Lecture: 3 Contact: 3 of several variables. Unconstrained optimization, gradient methods. Levels: Graduate Linear programming, simplex method, duality. Nonlinear constrained Schedule types: Lecture optimization. May not be used for degree credit with MATH 4553. Department/School: Mathematics Credit hours: 3 MATH 5423 Geometry and Algorithms in Three-Dimensional Modeling Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 2163 and MATH 3013 and (CS 1113 or ENGR 1412) Levels: Graduate 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 5513 Numerical Analysis of the mathematical background behind computer representation Prerequisites: MATH 2233 and MATH 3013 with grades of "C" or better and manipulation of 3D geometry and will apply their knowledge, via and knowledge of programming, or consent of instructor. both graphical user and programming interfaces, to design and 3D- Description: Machine computing, algorithms, and analysis of errors print models visualizing mathematical concepts. Written reports and applied to interpolation and approximation of functions solving equations oral presentation required. May not be used for degree credit with and systems of equations, discrete variable methods for integrals MATH 4423. and differential equations. May not be used for degree credit with Credit hours: 3 MATH 4513. (MATH 5513 was used to denote Numerical Analysis I prior Contact hours: Lecture: 3 Contact: 3 to 1992.) Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 5453 Mathematical Interest Theory Schedule types: Lecture Prerequisites: MATH 2153 and MATH 2233 with grades of "C" or better. Department/School: Mathematics Description: Fundamental concepts of financial mathematics including MATH 5543 Numerical Analysis for Differential Equations simple and compound interest, inflation, yield rates, and equations of Prerequisites: MATH 4233, MATH 4513 or CS 4513. value for annuities, stocks, bonds, and other financial instruments. Description: Advanced machine computing, algorithms, analysis of Determining equivalent measures of interest, determining yield rates, truncation and rounding errors, convergence and stability applied to estimating rates of return, amortization. May not be used for degree discrete variables, finite elements, and spectral methods in ordinary and credit with MATH 4453. partial differential equations. 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 12 Mathematics

MATH 5553 Numerical Analysis for Linear Algebra MATH 5623 Algebra II Prerequisites: MATH 3013, and MATH 4513 or CS 4513. Prerequisites: MATH 5613. Description: Advanced machine computing, algorithms, analysis of Description: A rigorous treatment of classical results in module theory, rounding errors, condition, convergence, and stability applied to direct multilinear algebra, and representation theory. and iterative solution of linear systems of equations, linear least squares Credit hours: 3 problems, and algebraic eigenvalue problems, including LU and QR Contact hours: Lecture: 3 Contact: 3 factorization, conjugate gradients, QR algorithm, and Lanczos method. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 5673 Combinatorics Schedule types: Lecture Prerequisites: MATH 3013 with a grade of "C" or better. Department/School: Mathematics Description: Introduction to graph theory and network theory, counting MATH 5563 Finite Element Methods for Partial Differential Equations techniques, generating functions, recurrence relations, and difference Prerequisites: MATH 4023; MATH 4263; and MATH 4513 or CS 4513 or equations. May not be used for degree credit with MATH 4663. equivalent. MATH 4143 or MATH 5043 preferred. Credit hours: 3 Description: Theory and practice of finite element methods, including Contact hours: Lecture: 3 Contact: 3 elliptic boundary value problems, weak formulations, the Ritz-Galerkin Levels: Graduate method, conforming and non-conforming finite elements, error estimates, Schedule types: Lecture and numerical experiments. Department/School: Mathematics Credit hours: 3 MATH 5713 Number Theory Contact hours: Lecture: 3 Contact: 3 Prerequisites: MATH 3613 with a grade of "C" or better. Levels: Graduate Description: Divisibility of integers, congruencies, quadratic residues, Schedule types: Lecture distribution of primes, continued fractions and the theory of ideals. May Department/School: Mathematics not be used for degree credit with MATH 4713. MATH 5580 Case Studies in Applied Mathematics Credit hours: 3 Prerequisites: MATH 2233, MATH 4013, and knowledge of computer Contact hours: Lecture: 3 Contact: 3 programming. Levels: Graduate Description: Selected mathematical problems from industry. Independent Schedule types: Lecture problem-solving, oral presentation of solutions, and technical report Department/School: Mathematics writing. Seminar-style format. Offered for variable credit, 1-3 credit hours, MATH 5753 Introduction to Cryptography maximum of 6 credit hours. Prerequisites: MATH 3013 and (MATH 3613 or CS 3653) with grades of Credit hours: 1-3 "C" or better. Contact hours: Contact: 1-3 Other: 1-3 Description: Classical and modern techniques for transmitting and Levels: Graduate managing information in the presence of eavesdroppers or adversaries Schedule types: Independent Study and the mathematical principles on which they are based. Symmetric and Department/School: Mathematics asymmetric ciphers such as RSA and public key cryptography. Modular MATH 5593 Methods of Applied Mathematics arithmetic, the factoring problem, and the discrete logarithm problem. Prerequisites: MATH 2233, MATH 4013, and knowledge of computer May not be used for degree credit with MATH 4753. programming. Credit hours: 3 Description: Continuous and discrete techniques in modern applied Contact hours: Lecture: 3 Contact: 3 mathematics. Positive definite matrices, eigenvalues and dynamical Levels: Graduate systems, discrete and continuous equilibrium equations, least squares Schedule types: Lecture estimation and the Kalman filter, potential flow, calculus of variations, Department/School: Mathematics network flows, and combinatorics. MATH 5803 Groups and Representations Credit hours: 3 Prerequisites: MATH 3013 and MATH 3613 with grades of "C" or better, or Contact hours: Lecture: 3 Contact: 3 consent of instructor. Levels: Graduate Description: An introduction to groups, group actions, symmetry groups, Schedule types: Lecture representations and characters. Further topics may include infinite Department/School: Mathematics symmetry groups, applications to chemistry and physics, finite isometry MATH 5613 Algebra I groups and geometry. May not be used for degree credit with MATH 4813. Prerequisites: MATH 4613 or MATH 5003. Credit hours: 3 Description: A rigorous treatment of classical results in group theory, ring Contact hours: Lecture: 3 Contact: 3 theory, and field theory. 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 13

MATH 5903 Seminar and Practicum in the Teaching of College MATH 6143 Functional Analysis I Mathematics Prerequisites: MATH 4613 or MATH 5003 or MATH 5023, MATH 5153, Prerequisites: Graduate standing in mathematics or consent of MATH 5303. instructor. Description: Theory of topological vector spaces including metrizability, Description: Foundations of college mathematics teaching, including consequences of completeness, Banach spaces, weak topologies, and lecturing, grading and exam preparation. Adapting classroom activities convexity. to better serve different types of learners. Current trends in mathematics Credit hours: 3 education such as calculus reform, cooperative learning, and technology Contact hours: Lecture: 3 Contact: 3 in the classroom. Previously offered as MATH 5902. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 6213 Harmonic Analysis Schedule types: Lecture Prerequisites: MATH 5153, MATH 5283. Department/School: Mathematics Description: Classical results giving connections among the size of a MATH 5913 Introduction to Research in Mathematics Education harmonic or analytic function on a complex domain, the existence and Prerequisites: MATH 3613 or MATH 4023 or equivalent. smoothness of its boundary values, and behavior of the Fourier series; Description: Examination and critique of research in mathematics selected extensions, related topics and applications. education. A comparative study of research design, analysis, and Credit hours: 3 reporting of both qualitative and quantitative research. 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 6233 Advanced Partial Differential Equations Department/School: Mathematics Prerequisites: MATH 5233 or consent of instructor. MATH 6000 Doctoral Research and Dissertation Description: Schwarz class, tempered distributions, basic linear Prerequisites: Consent of advisory committee. functional analysis, Holder spaces, Sobolev spaces, spaces involving Description: Directed reading and research culminating in the PhD or EdD time, Sobolev inequalities, existence and regularity theory of second-order thesis. Offered for variable credit, 1-9 credit hours, maximum of 24 credit elliptic, parabolic, and hyperbolic equations, semigroup theory. hours. Credit hours: 3 Credit hours: 1-9 Contact hours: Lecture: 3 Contact: 3 Contact hours: Contact: 1-9 Other: 1-9 Levels: Graduate Levels: Graduate Schedule types: Lecture Schedule types: Independent Study Department/School: Mathematics Department/School: Mathematics MATH 6263 Potential Theory MATH 6010 Advanced Seminar in Mathematics Prerequisites: MATH 5153 and MATH 5283. Prerequisites: Consent of instructor and student's advisory committee. Description: Subharmonic and superharmonic functions, potentials, Description: Directed reading on advanced topics in mathematics. energy problems (including problems with external fields), equilibrium Offered for variable credit, 1-3 credit hours, maximum of 12 credit hours. measures, capacities, Dirichlet problems, regularity, Green functions, Credit hours: 1-3 harmonic measures, conformal mappings, and applications. 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 6090 Doctoral Research Project Department/School: Mathematics Prerequisites: Consent of advisory committee. MATH 6283 Several Complex Variables Description: Directed reading and research culminating in preliminary Prerequisites: MATH 5283. doctoral research project. Offered for variable credit, 1-6 credit hours, Description: Elements of function theory of several complex variables, maximum of 6 credit hours. including extension phenomena, domains of holomorphy, notions of Credit hours: 1-6 convexity, holomorphic maps, and complex analytic varieties. 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 14 Mathematics

MATH 6290 Topics in Analysis MATH 6513 Theoretical Numerical Analysis Prerequisites: Consent of instructor. Prerequisites: MATH 5153, MATH 5543 or CS 5543, and MATH 5553 or Description: Advanced topics in analysis. Offered for variable credit, 1-3 CS 5553. credit hours, maximum of 9 credit hours. Description: An advanced theoretical treatment based on function spaces Credit hours: 1-3 and operator theory of algorithms for machine computing and analysis of Contact hours: Contact: 1-3 Other: 1-3 errors. Levels: Graduate Credit hours: 3 Schedule types: Independent Study Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 6323 Algebraic Topology I Schedule types: Lecture Prerequisites: MATH 5313. Department/School: Mathematics Description: Chain complexes, homology and cohomology groups, MATH 6590 Topics in Applied Mathematics the Eilenberg-Steenrod axioms, Mayer-Vietoris sequences, universal Prerequisites: Consent of instructor. coefficient theorems, the Eilenberg-Zilber theorem and Kunneth formulas, Description: Advanced topics in applied mathematics. Offered for variable cup and cap products, and duality in manifolds. credit, 1-3 credit hours, maximum of 9 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 6390 Topics in Topology MATH 6613 Commutative Algebra Prerequisites: Consent of instructor. Prerequisites: MATH 5623. Description: Advanced topics in topology. Offered for variable credit, 1-3 Description: Commutative rings, exactness properties of modules, tensor credit hours, maximum of 9 credit hours. products, integral dependence, chain conditions, completions, filtrations, Credit hours: 1-3 local rings, dimension theory, and flatness. 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 6433 Algebraic Geometry Department/School: Mathematics Prerequisites: MATH 5623. MATH 6623 Homological Algebra Description: Affine and projective varieties, dimension, algebraic curves, Prerequisites: MATH 5623. divisors and Riemann-Roch theorem for curves. Description: Closed and projective classes, resolution and derived Credit hours: 3 functors, adjoint theorem, construction of projective classes in the Contact hours: Lecture: 3 Contact: 3 categories of groups, rings and modules; categories, Abelian categories. Levels: Graduate Credit hours: 3 Schedule types: Lecture Contact hours: Lecture: 3 Contact: 3 Department/School: Mathematics Levels: Graduate MATH 6453 Complex Geometry Schedule types: Lecture Prerequisites: MATH 5283. Department/School: Mathematics Description: Complex manifolds, analytic sheaves, differential forms, MATH 6690 Topics in Algebra Dolbeault cohomology, Hodge theory, line bundles, divisors, Kodaira Prerequisites: Consent of instructor. embedding, and vanishing. Description: Advanced topics in algebra. Offered for variable credit, 1-3 Credit hours: 3 credit hours, maximum of 9 credit hours. Contact hours: Lecture: 3 Contact: 3 Credit hours: 1-3 Levels: Graduate Contact hours: Contact: 1-3 Other: 1-3 Schedule types: Lecture Levels: Graduate Department/School: Mathematics Schedule types: Independent Study MATH 6490 Topics in Geometry Department/School: Mathematics Prerequisites: Consent of instructor. MATH 6713 Analytic Number Theory Description: Advanced topics in geometry. Offered for variable credit, 1-3 Prerequisites: MATH 4283 or MATH 5283. credit hours, maximum of 9 credit hours. Description: Arithmetic functions, Zeta and L functions, distribution of Credit hours: 1-3 primes and introduction to modular forms. 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 Department/School: Mathematics Mathematics 15

MATH 6723 Algebraic Number Theory MATH 6990 Topics in Collegiate Mathematics Education Prerequisites: MATH 5013 or MATH 5623. Prerequisites: Consent of instructor. Description: Number fields, ideal theory, units, decomposition of primes, Description: Advanced topics in collegiate mathematics education. quadratic and cyclotomic fields, introduction to local fields. Offered for variable credit, 1-3 credit hours, maximum of 9 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 6790 Topics in Number Theory Prerequisites: Consent of instructor. Undergraduate Programs Description: Advanced topics in number theory. Offered for variable credit, • Mathematics, BA (http://catalog.okstate.edu/arts-sciences/ 1-3 credit hours, maximum of 9 credit hours. mathematics/ba/) Credit hours: 1-3 • Mathematics, BS (http://catalog.okstate.edu/arts-sciences/ Contact hours: Contact: 1-3 Other: 1-3 mathematics/bs/) Levels: Graduate • Mathematics: Actuarial and Financial Mathematics, BS (http:// Schedule types: Independent Study catalog.okstate.edu/arts-sciences/mathematics/actuarial-financial- Department/School: Mathematics bs/) MATH 6813 Lie Groups and Representations • Mathematics: Applied Mathematics, BS (http://catalog.okstate.edu/ Prerequisites: MATH 4153 or MATH 5053, MATH 4613 or MATH 5003, arts-sciences/mathematics/applied-mathematics-bs/) MATH 5303. • Mathematics: Pre-Law, BS (http://catalog.okstate.edu/arts-sciences/ Description: Differentiable manifolds, vector fields, Lie groups, mathematics/pre-law-bs/) exponential map, homogeneous spaces, representations of compact Lie groups, and maximal tori. • Mathematics: Pre-Medical Sciences, BS (http://catalog.okstate.edu/ Credit hours: 3 arts-sciences/mathematics/pre-medical-sciences-bs/) Contact hours: Lecture: 3 Contact: 3 • Mathematics: Secondary Teacher Certification, BS (http:// Levels: Graduate catalog.okstate.edu/arts-sciences/mathematics/secondary-teacher- Schedule types: Lecture certification-bs/) Department/School: Mathematics MATH 6823 Lie Algebras Graduate Programs Prerequisites: MATH 5013 and MATH 5023. The Department of Mathematics offers programs leading to the Master of Description: Matrix groups, Lie algebras, root systems, structure Science and Doctor of Philosophy degrees. of semisimple Lie algebras, universal enveloping algebra, and representations of lie algebras. Prerequisites Credit hours: 3 A student beginning graduate study in mathematics is expected to have Contact hours: Lecture: 3 Contact: 3 had, as an undergraduate, at least 18 semester hours in mathematics Levels: Graduate beyond elementary integral calculus including courses in differential Schedule types: Lecture equations, linear algebra, modern algebra and modern analysis. An Department/School: Mathematics applicant whose preparation is deficient may be admitted to the program, MATH 6890 Topics in Representation Theory if otherwise qualified, but will be required to correct the deficiency, Prerequisites: Consent of instructor. increasing somewhat the time required to complete work for the degree. Description: Advanced topics in representation theory. Offered for Prospective graduate students are advised to take at least introductory variable credit, 1-3 credit hours, maximum of 9 credit hours. courses in related fields such as physics, statistics and computer Credit hours: 1-3 science. Contact hours: Contact: 1-3 Other: 1-3 Levels: Graduate The Master of Science Degree Schedule types: Independent Study Department/School: Mathematics The department offers three tracks in the Master of Science degree, computational and applied mathematics, mathematics education and MATH 6923 Research in Undergraduate Mathematics Education pure mathematics. Each degree requires 32 credit hours of graduate Prerequisites: MATH 5913. course work in mathematics or related subjects. Two of these hours are Description: Continuation of MATH 5913 with an emphasis on design waived if a master's thesis is written. Each student must have a grade of of research in undergraduate mathematics education. Development of "A" or "B" in 18 hours of core coursework. research questions, review of the literature, data collection and analysis, development and evaluation of research proposals, reporting research results. The Doctor of Philosophy Degree Credit hours: 3 The department offers three tracks for the PhD degree: applied Contact hours: Lecture: 3 Contact: 3 mathematics, mathematics education and pure mathematics. Admission Levels: Graduate to the PhD program is granted only to students with superior records Schedule types: Lecture in their previous graduate or undergraduate study. A minimum of 90 Department/School: Mathematics semester credit hours of graduate credit beyond the bachelor's degree 16 Mathematics

is required for the PhD degree. This may include a maximum of 24 hours credit for the thesis. Each student has an individual doctoral committee that advises the student in the formulation of an approved plan of study for the degree. Each student must pass three comprehensive exams from a selection of core topic areas, or pass two such exams and complete a minor thesis.

The most important requirement for the PhD degree is the preparation of an acceptable dissertation. This dissertation must demonstrate the candidate's ability to do independent, original work in mathematics, or mathematics education. Minors • Actuarial Science (ACSC), Minor (http://catalog.okstate.edu/arts- sciences/mathematics/actuarial-science-minor/) • Mathematics (MATH), Minor (http://catalog.okstate.edu/arts- sciences/mathematics/mathematics-minor/) Faculty Christopher Francisco, PhD—Professor and Head Regents Professor: Alan Adolphson, PhD (emeritus); William Jaco, PhD (Grayce B. Kerr Chair); Jiahong Wu, PhD (AT&T Professor) Professors: Douglas B. Aichele, EdD (emeritus); Dale E. Alspach, PhD (emeritus); Leticia Barchini, PhD; Dennis Bertholf, PhD (emeritus); Birne Binegar, PhD; Herman Burchard, PhD (emeritus); James R. Choike, PhD (emeritus); Bruce C. Crauder, PhD; Benny Evans, PhD (emeritus); Amit Ghosh, PhD; Anthony Kable, PhD; Marvin S. Keener, PhD (emeritus); JaEun Ku, PhD; Weiping Li, PhD; Lisa A. Mantini, PhD; J. Robert Myers, PhD; Alan Noell, PhD; Michael Oehrtman, PhD (Noble Professor); Igor Pritsker, PhD (Vaughn Professor); David J. Ullrich, PhD (emeritus); John Wolfe, PhD (emeritus); David J. Wright, PhD; Roger Zierau, PhD Associate Professors: Mahdi Asgari, PhD; Paul Fili, PhD; Ning Ju, PhD; Jiři Lebl, PhD; Jeffrey Mermin, PhD; Edward Richmond, PhD; Jay Schweig, PhD; Henry Segerman, PhD Assistant Professors: John Paul Cook, PhD; Sean Curry, PhD; John Doyle, PhD; Neil Hoffman, PhD; Anand Patel, PhD; Michael Tallman, PhD; Xukai Yan, PhD; Xu Zhang, PhD Teaching Assistant Professors: Lee Ann Brown, MS; Allison Dorko, PhD; Detelin Dosev, PhD; Cynthia Francisco, MS; Melissa Mills, PhD; Donna Rae Tree, MS