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University of Utah

General Catalog Fall 2012
Posted Mar 02, 2012

Disclaimer: The course information below is current as of Mar 02, 2012, is intended for informational purposes only, and does not constitute a legal contract between the University of Utah and any person or entity.

This Web document is updated twice a year, on or about the first day of registration for Fall and Spring semesters.


1000  Understanding Mathemaphobia (1) Cross listed as UC 1000.
   This course is designed for the mathematics student who either suffers from a self-reported case of mathemaphobia or is simply interested in understanding the phenomenon to better teach mathematics. Through self-reflection, practice of mathematics skills, practice of test-taking skills, reading thought process surrounding mathematics, students will gain confidence, understanding and problem-solving skills.

1010  Intermediate Algebra (4) Prerequisites: "C" or better in MATH 990 OR Accuplacer EA score of 54 or better OR ACT Math score of 18 or better OR SAT Math score of 430 or better.
   Rapid review of elementary algebra; linear equations and inequalities, systems of linear equations; exponents, radicals, complex numbers, exponentials, logarithms; solving polynomial, rational, radical exponential and logarithmic equations; applications throughout these topics.

1030  Introduction to Quantitative Reasoning (3) Prerequisites: "C" or better in MATH 1010 OR Accuplacer CLM score of 50 or better OR ACT Math score of 23 or better OR SAT Math score of 540 or better. Fulfills Quantitative Reasoning (Math).
   This course helps students learn how to use some simple mathematical techniques effectively in their own field of study and apply those concepts to practical, real-life situations. Topics covered: sets and Venn diagrams, different systems of units and unit conversions, using percents and estimations, financial mathematics involved in loans and investments, linear and exponential modeling and applications, geometric measurements and scaling. This course is primarily for undergraduate students who will not take any further mathematics, except for statistics/probability.

1040  Introduction to Statistics and Probability (3) Prerequisites: "C" or better in (MATH 1010 OR MATH 1030 OR MATH 1050 OR MATH 1070 OR MATH 1080 MATH 1090) OR Accuplacer CLM score of 50 or better OR ACT Math score of 23 or better OR SAT Math score of 540 or better. Fulfills Quantitative Reasoning (Statistics/Logic).
   Topics covered: how to collect, organize, analyze, display, and interpret data; deviation, variance and standard deviation, Empirical rule; basic concepts of probability and counting, conditional probability, multiplication and addition rule; probability distributions, binomial distributions; standard normal (bell-shaped) distributions; correlation and linear regression.

1050  College Algebra (4) Prerequisites: "C" or better in (MATH 1010 OR MATH 1060 OR MATH 1080 OR MATH 1090) OR Accuplacer CLM score of 60 or better OR ACT Math score of 23 or better OR SAT Math score of 540 or better. Fulfills Quantitative Reasoning (Math).
   Functions, inverses and graphs; polynomial, rational, radical, exponential and logarithmic functions; systems of equations and matrices; applications; arithmetic and geometric sequences and series.

1060  Trigonometry (3) Prerequisites: "C" or better in (MATH 1010 OR MATH 1050 OR MATH 1080) OR Accuplacer CLM score of 60 or better OR ACT Math score of 23 or better OR SAT Math score of 540 or better. Fulfills Quantitative Reasoning (Math).
   Trigonometric functions, inverses, equations and identities with applications; introduction to vectors.

1070  Introduction to Statistical Inference (3) Prerequisites: "C" or better in (MATH 1010 OR MATH 1040 OR MATH 1050 OR MATH 1080 OR MATH 1090) OR Accuplacer CLM score of 50 or better OR ACT Math score of 23 or better OR SAT Math score of 540 or better. Fulfills Quantitative Reasoning (Statistics/Logic).
   The important topics used in making inferences from data will be presented and illustrated. As well as material on descriptive statistics, estimation of the mean, or of the proportion, in one or two populations, simple linear regression, and one-way analysis of variance are covered.

1080  Precalculus (5) Prerequisites: "C" or better in (MATH 1010 OR MATH 1050 OR MATH 1060) OR Math ACT score of at least 24 OR Math SAT score of at least 560 OR Accuplacer CLM score of 65 or better OR Department Consent.
   Provides in-depth review of college algebra and trigonometry to prepare for science-track calculus courses. Most topics from MATH 1050 and MATH 1060 are covered in this course.

1090  College Algebra for Business and Social Sciences (3) Prerequisites: "C" or better in (MATH 1010 OR MATH 1050 OR MATH 1080) OR Accuplacer CLM score of 60 or better OR ACT Math score of 23 or better OR SAT Math score of 540 or better. Fulfills Quantitative Reasoning (Math).
   Functions and graphs, polynomial and rational functions, matrices, Gaussian elimination, exponential and logarithmic functions, growth, periodic and continuously compounded interest, arithmetic and geometric series, annuities and loans.

1100  Quantitative Analysis (3) Prerequisites: "C" or better in (MATH 1050 OR MATH 1080 OR MATH 1090 OR MATH 1210) OR Accuplacer CLM score of 80 or better OR ACT Math score of 28 or better OR SAT Math score of 630 or better. Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Not for students who have completed more than one semester of calculus. Differentiation, maximization and minimization of functions, marginal analysis and the optimization of constrained functions, integration and applications.

1170  Calculus for Biologists I (4) Prerequisites: "C" or better in ((MATH 1050 AND MATH 1060) OR MATH 1080 OR MATH 1210) OR AP Calculus AB score of 3 or better OR Accuplacer CLM score of 95 or better OR ACT Math score of 28 or better OR SAT Math score of 630 or better. Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Derivation of dynamical models of biological systems and their analysis with differential and integral calculus. Discrete-time dynamical systems for growth, breathing, selection, the heart, etc. Differentiation and its applications to stability, approximation of functions, maximization, and limits. Differential equations describing growth, diffusion, and selection, and their solution with integral calculus. Computer lab using Maple.

1180  Calculus for Biologists II (4) Prerequisites: "C" or better in MATH 1170 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Higher dimensional and probabilistic models of biological systems and their analysis. Phase plane analysis of interacting populations and the neuron. Derivation and analysis of stochastic dynamical systems describing growth, diffusion, and selection. Introduction to probability theory including distributions, random variables, and probability density functions. Applications of binomial, exponential, Poisson, and normal distributions. Introduction to statistics including parameter estimation, maximum likelihood, hypothesis testing and regression. Computer lab using Maple.

1210  Calculus I (4) Prerequisites: "C" or better in ((MATH 1050 AND MATH 1060) OR MATH 1080) OR AP Calculus AB score of 3 or better OR Accuplacer CLM score of 95 or better OR ACT Math score of 28 or better OR SAT Math score of 630 or better. Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Functions and their graphs, differentiation of polynomial, rational and trigonometric functions. Velocity and acceleration. Geometric applications of the derivative, minimization and maximization problems, the indefinite integral, and an introduction to differential equations. The definite integral and the Fundamental Theorem of Calculus.

1220  Calculus II (4) Prerequisites: "C" or better in MATH 1210 OR MATH 1250 OR (MATH 1270 OR MATH 1311) OR AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3. Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Geometric applications of the integral, logarithmic, and exponential functions, techniques of integration, conic sections, improper integrals, numerical approximation techniques, infinite series and power series expansions, differential equations (continued).

1250  Calculus for AP Students I (4) Prerequisites: AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   MATH 1250 and MATH 1260 together replace the three semester sequence MATH 1210, MATH 1220, MATH 2210. Review of introductory calculus, applications of differential and integral calculus, introduction to differential equations, conic sections and polar coordinates, numerical approximation, sequences and series, power series.

1260  Calculus for AP Students II (4) Prerequisites: "C" or better in MATH 1250 OR AP Calculus BC score of at least 4 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Completion of MATH 1260 is equivalent to completing the entire three-semester Calculus I, II, III sequence. Vectors in the plane and in 3-space, differential calculus in several variables, integration and its applications in several variables, vector fields, and line, surface and volume integrals. Green's and Stokes' Theorems.

1310  Engineering Calculus I (4) Prerequisites: "C" or better in ((MATH 1050 AND MATH 1060) OR MATH 1080) OR AP Calc AB score of 3 or better OR ACT Math score of 28 or better OR SAT Math score of 630 or better OR Departmental Consent.
   Differential and integral calculus with a focus on engineering applications and projects: functions and models; rates of change in science and engineering, limits and derivatives; related rates; derivatives and shapes of graphs; optimization; Newton's method; definite integrals, anti-differentiation and Fundamental Theorem of Calculus; techniques of integration; numerical and symbolic integration with software; arclength, area and volumes via integration.

1311  Accelerated Engineering Calculus I (4) Prerequisites: AP Calculus AB score of 4 or better OR AP Calc BC score of 3 or better.
   Math 1311 and 1321 together are equivalent to the three semester sequence Math 1210, Math 1220, and Math 2210. This sequence is intended for engineering majors. Review of introductory calculus, applications of differential and integral calculus, introduction to differential equations, conic sections and polar coordinates, numerical approximation, sequences and series, power series.

1320  Engineering Calculus II (4) Prerequisites: "C" or better in (MATH 1270 OR MATH 1311) OR AP Calc BC score of 3 or better OR Departmental Consent.
   Differential and Integral Calculus II, with a focus on applications and projects for engineers: integral expressions for moments, centers of mass, and work; modeling with first order differential equations; infinite series and sequences; power series and Taylor series; vectors, dot and cross products, and the geometry of space; the calculus of vector functions and particle motion in space; differential calculus for functions of several variables, including linear approximation, partial and directional derivatives, chain rule, and multi-variable optimization.

1321  Accelerated Engineering Calculus II (4) Prerequisites: "C" or better in (MATH 1270 OR MATH 1311) OR AP Calculus BC score of 3 or better OR Department Consent.
   Completion of Math 1321 is equivalent to completing the entire three semester Calculus I, II, II sequence. Vectors in the plane and in 3-space, differential calculus in several variables, integration and its applications in several variables, vector fields, and line, surface and volume integrals, Green's and Stokes Theorems.

1900  Topics in Mathematics (1 to 4) Instructor's Consent
   Various special topics in mathematics to be treated at the appropriate level.

2090  Teaching Secondary School Math for Elementary Teachers (3) Prerequisites: "C" or better in ((MATH 1210 OR MATH 1220 OR MATH 1250 OR MATH 1260 OR (MATH 1270 OR MATH 1311) OR (MATH 1280 OR MATH 1321) OR MATH 2210) OR AP Calc AB score of at least 4 OR AP Calc BC score of at least 3) AND "C" or better in MATH 4020).
   Meets with 4090. In this course we discuss teaching methods for secondary classroom, including appropriate use technology. Important components are developing topics across the curriculum, connections between mathematical concepts, as well as other important issues in running one's classroom: setting norms, goals, assessing students work and knowledge, providing practice and direction, managing diverse populations. This is a hands on class with ample opportunities for teaching. First session course.

2200  Introduction to Discrete Mathematics (3) Prerequisites: "C" or better in (MATH 1220 OR MATH 1250 OR (MATH 1270 OR MATH 1311) OR MATH 2210) OR AP Calc BC score of 5.
   Fundamentals of logic, set theory, order, relations, functions. Elementary number theory, modular arithmetic. Combinatorics; counting permutations, generating functions, matrix operations. Basic algebraic structures; groups, rings. Discrete probability. Introduction to graphy theory, trees, search optimization problems. Boolean algebra.

2210  Calculus III (3) Prerequisites: "C" or better in (MATH 1220 OR MATH 1250) OR AP Calculus BC score of at least 4 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Vectors in the plane and in 3-space, differential calculus in several variables, integration and its applications in several variables, vector fields and line, surface, and volume integrals. Green's and Stokes' theorems.

2250  Differential Equations and Linear Algebra (4) Prerequisites: "C" or better in MATH 2210 OR MATH 1260 OR MATH 1280 OR ((MATH 1220 OR MATH 1250 OR MATH 1270 OR AP Calculus BC score of 5) AND PHYS 2210 OR PHYS 3210) Fulfills Quantitative Reasoning (Math & Stat/Logic).
   This is a hybrid course which teaches the allied subjects of linear algebra and differential equations. These topics underpin the mathematics required for most students in the Colleges of Science, Engineering, Mines & Earth Science.

2270  Linear Algebra (4) Prerequisites: "C" or better in MATH 2210 OR MATH 1260 OR MATH 1280 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Euclidean space, linear systems, Gaussian elimination, determinants, inverses, vector spaces, linear transformations, quadratic forms, least squares and linear programming, eigenvalues and eigenvectors, diagonalization. Includes theoretical and computer lab components.

2280  Introduction to Differential Equations (4) Prerequisites: "C" or better in MATH 2270 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Linear and nonlinear differential equations and systems of equations, with applications. Matrix exponential, fundamental solution matrix, phase-space and portraits, stability, initial- and boundary-value problems, introduction to partial differential equations. Requires familiarity with linear algebra. Includes theoretical and computer lab components.

2900  Honors Seminar in Mathematics (2) Prerequisites: "C" or better in MATH 1210 OR MATH 1250 OR MATH 1270 OR AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3
   Fostering the ability to understand theorems and their purpose by studying selected groups of theorems in contexts that are new to the students and not part of the regular introductory courses.

3000  Undergraduate Colloquium (1)
   Colloquium of presentations of topics of contemporary mathematical interest.

3010  Topics in the History of Mathematics (3) Prerequisites: "C" or better in (MATH 1210 OR MATH 1250 OR MATH 1270 OR MATH 1220 OR MATH 2210) OR AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3 Fulfills Comm/Wrtg & Phys/Life Sci Exploration.
   A brief look at the history of mathematics, focusing on the principal ideas of importance in the development of the subject.

3070  Applied Statistics I (4) Prerequisites: "C" or better in MATH 1220 OR MATH 1250 OR MATH 1270 OR AP Calculus BC score of at least 4 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   An introduction to basic probability theory, sampling from normal populations, large-sample problems, sampling from one or two populations, estimation, and testing. R is used to perform statistical analyses. There are three lectures and one 1 1/2 hour lab per week.

3080  Applied Statistics II (3) Prerequisites: "C" or better in MATH 3070 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Introduction to analysis of variance, regression analysis, correlation analysis, and nonparametric techniques. Continued use of R programming language. There are two lectures and one 1 1/2 hour lab per week.

3100  Foundations of Geometry (3) Prerequisites: "C" or better in MATH 2200 AND (MATH 2210 OR MATH 1260 OR MATH 1280) Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Modern axiomatic development of Euclidean geometry and of trigonometry, also incidence theorems, projective invariants, straight-edge and compass constructions, spherical and hyperbolic geometries.

3150  Partial Differential Equations for Engineering Students (2) Prerequisites: "C" or better in (MATH 2250 OR (MATH 2270 AND MATH 2280)) AND (MATH 2210 OR MATH 1260 OR MATH 1280)
   Fourier series and boundary-value problems for the wave, heat, and Laplace equations, separation of variables in rectangular and radial geometries, Fourier transform.

3160  Applied Complex Variables (2) Prerequisites: "C" or better in MATH 2250 OR (MATH 2270 AND MATH 2280)
   Analytic functions, complex integration, Cauchy integral theorem, Taylor and Laurent series, residues and contour integrals, conformal mappings with applications to electrostatics, heat, and fluid flow.

3170  R Lab I (1) Prerequisites: "C" or better in MATH 1220 OR MATH 1250 OR MATH 1270 OR AP Calculus BC score of at least 4
   For students who wish to participate only in the Lab component of MATH 3070.

3180  R Lab II (1) Prerequisites: "C" or better in MATH 3070 OR MATH 3170
   For students who wish to participate only in the Lab component of MATH 3080.

3210  Foundations of Analysis I (4) Prerequisites: "C" or better in (MATH 2210 OR MATH 1260 OR MATH 1280) AND (MATH 2200 OR MATH 2270 OR MATH 2250) Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Logic, methods of proof and mathematical argument in mathematical analysis. Rigorous reconsideration of the real-number system, infinte series and of continuity, differentiation and integration for functions of one variable. The emphasis is on improving the student's ability to understand and explain concepts in a logical and complete manner.

3220  Foundations of Analysis II (4) Prerequisites: "C" or better in MATH 3210 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Advanced multivariable calculus. Topics include continuity, compactness, differentiation and affine approximation, chain rule, Taylor series, extremization, error estimation, inverse and implicit function theorems, Riemann integration, Fubini's Theorem, change of variables formula. The emphasis is on further developing the student's ability to understand more abstract concepts and to write an effective and rigorous mathematical argument.

3300  Laboratory in Computational Science (3) Prerequisites: "C" or better in MATH 2270 OR MATH 2250
   Mathematical and computational experimentation to understand principles of physical, chemical, and biological processes. Develop hypotheses, and use Matlab to test, questions regarding diffusion, molecular interactions, populations dynamics, epidemics, and ranking of sports teams. Emphasis throughout on using mathematical reasoning to understand computer simulation results.

3900  Topics in Mathematics (1 to 4) Instructor's Consent
   Various special topics in mathematics to be treated at the appropriate level.

3910  Supervised Reading (1 to 6) Instructor's Consent
   A course of independent study overseen by a faculty member.

4010  Mathematics for Elementary School Teachers I (4) Prerequisites: "C" or better in (MATH 1050 OR MATH 1010) OR Accuplacer CLM score of 65 or better. Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   This is the first course in a two-course sequence for prospective elementary school teachers. This is a content course that provides teachers with a deeper understanding of the real number system and arithmetic operations for whole numbers, fractions, and decimals. This provides the conceptual framework that allows teachers to analyze and correct common student misunderstandings in Grades K-6. See the Utah State Core Curriculum at www.usoe.k12.ut.us. Teaching methods pertaining to this material are discussed in EDU 5360. The Mathematics Department is additionally requiring that the prerequisites for this course be taken no more than two years prior to registration.

4020  Mathematics for Elementary School Teachers II (4) Prerequisites: "C" or better in MATH 4010 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   This is a continuation of MATH 4010, but deals with a different part of the mathematics curriculum. It is a content course that gives teachers a better understanding of topics in geometry appropriate to Grades K-6, including measurement, symmetry, geometric shapes, congruence and similarity. The course presents ideas from an intuitive perspective that prepares teachers to discuss geometry with children, and from a computational perspective to enable teachers to work with students to calculate distance, area and volume in both customary and metric units, measure angles, construct figures, and more. A brief discussion of topics in statistics and probability for Grades K-6 is also included. See the Utah State Core Curriculum at www.usoe.k12.ut.us. Teaching methods pertaining to this material are discussed in EDU 5360. The Mathematics Department is additionally requiring that the prerequisites for this course be taken no more than two years prior to registration.

4030  Foundations of Algebra (3) Prerequisites: "C" or better in MATH 2200 AND (MATH 2210 OR MATH 1260 OR MATH 1280) Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   The integers, unique factorization, and modular arithmetic. Polynomial rings. Introduction to abstract algebraic systems.

4090  Teaching of Secondary School Mathematics (3) Prerequisites: "C" or better in MATH 3100 AND MATH 4030 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Meets with MATH 2090. In this course we discuss teaching methods for secondary classroom, including appropriate use of technology. Important components are developing topics across the curriculum, connections between mathematical concepts, as well as other important issues in running one's classroom: setting norms, goals, assessing students work and knowledge, providing practice and direction, managing diverse populations. This is a hands on class with ample opportunities for teaching. First session course.

4095  Practicum for Secondary Mathematics Teachers (2) Prerequisites: "C" or better in MATH 3100 AND MATH 4030 Co-requisite: MATH 4090
   This is a practicum course that will parallel MATH 4090. One purpose of this course is to help students develop an awareness of meaningful ways to teach geometry and algebra to students in the 7th through 12th grades. Another purpose of this course is to help students become reflective teachers who can look critically at textbooks, teaching materials, assessments and their own teaching for the purpose of better meeting the needs of students. This course will have a strong student teaching component.

4190  Secondary Mathematics Teaching Practicum (3) Prerequisites: "C" or better in MATH 3220 AND (MATH 4090 OR MATH 3105 OR MATH 4035)
   Attend Intermediate Algebra course, assist in grading, teach a weekly review session, meet weekly to discuss pedagogy and evaluations of teaching.

4200  Introduction to Complex Variables (3) Prerequisites: "C" or better in MATH 3220 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Complex functions and their differentiability, complex integrals, power series, the Cauchy theorem and formulas, residues and applications to evaluating integrals, conformal mappings and applications. Graduate students who need this course should consult the instructor.

4400  Introduction to Number Theory (3) Prerequisites: "C" or better in MATH 2270 OR MATH 2250 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   An overview of algebraic number theory, covering factorization and primes, modular arithmetic, quadratic residues, continued fractions, quadratic forms, and diophantine equations.

4500  Introduction to Applied Analysis (3) Prerequisites: "C" or better in MATH 3210
   This course introduces main concepts of analysis needed for further study of differential equations, numerical methods, and probability.

4510  Introduction to Topology and Geometry (3) Prerequisites: "C" or better in MATH 3220 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Introduction to metric spaces, Lipschitz maps, isometries, group of isometries of the Euclidean plane, surfaces as metric spaces, geodesics, topological spaces, continuity, compactness, connectedness, identification spaces.

4600  Mathematics in Physiology and Medicine (4) Prerequisites: "C" or better in MATH 2250 OR MATH 2280
   The goals of the class are (i) to introduce the students to a range of modern mathematical tools; (ii) to teach the students the skill of building tractable mathematical models of biological processes; (iii) to show how to combine the mathematical knowledge, the numerical simulations (in Matlab) and biological intuition to derive new insights into the functioning of living systems. Mathematical topics include introduction to linear algebra, complex numbers, geometric dynamical systems, bifurcation theory, probability, Markov chain, partial differential equations. Biological topics may include modeling heart and circulation, kidneys, circadian clocks, brain rhythms, HIV, antibiotic resistance in bacteria, regulation of gene expression, biological pattern formation.

4750  Elementary Mathematical Fluid Dynamics (3) Prerequisites: "C" or better in MATH 3150 AND (MATH 2250 OR MATH 2280)
   An elementary introduction to fluid dynamics for the advanced undergraduate sciences student. The course will discuss the mathematical description of a variety of interesting fluid phenomena.

4800  Undergraduate Research in Mathematics (3) Instructor's Consent
   Explore a topic of significant mathematical interest, or an application of mathematics to a significant problem in science, engineering, or business. Students help to present the material or the results of their own investigations, and write a report on their findings. Prerequisites vary depending on the topic.

4910  Internship in Mathematics (1 to 4) Instructor's Consent
   Mathematics-related work in industry, business, or government.

4950  Special Research Projects (2 to 6) Instructor's Consent
   Projects to be completed as part of the requirements for the Departmental Honors program in mathematics.

4999  Honors Thesis/Project (3) Instructor's Consent
   Restricted to students in the Honors Program working on their University Honors degree.

5000  Undergraduate Problem Seminar (1) Prerequisites: "C" or better in MATH 1210 OR MATH 1250 OR MATH 1270 OR AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3
   Difficult problems presented for solution sharpen skills and develops problem-solving techniques. Prepares students for Putnam Examination (given annually by the Mathematical Association of America).

5010  Introduction to Probability (3) Prerequisites: "C" or better in MATH 2210 OR MATH 1260 OR MATH 1280 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6805. Combinatorial problems, random variables, distributions, independence and dependence, conditional probability, expected value and moments, law of large numbers, and central limit theorems.

5030  Actuarial Mathematics (3) Prerequisites: "C" or better in MATH 5010 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Basic introduction to actuarial and insurance mathematics. Helps to prepare students for the third actuarial exam.

5040  Stochastic Processes and Simulation I (3) Prerequisites: "C" or better in MATH 5010 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6810. An introductory course in the theory and practice of random processes with special emphasis on problem solving and simulation analysis.

5050  Stochastic Processes and Simulation II (3) Prerequisites: "C" or better in MATH 5040 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6815. Second half of the course described under the listing for MATH 5040.

5075  Time Series Analysis (3) Prerequisites: "C" or better in MATH 5010
   Meets with MATH 6820. An introduction to the basic topics: difference equations and lag operators, stationary autoregressive moving average processes, forecasting, estimation of parameters, spectral analysis, Kalman filter, introduction to nonlinear time series, processes with deterministic trends, processes with unit roots, cointegration, time series models for heteroskedasticity, and time series with changes in regime.

5080  Statistical Inference I (3) Prerequisites: "C" or better in MATH 5010 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Sampling, sampling distributions, Central Limit Theorem, transformation of data, complete and sufficient statistics, point estimation, optimality.

5090  Statistical Inference II (3) Prerequisites: "C" or better in MATH 5080 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Interval estimation, hypothesis testing, likelihood method, errors, optimality, order statistics, nonparametric methods, rank statistics.

5110  Mathematical Biology I (3) Cross listed as BIOL 5011. Prerequisites: "C" or better in MATH 2280 OR MATH 2250 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6830. Mathematical modeling in the biological and medical sciences. Topics will include continuous and discrete dynamical systems describing interacting and structured populations, resource management, biological control, reaction kinetics, biological oscillators and switches, and the dynamics of infectious diseases.

5120  Mathematical Biology II (3) Cross listed as BIOL 5012. Prerequisites: "C" or better in MATH 5110 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6835. Mathematical models of spatial processes in biology including pattern formation in the embryo and during tissue differentiation, applications of traveling waves to population dynamics, epidemiology, and chemical reactions, and models for neural patterns.

5150  Mathematics Curriculum and Instruction I (3) Prerequisites: "C" or better in MATH 3100 AND MATH 4030 AND MATH 3070
   This is a two semester sequence of required courses to be taken in conjunction with the Secondary Teaching/Action Research Seminars. The sequence will provide students who have a strong mathematical background with an opportunity to examine their knowledge in light of its application in the context of teaching. The sequence will explore the main threads of secondary school mathematics from and advanced standpoint.

5160  Mathematics Curriculum and Instruction II (3) Prerequisites: "C" or better in MATH 5150
   This is a two semester sequence of required courses to be taken inconjunction with the Secondary Teaching/Action Research Seminars. The sequence will provide students who have a strong mathematical background with an opportunity to examine their knowledge in light of its application in the context of teaching. The sequence will explore the main threads of secondary school mathematics from an advanced standpoint.

5210  Introduction to Real Analysis (4) Prerequisites: "C" or better in MATH 3220 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Metric spaces, fixed-point theorems and applications, Lebesgue integral, normed linear spaces, approximation, the Fundamental Theorem of Calculus.

5215  Applied Fourier Analysis (3) Prerequisites: "C" or better in MATH 2270 AND MATH 2280
   Fourier series and integrals, uncertainty principle, approximation and convergance theorems, discrete Fouier transforms and the Fast Fourier transform, signal and image processing. A project/paper will be required.

5250  Matrix Analysis (3) Prerequisites: "C" or better in MATH 2270
   Linear transformations and their eigenvalues, factorizations and canonical forms, vector and matrix norms, special matrix types, matrix-valued functions, generalized inverses, matrix groups.

5310  Introduction to Modern Algebra I (3) Prerequisites: "C" or better in MATH 3210 AND (MATH 3220 OR MATH 4400 OR MATH 4510) Fulfills Quantitative Reasoning (Math & Stat/Logic).
   An introduction to groups, rings, and fields.

5320  Introduction to Modern Algebra II (3) Prerequisites: "C" or better in MATH 5310 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Second half of the course described under the listing for MATH 5310.

5405  Cryptography, Codes, and Computational Number Theory (3) Prerequisites: "C" or better in MATH 4400 AND MATH 5310
   Classic and modern methods of encryption, applications to public-key ciphers (RSA, El Gamnal, etc.), random number generators, attacks on encryption systems, error correcting codes; computational number theory. A project/paper will be required.

5410  Introduction to Ordinary Differential Equations (4) Prerequisites: "C" or better in MATH 3220 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6840. Linear ordinary differential equations: initial-value problems and behavior of solutions. Nonlinear equations: existence, uniqueness, perturbations, extension to the boundary. Introduction to dynamical systems and their relation to differential equations.

5420  Ordinary Differential Equations and Dynamical Systems (3) Prerequisites: "C" or better in MATH 5410 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6845. Continuation of the study of dynamical systems, through a discussion of stability and its absence, concrete examples. Sturm-Liouville theory, including the existence of complete orthormal systems of eigenfunctions.

5440  Introduction to Partial Differential Equations (3) Prerequisites: "C" or better in (MATH 3210 AND (MATH 2250 OR MATH 2280)) Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6850. Classical wave, Laplace, and heat equations. Fourier analysis, Green's functions. Methods of characteristics.

5470  Chaos and Nonlinear Systems (3) Prerequisites: "C" or better in MATH 2280 OR MATH 2250 Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Meets with MATH 6440. Introduction to chaotic motions, strange attractors, fractal geometry. Models from fluid dynamics and mechanical and electrical oscillators.

5500  Calculus of Variations with Applications (3) Prerequisites: "C" or better in (MATH 2280 OR (MATH 2250 AND MATH 3150))
   Introduces the Calculus of Variations and gives an introduction to a range of applications in physics, mechanics, signal processing, and some topics of geometry.

5520  Introduction to Algebraic and Geometric Topology (3) Prerequisites: "C" or better in MATH 5310 AND MATH 4510 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Surfaces, their topological classification, introduction to algebraic topology through the fundamental group, covering spaces, geometry of the universal covering spaces of surfaces (Euclidean, spherical, hyperbolc), Gauss-Bonnet theorem.

5600  Survey of Numerical Analysis (4) Prerequisites: "C" or better in (MATH 2210 OR MATH 1260 OR MATH 1280) AND (MATH 2270 OR MATH 2250) AND computing experience Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6855. Numerical linear algebra, interpolation, integration, differentiation, approximation (including discrete and continuous least squares, Fourier analysis, and wavelets), initial- and boundary-value problems of ordinary and partial differential equations.

5610  Introduction to Numerical Analysis I (4) Prerequisites: "C" or better in (MATH 2210 OR MATH 1260 OR MATH 1280) AND (MATH 2270 OR MATH 2250) Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6860. Numerical linear algebra, interpolation, integration, differentiation, approximation (including discrete and continuous least squares, Fourier analysis, and wavelets). Programming experience is necessary prior to taking this course.

5620  Introduction to Numerical Analysis II (4) Prerequisites: "C" or better in MATH 5610 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6865. Numerical solution of initial and boundary value problems of ordinary and partial differential equations.

5700  Capstone Course in Mathematics (3) Prerequisites: "C" or better in MATH 4030 AND MATH 3100
   The Capstone Course in Mathematics examines secondary school mathematics from an advanced point of view. The topics covered are drawn from Abstract Algebra, Analysis, and Geometry and are rooted in the core secondary curriculum of number and operations, algebra, geometry, and functions. Students learn to generalize definitions and theorems that help to unite and explain mathematics. As they explore familiar secondary mathematic problems from a higher perspective, they draw connections between ideas taught separately in different courses. Through their work in the course, they improve their ability to promote their students' understanding of mathematics and to make better decisions regarding the direction of their lessons and curriculum.

5710  Introduction to Applied Mathematics I (3) Prerequisites: "C" or better in (MATH 2250 AND MATH 3150 AND MATH 3160) OR (MATH 2280 AND MATH 4200) Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Symmetric linear systems, positive definite matrices, eigenvalue problems, equilibrium equations for discrete and continuous systems, boundary value problems in ODEs and PDEs, boundary integrals.

5720  Introduction to Applied Mathematics II (3) Prerequisites: "C" or better in MATH 5710 Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Fourier methods, initial value problems in ODEs and PDEs, conservation laws, network flows and combinatorics, optimization.

5740  Mathematical Modeling (3) Prerequisites: "C" or better in (MATH 2250 OR (MATH 2270 AND MATH 2280)) Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6870. Development of mathematical models for physical, biological, engineering, and industrial phenomena and problems, and their solution using a wide variety of tools. Taught through case studies.

5750  Topics in Applied Mathematics (3) Instructor's Consent Fulfills Quant Reason(Math & Stat/Log) & Quant Intensive BS.
   Meets with MATH 6880. Consult Math Department for specific offering. Possible topics include integral equations, calculus of variations, control theory, continuum mechanics, applied matrix theory, vector and tensor analysis, applications of probability and statistics. Will be offered occasionally on the basis of need or interest.

5760  Introduction to Mathematical Finance I (3) Prerequisites: "C" or better in MATH 5010 AND MATH 2280
   Meets with MATH 6890. A basic introduction to the theory of financial derivative pricing. Topics include no arbitrage principle, risk-neutral measure, Black-Scholes theory, numerical model implementation and parameter calibration.

5765  Introduction to Mathematical Finance II (3) Prerequisites: "C" or better in MATH 5760
   Meets with MATH 6895. Continuous-time finance fundamentals, topics include exotic options, interest rate term structure models, jump processes, credit models, and statistical arbitrage strategies.

5900  Topics in Mathematics (1 to 4) Instructor's Consent
   Various topics in mathematics to be treated at the appropriate level.

5910  Supervised Reading (1 to 6) Instructor's Consent Fulfills Quantitative Reasoning (Math & Stat/Logic).

5950  Senior Seminar in Mathematics (3) Instructor's Consent
   A seminar on advanced topics in mathematics, centering around senior theses and projects.

5960  Undergraduate Special Projects (4) Instructor's Consent Fulfills Quantitative Reasoning (Math & Stat/Logic).
   Special computer project to serve as a senior thesis for students in scientific-computing emphasis.

5969  Special Topics in Statistics (1 to 6) Cross listed as OIS 5969, ED PS 5969, FP MD 5969, ECON 5969, FCS 5969, PSY 5969, SOC 5969, STAT 5969. Instructor's Consent
   Topics vary. Taught by members of the University Statistics Committee. Check current class schedule for cross-listings.

6010  Linear Models (3) Prerequisites: "C" or better in MATH 5010 AND MATH 5080 AND MATH 5090 AND MATH 2270
   Univariate linear models with applications to regression and ANOVA.

6020  Multilinear Models (3) Prerequisites: "C" or better in MATH 6010
   Multivariate linear models with applications to regression and ANOVA.

6040  Mathematical Probability (3) Prerequisites: "C" or better in MATH 6210
   Analytical approach to probability theory, random variables and their distributions, limit theorems for sums of independent random variables.

6070  Mathematical Statistics (3) Prerequisites: "C" or better in MATH 2270 AND MATH 5080
   Topics from distribution theory, estimation, and hypothesis testing.

6080  Topics in Contemporary Mathematics (3) Prerequisite: Instructor's consent.
   This course is intended to broaden student's perspective of mathematical research areas, while simultaneously introducing important mathematical concepts. More than a survey course, each instructor will spend 4-6 weeks discussing a topic of contemporary mathematics in depth, and there will be two to three such modules in the course. The idea is to start from the beginning, developing the selected topic to the point that students can grasp some of the central ideas important at a research level. Students will be required to choose one of the topics from which they will be assigned to read two research papers, write a survey paper and present their topic to the peers and the faculty member from that field.

6090  Advanced Topics in the History of Mathematics (3) Prerequisite: Instructor's consent.
   This course is part of the curriculum specific to the emphasis in Mathematics Teaching. Each semester, one or two particular topics are discussed from a historical perspective, tracing the demise of failed interpretations as well as the development of the current understanding. Illuminating the difficulties associated with understanding a topic by examining wrong turns deepens understanding.

6130  Introduction to Algebraic Geometry I (3) Prerequisites: "C" or better in MATH 6310 AND MATH 6320
   Affine and projective varieties, tangent spaces and singularities, curve theory.

6140  Introduction to Algebraic Geometry II (3) Prerequisites: "C" or better in MATH 6130
   Surfaces, intersection theory, special varieties, introduction to schemes.

6150  Complex Manifolds (3) Prerequisites: "C" or better in MATH 6220
   Material will be selected from Riemann surfaces and algebraic curves, Kaehler geometry, Stein manifold theory, compact surfaces, etc.

6170  Introduction to Riemannian Geometry (3) Prerequisites: "C" or better in MATH 6510
   Riemannian metrics, connections, geodesics, normal coordinates, completeness, spaces of constant curvature, submanifolds, Bonnet's and Meyer's theorem, Cartan-Hadamard theorem, Alexandrov and Topogonov comparison theorems, closed geodesics, cut locus, sphere theorem.

6210  Real Analysis (3) Prerequisites: "C" or better in MATH 5210
   Measures and integrals, Lp-spaces, Hilbert spaces, Banach spaces, Fourier series.

6220  Complex Analysis (3) Prerequisites: "C" or better in MATH 4200 AND MATH 6210
   Analytic functions, complex integration, conformal mapping, families of analytic functions, zeros of analytic functions, analytic continuation.

6240  Lie Groups/Lie Algebras I (3) Prerequisites: "C" or better in MATH 6220
   Basic theory of Lie groups and Lie algebras.

6250  Lie Groups/Lie Algebras II (3) Prerequisites: "C" or better in MATH 6240
   Structure theory, classification, and finite dimensional representations of Lie groups. Compact Lie groups.

6310  Modern Algebra I (3) Prerequisites: "C" or better in MATH 5320
   Groups, rings, modules, homological algebra, fields, and Galois theory.

6320  Modern Algebra II (3) Prerequisites: "C" or better in MATH 6310
   Second half of the course described under the listing for MATH 6310.

6350  Commutative Algebra (3) Prerequisites: "C" or better in MATH 6320
   Various topics in commutative algebra. The course will be offered on the basis of need or interest. May be repeated for credit when the topics vary.

6370  Algebraic Number Theory (3) Prerequisites: "C" or better in MATH 6320
   This is a dedicated course for graduate students in number theory. List of Topics: Dedekind domains. Extension. Class group units: Minkowski's reduction theory and Dirichlet's unit theorem. L-functions. Cyclotomic fields. Statement of Artin Recoprocity Law.

6410  Ordinary Differential Equations (3) Prerequisites: "C" or better in MATH 5210
   Existence, uniqueness theory; stability theory; invariant sets and manifolds; periodic motions; bifurcation theory; boundary value problems; applications.

6420  Partial Differential Equations (3) Prerequisites: "C" or better in MATH 5210
   First-order equations: characteristics, transport equations, shocks, Hamilton-Jacobi theory. Boundary value problems for the Laplace equation: maximum principles, Green's functions, Hilbert space methods. Cauchy and initial-boundary value problems for the heat equation and wave equation: existence and basic properties.

6430  Advanced Partial Differential Equations (3) Prerequisites: "C" or better in MATH 6420
   Advanced topics from among the following: systems of conservations laws, nonlinear elliptic and parabolic equations, viscosity solutions of evolution problems, free boundary problems, applications.

6440  Advanced Dynamical Systems (3)
   Meets with MATH 5470. Basic abstract dynamics; stable, unstable, center manifold theory; index theories; KAM theory; chaos; dimensions of attractors; forced oscillations; applications.

6510  Differentiable Manifolds (3) Prerequisites: "C" or better in MATH 4510 AND MATH 5520
   Manifolds, tangent spaces, orientation, Whitney's embedding theorem, transversality, Sard's theorem, partitions of unity, tubular neighborhoods, fiber bundles, degree theory, vector fields, flows, Lie derivatives, Frobenius' integrability theorem, differential forms, DeRham cohomology.

6520  Introduction to Algebraic Topology (3) Prerequisites: "C" or better in MATH 5520 AND MATH 6510
   Simplicial and cell complexes, homology and cohomology with coefficients, excision, Mayer-Vietoris sequence, cup and cap products, DeRham theorem, Euler characteristic, Poincare-Hopf theorem, higher homotopy groups, long exact sequence of a fiber bundle, elementary homotopy theory.

6530  Introduction to Low Dimensional Topology & Geometric Group Theory (3) Prerequisite: MATH 6510, 6520 or consent of the instructor.
   The course covers the basic concepts in low dimensional topology and geometric group theory, such as hyperbolic structures on surfaces, mapping class group, geodesic laminations, Nielsen-Thurston theory, Bass-Serre theory, topology of free groups, arithmetic groups, and others. The exact syllabus is up to the instructor.

6550  Algebraic Topology (3) Prerequisites: "C" or better in MATH 6510 AND MATH 6520
   Topics depend on the instructor. Possibilities include: Morse theory, Lefschetz fixed-point theorem, simple-homotopy theory, obstruction theory, vector bundles, characteristic classes, spectral sequences, duality theorems, rational homotopy theory, topological K-theory.

6570  Geometric Topology (3) Prerequisites: "C" or better in MATH 6510 AND MATH 6520
   Topics depend on the instructor. Possibilities include: low-dimensional topology (geometric structures on surfaces, Nielsen-Thurston theory of surface homeomorphisms, topology and geometry of 3-manifolds, topology of 4-manifolds), surgery and the classification of high-dimensional manifolds.

6610  Analysis of Numerical Methods I (3) Prerequisites: "C" or better in MATH 5620
   Mathematical analysis of numerical methods in linear algebra, interpolation, integration, differentiation, approximation (including least squares, Fourier analysis, and wavelets), initial- and boundary-value problems of ordinary and partial differential equations.

6620  Analysis of Numerical Methods II (3) Prerequisites: "C" or better in MATH 6610
   Second half of the course described under the listing for MATH 6610.

6630  Numerical Solutions of Partial Differential Equations (3) Prerequisites: "C" or better in MATH 6610 AND MATH 6620 AND MATH 6420
   Analysis and implementation of numerical methods for solving partial differential equations. Issues of stability and accuracy. Linear and nonlinear problems.

6710  Applied Linear Operator and Spectral Methods (3) Prerequisites: "C" or better in MATH 5210 AND MATH 5410
   The theory of linear operators applied to matrix, differential and integral equations, the Fredholm alternative, spectral theory, inverse and pseudo-inverse operators, Hilbert-Schmidt theory and eigenfunction expansions.

6720  Applied Complex Variables and Asymptotic Methods (3) Prerequisites: "C" or better in MATH 5210 AND MATH 5410
   Cauchy-Riemann equations, Cauchy integral formulas, Taylor and Laurent series, multivalued functions, branch points and cuts, analytic continuation, Jordan's lemma, evaluation of real integrals; potential theory, stream functions, conformal mapping, special functions, Fourier, Laplace, Hilbert, and Z transforms, scattering theory, asymptopic analysis of integrals, Laplace's method, Watson's lemma, method of steepest descents.

6730  Asymptotic and Perturbation Methods (3) Prerequisites: "C" or better in MATH 6720
   Asymptotic analysis, initial-value problems, multiscale analysis and the averaging theorem, homogenization theory, boundary- and transition-layer problems, matched asymptotic expansions, relaxation oscillations and propagating transition layers. Applications to problems from the physical and life sciences.

6740  Bifurcation Theory (3) Prerequisites: "C" or better in MATH 6210 AND MATH 6220
   Degree theories; method of Liapunov and Schmidt; local and global bifurcation theory; Hopf bifurcation; Liusternik-Shnirelman theory; applications.

6750  Fluid Dynamics (3) Prerequisites: "C" or bette rin MATH 5440 OR MATH 6420
   Derivation of equations of fluid dynamics, Euler and Navier-Stokes equations, Bernoulli's theorem, Kelvin's circulation theorem, potential flow, exact solutions, hydrodynamic paradoxes, vorticity, compressibility, thermal convection, waves in fluids, fluid instabilities, turbulence.

6760  Continuum Mechanics: Solids (3)
   Linear and nonlinear elasticity theory, transport phenomena, electromagnetic and elastic wave propogation and variational principles. Additional possible topics include piezoelectricity, thermoelectricity, viscoelasticity, magnetic materials, the Hall effect, quasiconvexity and phase transitions, shape memory and composite materials.

6770  Mathematical Biology I (3)
   Topics will alternate between (a) ecology and population biology and (b) physiology and cell biology.

6780  Mathematical Biology II (3)
   Second half of the course described under the listing for MATH 6770, of which it is the continuation.

6790  Case Studies in Computational Engineering and Science (3) Prerequisites: "C" or better in MATH 5740
   Two to five faculty members from various disciplines will describe in detail a project in which they are engaged that involves all ingredients of computational engineering and science: a scientific or engineering problem, a mathematical problem leading to mathematical questions, and the solution and interpretation of these questions obtained by the use of modern computing techniques. Participating faculty will vary from year to year. To be offered on the basis of need.

6795  Seminar in Computational Engineering and Science (1 to 5) Prerequisites: "C" or better in MATH 6790
   Students in the final semester of the Computational Engineering and Science Program will present their own CES-related research. To be offered on the basis of need.

6805  Introduction to Probability (3) Prerequisites: "C" or better in MATH 2210
   Meets with MATH 5010. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6810  Stochastic Processes and Simulation I (3) Prerequisites: "C" or better in MATH 5010
   Meets with MATH 5040. For Ph.d. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6815  Stochastic Processes and Simulation II (3) Prerequisites: "C" or better in MATH 5010 AND MATH 5040
   Meets with MATH 5050. For Ph.d. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6820  Time Series Analysis (3) Prerequisites: "C" or better in MATH 5010
   Meets with MATH 5075. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6824  Statistical Inference I (3) Prerequisites: MATH 5010 OR MATH 6805
   Meets with MATH 5080. For PhD students only. Extra work is required, including statistical projects, based on material covered, using software.

6828  Statistical Inference II (3) Prerequisites: MATH 5080 OR MATH 6824
   Meets with MATH 5090. For PhD students only. Extra work is required, including statistical projects, based on material covered, using software.

6830  Mathematical Biology I (3) Prerequisites: "C" or better in MATH 2280 OR MATH 3150 OR Instructor Consent
   Meets with MATH 5110. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6835  Mathematical Biology II (3) Prerequisites: "C" or better in MATH 5110
   Meets with MATH 5120. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6840  Introduction to Ordinary Differential (4) Prerequisites: "C" or better in MATH 3220
   Meets with MATH 5410. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6845  Ordinary Differential Equations and Dynamical Systems (3) Prerequisites: "C" or better in MATH 5410 OR Instructor Consent
   Meets with MATH 5420. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6850  Introduction to Partial Differential Equations (3) Prerequisites: "C" or better in MATH 3220
   Meets with MATH 5440. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6855  Survey of Numerical Analysis (4) Prerequisites: "C" or better in MATH 2210 AND MATH 2250 AND MATH 2280
   Meets with MATH 5600. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6860  Introduction to Numerical Analysis I (4) Prerequisites: "C" or better in MATH 2210 AND (MATH 2250 OR MATH 2270) AND MATH 2280 AND Computing Experience
   Meets with MATH 5610. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6865  Introduction to Numerical Analysis II (4) Prerequisites: "C" or better in MATH 5610
   Meets with MATH 5620. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6870  Mathematical Model (3) Prerequisites: "C" or better in MATH 5600 OR CS 5220
   Meets with MATH 5740. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes. Development of mathematical models for physical biological, engineering, industrial and societal phenomena and problems, and their solution using a wide variety of tools. Taught through case studies.

6875  Methods of Optimization (3) Prerequisites: "C" or better in MATH 3150
   Meets with MATH 5450. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6880  Topics in Applied Mathematics (3)
   Meets with MATH 5750. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6890  Introduction to Mathematical Finance I (3) Prerequisites: "C" or better in MATH 2280 AND MATH 5010
   Meets with MATH 5760. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes.

6895  Introduction to Mathematical Finance II (3) Prerequisites: "C" or better in MATH 2280 AND MATH 5010
   Meets with MATH 5765. For Ph.D. students only. Extra work is required; this should be arranged with the instructor before the end of the second week of classes. Continuous-time finance fundamentals, topics include exotic options, interest rate term structure models, jump processes, credit models, and statistical arbitrage strategies.

6910  Supervised Reading (1 to 6)

6960  Special Projects (1 to 6)

6970  Thesis Research: Master's (1 to 9)

6980  Faculty Consultation (3)
   Usually only one sequence from each decade (e.g., 711 to 719) is offered in any year.

7210  Representations of Lie Groups I (3) Prerequisites: "C" or better in MATH 6210 AND MATH 6220
   Basic theory of unitary representations of Lie groups.

7220  Representations of Lie Groups II (3) Prerequisites: "C" or better in MATH 7210
   Infinite dimensional representations of semi-simple Lie groups. Theory of Harish-Chandra modules.

7240  Several Complex Variables I (3) Prerequisites: "C" or better in MATH 6220
   Local theory of functions of several complex variables.

7250  Several Complex Variables II (3) Prerequisites: "C" or better in MATH 7240
   Global theory of functions of several complex variables.

7280  Operator Theory (3) Prerequisites: "C" or better in MATH 6210 AND MATH 6220
   A study of linear operators, primarily in Hilbert spaces.

7310  Various Topics in Algebra (3) Prerequisite: Instructor's consent.
   This graduate course will be offered on the basis of need or interest, covering various topics in algebra. The material will vary according to instructor and student interest, with possible topics being noncommutative geometry, Weyl algebras and D-modules, cluster algebras, etc.

7710  Optimization (3)
   Discusses modern problems in calculus of variations and optimal control, especially in the structural optimizations, as well as the foundations of these disciplines. Offered on the basis of need or interest.

7730  Nonlinear Oscillations (3)
   Offered on the basis of need or interest.

7740  Nonlinear Waves (3)
   Offered on the basis of need or interest.

7760  Mathematics of Materials (3)
   Offered on the basis of need or interest.

7800  Topics in Algebraic Geometry (3)
   Various topics in the area of algebraic geometry, offered on the basis of need or interest.

7805  Seminar in Algebraic Geometry (1 to 3)

7810  Topics in Riemannian Geometry (1 to 3)
   Various topics in the area of Riemannian geometry, offered on the basis of need or interest.

7815  Seminar in Differential Geometry (1 to 3)

7825  Seminar in Analysis (1 to 3)

7830  Topics in Commutative Algebra (3)
   Various topics in the area of commutative algebra, offered on the basis of need or interest.

7835  Seminar in Algebra (1 to 3)

7840  Topics in Differential Equations (3)
   Various topics in the area of differential equations, offered on the basis of need or interest.

7845  Seminar in Differential Equations (1 to 3)

7850  Topics in Algebraic Topology (3)
   Various topics in algebraic topology, offered on the basis of need or interest.

7853  Topics in Geometric Topology (3)
   Various topics in the area of geometric topology, offered on the basis of need or interest.

7855  Seminar in Topology (1 to 3)

7860  Topics in Numerical Analysis (3)
   Various topics in the area of numerical analysis, offered on the basis of need or interest.

7870  Topics in Applied Mathematics (1)
   Various topics in applied mathematics, offered on the basis of need or interest.

7875  Seminar in Applied Mathematics (1 to 3)

7880  Topics in Probability (3)
   Various topics in the area of probability, offered on the basis of need or interest.

7885  Seminar in Probability and Statistics (1 to 3)

7890  Topics in Representation Theory (3)
   Various topics in representation theory, to be offered on the basis of need or interest. May be repeated for credit when the topics vary.

7895  Seminar in Representation Theory (1 to 3)
   No description.

7970  Thesis Research: Ph.D. (1 to 9)

7980  Faculty Consultation (3)

7990  Continuing Registration: Ph.D. (0)


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