Math Graduate Handbook

Handbook Sections

• Title Page
• Calendar of Events
• Graduation Deadlines
• General Information
• Financial Aid
• Tuition
• Living Expenses
• Housing
• Community
• Mathematics Program Offerings and Requirements
• Program purpose and objectives
• Application Requirements
• International Applicants
• Application Deadlines and Admission Requirements
• M. S. Program
• Ph. D. Program
• Master's Examination
• Minors
• Guidelines for Projects and Theses
• Advisement
• Evaluation of Student Progress
• Graduate Student Advisory Committee
• Masters Schedule of Study
• Ph. D. Schedule of Study
• Financial Support
• Graduate Seminar
• Course Offerings
• Faculty Areas of Interest

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GRADUATE MATHEMATICS

September 2007

Department of Mathematics

Brigham Young University

Provo, Utah 84602

Graduate Coordinator

William E. Lang

Graduate Examinations

Eric Swenson

Graduate Committee

William E. Lang, Chair

Roger Baker

Jasbir Chahal

Tiancheng Ouyang

Eric Swenson

Graduate Student Advisory Committee

Matthew Adams

Brent Kerby

Natalie Wilde

TA Training Coordinator

Vianey Villamizar

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Calendar of Graduate Events

Fall Semester 2007

August 29-31	Mathematics TA Student Workshop
September 3	Labor Day Holiday
September 4	Classes Begin
September 15	Masters Exam (9:00 AM; 294 TMCB)
November 22-23	Thanksgiving Day Holiday
December 13	Last day of class instruction
December 14-15	Reading days
December 17-21	Final examinations

Winter Semester 2008

January 7	Classes begin
January 19	Master's Exam (9 am, 294 TMCB)
January 20	Martin Luther King Day Holiday
February 18	President's Day Holiday
April 15	Last day of class instruction
April 16-179	Exam Preparation Days
April 18-19; 21-23	Final examinations
April 24	Graduation-university commencement
April 25	Graduation-college convocations

Spring Term 2008

April 29	Classes begin
May 10	Master's Exam (9:00 AM; 294 TMCB)
May 26	Memorial Day Holiday
June 16	Last day of class instruction
June 17	Exam Preparation Day
June 18-19	Final examinations

Summer Term 2008

June 23	Classes begin
July 4	Independence Day Holiday
July 24	Pioneer Day Holiday
August 11	Last day of class instruction
August 12	Exam Preparation Day
August 13-14	Final examinations
August 14	Graduation - university commencement
August 15	Graduation - college convocation

Fall Semester 2008

August 28-30	Mathematics TA Student Workshop
September 1	Labor Day Holiday
September 2	Classes Begin
September 13	Masters Exam (9:00 AM; 294 TMCB)
November 27-28	Thanksgiving Day Holiday
December 11	Last day of class instruction
December 12-13	Exam Preparation Days
December 15-19	Final examinations

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Graduation Deadlines

December Graduation 2007

September 28	Last day to apply for December graduation. Submit the application (Form 8a) to Lonette (292 TMCB).
November 2	Last day to schedule a final oral defense of dissertation, thesis or project with the department using the Department Scheduling of Final Oral Examination Form (Form 8c) and to submit a copy of their work to the department. If you choose to defend your work earlier, please do so AT LEAST 2 WEEKS PRIOR TO THE DATE YOU CHOOSE TO PRESENT.
November 16	Last day to have a final oral defense of dissertation or thesis for graduation.
November 30	Last day to submit dissertation or thesis and Approval for Submission of Dissertation to Thomas W. Sederberg (Associate Dean) in the Dean's Office for signature. For ETDs, the document in PDF format must be submitted online by logging into the ETD submission site. Please read all the instructions BEFORE submitting your work electronically. PAY SPECIAL ATTENTION TO BOOKMARKS since no thesis, dissertation or project will be accepted without them.). The dean's office will then review and approve the ETD.
December 7	Last day to submit final printed copies and/or ETD of dissertation or thesis with Form 8d to the Library Administration Office (2060 HBLL). The Math Department requires a bound copy of your work for the department as well as your advisor (unless he or she is content with the PDF version). Last day to complete any remaining requirements for a degree including payment of fees; and submitting grade changes for I's, T's, etc. and for departments to enter examination results (oral or written) on the computer. Also, DO NOT scan the signature pages. The PDF version should not be signed. The approval form serves this purpose. If you are submitting a project, you need to bring a final copy to Lonette (292 TMCB), back-to-back, no page numbers. You may also email her a PDF file (again no page numbers).

April Graduation 2008

January 25	Last day to submit your application for April graduation. Submit the application (Form 8a) to Lonette (292 TMCB).
February 22	Last day to schedule a final oral defense of dissertation, thesis or project with the department using the Department Scheduling of Final Oral Examination Form (Form 8c) and to submit a copy of their work to the department. If you choose to defend your work earlier, please do so AT LEAST 2 WEEKS PRIOR TO THE DATE YOU CHOOSE TO PRESENT.
March 7	Last day to have a final oral defense of dissertation or thesis for graduation.
March 14	Last day to submit dissertation or thesis and Approval for Submission of Dissertation to Thomas W. Sederberg (Associate Dean) in the Dean's Office for signature. For ETDs, the document in PDF format must be submitted online by logging into the ETD submission site. Please read all the instructions BEFORE submitting your work electronically. PAY SPECIAL ATTENTION TO BOOKMARKS since no thesis, dissertation or project will be accepted without them.). The dean's office will then review and approve the ETD.
March 21	Last day to submit final printed copies and/or ETD of dissertation or thesis with Form 8d to the Library Administration Office (2060 HBLL). The Math Department requires a bound copy of your work for the department as well as your advisor (unless he or she is content with the PDF version). Last day to complete any remaining requirements for a degree including payment of fees; and submitting grade changes for I's, T's, etc. and for departments to enter examination results (oral or written) on the computer. Also, DO NOT scan the signature pages. The PDF version should not be signed. The approval form serves this purpose. If you are submitting a project, you need to bring a final copy to Lonette (292 TMCB), back-to-back, no page numbers. You may also email her a PDF file (again no page numbers).

August Graduation 2008

May 23	Last day to submit your application for August graduation. Submit the application (Form 8a) to Lonette (292 TMCB).
June 20	Last day to schedule a final oral defense of dissertation, thesis or project with the department using the Department Scheduling of Final Oral Examination Form (Form 8c) and to submit a copy of their work to the department. If you choose to defend your work earlier, please do so AT LEAST 2 WEEKS PRIOR TO THE DATE YOU CHOOSE TO PRESENT.
July 3	Last day to have a final oral defense of dissertation or thesis for graduation.
July 11	Last day to submit dissertation or thesis and Approval for Submission of Dissertation to Thomas W. Sederberg (Associate Dean) in the Dean's Office for signature. For ETDs, the document in PDF format must be submitted online by logging into the ETD submission site. Please read all the instructions BEFORE submitting your work electronically. PAY SPECIAL ATTENTION TO BOOKMARKS since no thesis, dissertation or project will be accepted without them.). The dean's office will then review and approve the ETD.
July 18	Last day to submit final printed copies and/or ETD of dissertation or thesis with Form 8d to the Library Administration Office (2060 HBLL). The Math Department requires a bound copy of your work for the department as well as your advisor (unless he or she is content with the PDF version). Last day to complete any remaining requirements for a degree including payment of fees; and submitting grade changes for I's, T's, etc. and for departments to enter examination results (oral or written) on the computer. Also, DO NOT scan the signature pages. The PDF version should not be signed. The approval form serves this purpose. If you are submitting a project, you need to bring a final copy to Lonette (292 TMCB), back-to-back, no page numbers. You may also email her a PDF file (again no page numbers).

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General information about graduate study at Brigham Young University

With an enrollment of 27,000 full-time students, Brigham Young University is one of the nation's largest private universities. Founded as Brigham Young Academy in 1875 by the Church of Jesus Christ of Latter-day Saints, the university represents the importance of education to members of the Church. Enrollment is open to students of all faiths.

Costs and Financial Aid

Financial Aid

Most of the graduate students in mathematics are supported by teaching assistantships. The usual load for a teaching assistant is two three-hour sections for both Fall and Winter Semesters. The usual load for a Ph.D. candidate is the equivalent of two three-hour sections for one semester and one three-hour section the second semester if the student is making adequate progress on the qualifying examinations. Currently teaching assistants receive between $12,000 and $15,000 per academic year. Some research or travel money is available for those students who are making good progress toward a degree, have submitted a program of study, and have an advisor's endorsement.

To be considered for financial support, applications must be submitted by March 1 (September 15 for Winter semester).

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Tuition

A significant portion of the cost of operating the university is paid from the tithes of The Church of Jesus Christ of Latter-day Saints (LDS). Therefore, students and families of students who are tithe-paying members of the Church have already made a contribution to the operation of the university. Because others have not so contributed, they are charged a higher rate of tuition (in parentheses below). This practice is similar in principle to that of state universities that generally charge nonresidents at a higher rate than residents.

Tuition website

Tuition per semester 2007-2008

Full-Time	LDS: $2,430; Non-LDS: $4,860
Part-Time (per credit hour)	LDS: $270; Non-LDS: $540

Tuition per term 2007-2008

Full-Time	LDS: $1,215; Non-LDS: $2,430
Part-Time (per credit hour)	LDS: $270; Non-LDS: $540

Teaching and research assistants receive a tuition scholarship for mathematics courses fall and winter semesters if they are making good progress toward completion of their program.

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Living Expenses

Living Expenses for 2007-2008 full-time graduate study (Cost of Attendance)

Item	Single	Married
Books & Supplies (2 semesters)	$800	$800
Room and Board (12 months)	$4,500	$6,500
Misc. Personal Expenses (8 months)	$1,200	$1,200
Medical Insurance	$3801	$2,0161
TOTAL LIVING EXPENSES	$6,880	$10,516

¹BYU requires all three-quarter- and full-time students (registered for 9 credit hours or more for a semester; 4.5 credit hours for a term, including Salt Lake Center hours) to carry adequate medical insurance. Graduate students who are registered for 2.0 credit hours or more are eligible to enroll in the BYU Health Plan. The figure for married medical insurance does not include maternity coverage. For current costs and specific coverage, contact the Insurance Office at the Health Center: 2310 SHC, P. O. Box 24800, Provo, UT 84602-4800; (801) 422-7737, insurance@byu.edu.

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Housing

Student housing is available both on campus and in the surrounding communities; policies have been established with campus residence halls and with off-campus landlords to integrate living experiences with the complete educational experience.

On-campus Housing

Off-campus Housing

Student Family Housing

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Community

Brigham Young University is located in Provo, Utah. The university is a 30-60 minute drive from some of the best skiing in America, and numerous other outdoor recreational opportunities exist nearby. There are many cultural and athletic activities on campus, including an outstanding music program. Provo is 45 miles south of Salt Lake City, a major metropolitan area. In Salt Lake City, one can enjoy the Mormon Tabernacle Choir, the Utah Jazz, the Utah Symphony, and a large number of other attractions.

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Mathematics Program Offerings and Requirements

The Department of Mathematics offers a masters and a doctoral program. The Master of Science (M.S.) program prepares students for positions in business and industry, and also provides preparation for further graduate study leading to a doctoral degree at Brigham Young University or elsewhere.

The Doctor of Philosophy (Ph.D.) program prepares students for a career in research and teaching at the university level. The Ph.D. program in Mathematics was approved in 1986 when the Department received a program improvement grant to fund teaching assistantships in mathematics. The current research areas of the faculty include:

• Algebraic Geometry


• Applied Mathematics, Nonlinear PDEs and Dynamical Systems


• Combinatorics & Matrix Theory


• Geometric Topology, Geometric Group Theory, Combinatorial Group Theory


• Number Theory

With small classes and individual attention, the Department supports high quality research programs in the selected areas.

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Program purpose and objectives

The general objective of the Department of Mathematics at Brigham Young University, as related to the degrees offered by the department, is to teach mathematics and mathematical thinking at the level appropriate to each student, thus enabling students to employ critical analysis, thoughtful synthesis, logical deduction, and insightful problem-solving, not only within mathematics itself but in a wide variety of natural and man-made situations.

MS objectives

The Master of Science program is specifically designed to help students progress toward being independent mathematical thinkers and participate in advancing the frontiers of mathematical knowledge.

The Master of Science program also prepares students for positions in business and industry that require advanced mathematics skills, critical analysis, thoughtful synthesis, and insightful and independent problem solving.

PhD Objectives

The specific purpose of the Doctor of Philosophy program in Mathematics is to prepare students for a career in research and teaching at the university level, as well as to prepare them for professions that require independent mathematical research, advanced mathematical knowledge, critical analysis, thoughtful synthesis, and insightful and independent problem solving. It also gives students an opportunity to become full contributors to the important and exciting process of extending the frontiers of mathematical knowledge.

The underlying philosophy of the program is that graduate-level mathematics is both enabling and ennobling. Mathematical knowledge, logical reasoning, and the ability to solve problems and discover mathematical truth are powerful and important skills that allow students success in a wide range of academic, professional, or business-related careers. But more importantly, deep and careful mathematical thought expands both the mind and the soul. It increases our understanding of many things, both physical and spiritual. Our purpose in this program is to enrich the spiritual and temporal lives of our students by sharing the beauty and power of mathematics with them.

The accomplishment of these objectives requires the students to gain a deep understanding of and appreciation for mathematics, its versatility, depth, and power. They must also understand many of the important ideas of the main mathematical sub-disciplines, and relations of mathematics to other subjects. Finally, the students should be able to work independently--without the direct supervision and guidance of a senior mathematician. The development of this independence is certainly begun at the undergraduate and masters levels, but for most students it can only be fully achieved at the doctoral level. Thus, although coursework plays some role in the requirements for the PhD in mathematics, the most important element is the dissertation, a significant and substantial work of original mathematical research.

Specific goals of the programs

MS: The specific goals of the MS in Mathematics are to help each individual student

1. Achieve an understanding of graduate-level mathematics, including several of the areas, Analysis, Algebra, Topology, and Applied Mathematics.
2. Achieve depth and application in a specialized area.
3. Develop mathematical research skills.
4. Develop problem-solving skills applicable to a wide variety of settings.
5. Learn to communicate complex ideas effectively and demonstrate sound reasoning in both quantitative and qualitative settings.
6. Acquire the mathematical foundation necessary to enter a variety of opportunities in occupations and further schooling.
7. Relate knowledge of mathematics and mathematical processes to physical, natural, and social sciences, humanities, and other human endeavors.
8. Develop a reasoned relationship between secular knowledge and spiritual insight that fosters faith and commitment to the gospel of Jesus Christ and leads to lifelong learning and service.

PhD: The specific goals of the PhD in Mathematics are to help each individual student

1. Achieve a broad understanding of graduate-level mathematics, including several of the areas, Analysis, Algebra, Topology, and Applied Mathematics.
2. Achieve depth, and a thorough knowledge of current developments in a specialized area.
3. Develop mathematical research skills at the doctoral level, discovering significant new results in mathematics, or solving outstanding problems.
4. Develop expository skills that will allow communication of future research results with the academic world.
5. Learn to communicate complex ideas effectively and to reason soundly in both quantitative and qualitative settings.
6. Acquire the expertise necessary to continue to contribute to the frontiers of mathematical knowledge
7. Relate knowledge of mathematics and mathematical processes to physical, natural, and social sciences, humanities, and other human endeavors.
8. Develop a reasoned relationship between secular knowledge and spiritual insight that fosters faith and commitment to the gospel of Jesus Christ and leads to lifelong learning and service.

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Application and Admissions

University Application Requirements

Admission to graduate study is highly selective and is granted to a specific program for a specific semester or term. As a minimum, applicants who wish to be considered for admission must do the following:

U.S. Applicants

1. Submit a complete application before the application deadline. An application is not considered complete until the application fee has been paid and all official transcripts, letters of recommendation, the statement of intent, and the confidential report are in, as well as parts A and D of the admissions application.


2. Agree to maintain university standards of personal conduct.


3. Have received or be about to receive a baccalaureate degree from an accredited U.S. or Canadian university. The Office of Graduate Studies must receive an official transcript showing that the degree has been conferred. Without such verification, registration will not be permitted beyond the first semester. U.S. students with a degree from a foreign university equivalent to an American baccalaureate must submit official transcripts from all institutions attended and an accompanying certified translation.


4. Have earned at least a 3.0 GPA in the last 60 semester hours of course work.


5. All applicants for whom English is not the native language: Submit evidence of proficiency in English---a score of at least 580 on the TOEFL. To be competitive for financial support a TOEFL score of at least 600 or a computer equivalent score of at least 237 is preferred.


6. Satisfy departmental requirements for consideration. See all the sections under Mathematics Department Application and Admission Requirements.

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International Applicants (all non-U.S.)

Note: Brigham Young University will not process applications from applicants entering the United States with a B visa. An admitted student will receive an I-20 or IAP-66 form (Certificate of Eligibility) with the official letter of acceptance; the I-20 and IAP-66 are used to obtain a student visa (F-1 or J-1).

1. Submit a complete application before the application deadline. An application is not considered complete until the application fee has been paid and all official transcripts, official evidence of degrees earned, letters of recommendation (Part C), the statement of intent, official TOEFL score, financial certification, and the Code of Honor commitment and confidential report (Part B) are in, as well as Parts A and D of the admissions application.


2. Agree to maintain university standards of personal conduct.


3. Submit official transcripts from each institution attended, with accompanying certified English translation.


4. Submit a copy of a diploma (preparation completed at least equivalent to a U.S. bachelor's degree), with accompanying official English translation.


5. Have earned at least a 3.0 GPA (on a 4.0 scale) for all previous undergraduate work.


6. Submit a TOEFL score of at least 580. To be competitive for financial support a TOEFL score of at LEAST 600 or a computer equivalent score of at least 237 is preferred. This is required of all applicants for whom English is not the native language. Students with a bachelor's degree from a U.S. or Canadian university are usually exempt from this requirement.


7. Submit a completed Financial Certification and Visa Information form, with supporting documents. Applicants must provide proof of sufficient funds for the total length of their program of study.


8. Satisfy departmental requirements for consideration. See all the sections under Mathematics Department Application and Admission Requirements.

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Mathematics Department Application and Admission Requirements (all programs)

Applications deadlines are March 1 (for Fall, Summer), September 15 (for Winter), and February 15 (for Spring).

In addition to the university's application requirements, the Mathematics department requires the following entrance examinations. Please note that some of these exams are offered only 2-3 times per year and scores may not be reported for several weeks after the examination, so the exams should be taken well before the application deadlines.

Entrance examinations required

• General GRE.
• Advanced mathematics GRE (i.e. Math Subject Test).
• TOEFL (for applicants whose native language is not English).

Prerequisites

Before admission to graduate study in mathematics, all students must complete the following prerequisites:

• Credit at least equivalent to a BYU baccalaureate degree in mathematics.
• A year's sequence in abstract algebra.
• A year's sequence in advanced calculus (or undergraduate analysis).

Program Requirements

Forms

All forms needed for graduate studies may be downloaded from the following website:

http://www.byu.edu/gradstudies/forms/forms.php

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Mathematics M.S. Degree

Approved Courses (Both Thesis and Non-Thesis Programs)

Approved graduate mathematics courses include all classes numbered 500 and above, with the exceptions of 501, 502. All courses must be passed with a grade of C+ or better. No credit is given for prerequisite courses such as Math 316 or Math 372.

Thesis Program Requirements

1. Credit hours (30): Minimum 24 course work hours in approved graduate mathematics with a grade of C+ or better in each, including 12 hours in courses numbered 600 or above and 6 thesis hours (Math 699R).


2. Examination: Pass a written master's examination. The first attempt at the examination should be made by the end of the student's first semester of the second year after which one more attempt at the examination is allowed. Students are encouraged to take the exam as early in their program as possible and early attempts count only if the exam is passed.


3. Thesis


4. Oral defense of thesis

Non-Thesis Program Requirements

There are three different options in the non-thesis program: Traditional Mathematics Option, Minor Option, and Applied Option. The requirements for each are as follows:

1. Credit hours: Complete one of the following options.


1. Traditional Mathematics Option (32): Minimum 30 course work hours in approved graduate mathematics with a grade of C+ or better in each, including 18 hours in courses numbered 600 or above and two hours for the project (698R). No credit is given for prerequisite courses such as Math 316 or Math 372.


2. Minor Option (35): Minimum 24 course work hours in approved graduate mathematics with a grade of C+ or better in each, including 6 hours in courses numbered 600 or above, 9 hours in an approved minor and two hours for the project (698R).


3. Applied Option (38): Minimum 24 course work hours in approved graduate mathematics with a grade of C+ or better in each, including 6 hours in courses numbered 600 or above, 12 hours in areas related to applications of mathematics and two hours for the project (698R). The 12 hours of applications must be approved by the graduate coordinator.


2. Examination: Pass a written master's examination. The first attempt at the examination should be made by the end of the student's first semester of the second year after which one more attempt at the examination is allowed. Students are encouraged to take the exam as early in their program as possible and early attempts count only if the exam is passed.


3. Project, Paper and Presentation: Complete a project (Math 698R) focused on an area of advanced mathematics, write a paper about the project, and present a 45-minute talk based on the paper.

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Mathematics Ph.D. Degree

Requirements for Doctoral Degree

1. Credit Hours (54): Minimum 36 coursework hours in mathematics courses numbered 600 or above with a grade of B or better in each plus 18 dissertation hours (Math 799R). No credit is given for mathematics courses with numbers lower than 510.


2. Required Courses: Complete at least 3 hours each in algebra, analysis, applied mathematics, and geometry/topology.


3. Examinations:
   1. Written Examinations: At the beginning of the second year after admission to the Ph.D. program, the student is required to pass examinations in three of the four areas of algebra, analysis, applied mathematics, and geometry/topology. Four hours are allotted to each examination. A failed examination may be repeated once at the beginning of the winter semester of the student's second year, after which permission must be obtained from the department graduate committee to retake the examination. Passed examinations need not be repeated. Syllabi are available for each examination.
   
   
   2. Oral Examination: A student must pass an oral qualifying examination covering the background necessary for research in a specific area. The student, having chosen a research area and having a dissertation advisor approved, will, with the advisor, outline suitable examination topics. These topics must be approved by an examination committee of three (including advisor) appointed by the department graduate committee, which conducts the examination.
   
   
   3. Defense of Dissertation: A final oral defense of the dissertation is conducted by a faculty committee consisting of the student's research advisor, two other readers of the dissertation (one of whom may be an outside examiner), and two other members of the faculty.
   
   
4. Language Requirement: Demonstrate proficiency in an approved foreign language that is currently in major use in the mathematical literature. The approved languages are French, German, Russian, Italian, Japanese, and Chinese. In certain cases another language may be substituted for one of these if the department graduate committee approves. The committee will consider the current usage in the student's specialty area. The preferred avenue for the completion of the language requirements is the intensive reading course offered by the language department involved (such as French 121).
   
   Two other alternatives are considered suitable:
1. Course credit for the standard undergraduate sequence at the level of the GE math/foreign language requirement (or exam credit at the same level).


2. Exam of mathematics translation with occasional use of a dictionary. The examinations are prepared and offered by the Mathematics Department on a by request basis. They are designed to test a student's ability to translate foreign mathematical literature into scientifically correct English.


5. Dissertation

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Master's Examination

The content of the examination is based on Algebra (Math 371, 372 and 343), Analysis (Math 315, 316, 334, 541, 542), and Topology (Math 451, 553, 554). Previous exams may be used as study guides.

The first attempt at the examination should be made by the end of the student's first semester of the second year, after which one more attempt at the examination is allowed. Students are encouraged to take the exam as early in their program as possible and early attempts count only if the exam is passed.

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MS Minors

MS Minor Option: Approved Minors

An approved minor, for the minor option of the MS program, is one that is both university-approved and approved by the graduate committee. The university rules for a minor include the following:

If a minor is desired, a student must:

1. Obtain the approval of the department chair of the major and the minor departments.
2. Select a graduate faculty member (approved by the department chair of the minor department) to serve as a committee member.
3. Register for and complete 9 semester hours of approved graduate credit in the minor.
4. Pass an oral or a written comprehensive examination in the minor field (prepared by the minor committee member).

MS Applied Option: Approved Minors

The following is a list of pre-approved courses for the applied option. The graduate coordinator may approve other courses on a case-by-case basis. The student is responsible for making sure that he/she can meet the prerequisites for each class taken.

Chemistry

The approved classes are:

Chem 561	Chemical Thermodynamics
Chem 565	Introductory Quantum Chemistry
Chem 569	Fundamentals of Spectroscopy
Chem 699R	Quantum Chemistry
Chem 769R	Statistical Mechanics

Physics

The approved classes are:

Phscs 512	Computational Physics
Phscs 545	Introduction to Plasma Physics
Phscs 617	Advanced Topics in Theoretical Physics
Phscs 618	Advanced Topics in Theoretical Physics
Phscs 619	Advanced Topics in Theoretical Physics
Phscs 621	Dynamics
Phscs 625	Theory of Relativity
Phscs 631	Statistical Mechanics
Phscs 632	Statistical Mechanics
Phscs 641	Mathematical Theory of Electricity and Magnetism
Phscs 642	Mathematical Theory of Electricity and Magnetism
Phscs 651	Quantum Mechanics
Phscs 652	Quantum Mechanics
Phscs 751	Advanced Quantum Theory
Phscs 752	Advanced Quantum Theory

Statistics

The core is:

Stat 522	Theory of Linear Models
Stat 525	Statistical Inference
Stat 535	Applied Linear Models

Other approved courses include:

Stat 511	Statistical Methods for Research 1
Stat 512	Statistical Methods for Research 2
Stat 536	Modern Regression Methods
Stat 537	Generalized Linear Models
Stat 541	Advanced Probability
Stat 545	Stochastic Processes

Economics

The approved classes are:

Econ 580	Advanced Price Theory
Econ 586	Mathematical Economics
Econ 588	Econometrics

Computer Science

CS 557	Computer-Aided Geometric Design
CS 561	Theoretical Foundations of Computer Science

together with any other computer science course numbered above 500.

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Guidelines for M.S. Degree Projects and Theses

Content

A mathematics MS project should entail learning mathematics not normally taught in graduate or undergraduate classes. It may be of an expository nature or may involve the investigation of mathematical structures in some depth. It need not include original research, but it should include some proofs.

A mathematics MS thesis should be a substantial mathematical work. This does not refer to length, but rather to content. One would hope for original work sufficient for publication in some kind of college mathematics journal. The thesis should be the work of the student and should not have been written primarily by the advisor. Other than original work the thesis might be an account of work at the frontier of research in a particular area, perhaps including new examples worked out in detail. The content of the thesis should be demanding for a mathematician from an area different from the area of the thesis.

Computational/algorithmic projects or theses are also possible, however the mathematical content needs to be the core of the writing.

In both of these the students should bite off too much rather than too little. Students should be stretched and will be called to account for the logical content of their written work. They should contribute in some way to mathematics and not just regurgitate.

Students should be aware of the limitations of their methodology (e.g. statistical significance) and, on the other hand, the possibilities for amplification of their results. They should have some idea about how what they have done fits into the general subject, i.e., context is also important.

Presentation or Defense

The student should give a presentation in which the essential ideas of the written work are exposed and put in context. The student should be able to answer straightforward questions on the basic parts of their work, thus indicating a thorough understanding. The talk should include some proofs.

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Advisement

Academic Sponsor

Once accepted into the graduate program, students are assigned a department sponsor who guides their first registration and individual study until the student selects an advisory committee, which is appointed in the first semester. Students should contact their academic sponsor well before their first semester of graduate study so that they can be sure to enroll in courses best suited to their individual case.

Advisor and Advisory Committee

The advisor plays a significant role in guiding the student through the program and helping the student become an independent mathematician. The advisor helps the student choose a project, thesis, or dissertation topic, and gives guidance and supervision throughout.

Choosing an Advisor

The main component in choosing a professor to be an advisor should be matching the student's research interests with the type and quality of research done by the professor. In order to determine the type of research currently being done by faculty members, students should attend the various seminars offered. Once a student has determined someone with similar interests, she/he should consult with the potential advisor and ensure that professor is willing to act as an advisor.

Advisory Committee

During the first semester, students should work with the selected advisor to arrange for the appointment of an advisory committee. Master's (thesis and non thesis) committees consist of a chair and at least two other members; doctoral committees have a chair and at least four other members. The Department may require additional members. One member must be from the minor department if a student declares a minor.

Study List

The goal of the graduate program in mathematics is for the student to become an independent mathematician. This is not accomplished by just taking a random selection of courses but by carefully working with an advisory committee to create a program that meets the student's interests and has a solid mathematical foundation.

A study list must be submitted and approved by the students' advisory committee before the beginning of the student's second semester. Financial support will be reduced and may be withdrawn if a study list is not submitted on time. The Graduate Study List gives the approved courses of study for the graduate degree. It is possible at any time to amend the study list form for courses not yet taken. The study list is obtained from the department graduate secretary. After the list has been filled out and the appropriate signatures have been obtained, the list should be returned to the department graduate secretary.

In addition to the official study list, students should submit, by the end of November of each year, a tentative schedule of when they plan to take each remaining course on their study list. This allows the graduate committee to ensure that graduate course offerings for the coming year will meet students' needs.

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Evaluation of Student Progress

The Math Department encourages students to complete their degree programs in a timely fashion. The evaluation process is as follows:

I. The Math Department will monitor graduate student progress twice a year (fall semester and spring term).

1. The graduate committee will review the progress of each student.
2. Students will be rated as making satisfactory, marginal, or unsatisfactory progress.
3. Students will be notified in writing of their progress.
4. Students making marginal or unsatisfactory progress will be informed by certified letter with return receipt:
   • What they need to do to make satisfactory progress.
   • When each task needs to be accomplished.
   • What faculty member(s) they should contact for more information or support.
   • What will happen if these tasks are not accomplished (e.g., an unsatisfactory rating for the next semester, termination from the program, etc.).

II. Definitions of marginal and unsatisfactory ratings:

1. Marginal progress may include the following:
   • Failure to submit program of study form
   • Failure to establish a graduate committee
   • Registering for thesis hours when little or no work has been done
   • Failure to submit an approved thesis/dissertation prospectus
   • Minimal contact with chair or advisory committee members
   • Prospectus or thesis/dissertation draft not approved
   • Limited progress toward courses and requirements on Program of Study
   • Poor performance in clinical/externship/applied experience
   • Poor performance in research
2. Unsatisfactory progress may include the following:
   • Grade in a course falling below B-
   • Failure to complete program of study form
   • Failure to establish a graduate committee
   • Failing a course
   • Registering for thesis hours when little or no work has been done
   • Failure to submit an approved thesis/dissertation prospectus
   • Failure of comprehensive exams
   • Minimal or no contact with chair or advisory committee members
   • Prospectus or thesis/dissertation draft not approved
   • Lacking progress toward courses and requirements on study list
   • Poor performance in clinical/externship/applied experience
   • Rated as marginal in previous review and has not remediated weak areas
   • Concerns about ethical or professional behavior
   • Poor performance in research
   • Failure to resolve any problems or fulfill any requirements indicated in a previous marginal or unsatisfactory review.

III. If a student receives a marginal and an unsatisfactory or two unsatisfactory ratings in succession the department will:

1. terminate the student's program at the conclusion of the semester OR
2. submit a petition to Graduate Studies making a convincing case that the student be given another semester to demonstrate satisfactory progress. A copy of a contract listing student and faculty responsibilities and a time line should be attached.

IV. If a student receives a marginal rating in one semester and is not making satisfactory progress in the next semester, the student will be rated as making unsatisfactory progress. In other words, a student will not be rated as making marginal progress in two sequential semesters. Failing to correct marginal progress is unsatisfactory.

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Graduate Student Advisory Committee

The Graduate Student Advisory Committee exists to improve the graduate program by:

1. Advising graduate students concerning classes, requirements for degrees, and other aspects of the graduate program.
2. Making recommendations concerning the graduate program to the Department of Mathematics.
3. Assisting the Department in making its policies and requirements fully understood by the graduate students.
4. Organizing the weekly graduate seminar.

This committee consists of three graduate students, elected in the fall of each year by the mathematics graduate students. If there are not sufficient nominations, the Graduate Committee may nominate or select members of this committee.

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M.S. Degree Recommended Schedule of Study

Below is a recommended schedule of courses for students in the master's program. Students should consult with their advisor to determine whether some deviation from this plan is better suited to their individual needs. The standard load for a student with a teaching or research assistantship is 9 credit hours of graduate-level mathematics courses per semester. Students who enroll in fewer mathematics courses may have trouble completing their program requirements in a timely manner. Students not enrolled in at least 6 hours of mathematics courses per semester are generally not making satisfactory progress toward completion of their degree and may have their funding reduced or their degree candidacy terminated.

Semester 1 (Fall)

• Take Math 541, Math 671, and Math 551.
• Attend the weekly graduate seminar.
• Choose an advisory committee and prepare a study list.

Semester 2 (Winter)

• Take Math 542, Math 672, and Math 552, or other courses as directed by your advisor.
• Attend the weekly graduate seminar.
• Pass the master's exam.

Spring/Summer

• Begin the thesis or project.
• Take readings courses relevant to the thesis or project, as directed by your advisory committee.

Semester 3 (Fall)

• Take at least 3 hours of 600-level courses.
• Take 6 more hours of courses according to your study list (some may be thesis or project hours).
• Attend a weekly research seminar as directed by your advisor.
• Continue work on your thesis or project.

Semester 4 (Winter)

• Take at least 3 hours of 600-level courses.
• Take 6 more hours of courses according to your study list (some may be thesis or project hours).
• Attend a weekly research seminar as directed by your advisor.
• Finish and defend the thesis or project.

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Ph.D. Degree Recommended Schedule of Study

The following schedule is recommended for teaching assistants in the Ph.D. program. Except where there are extenuating circumstances, teaching assistants who fall more than one year behind this schedules should not expect their teaching assistantships to be renewed. Students who have strong potential but lack adequate preparation may petition to have a year zero added in which they complete their preparation for the Ph.D. program. During this year, their teaching duties and pay will be similar to master's students. Students who have passed fewer than two of the three required qualifying examinations by February of their second year will not be allowed to continue. Students who have passed only two of the three examinations by February of the second year may request special permission to continue for an additional year by making a written request to the student's graduate committee. The student's committee reviews the request and submits a written recommendation to the departmental graduate committee. In addition students who have completed an M.S. degree at BYU are required to pass at least one examination by February of their first year of study in the Ph.D. program in order to continue beyond the first year.

YEAR 1

• Take three 600-level year-long mathematics sequences. It is suggested that these sequences include analysis (641-642) and algebra (671-672).
• Attend the weekly graduate seminar (or a research seminar, as directed by your advisor).
• Select an area of specialty an advisor and advisory committee.
• Prepare a study list in consultation with your advisor (due by the first week of second year).
• Pass three written qualifying examinations by the end of the year.

YEAR 2

• Take 9 credit hours of advanced graduate courses each semester, ideally in year-long sequences (Dissertation hours may suffice for some of these credit hours)
• Attend a weekly research seminar, as directed by your advisor.
• Begin work on the language requirement.
• Complete the oral qualifying examination.

YEAR 3

• Continue taking advanced graduate courses.
• Actively participate in research seminars.
• Begin work toward a dissertation.
• Complete the language requirement.

YEAR 4

• Devote primary attention to finishing the dissertation.
• Continue participating in advanced courses and seminars.
• Find research topics to pursue beyond a dissertation and begin to develop a long-term research plan.
• Complete the requirements for the doctoral degree.

Note: It is expected that students attend a seminar of their choice as well as colloquia throughout their programs.

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Financial Support

Most graduate students in mathematics are supported by teaching assistantships. Currently teaching assistants receive between $12,000 and $15,000 per academic year. Some research assistantships are also available, and travel money is available for those students who are making good progress toward a degree, have submitted a program of study, and have an advisor's endorsement.

Guidelines for the Continuation of Financial Support

The Department of Mathematics continues financial support to graduate teaching assistants as much as possible under its budget limitations. Financial support is provided to attract excellent students and to maintain them until completion of a graduate degree. A description of departmental policy regarding continuation of support is given below. The Department reserves the option of flexible interpretation and redefinition of policy.

Continued financial support is recommended for graduate teaching assistants who are making satisfactory progress in an approved program of study and who are judged satisfactory in their teaching duties. Responsible and capable teaching performance is essential for continuation. Incompetent teaching will not be supported, and cases of conspicuous irresponsibility or neglect will be cause for immediate termination.

Teaching Assistants in the Master's Degree Program

1. For students in their first year of study for a master's degree, evaluations are made at the end of the fall semester by the Graduate Committee. Decisions are based on teaching performance and on progress in graduate courses. A student must make satisfactory progress in at least six hours of graduate mathematics each semester throughout the program unless special permission is granted.
   
2. Teaching assistants generally are supported for two years in the master's degree program. These appointments automatically terminate, without any special notice, at the end of the second year. In rare cases a student may request support for an additional semester or year by making a written request and an explanation of extenuating circumstances to the student's graduate committee. The student's committee reviews the request and submits a written recommendation to the departmental graduate committee.

Teaching Assistants in the Ph.D. Program

1. For students in years zero or one, evaluations are made by the Graduate Committee at the end of fall semester. Decisions are based on teaching performances and progress in graduate courses.
   
2. Teaching assistants beyond their first year in the Ph.D. program will be evaluated by the graduate committee early in the Winter Semester. Decisions are based on teaching performances and on progress toward a Ph.D. degree, following the schedule outlined earlier. In some cases, renewals may be contingent upon the completion of specific requirements, e.g., a satisfactory performance on the qualifying examination.

Employment Outside the Mathematics Department

You should find your combined obligations in teaching and studying to be a full-time undertaking. The Department of Mathematics does not permit teaching assistants to assume any additional form of employment.

Teaching Loads and Tuition Waivers

The normal teaching load for a teaching assistant in the master's degree program is the equivalent of two three-hour sections for both semesters. For Ph.D. students the teaching load is the equivalent of two three-hour sections for one semester and one three-hour section for the other semester. In some cases a slightly lighter load might be assigned without a reduced stipend.

Full tuition for mathematics courses will generally be provided in addition for teaching and research assistants for fall and winter semesters, provided they make adequate progress in their program of study and regularly attend the graduate seminar. Tuition may also be paid in spring and summer, depending on department budget constraints.

The department will not pay additional tuition for courses that are not on the student's program of study. For example, a student enrolled in 6 hours of mathematics courses and 3 hours of dance courses will have his/her tuition paid only for the 6 hours of mathematics courses. However, a student who is enrolled full-time (9 hours) in mathematics courses will have her/his full-time tuition paid by the mathematics department and thus may take additional non-mathematics courses without charge.

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Courses and Seminars

Part of becoming an independent mathematician is becoming exposed to a broad range of mathematical research as well as studying some specific areas in greater depth. Therefore, it is expected that students attend colloquia and a seminar of their choice. Students receiving tuition awards are expected to attend the graduate seminar (or, with the approval of their advisor, a research seminar) at least 11 weeks per semester.

The graduate seminar is a weekly seminar organized by the Graduate Student Advisory Committee. Its purpose is to acquaint students to the faculty and their research, prepare students for the department colloquia, and to permit students an opportunity to share their research with other students. As a student advances in the program, it will generally be expected that she/he will attend a regular research seminar instead or in addition.

The research seminars usually include the following.
Algebraic Geometry
Number theory,
Partial Differential Equations
Mathematical Physics
Geometric Analysis
Topology

Other seminars also run from time to time. Please see the Seminar Page for more information.

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Course Offerings

We have 15 core courses that are regularly scheduled and that are mainly for first year students. The remaining courses (about 13) are determined according to the needs of the current graduate students, in the manner described below.

Core Courses

The core courses are of two sorts:

First, 11 courses will be taught every year.

510 Linear Algebra
511 512 Numerical Analysis
541 542 Real Analysis
551 552 Topology
532 Complex Analysis
547 PDE
570 Matrix Analysis
671 672 Algebra

Second, 8 courses will be taught on alternate years (i.e. 4 per year).

521 522 Applied Math (every other year, alternate with 534)
534 Dynamical Systems (every other year, alternate with 521,522)

587 588 Number Theory (every other year, alternate with 561,562)
561 562 Algebraic geometry (every other year, alternate with 587,588)

Non-core courses

All other courses are determined in January, seven months before the new academic year starts, in the following manner:

All students should submit their program of study by the end of November of their first year. Students must also submit an additional list to the secretary giving a schedule of when the student plans to take the courses in her/his program of study. Students should consult with their advisors to select the most beneficial courses, and to decide when they should take them. The graduate committee uses these lists to determine which classes will be taught the next year, and to ensure that students' coursework needs are met.

Rough Guide to Past Course Offerings

Fall Odd	Winter Even		Fall Even	Winter Odd
511	512		511	512
521	522		521	522
	532			532
541	542		541	542
	547			547
551	552		551	552
			561	562
	570			570
			621	622
590	591		590	591
634	635		634	635
641	642		641	642
	643R
645	646
			647	648
651	652
			655	656
663	664
671	672		671	672
676	677
			687R	688R
	751R			751R

Course Descriptions of Approved Courses

511. Numerical Methods for Partial Differential Equations. (3)
Prerequisite: Math 311, 303 or 347.
Finite difference and finite volume methods for partial differential equations. Stability, consistency, and convergence theory.

512. Numerical Analysis. (3)
Prerequisite: Math 311, 343, or instructor's consent.
Numerical matrix algebra, orthogonalization and least squares methods, unsymmetric and symmetric eigenvalue problems, iterative methods, Lanczos methods, advanced solvers for partial differential equations.

513R. Advanced Topics in Applied Mathematics. (3)
Prerequisite: instructor's consent.

521, 522. Methods of Applied Mathematics. (3)
Prerequisite: Math 334, 343; or equivalents.
Survey of current methods, continuous and discrete, including linear algebra, estimation, differential equations of equilibrium, eigenvalue and initial value problems; finite element, spectral, transform and difference methods; Fourier series, the Fourier matrix, fast Fourier transform; convolution.

530. Calculus of Variations. (3)
Prerequisite: Math 334; 343. Recommended: Math 315, 347. Euler-Lagrange equation, sufficient conditions, Hamilton’s principle of least action, Dirichlet’s principle; applications to mechanics, geometry, economics, eigenvalue problems, direct methods.

532. Complex Analysis. (3)
Prerequisite: Math 332 or instructor's consent.
Theory of complex analysis at the beginning graduate level. Topics: Cauchy integral equations, Riemann surfaces, Picard's theorem, etc.

534. Introduction to Dynamical Systems I. (3)
Prerequisite: Math 315, 334; or equivalent.
Discrete dynamical systems; iterations of maps on the line and the plane; bifurcation theory; chaos, Julia sets, and fractals. Computational experimentation.

535. Introduction to Dynamical Systems 2. (3)
Continuous dynamical systems; introduction to invariant manifold theory; bifurcation theory; low-dimensional chaotic systems; attractors.

541, 542. Real Analysis. (3)
Prerequisite: Math 214, 315, 343 for 541; Math 541 for 542.
Rigorous treatment of differentiation and integration theory, Lebesque measure, Banach spaces.

543. Advanced Probability. (3)
Prerequisite: Math 214, Stat 441.
Advanced combinatorial methods, random walk, Markov chains, and stochastic processes.

547. Partial Differential Equations. (3)
Prerequisite: Math 214, 334; or equivalents.
Topics from elliptic equations, heat equations; wave equations, stability, Fourier methods, energy methods, existence of solutions, etc.

551, 552. Introduction to Topology. (3)
Prerequisite: Math 315 for 551; Math 551 for 552.
Axiomatic treatment of linearly ordered spaces, metric spaces, arcs, and Jordan curves; types of connectedness.

561, 562. Introduction to Algebraic Geometry. (3)
Prerequisite: Math 671 or concurrent enrollment.
Projective varieties, curves, surfaces, differential forms, and divisors.

565. Differential Geometry. (3)
Prerequisite: Math 214, 315.
Curves, surfaces, first and second fundamental forms, Gauss map, curvatures, geodesics, minimal surfaces, and the Gauss-Bonnet theorem.

570. Matrix Analysis. (3)
Prerequisite: Math 343; for 302, 303; or equivalents.
Special classes of matrices, canonical forms, matrix and vector norms, localization of eigenvalues, matrix functions, applications.

587. Introduction to Analytic Number Theory (3)
Prerequisite: Math 332
Arithmetical functions; distribution of primes; Dirichlet characters; Dirichlet's theorem; Gauss sums; primitive roots; Dirichlet L-functions; Riemann zeta function; prime number theorem; partitions.

588. Introduction to Algebraic Number Theory. (3)
Prerequisite: Math 372
Algebraic integers; different and discriminant; decomposition of primes; class group; Dirichlet unit theorem; Dedekind zeta function; cyclotomic fields; valuations; completions.

621, 622. Matrix Theory. (3)
Prerequisite: Math 570
Zero-one matrices, spectra of graphs, Laplacian matrix, irreducible and primitive matrices, cycle expansion of the determinant, matrix completion problems, permanents, generalized matrix functions.

631, 632. Complex Analysis. (3)
Prerequisite: Math 332, 542 for 631; Math 631 for 632.

634, 635. Theory of Ordinary Differential Equations. (3)
Prerequisite: Math 315, 334.

641, 642. Functions of Real and Complex Variables. (3)
Prerequisite: Math 542 or instructor's consent for 641; Math 641 for 642.

643R. Special Topics in Analysis. (3)
Prerequisite: Math 642 or instructor's consent.
Continued fractions, stochastic processes, generalized functions, etc.

644. Harmonic Analysis. (3)
Prerequisite: Math 532, 542.
Harmonic analysis on the torus and in Euclidean space; pointwise and norm convergence of Fourier series and functional-analytic aspects of Fourier transforms emphasized.

645, 646. Functional Analysis. (3)
Prerequisite: Math 641 for 645; Math 645 for 646.

647, 648. Theory of Partial Differential Equations. (3)
Prerequisite: Math 347, 542 for 647; Math 647 for 648.

651, 652. General Topology 1, 2. (3)
Prerequisite: Math 552.

655. Algebraic Topology 1. (3)
Prerequisite: instructor's consent.

656. Algebraic Topology 2. (3)
Prerequisite: Math 655.

663, 664. Algebraic Geometry. (3)
Prerequisite: Math 672; Math 676 or concurrent enrollment.
Varieties, sheaves, and schemes; their cohomology and classification; applications.

671, 672. Algebra. (3)
Prerequisite: Math 372 for 671; Math 671 for 672.

675R. Special Topics in Algebra. (3)
Prerequisite: Math 672.

676. Commutative Algebra. (3)
Prerequisite: Math 671, 672.
Commutative rings, modules, tensor products, localization, primary decomposition, Noetherian and Artinian rings, application to algebraic geometry and algebraic number theory.

677. Homological Algebra.
Prerequisite: Math 671, 672.
Chain complexes, derived functors, cohomology of groups, ext and tor, spectral sequences, etc. Application to algebraic geometry and algebraic number theory.

687R. Topics in Analytic Number Theory. (3)
Prerequisite: Math 387, 372, 532, and instructor's consent.
Current topics of research interest.

688R. Topics in Algebraic Number Theory. (3)
Prerequisite: Math 372, 387 and instructor's consent.
Current topics of research interest.

695R. Readings in Mathematics. (1-2)

698R. Master's Project. (2)

699R. Master's Thesis. (1-9)

751R. Advanced Special Topics in Topology. (3)
Prerequisite: instructor's consent and Math 651, 652.
Current topics in topology of research interest.

799R. Doctoral Dissertation. (Arr.)

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Graduate Faculty and Areas of Interest

Algebraic Geometry

• Tyler Jarvis: Algebraic Curves, Moduli Spaces
• William E. Lang: Algebraic Surfaces

Applied Mathematics, Nonlinear PDEs and Dynamical Systems

• Lennard Bakker: Dynamical Systems and Celestial Mechanics
• Shue-Sum Chow: Numerical Analysis
• Todd Fisher: Dynamical Systems
• Scott Glasgow: Optics: classical and quantum
• Christopher P. Grant: Nonlinear Partial Differential Equations, Dynamical Systems
• Jeff Humpherys: Applied Mathematics, Nonlinear Partial Differential Equations, Dynamical Systems
• Kenneth Kuttler: Abstract Methods for Nonlinear Partial Differential Equations and Inclusion
• Kening Lu: Applied Mathematics, Nonlinear Partial Differential Equations, Dynamical Systems
• Tiancheng Ouyang: Nonlinear Partial Differential Equations
• Vianey Villamizar: Numerical Solution of PDEs, Wave Scattering, Asymptotic Methods

Applications of Mathematics to Biology and Medicine

• John Dallon: Mathematical Biology
• William Smith: Mathematical Biology, Partial Differential Equations, Functional Analysis

Combinatorics and Matrix Theory

• Wayne W. Barrett: Combinatorial Matrix Theory, Positive Definite Matrices
• Rodney W. Forcade: Combinatorics, Number Theory, Graph Theory
• L. Kirk Tolman: Ordered Rings and Fields, Graph Theory

Geometric Topology, Geometric Group Theory, Topology, Combinatorial Group Theory

• James W. Cannon: Geometric Topology, Geometric Group Theory, Discrete Conformal Mapping
• Gregory Conner: Geometric Group Theory, Topology, Combinatorial Group Theory
• Michael Dorff: Minimal surfaces, Geometric Function Theory
• Lawrence Fearnley: Topology, Limits, Spaces, Topology of Manifolds
• Denise Halverson: Geometric Topology
• Stephen Humphries: Low-dimensional Topology, Group Theory
• Jessica Purcell: Three-dimensional manifolds, hyperbolic geometry, and knot theory.
• Eric Swenson: Geometric Group Theory, Topology
• David G. Wright: Geometric Topology, Mathematics Education

Number Theory

• Roger Baker: Number Theory
• David A. Cardon: Analytic Number Theory, Algebraic Number Theory, Automorphic Forms
• Jasbir S. Chahal: Number Theory
• Darrin Doud: Number Theory
• Rodney W. Forcade: Combinatorics, Number Theory, Graph Theory
• Xian-Jin Li: Analytic Number Theory