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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.
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.
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.
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:
Faculty
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.
| 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 have not taken AP or CLEP tests will be placed as follows:
| ACT | |
|---|---|
| Score | Placement |
| Below 17 | MATH 950 |
| 17 to 22 | MATH 1010 |
| 23 or above | MATH 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.
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).
1. Ordinary Major 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) Three courses from the following list: 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) Three courses from the following list:
MATH 5010 Probability (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
For a major, a grade of C or better is required in all mathematics
courses.
MATH 1210, 1220, 2210 Calculus I,II,III(4,4,3) 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.
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.
2. The total number of semester hours required for the masters
degree in pure mathematics should fall in the range 30-36
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. 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.
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)
Requirements for the 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)
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)
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)
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)
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)
Requirements for the Minor
MATH 3210, 3220 Foundations of Analysis I,II(3,3)
Graduate Program
Requirements for Graduate Degrees
M.S. in Pure Mathematics
Course Requirements
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:
M.S. in Applied Mathematics
Course Requirements
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.
MATH Courses