# DEGREE OPTIONS

**DEGREE REQUIREMENTS**

The Ph.D. Program in the Department of Mathematics enjoys an excellent reputation in a diversified set of subjects, such as algebraic geometry, commutative algebra, differential geometry, geometric topology, group and representation theory, and number theory in pure areas, and materials and fluids, mathematical biology, mathematical finance, numerical analysis, partial differential equations, probability, and statistics in applied areas.

The following is a list of departmental requirements, in addition to the requirements of the Graduate School, for candidates seeking a Ph.D. degree in mathematics.

- at least 42 credit hours numbered 6000 or above
- three written qualifying examinations
- an oral qualifying examination
- two semesters of teaching
- the final oral examination

More details can be found in the Graduate Bulletin.

**Coursework**

The course requirements for the Ph.D. degree consist of at least seven sequences (each sequence contains two consecutive courses on a subject) numbered 6000 or above, or their equivalent, approved by the student’s supervisory committee. They should include at least 14 credit hours of courses numbered 7800-7970 (topics courses, seminars, and thesis research). Exceptions must be approved on an individual basis by the Graduate Committee upon the recommendation by the student’s supervisory committee.

**Written Qualifying Examinations**

The written qualifying examinations are given twice a year, in January and August, just before the start of the Spring and Fall semesters. A Ph.D. candidate is required to pass three written qualifying examinations chosen from the following set of subjects (corresponding course numbers are included in parenthesis):

- algebra (6310-6320)
- applied mathematics (6710-6720)
- differential equations (6410-6420)
- numerical analysis (6610-6620)
- probability (6040)
- real and complex analysis (6210-6220)
- statistics (6070)
- topology and geometry (6510-6520)

Each exam lasts three hours and is written at a first-year graduate level. Entering students are recommended to take the 6000-level course corresponding to a particular exam and use the course materials to prepare for the exams. Students with particularly strong backgrounds can choose to take the exams without taking the courses. Copies of past exams from the last ten years can be obtained by contacting the Graduate Coordinator.

**Oral Qualifying Examination**

This exam is conducted by the student’s supervisory committee and it can take one of the following two formats: a general exam to measure the student’s overall mathematical maturity and breadth, or a presentation of the proposed dissertation project. The exam also evaluates the student’s skill at chalkboard exposition and verbal exchange.

**Teaching Requirement**

Each Ph.D. candidate is required to teach a minimum of two courses or equivalent tutorials, or supervise laboratory sessions.

**Final Oral Examination**

This examination consists of a public thesis defense that summarizes the candidate's thesis work.

## ADMISSION REQUIRMENTS

Admission to graduate status in the Ph.D. program requires that students hold a Bachelor's
degree in Mathematics, or its equivalent, with a **grade point average of at least 3.0** and that they show promise of success in graduate work. The prerequisites for the
various programs vary. Qualified applicants typically possess a Bachelor's or Master's
degree in mathematics. Students should be prepared to take the courses that directly
lead to qualifying exams.

### GRE Exams

Applicants to the Ph.D. program are not required to submit subject or general GRE scores. However, we strongly encourage all applicants to submit this test, and applications without such scores are frequently at a substantial disadvantage. Students in pure mathematics are especially encouraged to submit their subject GRE scores. If you have questions about whether to submit your scores, contact Jingyi Zhu, Chair of the Graduate Recruitment Committee or Elena Cherkaev, Director of Graduate Studies.

### English Tests

All applicants must meet the University of Utah's minimum requirements for English
proficiency, click here.

Additionally, successful applicants for Teaching Assistantships must be proficient
in their spoken and listening English skills. Those skills are usually reflected in
the submitted TOEFL scores (or equivalent). In most cases, for those subsections of
the TOEFL, we look for scores of at least about 20, and optimally, of at least about
23.

## FILLING OUT THE APPLICATION

For instructions on filling in the Graduate Mathematics Application Form: Click Here

**Questions?: ****Paula Tooman, Graduate Program Coordinator- tooman@math.utah.edu OR Elena Cherkaev, Director of Graduate Studies- elena@math.utah.edu**

## DEGREE REQUIREMENTS

The M.A. and M.S. degree requirements are identical except that the M.A. degree requires an additional language proficiency. The following is a list of departmental requirements for candidates seeking a M.S. or M.A. degree in mathematics.

**Minimum Degree Hours: 30**

### Coursework:

**For the Master's degree in pure mathematics:**

- MATH 5210 - Introduction to Real Analysis 4 Credit(s)
- MATH 5310 - Introduction to Modern Algebra I 3 Credit(s)
- MATH 5320 - Introduction to Modern Algebra II 3 Credit(s)
- One 6000-level sequence consisting of two one-semester courses
- Four additional one-semester courses at the 5000- or 6000-level

**For the Master's degree in applied mathematics:**

- MATH 5210 - Introduction to Real Analysis 4 Credit(s) and
- one 6000-level course
**OR** - two 6000-level courses

### Written Qualifying Examinations:

The written qualifying examinations are given twice a year, in January and August, just before the spring or the fall semester starts. A candidate can fulfill the graduation requirements by passing two written qualifying examinations, chosen from the following set of subjects (corresponding course numbers included in parentheses):

- algebra (6310–6320)
- applied mathematics (6710–6720)
- differential equations (6410–6420)
- geometry and topology (6510–6520)
- numerical analysis (6610–6620)
- probability (6040)
- real and complex analysis (6210–6220)
- statistics (6070)

Each exam lasts three hours and is written at a first year graduate level. Entering students are required to take the 6000-level course corresponding to a particular exam and use the course materials to prepare for the exams. Copies of past exams are posted (as PDF files) on the Graduate Program homepage (see Qualifying Examinations).

### Oral Comprehensive Examination and Additional Requirements:

An oral comprehensive exam can be chosen as an option to fulfill the Master’s degree requirements. This exam is conducted by the student’s supervisory committee. In case a candidate chooses the option of oral comprehensive exam, the student must complete nine (9) additional credits of a Masters Project, which can be one of the following:

## ADMISSION REQUIRMENTS

Admission to graduate status in the Master's program requires that students hold a
Bachelor's degree in Mathematics, or its equivalent, with a **grade point average of at least 3.0** and that they show promise of success in graduate work. The prerequisites for the
various programs vary. Master of Arts / Master of Science degrees, qualified applicants
typically possess a Bachelor's or Master's degree in mathematics. Students should
be prepared to take the courses that directly lead to qualifying exams.

### GRE Exams

Applicants to the Master's program are not required to submit subject or general GRE score. However, we strongly encourage all applicants to submit this test, and applications without such scores are frequently at a substantial disadvantage. Students in pure mathematics are especially encouraged to submit their subject GRE scores. If you have questions about whether to submit your scores, contact Jingyi Zhu, Chair of the Graduate Recruitment Committee or Elena Cherkaev, Director of Graduate Studies.

### English Tests

All applicants must meet the University of Utah's minimum requirements for English
proficiency, click here.

Additionally, successful applicants for Teaching Assistantships must be proficient
in their spoken and listening English skills. Those skills are usually reflected in
the submitted TOEFL scores (or equivalent). In most cases, for those subsections of
the TOEFL, we look for scores of at least about 20, and optimally, of at least about
23.

## FILLING OUT THE APPLICATION

For instructions on filling in the Graduate Mathematics Application Form: Click Here

**Questions?: ****Paula Tooman, Graduate Program Coordinator- tooman@math.utah.edu OR Elena Cherkaev, Director of Graduate Studies- elena@math.utah.edu**

## DEGREE REQUIREMENTS

The Master of Statistics (M-Stat) program is administered by the University Statistics Committee and applications should be made through the Graduate Admissions Office. Upon admission by the University Statistics Committee, the student is also admitted to the Mathematics Department Master's program. The degree of Master of Statistics (Mathematics) is awarded by the Mathematics Department.

### Coursework

- MATH 5010 - Introduction to Probability 3 Credit(s)
- MATH 5080 - Statistical Inference I 3 Credit(s)
- MATH 5090 - Statistical Inference II 3 Credit(s)
- MATH 6010 - Linear Models 3 Credit(s)
- MATH 6020 - Multilinear Models 3 Credit(s)
- MATH 6070 - Mathematical Statistics 3 Credit(s)
- MATH 6960 - Special Projects 1 - 6 Credit(s) (Masters Project)
- Electives approved by the supervisory committee, 12 credits
- Final project approved by supervisory committee

## ADMISSION REQUIRMENTS

- Bachelor’s Degree in Mathematics, or equivalent
- MATH 3070, 3080, or equivalent

## FILLING OUT THE APPLICATION

For instructions on filling in the Graduate Mathematics Application Form: Click Here

**Questions?: ****Paula Tooman, Graduate Program Coordinator- tooman@math.utah.edu OR Elena Cherkaev, Director of Graduate Studies- elena@math.utah.edu**

The University of Utah Department of Mathematics offers a general Masters of Science degree, as well as some specialized master’s degrees. Newest addition to this list the Master of Science in Mathematics with emphasis in teaching. The applications should be made through the Graduate School. Upon admission by the Mathematics Education Committee, the student is also admitted to the Mathematics Department Master’s program. The degree of Master of Mathematics (Teaching) is awarded by the Mathematics Department.

## 2019 COHORT MASTERS OF SCIENCE MATHEMATICS TEACHING (MSMT)

**(Formerly known as MSSST Program)**

**APPLICATION FOR 2019-2021 COHORT WILL BE OPEN SOON.**

For applicants who are licensed secondary mathematics teachers. The Department of Mathematics of the University of Utah offers a M.S. Mathematics Teaching degree. Admission to this Master’s degree helps practicing teachers acquire a deeper and broader science background. Applicants must be accepted by the Graduate School and Math Ed. Committee. Course work for this degree is designed to extend teachers’ mathematical knowledge for teaching at the secondary level.

## ADMISSION REQUIRMENTS

1. Licensed teachers with a level 4 endorsement (level 3 teachers will be considered, but may need additional course work).

2. Completion of the Praxis 5161 Mathematics (post 2012) or Praxis 0061 (pre-2012) Math Content Knowledge Exam. A score of at least 165 (5161) or 143 (0061) is required.

3. At least two years of teaching experience as of the application deadline. Applicants must be recommended by a professional educator who can judge their performance.

4. Satisfy University requirements for Graduate School admissions.

*The Mathematics Education Committee may advise candidates to take additional courses
to ensure readiness for the required course work in the program.*

### PLANNED SCHEDULE FOR 2019 COHORT

The M.S. in Mathematics Teaching degree requires a total of 39 credit hours: 30 are core courses, the remaining 9 credits are to be electives with at least 6 from the discipline-specific mathematics courses at 5000 level or above level (any exceptions must be approved by the Graduate Program Coordinator). In addition, candidates must take and pass a mid-program exam and submit and defend a final program project.

#### FIRST ACADEMIC YEAR

(Tentative Schedule)

*SUMMER Semester (June 5 - August 2): *

Session I: Math 5140 - Foundations of Mathematics for Teachers I (June 5 - June 21)

Session II: Math 5270 - Transformational Geometry (June 24 - July 12)

Session III: Math 5280 - Statistics and Probability (July 15 - August 2)

*Mid-Program Exam (before, during, or immediately following the Semester):*

--Prepared written response to questions.

*FALL Semester (1 night a week):*

Math 5150 - Foundations of Mathematics II

Math 5155 - Curriculum and Instruction Practicum

*SPRING Semester (1 night a week)::*

Math 5160 - Foundations of Mathematics for Teachers III (High School)

**SECOND ACADEMIC YEAR **

*SUMMER Semester (1 night a week):*

Session I: Math 6100 - Concepts of Calculus

Session II: Math 6090 - Topics in the History of Mathematics

Session III: Math 6080 - Topics in Contemporary Mathematics

*Final Program Exam:*

--Prepared written response to questions.

--Oral examination

--Presentation of project plan by student. The plan must be approved by the student’s committee before the project research begins. The student’s committee is composed of at least two members of the Mathematics Department.

*FALL Semester (1 night a week):*

Math 5740 - Mathematical Modeling

Math 6960 - MS project preparation course I

*SPRING Semester (1 night a week):*

Math 5700 - Capstone Course

Math 6960 - MS Project Preparation Course II

**Note: MATH 6960 -Master's Project courses are 3 credits each. Before graduating you must complete 6 credits total. Students
conduct research and report to their advisor on their findings in a Master's project.**

** Final Examination:** Successful performance on a final defense of their Master's Degree project that covers
work presented for the Master's degree and defense of the project.

**FILLING OUT THE APPLICATION**

Please follow the instructions below while filling out the application.

**APPLICATION FOR 2019-2021 COHORT WILL BE OPEN SOON.**

- Create an account to start the application for the Master of Science in Mathematics Teaching program.
- In the
**Program Information**section, the first heading is*Program of Interest*. Select "Salt Lake City Campus" under "Campus." Also, under the same section select**"Science Program for Secondary School Teacher MS"**under "Intended graduate program and degree." - The next section on this page is
*Emphasis Area*. Select “Mathematics.” - The last section on this page is
*Application Term and Year*. Select “Summer 2017.” - Complete all other fields on the remaining pages of the application. Upload transcripts, an official copy of your ETS notification of score on Praxis 5161 (post-2012) or 0061 (pre-2012), and a Statement of Purpose.
- Once you have submitted your application email Gail Howick (howick@math.utah.edu) to confirm your application has been completed.

## 2017 COHORT MASTERS OF SCIENCE MATHEMATICS TEACHING (MSMT)

**(Formerly known as MSSST Program)**

### PLANNED SCHEDULE FOR 2017 COHORT

The M.S. in Mathematics Teaching degree requires a total of 39 credit hours: 30 are core courses, the remaining 9 credits are to be electives with at least 6 from the discipline-specific mathematics courses at 5000 level or above level (any exceptions must be approved by the Graduate Program Coordinator). In addition, candidates must take and pass a mid-program exam and submit and defend a final program project.

#### FIRST ACADEMIC YEAR

*SUMMER Semester (June 7 - August 4): *

Session I: Math 5140 - Foundations of Mathematics for Teachers I (June 7-June 23)

Session II: Math 5270 - Transformational Geometry (June 26-July 14)

Session III: Math 5280 - Statistics and Probability (July 17-August 4)

*Mid-Program Exam (before, during, or immediately following the Semester):*

--Prepared written response to questions.

*FALL Semester (1 night a week):*

Math 5150 - Foundations of Mathematics II

Math 5155 - Curriculum and Instruction Practicum

*SPRING Semester (1 night a week)::*

Math 5160 - Foundations of Mathematics for Teachers III (High School)

**SECOND ACADEMIC YEAR **

*SUMMER Semester (1 night a week):*

Session I: Math 6100 - Concepts of Calculus

Session II: Math 6090 - Topics in the History of Mathematics

Session III: Math 6080 - Topics in Contemporary Mathematics

*Final Program Exam:*

--Prepared written response to questions.

--Oral examination

--Presentation of project plan by student. The plan must be approved by the student’s committee before the project research begins. The student’s committee is composed of at least two members of the Mathematics Department.

*FALL Semester (1 night a week):*

Math 5740 - Mathematical Modeling

Math 6960 - MS project preparation course I

*SPRING Semester (1 night a week):*

Math 5700 - Capstone Course

Math 6960 - MS Project Preparation Course II

**Note: MATH 6960 -Master's Project courses are 3 credits each. Before graduating you must complete 6 credits total. Students
conduct research and report to their advisor on their findings in a Master's project.**

** Final Examination:** Successful performance on a final defense of their Master's Degree project that covers
work presented for the Master's degree and defense of the project.

**Questions?: Maggie Cummings- cummings@math.utah.edu.**

# QUESTIONS?

### Elena Cherkaev

**Dir. of Graduate Studies**

**Can Answer Questions About:**

- Ph.D. in Mathematics
- M.A. and M.S. Mathematics Degrees
- Master of Statistics

### Paula Tooman

**Graduate Program Coord.**

**Can Answer Questions About:**

- Ph.D. in Mathematics
- M.A. and M.S. Mathematics Degrees
- Master of Statistics

### Lajos Horvath

**Professor**

**Can Answer Questions About:**

- Master of Statistics

### Maggie Cummings

**Instructor (Lecturer)**

**Can Answer Questions About:**

- M.S. in Mathematics Teaching