Professors. F. Adler, P. Alfeld, A. Bertram, M. Bestvina, P. Bressloff, R. Brooks, J. Carlson, A. Cherkaev, E. Cherkaev, D. Dobson, S. Ethier, A. Fogelson, E. Folias, S. Gersten, K. Golden, F. Gross, G. Gustafson, H. Hecht, L. Horvath, M. Kapovich, D. Khoshnevisan, N. Korevaar, J.D. Mason, D. Milicic, P. Roberts, H. Rossi, G. Savin, K. Schmitt, N. Smale, J. Taylor, D. Toledo, A. Treibergs, P. Trombi, D. Tucker.  

Professor Emeriti. C.E. Burgess, W. Coles, P. Fife, J. Wolfe, L. Glaser.   

Associate Professors. A. Balk, K. Bromberg, C. Hacon, C. Khare, Y.P. Lee, W. Niziol, A. Singh, P Trapa, J. Zhu.  

Assistant Professors. A. Borisyuk, T. deFernex, F. Rassoul-Agha, J. Tanner.  

Research Professors. N. Beebe, E. Cherkaev, R. Horn.  

Research Associate Professors. R. Morelli, R. Palais.  

Research Assistant Professor. T. Robbins.  

Adjunct Professor. M. Lewis. 

Adjunct Associate Professor. D. Eyre.  

Professor (Lecturer).  A. Roberts.

Advisors. Undergraduate Advisor, Aleksandra Jovanovic-Hacon, 204 JWB, 581-6837, ahacon@math.utah.edu; Graduate Advisor, Jingyi Zhu 323 JWB, 581-6120, (e-mail) zhu@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 

28 or above     Take MATH 1100, 1210

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. Students contesting their ACT/SAT placement may also use these tests.

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 math courses must be strictly observed, and a grade of a C or higher in prerequisite courses (or passing score through the Accuplacer exam) is required.  Exceptions must be approved by the Mathematics Department. Math course(s) for which a student has preregistered but did not achieve a grade of C or higher in the prerequisite course(s) will be automatically dropped from his/her schedule. 

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

Degree.  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 advisor or a departmental mentor, seven 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 two courses in statistical methodology courses offered by other departments. Depending on the mathematics emphasis chosen, this amounts to 48-55 hours of mathematics credits.

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; 2270, 2280; and 3210, 3220. They should contact the departmental undergraduate advisor 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 advisor 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 one time (up to 4 credits) is graded CR 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)

MATH 2270 Linear Algebra (4)

MATH 2280 Differential Equations (4)

MATH 3210, 3220 Foundations of Analysis I, II (4, 4)

Seven semester courses in mathematics numbered 4200 or higher except 4910, 4950, 4999, 5000, 5900, 5960, 5969. MATH 5910 must be approved in advance by the Undergraduate Advisor (18-24)

Total Math Hours: 48-55

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

2. Major with an Emphasis in Statistics
MATH 1210, 1220, 2210 Calculus I, II, III (4,4,3) or
MATH 1250, 1260 (4,4)
MATH 2270 Linear Algebra (4)
MATH 3070, 3080 Applied Statistics I, II (4,3)
MATH 3210, 3220 Foundations of Analysis I, II (4, 4)
MATH 5010 Probability (3)
MATH 5080, 5090 Statistical Inference I, II (3,3)
Four 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 (4)
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)
MATH 5750 Topics in Applied Mathematics (3)
Total Math Hours: 51-55

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

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)
MATH 2270 Linear Algebra (4)
MATH 2280 Differential Equations (4)
MATH 3210, 3220 Foundations of Analysis I, II (4, 4)
MATH 5610, 5620 Introduction to Numerical Analysis I, II (4,4)
MATH 5960 Special Projects (3)
Four 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 5740 Mathematical Modeling (3)
MATH 5710, 5720 Applied Mathematics (3,3)
Total Math Hours: 50-54
PHYS 2210, 2220 or 3210, 3220 Physics for Scientists, Engineers (4,4) Additional Allied Course (3)

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

Requirements for the Minor

Requirements

MATH 1210, 1220, 2210 Calculus I, II, III (4,4,3)

MATH 3210, 3220 Foundations of Analysis I, II (4, 4)

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.

Mathematics Teaching Major

I. Core Requirements

Choose one math sequence from the following:

a. MATH 1210, 1220, 2210 Calculus I,II,III (4,4,3)

b. MATH 1250, 1260 Calculus (AP students) I,II (4,4)

Required Courses:

MATH 2160 Introduction to Scientific Computing (3)

MATH 3010 Topics in the History of Mathematics (3)

MATH 3070 Applied Statistics I (3)

MATH 3100 Foundations of Geometry (3)

MATH 3105 Geometry Practicum (1)

MATH 2270 Linear Algebra (4)

MATH 2280 Differential Equations (4)

MATH 3210, 3220 Foundations of Analysis I, II (4, 4)

MATH 4030 Foundations of Algebra (3)

MATH 4035 Algebra Practicum (1)

MATH 4090 Teaching of Secondary School Mathematics (3)

MATH 5700 Capstone (3)

Complete one of the following courses: (The Mathematics Department strongly recommends students finish the physics sequence started)

a.                   PHYS 2210 Physics for Scientists and Engineers I (4)

b.                  PHYS 3210 Physics for Scientists I (4)

II. Certification Course Work

III. Comprehensive Exam. To graduate with a mathematics teaching major students must receive a score of 143 or higher score on the Praxis Exam #10061: “Mathematics: Content Knowledge.” To register see www.ets.org/praxis.

I. Core Requirements

MATH 1050 College Algebra (4)

AND/OR

MATH 1060 Trigonometry (2)

Choose one sequence from the following:

a. MATH 1210, 1220, 2210 Calculus I,II,III (4,4,3)

b. MATH 1250, 1260 Calculus (AP students) I,II (4,4)

Required Courses:

MATH 3100 Foundations of Geometry (3)

MATH 3105 Geometry Practicum (1)

MATH 4030 Foundations of Algebra (3)

MATH 4035 Algebra Practicum (1)

MATH 2270 Linear Algebra (4)

MATH 3070 Applied Statistics I (3)

MATH 4090 Teaching of Secondary School Mathematics (3)

II. Certification Course Work

Students must complete pre-cohort and cohort education course work through the Department of Teaching and Learning.

Departmental Honors Major

Lower Division Component
MATH 1250/1260 Calculus (8) OR
MATH 1210/1220/2210 (11)
MATH 2900 Freshman/Sophomore Seminar (2)
MATH 2270 Linear Algebra (4)
MATH 2280 Differential Equations (4)
MATH 3000 Undergraduate Colloquium (1)
PHYS 2210, 2220 OR 3210, 3220 (8)

Upper Division Component
MATH 3210 Foundations of Analysis I (4)
MATH 3220 Foundations of Analysis II (4)
MATH 5210 Real Analysis (4)
MATH 4200 Complex Analysis (3)
MATH 4999 Honors Thesis Project (3-6)

Upper Division Electives
Select at least 18 credits from among the following courses (these must include at least two of the listed full year sequences, MATH 5000, 5960, and 5969 do no count toward an honors degree, and MATH 5910 must be approved in advance by the Honors Advisor in order to count toward graduation):
MATH 4400 Intro to Number Theory (3)
MATH 4510 Intro to Topology (3)
MATH 4530 Curves and Surfaces (3)
MATH 4510-5520 Topology (3, 3)
MATH 5310-5320 Modern Algebra (3, 3)
MATH 5410-5420 Ordinary Diff, Equations (4, 3)
MATH 5610-5620 Numerical Analysis (4, 4)
MATH 5710-5720 Applied Mathematics (3, 3)
MATH 5010-5040 Probability and Statistics (3, 3)
MATH 5010-5080 Probability and Statistics (3, 3)

To receive an honors degree in mathematics, a student must receive at least a B in each course required for the program, and must maintain a GPA of at least 3.5 in these courses, as well as a 3.5 overall grade point average.

Graduate Program

Degree. M.A., M.S., M.Phil., Ph.D. in mathematics; M.Stat. in statistics. For additional information, see the Graduate Information section of this catalog.  

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. Applicants 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
2. Take an oral examination and complete a master’s project. The options available for this project are as follows: a. Master’s thesis. b. A curriculum project. c. Taking additional courses at the 6000- or 7000-level.
3. The total number of semester hours required for the master’s 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 5000- 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. For details see Science in the Colleges section of this catalog.

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). For details see Science in the Colleges section of this catalog.

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 credit 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 Course Descriptions