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.

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.

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.

Oasis Title: PREP FOR CPE.

Prerequisite or corequisite: ACAM(MATH) 0098 or ACAM(MATH) 0099.

Preparation for CPE through review of math fundamentals and geometry.

Non-traditional format: This course carries institutional credit and will not count toward graduation.

Offered fall, spring, and summer semesters every year.

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.

Oasis Title: INTRO 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.

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.

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.

Oasis Title: ANALY GEO AND CALC.

Not open to students with credit in MATH 2300H or MATH 2400H.

Prerequisite: MATH 1113.

Prerequisite or 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.

Oasis Title: DIFF CALC LAB.

Prerequisite or corequisite: MATH 2200 or MATH 2300H or MATH 2400H.

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.

Oasis Title: INTEGRAL CALCULUS.

Not open to students with credit in MATH 2110 or MATH 2310H or MATH 2410H or MATH 2260.

Prerequisite: MATH 2200 or MATH 2300H or MATH 2400H.

Prerequisite or 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.

Oasis Title: INT CALC LAB.

Prerequisite or corequisite: MATH 2210 or MATH 2310H or MATH 2410H.

Computer projects exploring topics related to the course content of Integral Calculus.

Offered fall, spring, and summer semesters every year.

Oasis Title: CALC I SCI ENG.

Not open to students with credit in MATH 2200 or MATH 2300H or MATH 2400H.

Prerequisite: MATH 1113 or permission of department.

Limits, derivatives, differentiation of algebraic and transcendental functions; linear approximation, curve sketching, optimization, indeterminate forms. The integral, Fundamental Theorem of Calculus, areas. Emphasis on science and engineering applications.

Offered fall and spring semesters every year.

Oasis Title: CALC II SCI ENG.

Not open to students with credit in MATH 2410H.

Prerequisite: MATH 2250.

Vector functions, velocity, acceleration, and physical applications. Techniques of integration and differential equations. Applications of integration: arclength, volumes, work, center of mass; polar coordinates and Kepler's laws. Polynomial approximation and Taylor series. Vectors in three-dimensional space, lines, planes, linear functions, and determinants.

Offered fall and spring semesters every year.

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.

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.

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.

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.

Oasis Title: MULTIVARIABLE CALC.

Not open to students with credit in MATH 3510.

Prerequisite: MATH 2210 or MATH 2260 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.

Oasis Title: DISCRETE MATH BIOL.

Discrete mathematics topics especially pertinent to applications in computational biology and genetics. Topics include basic set theory and logic, introductory linear algebra, difference equations and stability, counting and discrete probability and distributions, large data structures. Specific biological models are introduced to motivate topics.

Offered fall and spring semesters every year.

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 every year.

Oasis Title: ELEM DIFF EQNS.

Prerequisite: MATH 2210 or MATH 2260 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.

Oasis Title: INTRO TO LINEAR ALG.

Not open to students with credit in MATH 3500.

Prerequisite: MATH 2210 or MATH 2260 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.

Oasis Title: SEQUENCES & SERIES.

Prerequisite: MATH 2210 or MATH 2260 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.

Oasis Title: INTRO HIGHER MATH.

Prerequisite: MATH 2210 or MATH 2260 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.

Oasis Title: ADV PROB SOLV.

Prerequisite or corequisite: MATH 3000 or MATH 3100 or MATH 3200 or MATH 3500.

Strategies and tactics for solving advanced problems in undergraduate mathematics. Methods will be demonstrated through examples and exercises. (Will not count towards the mathematics degree.)

Offered fall and spring semesters every year.

Oasis Title: MULTIVAR MATH I.

Not open to students with credit in MATH 3000.

Prerequisite: MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410H.

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.

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.

Oasis Title: MATH METHODS FOR CS.

Prerequisite: (MATH 2210 or MATH 2310H or MATH 2410H) and CSCI 1301-1301L.

Mathematical tools and methods for computer science, with emphasis on proof-writing. Logic, set theory, function theory, induction, and other techniques of mathematical proof are developed within the context of discrete mathematics. Topics chosen from combinatorics, graph theory, discrete probability, algorithms, and linear algebra.

Offered fall and spring semesters every year.

Oasis Title: MOD ALG & GEOM I.

Undergraduate prerequisite: (MATH 3000 or MATH 3500) and (MATH 3200 or MATH 3610).

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.

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.

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.

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.

Oasis Title: REAL ANALYSIS.

Undergraduate prerequisite: MATH 3100 and (MATH 3200 or MATH 3610).

Metric spaces and continuity; differentiable and integrable functions of one variable; sequences and series of functions.

Offered fall semester every year.

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.

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.

Oasis Title: FUNCTIONAL ANALYSIS.

Undergraduate prerequisite: [MATH 4100/6100 and (MATH 3000 or MATH 3500)] or permission of department.

Introduction to analysis in infinite dimensional vector spaces useful in mathematics and other disciplines. Topics may be chosen from: metric spaces, completeness and compactness and applications; basic Banach space functionals and operators and applications; basic Hilbert space theory, self-adjoint compact operators, and applications.

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.

Oasis Title: POINT SET TOPOLOGY.

Undergraduate prerequisite: MATH 3100 and (MATH 3200 or MATH 3610).

Topological spaces, continuity; connectedness, compactness; separation axioms and Tietze extension theorem; function spaces.

Offered every year.

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.

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.

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.

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.

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.

Oasis Title: NUMER ANALYSIS I.

Undergraduate prerequisite: MATH 3000 or MATH 3500.

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.

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.

Oasis Title: COMP AIDED DESIGN.

Undergraduate prerequisite: MATH 2500 or MATH 3510.

Bezier curves and spline curves, tensor product Bezier and spline surfaces, Bezier triangular surfaces and triangular spline surfaces, Coons patches, basic differential geometry for curves and surfaces, computer implementation of these curves and surfaces.

Offered spring semester every even-numbered year.

Oasis Title: PROBABILITY.

Undergraduate prerequisite: (MATH 2260 and MATH 2500) or (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.

Oasis Title: INTRO QUANT COMP.

Prerequisite: CSCI 2670 and MATH 3000.

An introduction to quantum computation.

Oasis Title: ALGORITHMS.

Undergraduate prerequisite: MATH 3000 and (CSCI(MATH) 2610 or MATH 3200 or MATH 3610).

Discrete algorithms (number-theoretic, graph-theoretic, combinatorial, and algebraic) with an emphasis on techniques for their mathematical analysis.

Not offered on a regular basis.

Oasis Title: COMBINATORICS.

Undergraduate prerequisite: (MATH 3000 or MATH 3500) and (CSCI(MATH) 2610 or MATH 3200 or MATH 3610).

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.

Oasis Title: GRAPH THEORY.

Undergraduate prerequisite: (MATH 3000 or MATH 3500) and (CSCI(MATH) 2610 or MATH 3200 or MATH 3610).

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.

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.

Oasis Title: MATH OF FINANCE.

Undergraduate prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.

The mathematical methods and models used in the fields of financial analysis and actuarial science. Covers the theory of interest, models of financial markets including derivative markets, an introduction to risk and models and actuarial mathematics.

Offered spring semester every year.

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.

Oasis Title: MATH AND MUSIC.

Undergraduate prerequisite: (MATH 2210 or MATH 2310H or MATH 2410H) and (MATH 2500 or MATH 2700).

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. There is a serious writing component.

Not offered on a regular basis.

Oasis Title: MAT BIOLOGY.

Undergraduate prerequisite: MATH 2500 and (MATH 4700/6700 or (MATH 2700 and permission of department)).

Graduate prerequisite: Permission of department.

Mathematical models in the biological sciences, systems, phase-plane analysis, diffusion, convective transport, bifurcation analysis. Possible applications will include population models, infectious disease and epidemic models, acquired immunity and drug distribution, tumor growth, and analysis of arterial flow dynamics.

Offered spring semester every odd-numbered year.

Oasis Title: MATH OPTION PRICING.

Prerequisite: (MATH 2500 and MATH 3000) or MATH 3510 or permission of department.

Bonds, stock markets, derivatives, arbitrage, and binomial tree models for stocks and options, Black-Scholes formula for options pricing, hedging. Computational methods will be incorporated.

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.

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.

Oasis Title: RESEARCH MATH.

Research in mathematics directed by a faculty member in the department of mathematics. A final report is required.

Non-traditional format: Students will meet with faculty members on a regular basis.

Offered every year.

Oasis Title: DIRECTED READINGS.

Prerequisite: Senior standing and permission of Honors.

Individual study, reading, projects, or research under the direction of a project director.

Non-traditional format: Directed study.

Not offered on a regular basis.

Oasis Title: DIRECTED READINGS.

Prerequisite: Senior standing and permission of Honors.

Individual study, reading, projects, or research under the direction of a project director.

Non-traditional format: Directed study.

Not offered on a regular basis.

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.

Oasis Title: ARITH & PROB SOLV.

Not open to students with credit in MATH 1700 or MATH 5020/7020.

Topics in mathematics designed for future elementary school teachers. Problem solving. Number systems: whole numbers, integers, rational numbers (fractions) and real numbers (decimals), and the relationships between these systems. Understanding multiplication and division, including why standard computational algorithms work. Properties of arithmetic. Applications of elementary mathematics.

Offered fall and spring semesters every year.

Oasis Title: GEOM & PROB SOLV.

Not open to students with credit in MATH 5030/7030.

Undergraduate prerequisite: MATH 5001/7001.

A deep examination of mathematical topics designed for future elementary school teachers. Length, area, and volume. Geometric shapes and their properties. Probability. Elementary number theory. Applications of elementary mathematics.

Offered fall and spring semesters every year.

Oasis Title: ALG & PROB SOLV.

Prerequisite: MATH 5002/7002.

A deep examination of topics in mathematics that are relevant for elementary school teaching. Probability, number theory, algebra and functions, including ratio and proportion. Posing and modifying problems.

Offered fall and spring semesters every year.

Oasis Title: IDEAS OF ARITHMETIC.

Not open to students with credit in MATH 5001/7001.

Undergraduate prerequisite: MATH 2200.

Operations of arithmetic for middle school teachers; number systems; set theory to study mappings, functions, and equivalence relations.

Offered fall semester every year.

Oasis Title: GEOM AND MEAS.

Not open to students with credit in MATH 5002/7002.

Undergraduate prerequisite: MATH 2200.

Principles of geometry and measurement for middle school teachers.

Offered spring semester every year.

Oasis Title: ALG MID SCH TEACH.

Undergraduate prerequisite: MATH 2200 and MATH 5020/7020 and MATH 5030/7030.

Algebra for middle school teachers. Relationships between quantities and the interpretation of such relationships numerically, graphically, algebraically, and functionally. Emphasis on problem solving and applications, connections with geometry, arithmetic and data analysis, and math competitions such as Mathcounts.

Offered fall semester every year.

Oasis Title: CALC FOR AP TEACH.

Undergraduate prerequisite: MATH 2500 or MATH 3510.

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.

Oasis Title: FNDNS GEOMETRY I.

Undergraduate prerequisite: (MATH 3000 or MATH 3500) and (MATH 3200 or MATH 3610).

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.

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.

Oasis Title: PROB/STAT FOR TEACH.

Undergraduate prerequisite: MATH 2200.

Fundamental ideas of probability with particular emphasis on their applications in statistics.

Not offered on a regular basis.

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.

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.

Oasis Title: GRAD STUDENT SEM.

Advanced supervised experience in an applied setting. This course may not be used to satisfy a student's approved program of study.

Non-traditional format: Seminar.

Offered fall, spring, and summer semesters every year.

Oasis Title: CALCULUS IDEAS I.

Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.

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.

Oasis Title: CALCULUS IDEAS II.

Prerequisite: MATH 2210 or MATH 2310H or MATH 2410H.

A continuation of Basic Ideas of Calculus I focusing on functions of several variables.

Offered every year.

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.

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.

Oasis Title: FOUND GRAD MATH.

Prerequisite: Permission of department.

An intensive review of techniques and material essential for graduate study in mathematics, including background in calculus and linear algebra. Emphasis is on small group study and presentations. Topics include proofs, induction, the metric structure of the reals, the Bolzano-Weierstrass theorem, and the diagonalization theorem.

Non-traditional format: The intention is to limit lectures by the instructor to a minimum essential for progress of the course. The traditional lecture format will be replaced by whole group discussions and planning, directed study in small groups, and student presentations. Class enrollment for this course will normally be limited to ten students.

Offered fall, spring, and summer semesters every year.

Oasis Title: ALGEBRA I.

Prerequisite: MATH 4010/6010 or permission of department.

Groups and rings, including Sylow theorems, classifying small groups, finitely generated abelian groups, Jordan-Holder theorem, solvable groups, simplicity of the alternating group, euclidean domains, principal ideal domains, unique factorization domains, noetherian rings, Hilbert basis theorem, Zorn's lemma, and existence of maximal ideals and vector space bases.

Offered fall semester every year.

Oasis Title: PROBLEMS IN ALGEBRA.

Corequisite: MATH 8000.

Techniques and approaches to problems in algebra as an aid to mastery of the basic theory.

Non-traditional format: Significant outside preparation will be expected.

Offered every year.

Oasis Title: ALGEBRA II.

Prerequisite: MATH 8000.

Modules and fields, including noetherian modules, finitely generated modules over principal ideal domains, canonical forms of matrices, spectral theorems, tensor products, algebraic and transcendental field extensions, galois theory, solvability of polynomials, symmetric functions, cyclotomic extensions, finite fields, solution formulas for polynomials of low degree.

Offered spring semester every year.

Oasis Title: COMMUTATIVE 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.

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.

Oasis Title: REPS OF FIN GROUPS.

Prerequisite: MATH 8010.

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.

Not offered on a regular basis.

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.

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.

Oasis Title: PROBLEMS IN REAL.

Corequisite: MATH 8100.

Techniques and approaches to problems in real analysis as an aid to mastery of basic theory.

Non-traditional format: Significant outside preparation will be expected.

Offered every year.

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.

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.

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.

Oasis Title: PROBLEMS IN COMPLEX.

Corequisite: MATH 8150.

Techniques and approaches to problems in complex analysis as an aid to mastery of the basic theory.

Non-traditional format: Significant outside preparation will be expected.

Offered every year.

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.

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.

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.

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.

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.

Oasis Title: PROBLEMS IN TOPOLOG.

Corequisite: MATH 8200.

Techniques and approaches to problems in topology as an aid to mastery of the basic theory.

Non-traditional format: Significant outside preparation will be expected.

Offered every year.

Oasis Title: TOP OF MANIFOLDS.

Prerequisite: MATH 8200.

Poincare duality, deRham's theorem, topics from differential topology.

Offered every year.

Oasis Title: HOMOTOPY THEORY.

Prerequisite: MATH 8200.

Topics in homotopy theory, including homotopy groups, CW complexes, and fibrations.

Offered every year.

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.

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.

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.

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.

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.

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.

Oasis Title: TOPICS ALG GEOMETRY.

Prerequisite: MATH 8300.

Advanced topics such as algebraic surfaces, or cohomology and sheaves.

Offered every year.

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.

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.

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.

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.

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.

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.

Oasis Title: PROBLEMS IN NUMERIC.

Corequisite: MATH 8500.

Techniques and approaches to problems in numerical analysis as an aid to mastery of the basic theory.

Offered every year.

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.

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.

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.

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.

Oasis Title: PROBLEMS IN PROB.

Corequisite: MATH 8600.

Techniques and approaches to problems in probability as an aid to mastery of the basic theory.

Non-traditional format: Significant outside preparation will be expected.

Offered every year.

Oasis Title: TOPICS QUANT COMP.

Prerequisite: CSCI 6610 and CSCI(MATH)(PHYS) 4612/6612.

The selection of topics varies from year to year. Students will make presentations based on journal articles or original research.

Oasis Title: STOCH PROCESSES.

Prerequisite: MATH 8100.

Conditional expectation, Markov processes, martingales and convergence theorems, stationary processes, introduction to stochastic integration.

Offered every year.

Oasis Title: STOCHASTIC ANALYSIS.

Prerequisite: MATH 8100.

Conditional expectation, Brownian motion, semimartingales, stochastic calculus, stochastic differential equations, stochastic control, stochastic filtering.

Offered every year.

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.

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.

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.

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.

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.

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.

Oasis Title: COLLAB RESEARCH.

Research in a group setting on a topic of current interest in mathematics, under the direction of one or more faculty members. Emphasis will be given to problems that may be accessible to elementary methods. An introduction to basic research methods in mathematics, as well as expository and literature-search skills. Required for all first year graduate students.

Non-traditional format: The course is a 3 credit hour seminar since it includes both a weekly meeting of separate research groups and a joint weekly meeting of all the groups. The course is repeatable for 18 credit hours since the groups are required both semesters for first year students and are also appropriate for continuing students. By design the research experience will be different each semester as the group, topic, or investigation changes. The interaction among students and faculty is considered an important aspect of the seminar. The research group format is the main feature of recent reforms in the mathematics curriculum.

Offered fall, spring, and summer semesters every year.

Oasis Title: SEMINAR IN ALGEBRA.

Prerequisite: Permission of department.

A study of some phase of current research in algebra.

Offered every year.

Oasis Title: SEMINAR IN ANALYSIS.

Prerequisite: Permission of department.

A study of some phase of current research in analysis.

Offered every year.

Oasis Title: SEMINAR IN TOPOLOGY.

Prerequisite: Permission of department.

A study of some phase of current research in topology.

Offered every year.

Oasis Title: SEMINAR IN ALG GEOM.

Prerequisite: Permission of department.

A study of some phase of current research in algebraic geometry.

Offered every year.

Oasis Title: SEMINAR IN NUM TH.

Prerequisite: Permission of department.

A study of some phase of current research in number theory.

Offered every year.

Oasis Title: SEMINAR IN NUM ANLY.

Prerequisite: Permission of department.

A study of some phase of current research in numerical analysis.

Offered every year.

Oasis Title: SEMINAR IN PROB.

Prerequisite: Permission of department.

A study of some phase of current research in probability.

Offered every year.

Oasis Title: SEMINAR IN AP MATH.

Prerequisite: Permission of department.

A study of some phase of current research in applied mathematics.

Offered every year.

Oasis Title: SEMINAR IN GEOMETRY.

Prerequisite: Permission of department.

A study of some phase of current research in geometry.

Offered every year.

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.

Oasis Title: DOC GRAD STU SEM.

Advanced supervised experience in an applied setting. This course may not be used to satisfy a student's approved program of study.

Non-traditional format: Seminar.

Offered fall, spring, and summer semesters every year.

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.