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 departmental 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 departmental 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 Take MATH 950
17 to 22 Take MATH 1010
23 or above Take MATH 1050, 1060, 1090, 1100, or 1210,
according to high school preparation

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 40-49 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 Internships. 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; 2270, 2280; 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 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)
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: 40-48
PHYCS 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)
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: 43-49
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)
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 5740 Mathematical Modeling (3)
MATH 5710, 5720 Applied Mathematics (3,3)
Total Math Hours: 42-46
PHYCS 2210, 2220 or 3210, 3220 Physics for Scientists, Engineers (4,4)
Allied Course (3)

*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
Requirements
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. 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
Mathematics Teaching Major and Minor