Course Listing For MATH

(MATH)ACAM 0097. Intermediate Algebra I. 3 hours.
Oasis Title: INTERMED ALG I.
Concepts of fractions, decimals, percents, and signed numbers. Methods for solving first degree equations, systems, and related applications, and graphing linear equations.
Non-traditional format: This course carries institutional credit and will not count toward graduation.
Offered fall, spring, and summer semesters every year.

(MATH)ACAM 0098. Intermediate Algebra II. 3 hours.
Oasis Title: INTERMED ALG II.
Concepts of factoring, functions, polynomials. Methods for solving second degree and rational equations and related applications. Operations regarding polynomials, exponents, and radicals.
Non-traditional format: This course carries institutional credit and will not count toward graduation.
Offered fall, spring, and summer semesters every year.

(MATH)ACAM 0099. Introduction to College Algebra. 3 hours.
Oasis Title: INTRO COLLEGE ALG.
Concepts of factoring, exponents, polynomials, radicals, fractions, and graphing. Methods for solving equations: rational, first and second degree, absolute value, inequalities, and systems and their related applications.
Non-traditional format: This course carries institutional credit and will not count toward graduation.
Offered fall, spring, and summer semesters every year.

MATH 1060. Mathematics of Decision Making. 3 hours.
Oasis Title: MAT DECISION MAKING.
Applications of modern mathematics to management and decision making including the solution of optimization problems using network theory, methods for optimal scheduling, voting methods, game theory, and related strategies. Applications include planning of postal delivery routes, placement of cable television lines, United States Congressional apportionment, and dispute resolution.
Offered fall, spring, and summer semesters every year.

MATH 1090. Trigonometry. 3 hours.
Oasis Title: TRIGONOMETRY.
Not open to students with credit in MATH 1113.
Trigonometry with an emphasis on geometric applications.
Non-traditional format: This course is also offered through University System of Georgia Independent Study (USGIS).
Offered fall and spring semesters every year.

MATH 1101. Mathematical Modeling. 3 hours.
Oasis Title: MATH MODELING.
Mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. The investigation and analysis of applied problems and questions, and of effective communication of quantitative concepts and results.
Non-traditional format: This course is also offered through University System of Georgia Independent Study (USGIS).
Offered fall, spring, and summer semesters every year.

MATH 1113. Precalculus. 3 hours.
Oasis Title: PRECALCULUS.
Preparation for calculus, including an intensive study of algebraic, exponential, logarithmic, and trigonometric functions and their graphs. Applications include simple maximum/minimum problems, exponential growth and decay, and surveying problems.
Non-traditional format: This course is also offered through University System of Georgia Independent Study (USGIS).
Offered fall, spring, and summer semesters every year.

MATH 1700. Arithmetic and Problem Solving. 3 hours.
Oasis Title: ARITH & PROB SOLV.
Prerequisite: MATH 1101.
Problem solving and critical thinking involving mathematics particularly appropriate for prospective elementary school teachers. Emphasis will be placed on properties of number systems, basic geometric concepts, and challenging problems involving elementary mathematics.
Offered fall, spring, and summer semesters every year.

MATH 2110. Calculus for Economics. 3 hours.
Oasis Title: CALC FOR ECONOMICS.
Not open to students with credit in MATH 2210 or MATH 2210L or MATH 2310H or MATH 2410H.
Prerequisite: MATH 2200 and MATH 2200L.
Topics specifically chosen to meet the needs of the student of economics: the definite integral, functions of several variables, partial derivatives, Lagrange multipliers, and matrices.
Offered spring semester every year.

MATH 2200. Analytic Geometry and Calculus. 3 hours.
Oasis Title: ANALY GEO AND CALC.
Not open to students with credit in MATH 2300H or MATH 2400H.
Prerequisite: MATH 1113.
Corequisite: MATH 2200L.
Introductory differential calculus and its applications. Topics include limits, continuity, differentiability, derivatives of trigonometric, exponential and logarithmic functions, maximum-minimum problems, curve sketching, Newton's method, and antiderivatives.
Non-traditional format: This course is also offered through University System of Georgia Independent Study (USGIS).
Offered fall, spring, and summer semesters every year.

MATH 2200L. Differential Calculus Laboratory. 1 hour. 2 hours lab per week.
Oasis Title: DIFF CALC LAB.
Corequisite: MATH 2200 or MATH 2300H.
Computer projects exploring topics related to the course content of Analytic Geometry and Calculus.
Non-traditional format: This course is also offered through University System of Georgia Independent Study (USGIS).
Offered fall, spring, and summer semesters every year.

MATH 2210. Integral Calculus. 3 hours.
Oasis Title: INTEGRAL CALCULUS.
Not open to students with credit in MATH 2110 or MATH 2310H or MATH 2410H.
Prerequisite: MATH 2200 or MATH 2300H or MATH 2400H.
Corequisite: MATH 2210L.
Introductory integral calculus and its applications. Topics include Riemann sums, the Riemann integral, the Fundamental Theorem of calculus, techniques of integration, arc length, surface area, volumes, force, work, and an introduction to differential equations.
Offered fall, spring, and summer semesters every year.

MATH 2210L. Integral Calculus Laboratory. 1 hour. 2 hours lab per week.
Oasis Title: INT CALC LAB.
Corequisite: MATH 2210 or MATH 2310H.
Computer projects exploring topics related to the course content of Integral Calculus.
Offered fall, spring, and summer semesters every year.

MATH 2300H. Differential Calculus (Honors). 3 hours.
Oasis Title: DIFF CALC HONORS.
Not open to students with credit in MATH 2200.
Prerequisite: MATH 1113 and permission of Honors.
Corequisite: MATH 2200L.
Honors differential calculus and its applications.
Offered fall semester every year.

MATH 2310H. Integral Calculus (Honors). 3 hours.
Oasis Title: INT CALC (HONORS).
Not open to students with credit in MATH 2110 or MATH 2210 or MATH 2410H.
Prerequisite: (MATH 2200 or MATH 2300H or MATH 2400H) and permission of Honors.
Corequisite: MATH 2210L.
Honors integral calculus.
Offered spring semester every year.

MATH 2400H. Differential Calculus with Theory (Honors). 4 hours.
Oasis Title: DIF CALC THRY HNRS.
Not open to students with credit in MATH 2110 or MATH 2210 or MATH 2310H.
Prerequisite: Permission of Honors.
A more rigorous and extensive treatment of differential calculus. Topics include the real numbers, the least upper bound property, limits, continuity, differentiability, and applications. Students with a strong background and interest in mathematics are encouraged to take this course; prior experience with calculus is not required.
Offered fall semester every year.

MATH 2410H. Integral Calculus with Theory (Honors). 4 hours.
Oasis Title: INT CALC THRY HNRS.
Not open to students with credit in MATH 2110 or MATH 2210 or MATH 2310H.
Prerequisite: MATH 2400H and permission of Honors.
A more rigorous and extensive treatment of integral calculus. Topics include the Fundamental Theorem of calculus, applications of integration, logarithms and exponentials, Taylor polynomials, sequences, series, and uniform convergence.
Offered spring semester every year.

MATH 2500. Multivariable Calculus. 3 hours.
Oasis Title: MULTIVARIABLE CALC.
Not open to students with credit in MATH 3510.
Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.
Calculus of functions of two and three variables including vectors in two and three dimensions, parametric curves, continuity and differentiability of functions of several variables, directional derivatives, Lagrange multipliers, multiple integration, polar coordinates, Green's theorem, and Stokes' theorem.
Offered fall, spring, and summer semesters every year.

(MATH)CSCI 2610. Discrete Mathematics for Computer Science. 4 hours.
Oasis Title: DISCRETE MATH.
Prerequisite: CSCI 1301-1301L.
The fundamental mathematical tools used in computer science: sets, relations, and functions; propositional logic, predicate logic, and inductive proofs; summations, recurrences, and elementary asymptotics; counting and discrete probability; undirected and directed graphs; introductory linear algebra, with applications in computer science.
Offered spring semester every year.

MATH 2700. Elementary Differential Equations. 3 hours.
Oasis Title: ELEM DIFF EQNS.
Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.
First and second order ordinary differential equations, including physical and biological applications, numerical solutions, and mathematical modeling.
Offered fall, spring, and summer semesters every year.

MATH 3000. Introduction to Linear Algebra. 3 hours.
Oasis Title: INTRO TO LINEAR ALG.
Not open to students with credit in MATH 3500.
Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.
Theory and applications of systems of linear equations, vector spaces, and linear transformations. Fundamental concepts include: linear independence, basis, and dimension; orthogonality, projections, and least squares solutions of inconsistent systems; eigenvalues, eigenvectors, and applications to Markov chains, difference equations, and quadratic forms.
Offered fall, spring, and summer semesters every year.

MATH 3100. Sequences and Series. 3 hours.
Oasis Title: SEQUENCES & SERIES.
Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.
Precise definitions of limit and convergence concepts; practical tests for convergence of infinite series; power series representations and numerical error estimates; applications to calculus and explicit summation formulae; trigonometric series.
Offered fall and spring semesters every year.

MATH 3200. Introduction to Higher Mathematics. 3 hours.
Oasis Title: INTRO HIGHER MATH.
Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.
Preparation in mathematical reasoning and proof-writing necessary for upper division course work in mathematics. Topics include logic, integers and induction, sets and relations, equivalence relations and partitions, and functions (including injectivity and surjectivity).
Offered fall, spring, and summer semesters every year.

MATH 3500. Multivariable Mathematics I. 3 hours.
Oasis Title: MULTIVAR MATH I.
Not open to students with credit in MATH 3000.
Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.
Prerequisite or corequisite: MATH 3200.
Vector algebra and geometry; fundamental concepts of linear algebra; linear transformations; differential calculus of functions of several variables; eigenvalues and applications. The sequence of Multivariable Mathematics gives an integrated and more conceptual treatment of the material in Multivariable Calculus and Introduction to Linear Algebra.
Offered fall semester every year.

MATH 3510. Multivariable Mathematics II. 3 hours.
Oasis Title: MULTIVAR MATH II.
Not open to students with credit in MATH 2500.
Prerequisite: MATH 3500.
Inverse function theorem and Jacobians; integration in several variables, the change of variables theorem; line integrals, surface integrals, and Stokes' Theorem; applications to physics.
Offered spring semester every year.

MATH 4000/6000. Modern Algebra and Geometry I. 3 hours.
Oasis Title: MOD ALG & GEOM I.
Undergraduate prerequisite: (MATH 3000 and MATH 3200) or permission of department.
Abstract algebra, emphasizing geometric motivation and applications. Beginning with a careful study of integers, modular arithmetic, and the Euclidean algorithm, the course moves on to fields, isometries of the complex plane, polynomials, splitting fields, rings, homomorphisms, field extensions, and compass and straightedge constructions.
Offered fall, spring, and summer semesters every year.

MATH 4010/6010. Modern Algebra and Geometry II. 3 hours.
Oasis Title: MOD ALG & GEOM II.
Undergraduate prerequisite: MATH 4000/6000.
More advanced abstract algebraic structures and concepts, such as groups, symmetry, group actions, counting principles, symmetry groups of the regular polyhedra, Burnside's Theorem, isometries of R^3, Galois Theory, and affine and projective geometry.
Offered spring semester every year.

MATH 4050/6050. Advanced Linear Algebra. 3 hours.
Oasis Title: ADV LIN ALG.
Undergraduate prerequisite: MATH 4000/6000.
Orthogonal and unitary groups, spectral theorem; infinite dimensional vector spaces; Jordan and rational canonical forms and applications.
Not offered on a regular basis.

MATH 4080/6080. Advanced Algebra. 3 hours.
Oasis Title: ADVANCED ALGEBRA.
Undergraduate prerequisite: MATH 4010/6010 or permission of department.
Linear algebra, groups, rings, and modules, intermediate in level between Modern Algebra and Geometry II and Algebra. Topics include the finite-dimensional spectral theorem, group actions, classification of finitely generated modules over principal ideal domains, and canonical forms of linear operators.
Offered fall semester every even-numbered year.

MATH 4100/6100. Real Analysis. 3 hours.
Oasis Title: REAL ANALYSIS.
Undergraduate prerequisite: (MATH 3100 and MATH 3200) or permission of department.
Metric spaces and continuity; differentiable and integrable functions of one variable; sequences and series of functions.
Offered fall semester every year.

MATH 4110/6110. The Lebesgue Integral and Applications. 3 hours.
Oasis Title: LEBESGUE INTEGRAL.
Undergraduate prerequisite: MATH 4100/6100 or MATH 4200/6200 or permission of department.
The Lebesgue integral with applications to Fourier analysis and probability.
Offered spring semester every even-numbered year.

MATH 4120/6120. Multivariable Analysis. 3 hours.
Oasis Title: MULTIVAR ANALYSIS.
Undergraduate prerequisite: MATH 3510 or MATH 4100/6100 or MATH 4200/6200.
The derivative as a linear map, inverse and implicit function theorems, change of variables in multiple integrals; manifolds, differential forms, and the generalized Stokes' Theorem.
Offered spring semester every odd-numbered year.

MATH 4150/6150. Complex Variables. 3 hours.
Oasis Title: COMPLEX VARIABLES.
Undergraduate prerequisite: (MATH 2500 and MATH 3100) or MATH 3510.
Differential and integral calculus of functions of a complex variable, with applications. Topics include the Cauchy integral formula, power series and Laurent series, and the residue theorem.
Offered every year.

MATH 4200/6200. Point Set Topology. 3 hours.
Oasis Title: POINT SET TOPOLOGY.
Undergraduate prerequisite: MATH 3100 and MATH 3200.
Topological spaces, continuity; connectedness, compactness; separation axioms and Tietze extension theorem; function spaces.
Offered every year.

MATH 4220/6220. Differential Topology. 3 hours.
Oasis Title: DIFF TOPOLOGY.
Undergraduate prerequisite: MATH 4120/6120 and (MATH 4100/6100 or MATH 4200/6200).
Manifolds in Euclidean space: fundamental ideas of transversality, homotopy, and intersection theory; differential forms, Stokes' Theorem, deRham cohomology, and degree theory.
Offered fall semester every odd-numbered year.

MATH 4250/6250. Differential Geometry. 3 hours.
Oasis Title: DIFF GEOMETRY.
Undergraduate prerequisite: (MATH 2500 and MATH 3000) or MATH 3510.
The geometry of curves and surfaces in Euclidean space: Frenet formulas for curves, notions of curvature for surfaces; Gauss-Bonnet Theorem; discussion of non-Euclidean geometries.
Offered every year.

MATH 4300/6300. Introduction to Algebraic Curves. 3 hours.
Oasis Title: INTRO TO ALG CURVES.
Undergraduate prerequisite: MATH 4000/6000 or permission of department.
Polynomials and resultants, projective spaces. The focus is on plane algebraic curves: intersection, Bezout's theorem, linear systems, rational curves, singularities, blowing up.
Not offered on a regular basis.

MATH 4400/6400. Number Theory. 3 hours.
Oasis Title: NUMBER THEORY.
Undergraduate prerequisite: MATH 4000/6000.
Euler's theorem, public key cryptology, pseudoprimes, multiplicative functions, primitive roots, quadratic reciprocity, continued fractions, sums of two squares and Gaussian integers.
Offered spring semester every year.

MATH 4450/6450. Cryptology and Computational Number Theory. 3 hours.
Oasis Title: COMP NUMBER THY.
Undergraduate prerequisite: MATH 4000/6000.
Recognizing prime numbers, factoring composite numbers, finite fields, elliptic curves, discrete logarithms, private key cryptology, key exchange systems, signature authentication, public key cryptology.
Not offered on a regular basis.

MATH 4500/6500. Numerical Analysis I. 3 hours.
Oasis Title: NUMER ANALYSIS I.
Undergraduate prerequisite: MATH 3000.
Undergraduate prerequisite or corequisite: MATH 3100.
Methods for finding approximate numerical solutions to a variety of mathematical problems, featuring careful error analysis. A mathematical software package will be used to implement iterative techniques for nonlinear equations, polynomial interpolation, integration, and problems in linear algebra such as matrix inversion, eigenvalues and eigenvectors.
Offered fall and spring semesters every year.

MATH 4510/6510. Numerical Analysis II. 3 hours.
Oasis Title: NUMER ANALYSIS II.
Undergraduate prerequisite: (MATH 2500 or MATH 3510) and MATH 2700 and MATH 4500/6500.
Numerical solutions of ordinary and partial differential equations, higher-dimensional Newton's method, and splines.
Offered spring semester every year.

MATH 4600/6600. Probability. 3 hours.
Oasis Title: PROBABILITY.
Undergraduate prerequisite: (MATH 2500 and MATH 3100) or MATH 3510.
Discrete and continuous random variables, expectation, independence and conditional probability; binomial, Bernoulli, normal, and Poisson distributions; law of large numbers and central limit theorem.
Offered every year.

MATH(CSCI) 4630/6630. Mathematical Analysis of Computer Algorithms. 3 hours.
Oasis Title: ALGORITHMS.
Undergraduate prerequisite: MATH 3000 and (MATH 3200 or CSCI(MATH) 2610).
Discrete algorithms (number-theoretic, graph-theoretic, combinatorial, and algebraic) with an emphasis on techniques for their mathematical analysis.
Not offered on a regular basis.

MATH(CSCI) 4670/6670. Combinatorics. 3 hours.
Oasis Title: COMBINATORICS.
Undergraduate prerequisite: MATH 3000 and (MATH 3200 or CSCI(MATH) 2610).
Basic counting principles: permutations, combinations, probability, occupancy problems, and binomial coefficients. More sophisticated methods include generating functions, recurrence relations, inclusion/exclusion principle, and the pigeonhole principle. Additional topics include asymptotic enumeration, Polya counting theory, combinatorial designs, coding theory, and combinatorial optimization.
Offered every year.

MATH(CSCI) 4690/6690. Graph Theory. 3 hours.
Oasis Title: GRAPH THEORY.
Undergraduate prerequisite: MATH 3000 and (MATH 3200 or CSCI(MATH) 2610).
Elementary theory of graphs and digraphs. Topics include connectivity, reconstruction, trees, Euler's problem, hamiltonicity, network flows, planarity, node and edge colorings, tournaments, matchings, and extremal graphs. A number of algorithms and applications are included.
Offered every year.

MATH 4700/6700. Qualitative Ordinary Differential Equations. 3 hours.
Oasis Title: QUAL ORD DIFF EQNS.
Undergraduate prerequisite: MATH 2700 and (MATH 3000 or MATH 3500).
Transform methods, linear and nonlinear systems of ordinary differential equations, stability, and chaos.
Offered every year.

MATH 4720/6720. Introduction to Partial Differential Equations. 3 hours.
Oasis Title: INTRO TO PDES.
Undergraduate prerequisite: MATH 2700 and (MATH 2500 or MATH 3510).
The basic partial differential equations of mathematical physics: Laplace's equation, the wave equation, and the heat equation. Separation of variables and Fourier series techniques are featured.
Offered every year.

MATH 4760/6760. Mathematics and Music. 3 hours.
Oasis Title: MATH AND MUSIC.
Undergraduate prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.
This course is intended for undergraduates (math majors, music majors, and others) interested in the mathematical aspects of music. At least some familiarity with musical notation is a prerequisite. Topics to be discussed include the structure of sound, the construction of scales, and synthesis.
Not offered on a regular basis.

MATH 4780/6780. Mathematical Biology. 3 hours.
Oasis Title: MAT BIOLOGY.
Undergraduate prerequisite: MATH 2700 and (MATH 3000 or MATH 3500).
Mathematical models in the biological sciences: compartmental flow models, dynamic system models, discrete and continuous models, deterministic and stochastic models.
Not offered on a regular basis.

MATH 4850/6850. History of Mathematics. 3 hours.
Oasis Title: HISTORY OF MATH.
Undergraduate prerequisite: Senior standing.
The development of mathematical thought from ancient times to the present, paying particular attention to the context of today's mathematics curriculum.
Not offered on a regular basis.

MATH 4900/6900. Topics in Mathematics. 3 hours. Repeatable for maximum 6 hours credit.
Oasis Title: TOPICS IN MATH.
Undergraduate prerequisite: Senior standing.
A special topic not otherwise offered in the mathematics curriculum.
Not offered on a regular basis.

MATH 4960H. Directed Readings and/or Projects (Honors). 3 hours.
Oasis Title: DIRECTED READINGS.
Prerequisite: Senior standing and permission of Honors.
Individual study, reading, or projects under the direction of a project director.
Non-traditional format: Directed study.
Not offered on a regular basis.

MATH 4970H. Directed Readings and/or Projects (Honors). 3 hours.
Oasis Title: DIRECTED READINGS.
Prerequisite: Senior standing and permission of Honors.
Individual study, reading, or projects under the direction of a project director.
Non-traditional format: Directed study.
Not offered on a regular basis.

MATH 4990H. Honors Thesis. 3 hours.
Oasis Title: HONORS THESIS.
Prerequisite: Permission of Honors.
Individual research in the major or in a closely related field.
Non-traditional format: Thesis course.
Offered fall, spring, and summer semesters every year.

MATH 5020/7020. Arithmetic for Middle School Teachers. 3 hours.
Oasis Title: IDEAS OF ARITHMETIC.
Undergraduate prerequisite: MATH 2200 and MATH 2200L.
Operations of arithmetic for middle school teachers; number systems; set theory to study mappings, functions, and equivalence relations.
Not offered on a regular basis.

MATH 5030/7030. Geometry and Measurement for Middle School Teachers. 3 hours.
Oasis Title: GEOM AND MEAS.
Undergraduate prerequisite: MATH 2200 and MATH 2200L.
Principles of geometry and measurement for middle school teachers.
Not offered on a regular basis.

MATH 5070/7070. Calculus for Advanced Placement Teachers. 3 hours.
Oasis Title: CALC FOR AP TEACH.
Undergraduate prerequisite: MATH 2500.
Variable calculus designed to prepare in-service secondary school teachers for effective instruction of advanced placement students. Emphasizes concepts and principles underlying differential and integral calculus of a single variable.
Not offered on a regular basis.

MATH 5200/7200. Foundations of Geometry I. 3 hours.
Oasis Title: FNDNS GEOMETRY I.
Undergraduate prerequisite: MATH 3000 and MATH 3200.
Advanced elementary geometry for prospective teachers of secondary school mathematics: axiom systems and models; the parallel postulate; neutral, Euclidean, and non-Euclidean geometries.
Offered fall and spring semesters every year.

MATH 5210/7210. Foundations of Geometry II. 3 hours.
Oasis Title: FNDNS GEOMETRY II.
Undergraduate prerequisite: MATH 5200/7200.
Further development of the axioms and models for Euclidean and non-Euclidean geometry; transformation geometry.
Offered spring semester every year.

MATH 5560/7560. Probability and Statistics for Teachers. 3 hours.
Oasis Title: PROB/STAT FOR TEACH.
Undergraduate prerequisite: MATH 2200 and MATH 2200L.
Fundamental ideas of probability with particular emphasis on their applications in statistics.
Not offered on a regular basis.

MATH 6800. Directed Reading and/or Projects. 1-6 hours. Repeatable for maximum 30 hours credit.
Oasis Title: DIR READ AND/OR PRO.
Directed reading and/or project at the master's level.
Non-traditional format: Directed study.
Offered every year.

MATH 7000. Master's Research. 1-6 hours. Repeatable for maximum 30 hours credit.
Oasis Title: MASTER'S RESEARCH.
Prerequisite: Permission of department.
Research while enrolled for a master's degree under the direction of faculty members.
Non-traditional format: Independent research under the direction of a faculty member.
Offered fall, spring, and summer semesters every year.

MATH 7040. Basic Ideas of Calculus I. 3 hours.
Oasis Title: CALCULUS IDEAS I.
Prerequisite: MATH 2210 and MATH 2210L.
Survey of one-variable calculus in preparation for teaching calculus at the secondary level: combines review of basic techniques with careful study of underlying concepts.
Offered every year.

MATH 7050. Basic Ideas of Calculus II. 3 hours.
Oasis Title: CALCULUS IDEAS II.
Prerequisite: MATH 7040.
A continuation of Basic Ideas of Calculus I focusing on functions of several variables.
Offered every year.

MATH 7100. Technical Report. 3 hours.
Oasis Title: TECHNICAL REPORT.
For use with the Master's degree in Applied Mathematical Science - Mathematics option.
Non-traditional format: Independent research under the direction of a faculty member.
Offered fall, spring, and summer semesters every year.

MATH 7300. Master's Thesis. 1-9 hours. Repeatable for maximum 18 hours credit.
Oasis Title: MASTER'S THESIS.
Prerequisite: Permission of department.
Thesis writing under the direction of the major professor.
Non-traditional format: Independent research and thesis preparation.
Offered every year.

MATH 8000. Algebra. 3 hours.
Oasis Title: ALGEBRA.
Prerequisite: MATH 4080/6080 or permission of department.
A course in groups, fields and rings, designed to prepare the student for the algebra prelims. Some topics covered include the Sylow theorems, solvable and simple groups, Galois theory, finite fields, Noetherian rings and modules.
Offered every year.

MATH 8010. Representation Theory of Finite Groups. 3 hours.
Oasis Title: REPS OF FIN GROUPS.
Prerequisite: MATH 8000.
Irreducible and indecomposable representations, Schur's lemma, Maschke's theorem, the Wedderburn structure theorem, characters and orthogonality relations, induced representations and Frobenius reciprocity, central characters and central idempotents, Burnside's p^a q^b theorem, Frobenius normal p-complement theorem.
Offered every year.

MATH 8020. Communative Algebra. 3 hours.
Oasis Title: COMMUNATIVE ALGEBRA.
Prerequisite: MATH 8000.
Localization and completion, Nakayama's lemma, Dedekind domains, Hilbert's basis theorem, Hilbert's Nullstellensatz, Krull dimension, depth and Cohen-Macaulay rings, regular local rings.
Offered every year.

MATH 8030. Topics in Algebra. 3 hours. Repeatable for maximum 9 hours credit.
Oasis Title: TOPICS IN ALGEBRA.
Prerequisite: MATH 8000 or permission of department.
Topics in abstract algebra at the level of current research.
Offered every year.

MATH 8080. Lie Algebras. 3 hours.
Oasis Title: LIE ALGEBRAS.
Prerequisite: MATH 8000.
Nilpotent and solvable Lie algebras, structure and classification of semisimple Lie algebras, roots, weights, finite-dimensional representations.
Offered every year.

MATH 8100. Real Analysis I. 3 hours.
Oasis Title: REAL ANALYSIS I.
Prerequisite: MATH 4100/6100 or permission of department.
Measure and integration theory with relevant examples from Lebesgue integration, Hilbert spaces (only with regard to L^2), L^p spaces and the related Riesz representation theorem. Hahn, Jordan and Lebesgue decomposition theorems, Radon-Nikodym Theorem and Fubini's Theorem.
Offered every year.

MATH 8110. Real Analysis II. 3 hours.
Oasis Title: REAL ANALYSIS II.
Prerequisite: MATH 8100.
Topics including: Haar Integral, change of variable formula, Hahn-Banach theorem for Hilbert spaces, Banach spaces and Fourier theory (series, transform, Gelfand-Fourier homomorphism).
Offered every year.

MATH 8130. Topics in Analysis. 3 hours. Repeatable for maximum 18 hours credit.
Oasis Title: TOPICS IN ANALYSIS.
Prerequisite: MATH 8100 or MATH 8150.
Topics in analysis at the level of current research.
Not offered on a regular basis.

MATH 8150. Complex Variables I. 3 hours.
Oasis Title: COMPLEX VARIABLES I.
The Cauchy-Riemann Equations, linear fractional transformations and elementary conformal mappings, Cauchy's theorems and its consequences, including Morera's theorem, Taylor and Laurent expansions, maximum principle, residue theorem, argument principle, Rouche's theorem and Liouville's theorem.
Offered every year.

MATH 8160. Complex Variables II. 3 hours.
Oasis Title: COMPLEX VAR II.
Prerequisite: MATH 8150.
Topics including Riemann Mapping Theorem, elliptic functions, Mittag-Leffler and Weierstrass Theorems, analytic continuation and Riemann surfaces.
Offered every year.

MATH 8170. Functional Analysis I. 3 hours.
Oasis Title: FUNC ANALYSIS I.
Prerequisite: MATH 8100.
Hilbert spaces and Banach spaces, spectral theory, topological vector spaces, comvexity and its consequences, including the Krein-Milman theorem.
Offered every year.

MATH 8180. Functional Analysis II. 3 hours.
Oasis Title: FUNC ANALYSIS II.
Prerequisite: MATH 8170 or permission of department.
Operator theory, spectral theorem for normal operators, distribution theory, the Schwartz spaces, topics from C*-algebras and von Neumann algebras.
Offered every year.

MATH 8190. Lie Groups. 3 hours.
Oasis Title: LIE GROUPS.
Prerequisite: MATH 8000 and MATH 8250.
Classical groups, exponential map, Poincare-Birkhoff-Witt Theorem, homogeneous spaces, adjoint representation, covering groups, compact groups, Peter-Weyl Theorem, Weyl character formula.
Offered every year.

MATH 8200. Algebraic Topology. 3 hours.
Oasis Title: ALGEBRAIC TOPOLOGY.
Prerequisite: MATH 4200/6200.
The fundamental group, van Kampen's theorem, and covering spaces. Introduction to homology: simplicial, singular, and cellular. Applications.
Offered every year.
Offered every even-numbered year.
Offered every odd-numbered year.

MATH 8210. Topology of Manifolds. 3 hours.
Oasis Title: TOP OF MANIFOLDS.
Prerequisite: MATH 8200.
Poincare duality, deRham's theorem, topics from differential topology.
Offered every year.

MATH 8220. Homotopy Theory. 3 hours.
Oasis Title: HOMOTOPY THEORY.
Prerequisite: MATH 8200.
Topics in homotopy theory, including homotopy groups, CW complexes, and fibrations.
Offered every year.

MATH 8230. Topics in Topology and Geometry. 3 hours. Repeatable for maximum 9 hours credit.
Oasis Title: TOPICS IN TOP & GEO.
Prerequisite: MATH 8200 or permission of department.
Advanced topics in topology and/or differential geometry leading to and including research level material.
Offered every year.

MATH 8250. Differential Geometry I. 3 hours.
Oasis Title: DIFF GEOMETRY I.
Prerequisite: MATH 4200/6200.
Differentiable manifolds, vector bundles, tensors, flows, and Frobenius' theorem. Introduction to Riemannian geometry.
Offered every year.

MATH 8260. Differential Geometry II. 3 hours.
Oasis Title: DIFF GEOMETRY II.
Prerequisite: MATH 8250.
Riemannian geometry: connections, curvature, first and second variation; geometry of submanifolds. Gauss-Bonnet theorem. Additional topics, such as characteristic classes, complex manifolds, integral geometry.
Offered every year.

MATH 8300. Introduction to Algebraic Geometry. 3 hours.
Oasis Title: INTRO ALG GEOMETRY.
Prerequisite: MATH 8000.
An invitation to algebraic through a study of examples. Affine and projective varieties, regular and rational maps, Nullstellensatz. Veronese and Segre varieties, Grassmannians, algebraic groups, quadrics. Smoothness and tangent spaces, singularities and tangent cones.
Offered every year.

MATH 8310. Geometry of Schemes. 3 hours.
Oasis Title: GEOMETRY OF SCHEMES.
Prerequisite: MATH 8020 and MATH 8300.
The language of Grothendieck's theory of schemes. Topics include the spectrum of a ring, "gluing" spectra to form schemes, products, quasi-coherent sheaves of ideals, and the functor of points.
Offered every year.

MATH 8320. Algebraic Curves. 3 hours. Repeatable for maximum 9 hours credit.
Oasis Title: ALGEBRAIC CURVES.
Prerequisite: MATH 8300.
The theory of curves, including linear series and the Riemann Roch theorem. Either the algebraic (variety), arithmetic (function field), or analytic (Riemann surface) aspect of the subject may be emphasized in different years.
Offered every year.

MATH 8330. Topics in Algebraic Geometry. 3 hours. Repeatable for maximum 9 hours credit.
Oasis Title: TOPICS ALG GEOMETRY.
Prerequisite: MATH 8300.
Advanced topics such as algebraic surfaces, or cohomology and sheaves.
Offered every year.

MATH 8400. Algebraic/Analytic Number Theory I. 3 hours.
Oasis Title: ALG/AN NUMBER TH I.
Prerequisite: MATH 4080/6080 or permission of department.
The core material of algebraic number theory: number fields, rings of integers, discriminants, ideal class groups, Dirichlet's unit theorem, splitting of primes; p-adic fields, Hensel's lemma, adeles and ideles, the strong approximation theorem.
Offered every year.

MATH 8410. Algebraic/Analytic Number Theory II. 3 hours.
Oasis Title: ALG/AN NUMBER TH II.
Prerequisite: MATH 8400 or permission of department.
A continuation of Algebraic and Analytic Number Theory I, introducing analytic methods: the Riemann Zeta function, its analytic continuation and functional equation, the Prime number theorem; sieves, the Bombieri-Vinogradov theorem, the Chebotarev density theorem.
Offered every year.

MATH 8430. Topics in Arithmetic Geometry. 3 hours. Repeatable for maximum 18 hours credit.
Oasis Title: ARITHMETIC GEOMETRY.
Prerequisite: Permission of department.
Topics in Algebraic number theory and Arithmetic geometry, such as class field theory, Iwasawa theory, elliptic curves, complex multiplication, cohomology theories, Arakelov theory, diophantine geometry, automorphic forms, L-functions, representation theory.
Offered every year.

MATH 8440. Topics in Combinatorial/Analytic Number Theory. 3 hours. Repeatable for maximum 18 hours credit.
Oasis Title: COMB/ANLY NUMBER TH.
Prerequisite: Permission of department.
Topics in combinatorial and analytic number theory, such as sieve methods, probabilistic models of prime numbers, the distribution of arithmetic functions, the circle method, additive number theory, transcendence methods.
Offered every year.

MATH 8450. Topics in Algorithmic Number Theory. 3 hours. Repeatable for maximum 18 hours credit.
Oasis Title: TOPICS ALGO NUMBER.
Prerequisite: Permission of department.
Topics in computational number theory and algebraic geometry, such as factoring and primality testing, cryptography and coding theory, algorithms in number theory and arithmetic geometry.
Offered every year.

MATH 8500. Advanced Numerical Analysis I. 3 hours.
Oasis Title: ADV NUM ANALY I.
Prerequisite: MATH 4510/6510.
Prerequisite or corequisite: MATH 4100/6100.
Numerical solution of nonlinear equations in one and several variables, numerical methods for constrained and unconstrained optimization, numerical solution of linear systems, numerical methods for computing eigenvalues and eigenvectors, numerical solution of linear least squares problems, computer applications for applied problems.
Offered every year.

MATH 8510. Advanced Numerical Analysis II. 3 hours.
Oasis Title: ADV NUM ANALY II.
Prerequisite: MATH 8500.
Polynomial and spline interpolation and approximation theory, numerical integration methods, numerical solution of ordinary differential equations, computer applications for applied problems.
Not offered on a regular basis.

MATH 8520. Advanced Numerical Analysis III. 3 hours.
Oasis Title: ADV NUM ANALY III.
Prerequisite: MATH 8500.
Finite difference and finite element methods for elliptic, parabolic, and hyperbolic partial differential equations, convergence and stability of those methods, numerical algorithms for the implementation of those methods.
Not offered on a regular basis.

MATH 8550. Special Topics in Numerical Analysis. 3 hours. Repeatable for maximum 18 hours credit.
Oasis Title: TOPICS IN NUM ANALY.
Prerequisite: MATH 8500.
Special topics in numerical analysis, including iterative methods for large linear systems, computer aided geometric design, multivariate splines, numerical solutions for pde's, numerical quadrature and cubature, numerical optimization, wavelet analysis for numerical imaging. In any semester, one of the above topics will be covered.
Offered every year.

MATH 8600. Probability. 3 hours.
Oasis Title: PROBABILITY.
Prerequisite: MATH 8100.
Probability spaces, random variables, distributions, expectation and higher moments, conditional probability and expectation, convergence of sequences and series of random variables, strong and weak laws of large numbers, characteristic functions, infinitely divisible distributions, weak convergence of measures, central limit theorems.
Offered every year.

MATH 8620. Stochastic Processes. 3 hours.
Oasis Title: STOCH PROCESSES.
Prerequisite: MATH 8100.
Conditional expectation, Markov processes, martingales and convergence theorems, stationary processes, introduction to stochastic integration.
Offered every year.

MATH 8630. Stochastic Analysis. 3 hours.
Oasis Title: STOCHASTIC ANALYSIS.
Prerequisite: MATH 8100.
Conditional expectation, Brownian motion, semimartingales, stochastic calculus, stochastic differential equations, stochastic control, stochastic filtering.
Offered every year.

MATH 8700. Applied Mathematics: Applications in Industry. 3 hours. Repeatable for maximum 15 hours credit.
Oasis Title: AP MATH IN INDUSTRY.
Prerequisite: MATH 4720/6720.
Mathematical modeling of some real-world industrial problems. Topics will be selected from a list which includes air quality modeling, crystal precipitation, electron beam lithography, image processing, photographic film development, production planning in manufacturing, and optimal control of chemical reactions.
Offered every year.

MATH 8710. Applied Mathematics: Variational Methods/Perturbation Theory. 3 hours.
Oasis Title: AP MATH VAR/PERTURB.
Prerequisite: MATH 4100/6100.
Calculus of variations, Euler-Lagrange equations, Hamilton's principle, approximate methods, eigenvalue problems, asymptotic expansions, method of steepest descent, method of stationary phase, perturbation of eigenvalues, nonlinear eigenvalue problems, oscillations and periodic solutions, Hopf bifurcation, singular perturbation theory, applications.
Offered every year.

MATH 8740. Ordinary Differential Equations. 3 hours.
Oasis Title: ORDINARY DIFF EQNS.
Prerequisite: MATH 4100/6100.
Solutions of initial value problems: existence, uniqueness, and dependence on parameters, differential inequalities, maximal and minimal solutions, continuation of solutions, linear systems, self-adjoint eigenvalue problems, Floquet Theory.
Offered every year.

MATH 8750. Introduction to Dynamical Systems. 3 hours.
Oasis Title: DYNAMICAL SYSTEMS.
Prerequisite: MATH 8740.
Continuous dynamical systems, trajectories, periodic orbits, invariant sets, structure of alpha and omega limit sets, applications to two-dimensional autonomous systems of ODE's, Poincare-Bendixson Theorem, discrete dynamical systems, infinite dimensional spaces, semi-dynamical systems, functional differential equations.
Offered every year.

MATH 8770. Partial Differential Equations. 3 hours.
Oasis Title: PARTIAL DIFF EQNS.
Prerequisite: MATH 4100/6100.
Classification of second order linear partial differential equations, modern treatment of characteristics, function spaces, Sobolev spaces, Fourier transform of generalized functions, generalized and classical solutions, initial and boundary value problems, eigenvalue problems.
Offered every year.

MATH 8800. Directed Reading and/or Projects. 1-6 hours. Repeatable for maximum 30 hours credit.
Oasis Title: DIR READ AND/OR PRO.
Directed reading and/or project at the doctoral level.
Non-traditional format: Directed study.
Not offered on a regular basis.

MATH 8900. Seminar in Algebra. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN ALGEBRA.
Prerequisite: Permission of department.
A study of some phase of current research in algebra.
Offered every year.

MATH 8910. Seminar in Analysis. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN ANALYSIS.
Prerequisite: Permission of department.
A study of some phase of current research in analysis.
Offered every year.

MATH 8920. Seminar in Topology. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN TOPOLOGY.
Prerequisite: Permission of department.
A study of some phase of current research in topology.
Offered every year.

MATH 8930. Seminar in Algebraic Geometry. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN ALG GEOM.
Prerequisite: Permission of department.
A study of some phase of current research in algebraic geometry.
Offered every year.

MATH 8940. Seminar in Number Theory. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN NUM TH.
Prerequisite: Permission of department.
A study of some phase of current research in number theory.
Offered every year.

MATH 8950. Seminar in Numerical Analysis. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN NUM ANLY.
Prerequisite: Permission of department.
A study of some phase of current research in numerical analysis.
Offered every year.

MATH 8960. Seminar in Probability. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN PROB.
Prerequisite: Permission of department.
A study of some phase of current research in probability.
Offered every year.

MATH 8970. Seminar in Applied Mathematics. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN AP MATH.
Prerequisite: Permission of department.
A study of some phase of current research in applied mathematics.
Offered every year.

MATH 8980. Seminar in Geometry. 1-3 hours. Repeatable for maximum 30 hours credit.
Oasis Title: SEMINAR IN GEOMETRY.
Prerequisite: Permission of department.
A study of some phase of current research in geometry.
Offered every year.

MATH 9000. Doctoral Research. 1-9 hours. Repeatable for maximum 36 hours credit.
Oasis Title: DOCTORAL RESEARCH.
Prerequisite: Permission of department.
Research while enrolled for a doctoral degree under the direction of faculty members.
Non-traditional format: Independent research under the direction of a faculty member.
Offered fall, spring, and summer semesters every year.

MATH 9300. Doctoral Dissertation. 1-9 hours. Repeatable for maximum 40 hours credit.
Oasis Title: DOCT DISSERTATION.
Prerequisite: Permission of department.
Dissertation writing under the direction of the major professor.
Non-traditional format: Independent research and preparation of the doctoral dissertation.
Offered fall, spring, and summer semesters every year.