## Department of Mathematics

**Gregory Lyng, Department Head 202 Ross Hall Phone: (307) 766-4221, FAX: (307) 766-6838 Web site: www.uwyo.edu/math**

### Professors

**MYRON B. ALLEN III,** A.B. Dartmouth College 1976; M.A. Princeton University 1978; Ph.D. 1983; Professor of Mathematics 1992, 1983.** HAKIMA BESSAIH,** M.S. University of Algiers 1992; Ph.D. Scuola Normale Superiore of Pisa 1999; Professor of Mathematics 2015, 2004.

**CRAIG C. DOUGLAS,** B.A. University of Chicago 1977; M.S. Yale University 1978; M.Phil. 1981; Ph.D. 1982; SER Professor of Mathematics 2008.

** STEFAN HEINZ, **B.S. Humboldt University 1985; M.S. 1986; Ph.D. Heinrich-Hertz Institute 1990; Professor of Mathematics 2013, 2004.

**B.S. University of Wisconsin-Madison 1978; M.S. 1980; Ph.D. 1983; M.A. 1986; Ph.D. 1989; Professor of Mathematics 1999, 1991.**

FARHAD JAFARI,

FARHAD JAFARI,

**GREGORY LYNG,**B.A. Saint Olaf College 1996; M.A. Indiana University 1999; Ph.D. 2002; Professor of Mathematics 2015, 2005.

**G. ERIC MOORHOUSE,**B.S. University of Toronto 1980; M.S. 1984; Ph.D. 1987; Professor of Mathematics 2011, 1989.

**PETER POLYAKOV,**M.S. Moscow State University 1967; Ph.D. 1971; Professor of Mathematics 1998, 1993.

**BRYAN L. SHADER,**B.S. University of Wyoming 1984; M.S. University of Wisconsin-Madison 1987; Ph.D. 1990; Professor of Mathematics 2000, 1990.

### Associate Professors

**CHARLES ANGEVINE,** B.S. Brown University 1980; Ph.D. Cornell University 1983; Associate Professor of Mathematics 1989, 1984.

**MICHELLE T. CHAMBERLIN,** B.S. Colorado State University 1997; M.S. 1999; Ph.D. Purdue University 2002; Associate Professor of Mathematics 2012, 2007.

**FREDERICO da CUNHA FURTADO,** B.S. Federal University of Minas Gerais 1979; M.S. Federal University of Rio de Janeiro 1984; Ph.D. Courant Institute 1989; Associate Professor of Mathematics 2002, 1997.

**VICTOR GINTING,** B.S. Institut Teknologi Bandung Indonesia 1995; M.S. Texas A&M University 1998; Ph.D. 2004; Associate Professor of Mathematics 2012, 2007.

** CHRISTOPHER HALL,** B.S. University of Colorado, Boulder 1997; Ph.D. Princeton University 2003; Associate Professor of Mathematics 2013, 2009.

**LYNNE IPINA,**B.S. South Dakota State University 1972; M.S. New York University 1978; Ph.D. 1986; Associate Professor of Mathematics 1992, 1985.

**LONG LEE,**B.S. National Taiwan University, Taipei 1988; M.A. University of Maryland 1998; Ph.D. University of Washington 2002; Associate Professor of Mathematics 2011, 2005.

**RONGSONG LIU,**B.A. Henan Normal University 1999; M.A. Fudan University 2002; Ph.D. York University 2006; Associate Professor of Mathematics and Program in Ecology 2015, 2009.

**DAN STANESCU,**B.Eng. Polytechnic Institute, Romania 1986; M.Eng. McGill University, 1994; Ph.D. Concordia University 1999; Associate Professor of Mathematics 2008, 2003.

**JASON WILLIFORD,**B.A. University of Pennsylvania 1998; Ph.D. University of Delaware 2004; Associate Professor Mathematics 2014, 2009.

**MAN-CHUNG YEUNG,**B.S. Jinan University, China 1986; M.Ph. University of Hong Kong 1990; Ph.D. University of California-Los Angeles 1997; Associate Professor of Mathematics 2005, 2001.

### Assistant Professors

**TYRRELL McALLISTER,** B.S. University of California, Davis 2001; Ph.D. 2006; Assistant Professor of Mathematics 2009.

**ZHUANG NIU,** B.S. Wuhan University 1998; M.S. 2001; Ph.D. University of Toronto 2005; Assistant Professor of Mathematics 2012.

### Senior Lecturers

**JOHN SPITLER,** B.S. Vanderbilt University 1977; M.S. University of Wyoming 1998; Assistant Research Scientist 1994; Senior Lecturer in Mathematics 2009, 2000.

**WILLIAM WEBER,** B.S. Colorado State University 1979; B.S. University of Wyoming 1988; M.S. 1992; Senior Lecturer in Mathematics 2012, 2001.

### Associate Lecturers

**DAVID ANTON,** B.S. North Dakota State University 2001; M.S. University of Wyoming 2007; Associate Lecturer in Mathematics 2012, 2005.

**JEFFREY SELDEN,** B.S. New Mexico State University 1998; Ph.D. University of Arizona 2004; Associate Lecturer in Mathematics 2014, 2009.

### Assistant Lecturer

**NATHAN CLEMENTS,** B.S. Brigham Young University-Idaho 2007; M.S. Idaho State University 2009; D.A. 2012; Assistant Lecturer in Mathematics 2012.

### Adjunct Professors

Saman Aryana, Li Deng, John Hitchcock, Robert Kansky, David Meyer, Siguna Mueller, Gerald Schuster.

### Professors Emeriti

Leonard Asimow, Robert Buschman, Benito M. Chen-Carpentier, George C. Gastl, John H. George, Syed Husain, Eli Isaacson, Terry Jenkins, A. Duane Porter, Ben G. Roth, John Rowland, Raymond Smithson.

**"For the things of this world cannot be made known without a knowledge of mathematics.''--Roger Bacon**

Virtually every student at UW will take one or more math courses to fulfill graduation requirements. The intent is to illustrate the esthetics inherent in mathematics, and to provide students with the quantitative skills needed for today's careers.

Mathematics majors receive a broad and deep view of the mathematical sciences. They develop their mathematical thinking and communications skills in algebra, analysis, and applied math. They learn a variety of technological tools necessary for jobs in education, business, government, and industry. In addition to our math classes, the department offers a variety of opportunities to enrich the undergraduate experience. Students can participate in weekly seminars, summer research projects, Putnam Team competitions, and the math club.

### Mathematics Placement

All UW math courses have prerequisites which are detailed in the course listings below. These are to assure that each student has the best possible opportunity for success in the course. In accordance with this, all students registering for a math course will have their records checked in order to determine whether the prerequisite is satisfied.

A computerized prerequisite check is run prior to the start of every semester. Students who pre-registered for a math course but have not satisfied the prerequisites at the time of the check will be automatically dropped from the course.

Prerequisites for courses numbered 2200 or lower (except 1105 and 2120), and 2350 (Business Calculus), may be satisfied in one of four ways:

- Obtain a grade of C or better in a prerequisite course. Note that non-credit courses from out-of-state colleges are not accepted as prerequisites.
- Pass the Mathematics Placement Exam (MPE) at the stated level within one year of the start of the course.
- Obtain a sufficiently high score on one of the following standardized exams within three years of the start of the course: ACT math score or SAT quantitative score.
- Obtain a sufficiently high score on one of the following standardized exams: AP Calculus, CLEP, or IB.

More information on mathematics placement may be obtained from the Center for Advising on Mathematics Placement (CAMP), 202 Ross Hall, 766-4221, or at www.uwyo.edu/mpe.

### Duplication of Courses (MATH 1400, 1405, 1450)

To avoid loss of credit because of duplication of course content, please note the following: (a) students with credit for both MATH 1400 and MATH 1405 will not receive new credit by taking 1450; (b) students with credit for one of MATH 1400 or MATH 1405 will receive only 2 additional credits by taking MATH 1450; (c) students with credit for MATH 1450 will receive only 1 additional credit by taking both MATH 1400 and MATH 1405. Note that the GPA calculation for these situations is unusual, and students should ask the Registrar’s Office for details.

Note that MATH 1450 counts as one attempt at each of MATH 1400 and 1405 for the purposes of repeating classes.

### Undergraduate Major

A degree in mathematics should prepare students to enter either graduate studies or the workforce with a skill set that could only come from an intense study of both quantitative reasoning and rigorous proof. This can be accomplished by focusing on the following goals for our undergraduate major:

- Develop mathematical thinking and communication skills
- Develop skills with a variety of technological tools
- Provide a broad view of the mathematical sciences
- Require study in depth

The required lower division core courses for a mathematics major are Calculus 1, 2, and 3 (MATH 2200,2205,2210), Differential Equations (MATH 2310), Linear Algebra (MATH 2250), and the Math Major Seminar (MATH 2800).

At the upper division, all mathematics majors must take Analysis 1 (MATH 3205), Algebra 1 (MATH 3500) and Introduction to Scientific Computing (MATH 3340). These courses, known as the transition courses, introduce students to the three main areas of mathematics research currently represented in the department.

Every mathematics major must select one two-course sequence (MATH 4200/4205, MATH 4510/4520, or MATH 4340/4440) that builds on the corresponding transition course. This sequence provides the student with an opportunity to study one of these areas in greater depth.

Finally, an additional 12 credits of upper division math courses (3000 and above) are required. It is recommended that these courses be selected to provide a broad view of mathematics.

Two of the math electives may be chosen from a list of approved courses that have significant math content, upon approval by the student’s advisor. More details about such courses are available on the math department’s web site, math.uwyo.edu.

Only grades of C or better will be accepted for the major.

### Undergraduate Minor

The minor in mathematics focuses on fundamental aspects of mathematics that are essential for further study in mathematics and are also useful in a variety of other disciplines. Students minoring in mathematics may customize the minor by choosing the appropriate transition course and upper-division electives to match their needs.

The required lower division core courses for a mathematics minor are Calculus 1, 2, and 3 (MATH 2200,2205,2210), Differential Equations (MATH 2310), Linear Algebra (MATH 2250), and the Math Major Seminar (MATH 2800).

At the upper division, all mathematics minors must take ONE of Analysis 1 (MATH 3205), Algebra 1 (MATH 3500) or Introduction to Scientific Computing (MATH 3340), as well as 6 additional credits of upper division math courses (3000 and above).

Two of the math electives may be chosen from a list of approved courses that have significant math content, upon approval by the student’s advisor. More details about such courses are available on the math department’s web site, math.uwyo.edu.

Only grades of C or better will be accepted for the minor.

### Undergraduate Interdisciplinary Computational Science Minor

In recognition of the importance of modeling and simulation in an increasing number of applications, the Undergraduate Interdisciplinary Computational Science Minor is intended to help prepare science, math, and engineering students for leading roles in their professions.

The Undergraduate Minor in Computational Science is based on the following requirements:

- The student must earn 15 credit hours in specified courses.
- Within the 15 credits, the student must earn 9 credits at the upper-division level (3000 or above).
- Within the 15 credits, the student must earn 6 credits outside of her/his major.
- Within the 15 credits, the student must earn at least 6 credits in core courses.
- Only grades of C or better will be accepted for the minor.

The 15 hours of coursework are divided between core and elective courses as listed below.

#### Core Courses

- Numerical Analysis (Math 4340/COSC 4340)
- High-Performance Computing (Offered as a topics course.)
- Scientific Computing (MATH 3340/COSC 3340).
- Statistical Computing and Modeling (STAT 4460).

#### Elective Courses

- Computational Biology (BOT 4550/5550)
- Algorithms and Data Structures (COSC 3020)
- Mathematical and Computational Methods in Physics (PHYS 4840)
- Molecular Modeling (CHEM 4560/5560)
- C with Numerical Methods for Engineers (ES 3070)
- Mathematical Modeling (MATH 4300)
- Introduction to Finite Element Methods (ME 4040)
- Principles of Database Systems (COSC 4820)

## Graduate Study

The Department of Mathematics offers programs leading to the degrees of master of arts, master of science, master of arts in teaching, master of science in teaching, and the doctor of philosophy.

The requirements for these degrees reflect our belief that mathematicians should have a broad foundation in core areas of algebra, analysis, and applied mathematics, as well as the experience of a more intensive investigation of a specialized area. We provide this within a flexible structure that recognizes the individual interests and varied backgrounds of our students.

### Program Specific Admission Requirements

To be competitive for admission, applicants must have strong backgrounds in mathematics. Generally, this means a bachelor's degree in mathematics or a closely related discipline. All applicants should have substantial coursework beyond the calculus sequence; courses in differential equations, linear algebra, and, in particular, courses in abstract algebra and analysis are highly recommended. A solid performance on the GRE Subject Test in Mathematics can demonstrate the applicant's mastery of these subjects. The GRE Subject Test in Mathematics is therefore recommended but not required.

The GRE General Test is required, with a minimum Quantitative Reasoning score of 157 and Verbal score of 143. International applicants need a composite TOEFL score of 76 or an IELTS score of 6.5.

ETS only reports TOEFL scores taken within two years of the date of request.### Requirements for Admission for M.A.T. or M.S.T.

Applicants are required to have:

- A valid teaching endorsement in any state or educational requirements satisfied for secondary teaching;
- courses equivalent to MATH 3205, 3500, 4000, and 4600;
- a course in computer programming.

Students who enter the program with a deficiency in the courses listed above must take them at UW, but these courses may not be counted toward the course requirements of the M.S.T./M.A.T. program.

### Graduate Interdisciplinary Computational Science Minor

In recognition of the importance of modeling and simulation in an increasing number of applications, the Graduate Interdisciplinary Computational Science Minor is intended to help prepare science, math, and engineering students for leading roles in their professions.

#### Requirements

- The student must earn 15 credit hours in specified courses.
- Within the 15 credits, the student must earn at least 12 credits in graduate level classes (5000).
- Within the 15 credits, the student must earn 6 credits outside of her/his department.
- Only grades of B or better will be accepted for a course counting towards the minor.
- For all students, the 15 hours of coursework will be divided into 9 credit hours of core courses and 6 credit hours of electives.

#### Core Courses

- Computational Methods in Applied Sciences I (MATH 5310/COSC 5310), 3 hrs.
- Introduction to High-Performance Computing (COSC 5010), 3 hrs.
- Computational Methods II (MATH 5340/COSC 5340), 3 hrs.
- Computational Biology (BOT 4550/5550), 4 hrs.
- Groundwater Flow and Transport Modeling (GEOL 4030/5030), 3 hrs.
- Computational Fluid Dynamics I (ME 5461), 3 hrs.
- Computational Fluid Dynamics II (ME 5462), 3 hrs.
- Computational Methods in Statistics (STAT 5660), 3 hrs.

#### Electives

- Analysis of Algorithms (COSC 5110), 3 hrs.
- Advanced Bayesian Statistics (STAT 5680), 3 hrs.
- Bayesian Data Analysis (STAT 5380), 3 hrs.
- High-Performance Computing in Geosciences, 2 hrs.
- Mathematics Modeling of Processes (MATH 5320), 3 hrs.
- Molecular Modeling (CHEM 4560/5560), 3 hrs.
- Mathematical and Computational Methods in Physics (PHYS 4840), 3 hrs.
- Mathematical Modeling (MATH 4300), 3 hrs.

### Graduate Assistantships

The mathematics department employs approximately 25 graduate assistants each year. Assistantships include a full tuition and fee waiver, a monthly living stipend, and health insurance. Ph.D. students normally receive a higher stipend than master's students.

Teaching assistants teach an undergraduate course each semester.

Students may also compete for research assistantships, provided that their interests align with an externally funded research project.

Summer support is not guaranteed but is usually available through teaching and research opportunities.

Renewal of funding and continuation in the mathematics graduate program is dependent upon the student's adequate progress towards graduation.

### Program-Specific Degree Requirements

*Master's Programs: M.A. and M.S. Plan A and Plan B*

Students in the program must:

- Maintain a 3.0 cumulative GPA.
- Complete 30 hours of formal mathematics coursework at the 5000 level.
- Within the 30 hours of 5000-level courses, complete the following courses with a grade of B or better: MATH 5200, 5230, 5310, 5400, 5500, and 5550.
- Within the 30 hours of 5000-level courses, pass 1 hour of MATH 5800-01, Professional Development.
- Within the 30 hours of 5000-level courses, the Plan A student must complete 4 hours of MATH 5960, Thesis Research. At least 26 hours of 5000-level coursework must be math-content courses (not thesis research).
- The student must pass the foundation exam.
- The student must prepare a master's thesis (Plan A) or a master's paper (Plan B) and give an oral defense.

*Master's Program: Second Option for Plan B Degree*

A second M.A. or M.S. option exists for the Plan B student. In lieu of writing a paper, the student takes a sequence of three 5000-level courses. The sequence must be approved by the student's advisor and the mathematics graduate committee. Two of the courses must be mathematics-department offerings, and the third may be either a mathematics course (including reading/topics courses) or a course from another department in a related field.

A student graduating under this option must:

- Maintain a 3.0 GPA.
- Complete 36 hours of courses at the 5000 level.
- Within the 36 hours, complete with a grade of B or better: MATH 5200, 5230, 5310, 5400, 5500, and 5550.
- Witin the 36 hours, pass 1 hour of MATH 5800-01, Professional Development.
- Within the 36 hours, complete with a grade of A or B a 3-course sequence as approved by the student's advisor and the graduate committee.
- Pass the foundation exam.
- Write a short paper and give a presentation on the 3-course sequence.

In approving the student's proposal for this option, the graduate committee and the advisor will consider how the writing and independent study spirit of the Plan B option are fulfilled within the recommended plan.

*Master of Arts in Teaching or Master of Science in Teaching*

This degree is intended for in-service high school or middle school math teachers. The M.S.N.S. (Master of Science in Natural Science) Math option, through the Science and Math Teaching Center of the College of Education, is an alternative for middle school teachers.

Candidates for the M.S.T. or M.A.T. must take at least 30 hours of coursework at the 4000 level or above, of which at least 18 hours must be math courses, and at least 24 hours must be in the College of Arts and Sciences.

GPA of 3.0 in math courses is required.

EDRE 5530 or 5550 is recommended as part of the student's program.

The student prepares a master's thesis (Plan A) or master's paper (Plan B) and gives an oral defense.

Students must have two years' teaching experience at the precollege level, which may be completed during the degree program.

### Doctoral Program

The student must maintain a 3.0 cumulative GPA.

The student must teach two semesters of college mathematics.

The student must complete a combination of 72 hours of coursework and dissertation research. Within the 72 hours, a maximum of 12 hours can be at the 4000 level, and 42 hours must be formal courses at the 5000 level. The courses must be mathematics courses or courses with significant mathematical content, as approved by the department's graduate committee.

Within the 42 hours of 5000-level courses, the student must:

Complete MATH 5200, 5230, 5310, 5400, 5500, and 5550 with a grade of B or better.

Take a broadening course as defined by the department and pass with a grade of B or better.

Take one hour of MATH 5800-01, Professional Development.

Take two hours of MATH 5800-02, Seminars and Colloquia.

Complete the courses distributed in three areas: algebra, analysis, and applied mathematics. The student must take at least two courses in each of two categories and at least one course from the third category. The department maintains a list of course categories.

In addition, the student must:

Pass the foundation exam, the qualifying exam in the student's research area, and the preliminary exam.

Write a dissertation containing the student's original mathematical results and present an oral defense of the research.