Department of Mathematics, University of Utah
UofUtah
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Department of Mathematics,
College of Science,
University of Utah,
Salt Lake City, Utah 84112-0090, USA.
801-581-6851, 801-581-4148 (fax)

1998-99 Catalog Information

This page contains a corrected and update transcription of the 1998-99 University of Utah Bulletin. Corrections to the paper version of the catalog are marked in red. Some of these changes may still have to be approved to make it into the 1999-2000 Catalog. Let me know by e-mail about any other errors that may still be there.

This web page was obtained by scanning the physical catalog. The text so obtained was edited by Ms. Liesel Thomas.

You can also examine the 1997-98 Catalog.

MATHEMATICS

Contents

College of Science

Department Office: 233 John Widtsoe Building, 581-6851

Mailing Address: 155 S. 1400 E, Salt Lake City, UT 84112-0090

Web Address: www.math.utah.edu

Department Chair, James A. Carlson, Ph.D.

Faculty

Distinguished Professors. P. Fife, J. Kollar.

Professors. P. Alfeld, M. Bestvina, R. Brooks, C.E. Burgess, J. Carlson, A. Cherkaev, C. H. Clemens, W. Coles, S. Ethier, A. Fogelson, E. Folias, S. Gersten, L. Glaser, K. Golden, F. Gross, G. Gustafson, H. Hecht, L. Horvath, M. Kapovich, J. Keener, N. Korevaar, J.D. Mason, D. Milicic, G. Milton, H. Othmer, P. Roberts, H. Rossi, T.B. Rushing, K. Schmitt, I. Taylor, D. Toledo, A. Treibergs, P. Trombi, D. Tucker, D. Willett.

Professors Emeritus. E.A. Davis, C. Wilcox, J. Wolfe.

Associate Professors. A. Bertram, D. Khoshnevisan, B. Kleiner, M. Lewis, G. Savin, N. Smale.

Assistant Professors. F. Adler, A. Balk, R. McLaughlin, R. Morelli, W. Niziol, J. Zhu.

Research Professor. Roger Horn

Assoc. Research Professor: Elena Cherkaeva.

Instructors. D. Allcock, J. Amoros, D. Bottino, K Glasner, V. Guirardel, C. Hacon, H. Kley, G. Muic, J Raquepas, K. Solna, K Whyte.

Adjunct Professors. M. Egger, J. Reading.

Adjunct Associate Professors. N. Beebe, D. Clark, C. Johnson, J. Johnson, L. Lewis, A. Roberts.

Adjunct Assistant Professors. S. Foresti, M. Pernice.

Advisers. Undergraduate Adviser, Leslie C. Glaser, 239 JWB, 581-6837, (e-mail)glaser@math.utah.edu Graduate Adviser, Peter Trombi, 323 JWB, 581-6120, (e-mail)trombi@math.utah.edu

The Department of Mathematics has prepared two publications (1) a brochure describing the department's undergraduate program, including the requirements for the various majors and minors in mathematics, and (2) a bulletin, Graduate Mathematics, which describes the graduate program of the department and gives guidelines for a student's progress through the various degree programs.


Placement and Prerequisites

Initial placement in mathematics at the University of Utah is made on the basis of the student's school transcript, ACT scores, and CLEP or AP test scores.

Students who receive a score of 3, 4, or 5 on either the AB or BC AP test in calculus are awarded 8 semester hours of mathematics credit. Placement information follows:
AP TEST
SCORE PLACEMENT
AB 3 MATH 1220
AB 4 MATH 1250
AB 5 MATH 1250 or 1260, with consent of instructor
BC 3 MATH 1260
BC 4 MATH 1260
BC 5 MATH 1260 or 2250 or 2270, with consent of department adviser

Students who begin in MATH 1260 may not receive credit for MATH 1210 or MATH 1250. Students who score less than 3 on one of the AP calculus examinations but believe they should be placed in a more advanced course than MATH 1210 should consult a department al adviser. Students who score above 50 on the CLEP college algebra or trigonometry test will have the corresponding course requirement (MATH 1050 or 1060) waived.

Students who have not taken AP or CLEP tests will be placed as follows:
ACT
Score Placement
Below 17 MATH 950
17 to 22MATH 1010
23 or aboveMATH 1050, 1060, 1090, 1100, or 1210

If the ACT was taken prior to October 1989, the minimum score required to take MATH 1010 is 16 and the minimum score required to take MATH 1050, 1060, 1090, 1100, or 1210 is 25.

A mathematics placement test is given at the University Testing Center and may be used to help determine placement if a recent ACT score is not available. Also available are an algebra test and a functions test for qualification to take MATH 1210.

A student who scores above 23 on the ACT test and has taken either college algebra or trigonometry in high school and received a grade of A or B will have the appropriate course requirement waived.

A student who received a grade of C in one of these courses but would like that course requirement waived should consult a mathematics adviser.

Transfer students and students resuming the study of mathematics after an interval of two years or more may be required to take appropriate placement tests. Consult the department for details.

Prerequisites for courses must be strictly observed, and a grade of at least C in prerequisite courses is required. Exceptions must be approved by the department. Students who enroll in a course without the prerequisites may have their registration canceled. If no prerequisite is announced for a course departmental approval is required.

High school students who plan college programs that require calculus and who wish to avoid delay in the completion of these programs should complete trigonometry and college algebra in high school to permit registration for MATH 1210 during their first semester.


Undergraduate Program

Degrees. B.A., B.S.

To become a mathematics major one must have an interest in and talent for mathematics. There are no special departmental or admission requirements. Mathematics majors must earn a grade of C or better in all required mathematics courses.

The basic major program consists of Calculus I, II, and III (MATH 1210, 1220, 2210 or some of MATH 1250, 1260 depending upon AP credit; college algebra and trigonometry are prerequisites for calculus), and four semesters of 2000- and 3000-level mathematics: linear algebra and differential equations (MATH 2270, 2280), and foundations of analysis (MATH 3210, 3220). The major student, other than a teaching major, then chooses, in consultation with the departmental adviser or a departmental mentor, six semester courses in mathematics numbered 4200 or higher. The allowed choices depend on the emphasis chosen. The regular major may select from the full list of 33 advanced semester courses.

The only allied requirement is a year of physics. Majors whose emphasis is statistics replace the physics requirement with eight hours of approved credit in statistical methodology courses offered by other departments. Depending on the mathematics emphasis chosen, this amounts to 37-48 hours of mathematics credits. The Department of Mathematics requires for graduation that each major demonstrate satisfactory performance on the advanced mathematics part of the GRE. This examination is used as the department's comprehensive examination. It should be taken before the last semester prior to graduation.

Mathematics Internship. The Department of Mathematics participates in the University's Cooperative Education Program (Co-op), which provides internship opportunities for students in business, industry, and government. The program involves either full-time employment during a semester when the student is not enrolled in school or part-time employment during a semester in which the student is enrolled part-time.

While exposing students to mathematics in non academic settings, the internship enables them to defray part of their education costs.

Students also become known by potential employers. Students who want to participate in the program through the Mathematics Department should be mathematics majors who have completed one-half of each of the sequences MATH 2210, 2220 and 3210, 3220. They should contact the departmental undergraduate adviser to get an application form and two faculty recommendation forms. Once approved by the Mathematics Department, the student is assisted by the Cooperative Education Center in preparing a resume and applying for a Co-op position. Placements are decided by the employer.

Interns register for MATH 4910 during the semesters they are involved with the program. The course carries variable credit, decided by the undergraduate adviser once the hours and duties of the internship are known. At the end of the semester, the intern writes a report describing the completed work and presents an evaluation written by his/her supervisor during the internship. The course, which may be taken a maximum of two times, is graded CH or NC (credit/no credit).


Requirements for the Major

1. Ordinary Major
MATH 1210, 1220, 2210 Calculus I, II, III (4,4,3)
or MATH 1250, 1260 (4,4)
or MATH 1215, 1225, 2210 (4,4,3)
MATH 2270 Linear Algebra (4)
MATH 2280 Differential Equations (4)
MATH 3210, 3220 Foundations of Analysis I, II (3,3) Six semester courses in mathematics numbered 4200 or higher (18-23)

Total Math Hours with a grade of C or better: 40-48

PHYCS 2210, 2220, or 3210 Physics for Scientists, Engineers (4,4)

Satisfactory performance on the department's comprehensive examination

2. Major with an Emphasis in Statistics

MATH 1210, 1220, 2210 Calculus I, II, 111 (4,4,3)
or MATH 1250, 1260 (4,4)
or MATH 1215, 1225, 2210 (4,4,3)
MATH 2270 Linear Algebra (4)
MATH 3070, 3080 Applied Statistics I, II (4,3)
MATH 3210, 3220 Foundations of Analysis I, II (3,3)
MATH 5010 Probability (3)
MATH 5080, 5090 Statistical Inference I, II (3,3)

Three courses from the following list:
MATH 4200 Complex Variables (3)
MATH 5030 Actuarial Math (3)
MATH 5040, 5050 Stochastic Processes I, II (3,3)
MATH 5210 Real Analysis (3)
MATH 5410 Ordinary Differential Equations (4)
MATH 5420 Dynamical Systems (3)
MATH 5610, 5620 Introduction to Numerical Analysis I, II (4,4)
MATH 5710, 5720 Applied Mathematics (3,3)

Total Math Hours with a grade of C or better: 43-49

The physics sequence should be replaced by statistics courses from other departments.

Satisfactory performance on the department's comprehensive examination

3. Major with an Emphasis in Scientific Computing

MATH 1210, 1220, 2210 Calculus I, II, III (4,4,3)
or MATH 1250, 1260 (4,4)
or MATH 1215, 1225, 2210 (4,4,3)
MATH 2270 Linear Algebra (4)
MATH 2280 Differential Equations (4)
MATH 3210, 3220 Foundations of Analysis I, II (3, 3)
MATH 5610, 5620 Introduction to Numerical Analysis I, II (4,4)
MATH 5960 Special Projects (3)

Three courses from the following list: MATH 5010 Probability (3)
MATH 5040, 5050 Stochastic Processes I, II (3,3)
MATH 5080, 5090 Statistical Inference I, II (3,3)
MATH 5110, 5120 Mathematical Biology (3,3)
MATH 5410 Ordinary Differential Equations (4)
MATH 5420 Dynamical Systems (3)
MATH 5440 Partial Differential Equations (3)
MATH 5710, 5720 Applied Mathematics (3,3)

Total Math Hours with a grade of C or better: 42-46

PHYCS 2210, 2220 or 3210, 3220 Physics for Scientists, Engineers (4,4)

Allied Course (3)

Satisfactory performance on the department's comprehensive examination

*Required for each major is satisfactory performance on the advanced mathematics part of the Graduate Record Examination, which is used as the department's comprehensive examination. This exam should be taken before the last semester prior to graduation.

For a major, a grade of C or better is required in all mathematics courses.

Requirements for the Minor

MATH 1210, 1220, 2210 Calculus I,II,III(4,4,3)
MATH 3210, 3220 Foundations of Analysis I,II(3,3)

Three other courses with a prerequisite of at least Calculus I and II

For a minor, a grade of C or better is required in all mathematics courses.

Teaching Major, Minor, Certification. Please refer to Education in the Colleges section for information on teaching major and minor course requirements and state secondary teacher certification.


Graduate Program

Degrees. M.A., M.S., M.Phil., Ph.D. in mathematics; M.Stat. in statistics.

Areas of Specialization. Algebra, algebraic geometry, analysis, applied mathematics, differential equations, differential geometry, numerical analysis, probability, statistics, and topology. Detailed information is available in Graduate Mathematics, available from the department office.

Admission Requirements. Admission to graduate status in either a master's or the Ph.D. program requires that students hold a bachelor's degree, or its equivalent, with a GPA of at least 3.0 and that they show promise of success in graduate work. Applicant s are urged to take the advanced mathematics portion of the GRE. Foreign students are required to take both the TOEFL and TSE tests.

Requirements for Graduate Degrees

M.S. in Pure Mathematics

Course Requirements

  1. MATH 5210 (real analysis)
  2. MATH 5310, 5320 (algebra)
  3. One 6000-level sequence consisting of two one-semester courses
  4. Four additional one-semester courses at the 5000- or 6000-level

Graduation Requirements

1. Pass two of the written qualifying exams
or
Take an oral examination and complete a master's project.
The options available for this project are as follows:
  1. Master's thesis.
  2. A curriculum project.
  3. Taking additional courses at the 6000- or 7000-level.

2. The total number of semester hours required for the masters degree in pure mathematics should fall in the range 30-36

M.S. in Applied Mathematics

Course Requirements

1. Either two 6000-level sequences in mathematics or MATH 5210 and three 6000-level one-semester courses, two of which must form a year-long sequence

2. Five additional one-semester courses at the 5Q00- or 6000-level

Graduation Requirements. Same as those for the M.S. in pure mathematics.

M. Stat.

1. MATH 5010, 5080, 5090.
2. MATH 6070.
3. One sequence chosen from either MATH 6010, 6020 or MATH 6210, 6040.
4. Six one-semester graduate-level courses approved by the student's supervisory committee.
5. MATH 6960 (master's project) (3-6 hours)
6. Written competency examination in applied statistics.
7. Oral examination on project.

M.S. for Secondary School Teachers

The College of Science offers a special option leading to a master's degree for secondary-school teachers with at least three years teaching experience in science or mathematics.

Graduate Certificate in Computational Engineering and Science (CES)

A joint program in computational engineering and science offered by the departments of Computer Science (College of Engineering) and Mathematics (College of Science).

Utah Genome Science Training Program

A joint program offered by the departments of Biology and Mathematics. For details see Science in the Colleges section of this catalog.

M. Phil.

The M. Phil. degree has the same requirements as the Ph.D. degree except that no doctoral dissertation is required. Consult the Bulletin of the University of Utah, The Graduate School, the Graduate Information section of this catalog, and the departmental director of graduate studies for details.

Ph.D.

Course Requirements. The course requirements for the Ph.D. degree consist of at least seven year-long sequences numbered 6000 or above, or their equivalent, approved by the student's supervisory committee. The seven sequences must include at least 15 credits. t hours of courses numbered 7800-7970 (topics courses, seminars, thesis research).

Written Qualifying Examination. The student must pass written examinations, each of three hours' duration, in three different areas of mathematics approved by the students supervisory committee. These exams are given just before the start of the fall semester. A student has two opportunities to pass the three exams.

Oral Qualifying Examination. The student must pass an oral examination during the academic year in which he/she completes the written examinations. This exam may be repeated once at the discretion of the student's supervisory committee. The oral exam is not a test of specific subject matter retention; rather, it is designed to measure the student's overall mathematical maturity and breadth, and his/her skill at chalkboard exposition and verbal exchange. In general the oral examination is concentrated in the area of specialization of the student and in related areas.

Language Requirements. The Department of Mathematics has no language requirements for the Ph.D. degree.

Thesis. The student must write a thesis on a topic approved by his/her supervisory committee.

Final Oral Examination. This is an oral examination which consists of a public thesis defense.


MATH Courses

1010 Intermediate Algebra (3) Recommended Prereq.: ACT score of at least 17 and either high school algebra or consent of the instructor. Rapid review of elementary algebra; exponents and radicals; linear functions, equations, inequalities; complex numbers; quadratic functions and equations; logarithm and exponential functions.

1030 Introduction to Quantitative Thinking (3) Recommend Prereq. MATH 1010. Fulfills: Quantitative Reasoning A Course. Mathematical methods for solving problems through specific case studies: isolation of relevant parameters, data analysis, representation and interpretation, simulations, geometric and time-varying models.

1040 Introduction to Statistics (3) Discussion, lecture. Recommend Prereq.: MATH 1010. Fulfills: Quantitative Reasoning B Course. The course covers descriptive statistics and elements of estimation and testing.

1050 College Algebra (4) Recommend Prereq.: MATH 1010. Fulfills: Quantitative Reasoning A Course. Functions and graphs, linear models and matrices, exponential and logarithm functions, arithmetic and geometric sequences.

1060 Trigonometry (2) Recommend Prereq.: MATH 1010. Trigonometric functions periodicity, polar coordinates, planar vectors.

1070 Elementary Statistics (3) Recommend Prereq.: MATH 1010. Fulfills: Quantitative Reasoning B Course. Students who have completed one quarter of calculus should take MATH 3070 instead of MATH 1070. Modern statistics, including summarization of data, introduction to probability, elementary methods of estimation, and statistical tests.

1075 The Mathematics of Chance (3) Recommend Prereq.: MATH 1010. Fulfills: Science Foundation, Quantitative Reasoning A Course. The development of probability (an historical look), probability and games of chance, applications of probability to statistics, genetics, other applications as time permits.

1080 Perspective on Mathematics (3) Recommend Prereq.: MATH 1010. Fulfills: Science Foundation, Quantitative Reasoning A Course. Topics from calculus, emphasizing the ideas of calculus rather than the technical aspects.

1090 College Algebra for Business, Social Sciences (3) Recommend Prereq.: MATH 1010. Fulfills; Quantitative Reasoning A Course. Functions and graphs linear and quadratic functions matrices, Gaussian elimination, Leontieff models, exponential and logarithmic functions, growth, periodic and continuously compounded interest, arithmetic and geometric series, annuities and loans.

1100 Quantitative Analysis (3) Recommended Prereq.: MATH 1090. Fulfills Quantitative Reasoning A Course, Quantitative Reasoning B Course. Not for students who have completed more than one quarter of calculus. Differentiation, maximization and minimization of functions, marginal analysis and the optimization of constrained functions, integration and applications.

1170 Mathematics for Life Scientists I (4) Recommended Prereq.: MATH 1050 and 1060+ Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Differential and integral calculus applied to biological problems. Derivation and analysis of discrete-time dynamical systems for growth, diffusion, and selection. Probability and statistics applied to biological problems. Computer lab using Maple.

1180 Mathematics for Life Scientists II. (4) Recommended Prereq.: MATH 1170 or consent of instructor. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Second half of the course described under the listing for MATH 1170.

1210 Calculus I (4) Recommended Prereq.: Either both MATH 1050 and 1060 or equivalent high school courses and ACT score of at least 23. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning 8 Course. 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.

1215 Calculus I with Maple (4) Recommended Prereq.: Either both MATH 1050 and 1060 or equivalent high school courses and ACT score of at least 23. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. This course is the same as MATH 1210 with an added Maple lab component.

1220 Calculus 11(4) Recommended Prereq.: MATH 1210 or 1215. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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).

1225 Calculus II with Maple (4) Recommended Prereq.: MATH 1210 with consent of instructor or MATH 1215. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. This course is the same as MATH 1220, with an added Maple lab component.

1250 Calculus for AP Students I (4) Departmental consent. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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) Departmental consent. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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.

1400 Rapid Calculus (5) Recommended Prereq.: One quarter of calculus. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Taught only Fall Semester 1998. Takes students who have completed MATH 111 (quarter system) through the rest of Calculus I and 11 in one semester. For topics see the descriptions of MATH 1210 and MATH 1220.

2070 Mathematics in Medicine (3) Discussion, lecture. Recommended Prereq: MATH 1170 or 1210. Fulfills: Science Integration Quantitative Reasoning A Course Quantitative Reasoning B Course. The course is designed to give students the quantitative tools needed to understand and solve problems and models in the medical sciences, using examples froth pharmaceutics, epidemiology, and physiology. The class format will be a combination of lecture s and discussion sessions.

2160 Introduction to Scientific Computing Using C (3) Recommended Prereq.: MATH 1210 or consent of instructor. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. A short introduction to those aspects of C and C++ essential for mathematics, followed by extensive work with mathematics problems in which computation plays an important role.

2210 Calculus 111(3) Recommended Prereq.: MATH 1220 or 1225. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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 Ordinary Differential Equations and Linear Algebra (3) Recommended Prereq.: MATH 2210 or 1260 or PHYCS 2210 or 3210. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. First and second order ODEs with applications to mechanics, electrical circuits, and populations. Qualitative analysis and stability. Elementary numerical methods. Laplace transforms. Linear algebra and its applications to solution spaces, systems of differential equations, and phase space analysis. Introduction to nonlinear systems and chaos.

2270 Linear Algebra (4) Laboratory, lecture. Recommended Prereq.: MATH 1220 or 1225 or 1260 Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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) Laboratory, lecture. Recommended Prereq.: MATH 2270 or consent of instructor. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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.

2500 Linear Algebra/Vector Calculus (3) Recommended Prereq.: One quarter of Engineering Mathematics (differential equations). Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Taught only in the Fall Semester of 1998. Takes students who have completed our MATH 251 (quarter system) through MATH 252.The topics will be linear algebra, matrix theory, and the basics of vector calculus.

3010 Topics in the History of Mathematics (3) Fulfills: Science Integration. A brief look at the history of mathematics, focusing on the principal ideas of importance in the development of the subject.

3070 Applied Statistics 1(4) Laboratory, lecture. Recommended Prereq. MATH 1210 or 1215 or 1250 Fulfills: Quantitative Intensive BS Course. Quantitative Reasoning A Course, Quantitative Reasoning B Course. An introduction to basic probability theory, sampling from normal populations, large-sample problems, sampling from one or two populations, estimation, and testing. SAS is used to perform statistical analyses. There are three lectures and one 1 1/2 hour lab per week.

3080 Applied Statistics 11(3) Laboratory, lecture. Recommended Prereq.: MATH 3070. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Introduction to analysis of variance, regression analysis, correlation analysis, and nonparametric techniques. Continued use of SAS programming language. There are two lectures and one 1 1/2 hour lab per week.

3090 Design of Experiments (3) Laboratory, lecture. Recommended Prereq.: MATH 3070. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Introduction to the design of experiments, multiple regression, factorial and nested designs. SAS is used for computations.

3100 Foundations of Geometry (3) Recommended Prereq.: MATH 2210. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Modern axiomatic development of Euclidean geometry and of trigonometry, also incidence theorems, projective invariants, straight-edge and compass constructions, spherical and hyperbolic geometries. Mathematics teaching majors should take the accompanying practicum, MATH 3105.

3105 Geometry Practicum (1) Recommended Prereq.: MATH 3100. Application of the geometry studied in MATH 3100 to the secondary-school classroom.

3150 Partial Differential Equations for Engineering Students (2) Recommended Prereq.: MATH 2250 or both 2270 & 2280. Fourier series and boundary-value problems for the wave, heat, and Laplace equations, separation of variables, Sturm-Liouville problems and orthogonal expansions, Bessel functions and Legendre polynomials. Fourier transform.

3160 Complex Variables for Engineering Students (2) Recommended Prereq.: MATH 2250. 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.

3210 Foundations of Analysis I (3) Recommended Prereq.: MATH 2210. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Methods of proof in mathematical analysis. Rigorous reconsideration of the real-number system, cardinality, continuity, differentiability, integrability, compactness, and connectedness. The emphasis is on improving the student's ability to understand and explain concepts in a logical and complete manner.

3220 Foundations of Analysis 11(3) Recommended Prereq.: MATH 3210. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Reconsideration of topics in several-variable calculus from a more advanced point of view. Topics include: differentiation and affine approximations, chain rule, Taylor series and multi-variable extremization, error estimation, Fubini's theorem, introduction to differential forms and the general Stokes' Theorem, inverse and implicit function theorems, applications to the study of curves and surfaces.

3730 Applied Linear Algebra (3) Laboratory lecture Recommended Prereq.: MATH 2250 or 2270 Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Vector spaces linear transformations. systems of linear equations, eigenvalues and eigenvectors, applications to Markov chains, linear difference and differential equations, numerical methods. There is also an applied computer lab Component.

4010 Teaching of Elementary School Mathematics l (4) Recommended Prereq.: MATH 1050. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Introduction to real-number arithmetic, intuitive and computational geometry, with an emphasis on communicating these concepts to children in grades K-6. Developing a more mature view of arithmetic skills, including the use of computers in teaching problem-solving skills.

4020 Teaching of Elementary School Mathematics 11(4) Recommended Prereq.: MATH 4010. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Second half of the course described under the listing for MATH 4010.

4040 Teacher Leader Training I (4) Recommended Prereq.: MATH 1050. Fulfills: Quantitative Reasoning A Course. Elementary probability and statistics, networks, and graphs. Intuitive and computational geometry. Introduction to trigonometry. Intuitive calculus.

4050 Teacher Leader Training II (4) Recommended Prereq.: MATH 4040. Fulfills: Quantitative Reasoning A Course. Second half of the course described under the listing for MATH 4040.

4090 Teaching of Secondary School Mathematics (3) Recommended Prereq.: MATH 2210. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Presentation of mathematical material at the appropriate level, remedial-instruction methods, curriculum development.

4200 Introduction to Complex Variables (3) Recommended Prereq.: MATH 3220. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Complex functions and their differentiability, complex integrals, power series, the Cauchy theorem and formulas, residues and applications to evaluating integrals, non formal mappings and applications. Graduate students in other departments who need this course should consult the instructor.

4300 Introduction to Algebra (3) Recommended Prereq.: MATH 2210. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. The integers, unique factorization, and modular arithmetic. Polynomial rings. Introduction to abstract algebraic systems. Mathematics teaching majors should also take the accompanying practicum, MATH 4305.

4305 Algebra Practicum (1) Recommended Coreq: MATH 4300. Application of the material studied in MATH 4300 to the secondary-school classroom.

4400 Introduction To Number Theory (3) Recommended Prereq.: MATH 2280. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. An overview of algebraic number theory, covering factorization and primes, modular arithmetic, quadratic residues: continued fractions, quadratic forms and diophantine equations.

4510 Introduction To Topology (3) Recommended Prereq MATH 3220 Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Introduction to the ideas of topologies, compactness, connectedness, separation axioms, metric spaces. Graduate students in other departments who need this course should consult the instructor.

4530 Curves and Surfaces in Euclidean Space (3) Recommended Prereq.: MATH 3220. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Frenet theory, Gaussian and mean curvatures, Gauss-Bonnet theorem, minimal surfaces, and surfaces of constant curvature. Graduate students in other departments who need this course should consult the instructor.

4750 Elementary Mathematical Fluid Dynamics (3) Recommended Prereq.: MATH both 2250 and 3150 or consent of instructor. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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.

4910 Internship in Mathematics (1 to 4) Departmental consent. Independent study. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Mathematics-related work in industry, business, or government.

4999 Honors Thesis/Project (3) Honors thesis project. Fulfills: Communication Writing. Restricted to students in the Honors Program working on their Honors degree.

5000 Undergraduate Problem Seminar (1) Recommended Prereq.: MATH 1210. 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) Recommended Prereq.: MATH 2210 or 1260. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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) Recommended Prereq.: MATH 5010. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Basic introduction to actuarial and insurance mathematics. Prepares students for the actuarial exam.

5040 Stochastic Processes and Simulation I (3) Recommended Prereq.: MATH 5010. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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) Recommended Prereq.: MATH 5040. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Second half of the course described under the listing for MATH 5040.

5080 Statistical Inference 1(3) Recommended Prereq.: MATH 5010. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Sampling, sampling distributions, point and interval estimation, tests of hypotheses, regression, ranking methods, order statistics, and other nonparametric methods.

5090 Statistical Inference 11(3) Recommended Prereq.: MATH 5080. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Second half of the course described under the listing for MATH 5080.

5110 Mathematical Biology l (3) Recommended Prereq.: MATH 2250 or 2280 or consent of Instructor. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Cross-listed as BIOL 6080. Topics from population biology, physiology, and developmental biology.

5120 Mathematical Biology II (3) Recommended Prereq.: MATH 5110. Fulfills: Quantitative Intensive BS Courses Quantitative Reasoning A Course, Quantitative Reasoning B Course. Second half of the course described under the listing for MATH 5110. Cross-listed as BIOL 6090.

5210 Introduction to Real Analysis (4) Recommended Prereq.: MATH 3220 and 4510. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Metric spaces, fixed-point theorems and applications, Lebesgue integral, normed linear spaces, approximation, the Fundamental Theorem of Calculus.

5250 Matrix Analysis (3) Recommended Prereq.: MATH 2270. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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 1(3) Recommended Prereq. MATH 2250 or 2270. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. An introduction to groups, rings, and fields.

5320 Introduction to Modern Algebra II (3) Recommended Prereq.: MATH 5310. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Second half of the course described under the listing for MATH 5310.

5410 Introduction to Ordinary Differential Equations (4) Recommended Prereq.: MATH 3220. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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) Recommended Prereq.: MATH 5410 Fulfills Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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 orthonormal systems of eigenfunctions.

5440 Introduction to Partial Differential Equations (3) Recommended Prereq.: MATH 3220. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Classical wave, Laplace, and heat equations. Fourier analysis, Green's functions. Methods of characteristics.

5470 Applied Dynamical Systems (3) Recommended Prereq.: MATH 2250 or Math 2270 or Math 2280. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Introduction to chaotic motions, strange attractors, fractal geometry,. Models from fluid dynamics and mechanical and electrical oscillators.

5520 Introduction to Algebraic/ Geometric Topology (3) Recommended Prereq.: MATH 4510 or equivalent. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Introduction to algebraic topology via the fundamental group of a topological space. Includes selected topics in geometric topology.

5600 Survey of Numerical Analysis (4) Recommended Prereq.: MATH 2210, either MATH 2250 or 2270, and computing experience. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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) Recommended Prereq.: MATH 2210, either MATH 2250 or 2270, and computing experience. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Numerical linear algebra, interpolation, integration, differentiation, approximation (including discrete and continuous least squares, Fourier analysis, and wavelets).

5620 Introduction to Numerical Analysis II (4) Recommended Prereq.: MATH 5610. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Numerical solution of initial and boundary value problems of ordinary and partial differential equations.

5650 Topics in Numerical Analysis (3) Recommended Prereq.: MATH 5600 or both 5610 and 5620. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Variable topics in numerical analysis depending on need and interest.

5660 Parallel Numerical Methods (4) Recommended Prereq.: MATH 5600 or both 5610 and 5620. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. An introduction to parallel computing (hardware, software, programming environments, algorithm design, performance evaluation) in the context of numerical linear algebra and the numerical solution of partial differential equations. Offered on the basis o f need or interest.

5710 Introduction to Applied Mathematics I (3) Recommended Prereq.: MATH 2250 and 3150 and 3160. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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 11(3) Recommended prereq.: MATH 5710. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Fourier methods, initial value problems in ODEs and PDEs, conservation laws, network flows and combinatorics, optimization.

5740 Mathematical Modeling (3) Recommended Prereq.: MATH 5600 or CP SC 5220. Fulfills: Quantitative Intensive BS Course, Quantitative Reasoning A Course, Quantitative Reasoning B Course. Development of mathematical models for physical, biological, engineering, and industrial phenomena and problems, using mainly ordinary and partial differential equations. Involvement of analytical and numerical tools suitable for analysis and visualization of the solutions of these problems, including packages such as LAPACK, EISPACK, Maple and Matlab.

5750 Topics in Applied Mathematics (3) Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. 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.

5910 Supervised Reading (1 to 6) Independent study. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course.

5960 Undergraduate Special Projects (4) Special projects. Fulfills: Quantitative Reasoning A Course, Quantitative Reasoning B Course. Special computer project to serve as a senior thesis for students in scientific-computing emphasis.

6010 Linear Models (3) Recommended Prereq.: MATH 5010 and 5080 and 5090 and 2270. Univariate linear models with applications to regression and ANOVA.

6020 Multi-linear Models (3) Recommended Prereq.: MATH 6010. Multivariate linear models with applications to regression and ANOVA.

6040 Mathematical Probability (3) Recommended Prereq.: MATH 6210. Analytical approach to probability theory, random variables and their distributions, limit theorems for sums of independent random variables.

6070 Mathematical Statistics (3) Recommended Prereq.: MATH 2270 and 5080. Topics from distribution theory, estimation, and hypothesis testing.

6130 Introduction to Algebraic Geometry I (3) Recommended Prereq.: MATH 6310 and 6320. Affine and projective varieties, tangent spaces and singularities, curve theory.

6140 Introduction to Algebraic Geometry II (3) Recommended Prereq.: MATH 6130. Surfaces, intersection theory, special varieties, introduction to schemes.

6150 Complex Manifolds (3) Recommended Prereq.: 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) Recommended Prereq.: MATH 6520. Riemannian metrics, connections, geodesics, normal coordinates, completeness, spaces of constant curvature, sub-manifolds, Bonnet's and Meyer's theorem, Cartan-Hadamard theorem, Alexandrov and Topogonov comparison theorems, closed geodesics, cut locus, sp here theorem.

6210 Real Analysis (3) Recommended Prereq.: MATH 5210. Measures and integrals, Lp-spaces, Hilbert spaces Banach spaces, Fourier series.

6220 Complex Analysis (3) Recommended Prereq.: MATH 4200 and 6210. Analytic functions, complex integration, Conformal mapping, families of analytic functions, zeros of analytic functions, analytic continuation.

6240 Lie Groups/Lie Algebras I (3) Recommended Prereq.: MATH 6220. Basic theory of Lie groups and Lie algebras.

6250 Lie Groups/Lie Algebras II (3) Recommended Prereq.: MATH 6240 Structure theory, classification, and finite dimensional representations of Lie groups. Compact Lie groups

6310 Modern Algebra 1 (3) Recommended Prereq.: MATH 5320 Groups, rings, modules, homological algebra, fields and Galois theory.

6320 Modern Algebra 11(3) Recommended Prereq.: MATH 6310. Second half of the course described under the listing for MATH 6310.

6330 Group Theory I (3) Recommended Prereq.: MATH 5320. Various topics in group theory will be studied. The course will be offered on the basis of need or interest.

6340 Group Theory II (3) Recommended Prereq.: MATH 6330. Second half of the course described under the listing for MATH 6330.

6350 Commutative Algebra (3) Recommended Prereq.: 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.

6410 Ordinary Differential Equations (3) Recommended Prereq.: MATH 5210. Existence, uniqueness theory; stability theory; invariant sets and manifolds; periodic and quasiperiodic motions; boundary value problems; ODEs in Banach spaces; applications.

6420 Partial Differential Equations (3) Recommended Prereq.: MATH 5210. First-order equations: characteristics, transport equations, shocks, Hamilton-Jacobi theory. Boundary value problems for the Laplace equation: maximum principles, Green's functions, Hubert 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) Recommended Prereq.: MATH 6420. Elliptic and parabolic equations: methods of functional analysis; weak solutions; regularity. Systems of conservation laws.

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

6510 Differentiable Manifolds (3) Recommended Prereq.: MATH 4510 and 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) Recommended Prereq.: MATH 5520 and 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.

6550 Algebraic Topology (3) Recommended Prereq.: MATH 6510 and 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) Recommended Prereq.: MATH 6510 and 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 an,:1 the classification of high-dimensional manifolds.

6610 Analysis of Numerical Methods 1(3) Recommended Prereq.: 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 11(3) Recommended Prereq.. MATH 6610. Second half of the course described under the listing for MATH 6210.

6630 Numerical Solutions of Partial Differential Equations (3) Recommended Prereq. MATH 6610 and 6620 and 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) Recommended Prereq.: MATH 5210 and 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 Appl Complex Variables, Asymptotic Methods (3) Recommended Prereq.: MATH 5210 and 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, asymptotic analysis of integrals, Laplace's method, Watson's lemma, method of steepest descents.

6730 Asymptotic and Perturbation Methods (3) Recommended Prereq.: 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) Recommended Prereq.: MATH 6210 and 6220. Degree theories; method of Liapunov and Schmidt; local and global bifurcation theory; Hopf bifurcation; Liusternik-Shnirelman theory; applications.

6750 Continuum Mechanics: Fluids (3) Recommended Prereq.: MATH 5440 or 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 propagation 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) Recommended Prereq.: 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) Recommended Prereq.: 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.

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) Recommended Prereq.: MATH 6210 and 6220. Basic theory of unitary representations of Lie groups.

7220 Representations of Lie groups 11(3) Recommended Prereq.: MATH 7210. Infinite dimensional representations of semi-simple Lie groups. Theory of Harish-Chandra modules.

7240 Several Complex Variables I (3) Recommended Prereq.: MATH 6220. Local theory of functions of several complex variables.

7250 Several Complex Variables II (3) Recommended Prereq.: MATH 7240. Global theory of functions of several complex variables.

7270 Topological vector spaces and distribution theory (3) Recommended Prereq.: MATH 6210 and 6220. Introduction to topological vector spaces and the theory of distributions, with applications to partial differential equations.

7280 Operator Theory (3) Recommended Prereq. : MATH 6210 and 6220. A study of linear operators, primarily in Hilbert spaces.

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.

7720 Asymptotic Methods (3) 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.

7750 Mathematics of Fluids (3) Offered on the basis of need or interest.

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

7770 Mathematical Modeling (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 (3) Various topics in the area of Riemannian geometry, offered on the basis of need or interest.

7813 Topics in Complex Geometry (3) Various topics in the area of complex geometry, offered on the basis of need or interest.

7815 Seminar in Differential Geometry (1 to 3)

7820 Topics in Analysis (3) Various topics in analysis, offered on the basis of need or interest.

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.

7833 Topics in Geometric Group Theory (3) Various topics in the area of geometric group theory, 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.

7865 Seminar in Numerical Analysis (1 to 3)

7870 Topics in Applied Mathematics (3) 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.

7883 Topics in Mathematical Statistics (3) Various topics in mathematical statistics, 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)

7970 Thesis Research: Ph. D. (1 to 9)

7980 Faculty Consultation (3)

7990 Continuing Registration: Ph. D. (0)


University of Utah, Department of Mathematics, 155 S 1400 E Rm 233, Salt Lake City, UT 84112-0090, USA 801-581-6851, 801-581-4148 (fax)       [02-Jul-1998].