These are the Department of Mathematical and Statistical Sciences Legacy Pages

Graduate Handbook

UC Denver Department of Mathematical & Statistical Sciences

Last Revision: December 11, 2009

CONTENTS

Degrees

Prerequisites for Graduate Studies in Applied Mathematics

Deadlines

Advising

Requirements for the M.S. Degree

1. General Requirements
2. Math Clinic
3. Advisory Committee
4. Thesis Option
5. Final Examination
6. Time Limits for Completion of Degree
7. Leave of Absence
8. Course Requirements by Area

a. Applied Statistics
b. Applied Probability
c. Computer Science
d. Discrete Mathematics
e. Mathematics of Engineering and Science
f. Numerical Analysis
g. Operations Research
h. Computational Biology

Requirements for the Ph.D. Degree

Admission to the Ph.D. Program

Graduation Requirements

1. Course requirements
2. Preliminary examinations
3. Ph.D. Committee
4. Residency and Participation
5. Comprehensive Examination
6. Thesis Proposal
7. Thesis
8. Language Requirement
9. Time Limits
10. Leave of Absence

Transitional Rules

Exceptions

Degrees

The Department of Mathematical & Statistical Sciences at UC Denver offers the Master of Science (M.S.) in Applied Mathematics and the Doctor of Philosophy (Ph.D.) in Applied Mathematics. These degrees are designed to give candidates a contemporary, in-depth education in applied mathematics and to provide research opportunities in the special fields of computational mathematics, computational biology, discrete mathematics, mathematics of science and engineering, operations research, optimization, probability, and statistics.

Prerequisites for Graduate Studies in Applied Mathematics

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Admission Deadlines

Advising

Upon acceptance into the graduate program, each student is assigned an academic advisor. A student may request and obtain a change in advisor by informing the Graduate Program Assistant.

A required orientation for all new graduate students is held the week before the fall semester begins. The orientation provides information about the department, the faculty, graduate program requirements, expectations and realities, and an opportunity for students to meet with individual faculty advisors.

During the first semester of graduate study each student is required to set up a tentative plan of study with the advisor's help. The plan of study, which becomes part of the student's file, should include a tentative list of courses to be taken each semester. Both the advisor and the student will sign the plan, which should be reviewed at least once each year with the current advisor. All course substitutions must be approved on the study plan. 

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Requirements for the M.S. Degree

1. General Requirements

Students must complete at least 30 semester hours, of which at least 24 hours must be in mathematics courses numbered 5000 or above. At most six hours may be in courses outside the Department of Mathematical & Statistical Sciences at the 4000 level or above, if approved by the student's advisor and by the Graduate Committee. The overall grade point average must be 3.0 or higher. Grades below a B- are not accepted (but they do contribute to the overall GPA).

By graduate school rules, courses taken more than five years prior to applying for candidacy (including transfer courses) must be validated by the graduate program director to ensure their content is still current. However, it is the policy of the Department of Mathematical and Statistical Sciences that the content of all mathematics courses taken at an accredited University is considered current for at least ten years. For courses taken more than ten years prior to applying for candidacy, the validation process will require an assessment of the student's knowledge of the subject matter.

Exception: Note that the Computational Biology option has a special provision that students may take up to 9 hours outside the Department of Mathematical & Statistical Sciences.

A maximum of 9 credit hours of coursework may be transferred into the M.S. program. Only courses completed with a grade of B- or better may be considered for transfer credit. Credit cannot be transferred until the student has established a satisfactory record of at least one term of full-time enrollment at UC Denver with a minimum GPA of 3.0. All transfer courses must be approved by the graduate committee. Courses taken while registered as a nondegree student are considered transfer courses.

By graduate school rules, courses taken while enrolled as a graduate student at any campus of the University of Colorado system is considered resident coursework. However, all courses taken outside of the Department of Mathematical and Statistical Sciences must be approved by the graduate committee to be applied toward the M.S. degree. In addition, courses taken at other campuses prior to enrollment in the M.S. program will be counted as part of the 9 credit hour limit on transfer courses. Courses taken outside the Department of Mathematical and Statistical Sciences while enrolled in the M.S. program should be approved in advance in order to be counted toward the M.S. degree. The following courses will not count toward a graduate degree in applied mathematics:

2. Math Clinic

All students are encouraged to participate in at least one Math Clinic. With the approval of the student's advisor, a clinic may be used in lieu of a stated area requirement. Details about current and upcoming projects are available from the Clinic Director.

3. Advisory Committee

By the end of the first year of graduate study, each student must choose an advisor to chair the advisory committee. With this advisor's help, the student will choose two additional members of the advisory committee. All three members must be on the UC Denver Graduate Faculty, and at least two must be members of the Department of Mathematical & Statistical Sciences.

4. Thesis Option

Each student is encouraged to write a thesis to which 4-6 of the 30 hours of course work may be devoted. Although original work is encouraged, the thesis may be expository in nature. The topic should be within a relevant area of applied mathematics and should be chosen with the approval of the advisor. The thesis should be prepared in TeX, LaTeX, or AMSTeX (thesis templates available), and it must comply in format with the specifications of the Graduate School. A typed copy of the thesis must be given to all members of the advisory committee at least three weeks before the defense. Eighteen days before the date of graduation, three complete copies of the thesis must be filed with the Graduate School. The student must provide a single .pdf file of the thesis with an attached statement giving the Department the right to distribute the thesis as it wishes.

5. Final Examination

All students must take and pass a final oral exam. The exam is given by the student's advisory committee.

For students choosing the thesis option, the exam consists of a one-hour thesis defense. The advisory committee may declare the thesis defense successful, but request further changes in the thesis and specify a deadline and the manner in which the revised thesis will be reviewed. In that case, the student does not need to register for further thesis credit hours, but the requirements for the Master's degree are not satisfied until the final version of the thesis is approved by the student's advisory committee and the Graduate School. If no member of the advisory committee raises further questions or objections within 30 days after the revised thesis has been received by the advisor, the thesis is considered approved by the advisory committee.

Students choosing the non-thesis option will give a one-hour presentation and answer questions on a relatively specific topic that has been selected in consultation with the advisor. Students completing a Master's degree while pursuing a Ph.D. degree are encouraged to choose a topic that will advance their Ph.D. research. A student who does not pass the exam on the first attempt may take it again after three months; however, the retake must be completed by the end of the next academic semester. Guidelines for oral presentations and thesis defenses are available in the Department of Mathematical & Statistical Sciences.

6. Time Limits for Completion of Degree

By graduate school rules, Master's degree students have five years from the date of admission to complete all degree requirements.

7. Leave of Absence

A student may request up to a one-year leave of absence from the M.S. program. The student must be in good standing, indicate the return date, give justification for the leave of absence, and agree to contact his/her advisor and the Graduate Committee at least once per semester. Each petition must be approved by the Graduate Committee.

A leave of absence pauses the clock, but does not extend deadlines automatically; extension of deadlines requires a separate petition to the Graduate Committee. Students who leave a graduate program for more than three consecutive semesters must reapply for admission.

8. Course Requirements by Area

The core courses Math 5070 (Applied Analysis) or Math 6131 (Real Analysis), and Math 5718 (Applied Linear Algebra) are required of all M.S. students. In addition, the requirements in one of the following areas must be satisfied. Substitutions may be made with the advisor's written approval. One course cannot be used to fulfill two requirements.

a. Applied Statistics

b. Applied Probability

c. Computer Science

d. Discrete Mathematics

e. Mathematics of Engineering and Science

f. Numerical Analysis

g. Operations Research

h. Computational Biology

Requirements for the Ph.D. Degree

Admission to the Ph.D. Program

Graduation Requirements

There are six phases to the Ph.D. program. A candidate must fulfill course requirements, pass the preliminary examinations, meet the academic residency and participation requirements, pass the comprehensive examination, give an oral thesis proposal, and write and defend a thesis.

1. Course Requirements

Ph.D. students must complete 42 credit hours of non-dissertation graduate courses. The following courses will not count toward a graduate degree in applied mathematics: Math 5000-5010, Math 5012-5015, Math 5017, Math 5198, and Math 5250.

The following courses are required as a part of the formal course work:  

• 4 PhD level courses (3 hours each).
• Math Clinic (Math 5779) (3 hours)
• 3 Readings Courses (Math 7921-7926) (1 credit hour each.)

The Readings Courses are one-hour seminar courses that are announced prior to the start of each semester. All courses should be chosen in consultation with an advisor. Course replacements and equivalencies should be approved by the Graduate Committee.

Within the coursework requirement, students must satisfy a breadth requirement by completing six graduate math courses from the following categories. No more than three of these courses can come from any one category:

1. Computational Mathematics
2. Discrete Mathematics
3. Operations Research (including Probability)
4. Statistics
5. General

A maximum of 30 credit hours of graduate coursework (including courses applied to a Master's degree), may be transferred into the Ph.D. program. Up to 6 credit hours of this 30 may be awarded for a Master's thesis. Only graduate courses completed with a grade of B- or better may be considered for transfer credit. Credit cannot be transferred until the student has established a satisfactory record of at least one term of full-time enrollment at UC Denver with a minimum GPA of 3.0. All transfer courses must be approved by the graduate committee. Courses taken while registered as a nondegree student are considered transfer courses. By graduate school rules, courses taken while enrolled as a graduate student at any campus of the University of Colorado system is considered resident coursework. However, all courses taken outside of the Department of Mathematical and Statistical Sciences must be approved by the graduate committee to be applied toward the Ph.D. In addition, courses taken at other campuses prior to enrollment in the Ph.D. program will be counted as part of the 30 credit hour limit on transfer courses. Courses taken outside the Department of Mathematical and Statistical Sciences while enrolled in the Ph.D. program should be approved before they are taken in order to be counted toward the Ph.D. degree.

All Ph.D. course work must be completed with at least a 3.25 grade point average. Grades below a B- are not acceptable for the Ph.D. A student who receives a grade of C+ or lower, or whose overall GPA as a doctoral student falls below 3.25 will be reviewed by the Graduate Committee and may be put on probation or suspended.

2. Preliminary examinations

Each student must pass two preliminary exams: one in Applied Analysis and one in Applied Linear Algebra. These are four-hour written exams that cover material roughly at the level of first-year graduate study. The exams are offered twice a year, from 10:00 am to 2:00 pm. The first set of exams are offered in January. The Applied Analysis preliminary exam will be held the Monday prior to the start of classes, and the Applied Linear Algebra exam is offered the Friday before the start of classes. The second exam offerings follow the spring semester. The Applied Linear Algebra exam is held the Friday before the start of the summer semester, and the Applied Analysis exam is offered the first Friday of the summer semester.

A student wishing to take a preliminary exam must sign up with the graduate program assistant at least one month prior to the administration of the exam. Students who cannot take the exam as planned must give notice of withdrawal at least one week prior to the exam.

Students have a maximum of three attempts to pass each exam (including attempts prior to enrolling in the Ph.D. program). The time limit clock starts the first semester a student is admitted into the program.

• Students entering the Ph.D. program without a master's degree in mathematics have three years to pass both preliminary exams.

• Students entering the Ph.D. program with a master's degree in mathematics have two years to pass both preliminary exams.

3. Ph.D. Advisory Committee

Each student must choose an advisor and, with the advisor's help, select other members of the Ph.D. advisory committee. This committee assumes the dual responsibility for advising and testing the student. In particular, under the direction of the advisor, each member of this commitee will:

1. Design and evaluate the Comprehensive Exam;
2. Advise on research and serve as the the examining committee for the student's dissertation defense.

The Ph.D. advisory committee consists of five graduate faculty members from the CU system, one of whom is the student's advisor. At least one committee member must have their primary and prior affiliations outside of the Department of Mathematical & Statistical Sciences. At least three committee members will be regular faculty members of the Department of Mathematical & Statistical Sciences. Exceptions to this must be approved by the graduate committee. Committee members may be from outside the CU system, but must be granted special membership on the graduate faculty for this purpose. The chair of the Ph.D. advisory committee must be a regular faculty member of the Department of Mathematical & Statistical Sciences. Under graduate school rules, the thesis advisor cannot be the chair of the committee. The thesis advisor may be affiliated with another university department, a government lab, or industry, subject to approval by the Graduate Committee, and subject to approval of a special appointment to the graduate faculty.

4. Enrollment and Participation

By Graduate School rules, all doctoral students must be enrolled for a minimum of six (6) semesters of full time scholarly work beyond the attainment of a bachelor's degree. Two of these six semesters may be replaced by a master's degree in mathematics from another institution; however, at least four (4) semesters of credit must be earned for work performed while enrolled at UC Denver. For this purpose a full course load is defined to be five semester hours of course work.

Ph.D. students are expected to participate in the life of the department by attending colloquia, seminars, orientations and other department activities and by spending time on campus interacting with other students and faculty outside of normal class hours. Students should discuss with their advisors how to fulfill the spirit of this requirement.

5. Comprehensive Examination

Application for candidacy to the Ph.D. program must be made at least two weeks before the comprehensive examination is taken. Candidacy will be granted after at least three semesters of residence have been earned, an advisory committee has been selected, all preliminary and comprehensive examinations have been passed, and essentially all course requirements (including the breadth requirement) have been satisfied.

The comprehensive exam has the following objectives: to determine mastery of graduate level mathematics, capacity to synthesize mathematical concepts, and ability to embark upon doctoral thesis research. The comprehensive exam has two parts:

1. The first part consists of a written exam of roughly (but not limited to) six hours. The written exam covers material from the student's intended area of research. The choice of area and the extent of coverage within that area will be determined by the student's advisory committee. The advisory committee will prepare and conduct the exam and determine the outcome. The written exam has three possible outcomes: pass, conditional pass, and failure.

2. Given a conditional pass on the written exam, the second part of the exam consists of an oral follow-up, not to exceed two hours in length. The student will be given a copy of the graded written exam, no later than seven days after that exam, and a list of topics in which the committee found the student deficient. The oral follow-up will cover questions on the written exam and topics on the list provided to the student. The oral exam is open to the public and must be scheduled and advertised through the graduate program assistant at least two weeks prior to the exam. The oral must be given within four weeks of returning the graded exam to the student, and it has two possible outcomes: pass or failure based on a majority vote of the committee.

"In the event of failure of either the written exam or oral follow-up, the student's advisory committee will determine the next step (dismissal from the program, retake of the oral follow-up and/or a retake of the written exam are possible outcomes). If a retake is allowed, the retake must be completed within 12 months. The Graduate Committee will hear grievances and appeals of the outcome of the comprehensive exam.

All members of the advisory committee must be present for the oral exam; however, a minority of members, but not the chairperson nor the student, may participate by interactive video. In the event of an emergency that prevents one committee member from attending the exam, the exam can proceed with the faculty who can attend. However, the student will need to meet with the absent committee member at an alternate time.

Admission to candidacy follows successful completion of the two parts of the comprehensive exam.

6. Thesis Proposal

Within six months of successful completion of the written exam and/or oral follow-up, the student must give an oral research proposal before the advisory committee. The purpose of this presentation is to determine the feasibility of the student's proposed thesis topic. The research proposal is open to the public and must be scheduled and advertised through the graduate program assistant at least two weeks prior to the presentation. The student will be provided a detailed summary of the committee's assessment and recommendations. At the discretion of the advisory committee, a student may be asked to give a subsequent oral proposal at a later date.

7. Thesis

Each student must complete at least 30 hours of thesis credit. Not more than 10 of these hours may be taken in any one semester. Not more than 10 thesis hours taken prior to the semester of the comprehensive examination may be applied to this requirement.

Candidates for the Ph.D. degree are required to write a dissertation containing original contributions and evidence of significant scholarship. The thesis is written under the guidance of an advisor who is a member of the graduate faculty of the University of Colorado. The thesis must comply in format with the specifications of the Graduate School and must be prepared in TeX, LaTeX, or AMSTeX (thesis templates available). Six weeks before the date of graduation, the Graduate School must be notified by the candidate of the dissertation title. Thirty days before the final thesis defense, the thesis must be available in written form. Eighteen days before the date of graduation, three complete copies of the thesis must be filed with the Graduate School. The student must provide the Department with a .pdf file of the thesis with an attached statement giving the Department the right to distribute the thesis.

At least thirty days before the date of graduation, the candidate must present and defend the dissertation before the student's advisory committee. The defense is open to the public and must be scheduled and advertised through the graduate program assistant at least two weeks in advance. The defense is open to the public and must be scheduled and advertised through the graduate program assistant at least two weeks prior to the exam. All members of the advisory committee must be present for the defense; however, a minority of members, but not the chairperson nor the student, may participate by interactive video. In the event of an emergency that prevents one committee member from attending the exam, the exam can proceed with the faculty who can attend. However, the student will need to meet with the absent committee member at an alternate time. The outcome of the defense can be "pass", "conditional pass", or "fail", as determined by a majority vote of the committee. If the student receives a conditional pass, the examining committee will define requirements that the student must satisfy to pass the defense. These requirements must be completed to the satisfaction of the committee within 60 days. Any extensions to this deadline requires a recommendation from the graduate committee and approval by the graduate school.

The committee may declare the thesis defense successful, but may request further minor changes in the thesis, and specify a deadline and the manner in which the revised thesis will be reviewed. In that case, the student does not need to register for additional thesis hours, but the requirements for the Ph.D. are not satisfied until the final version of the thesis is approved by the advisory committee and the Graduate School. If no member of the committee raises further questions or objections within 30 days after the revised thesis has been received by the advisor, the thesis will be considered approved by the advisory committee.

8. Language Requirement

The University of Colorado permits each department to decide whether or not to implement a foreign language requirement. The Department of Mathematical & Statistical Sciences has approved the following policy:

Recognizing that the need of a foreign language to do research varies from no languages in many areas to one or two languages in a few areas, the department has no formal language requirement. Instead, the necessity for some level of proficiency in a foreign language is left to the discretion of each student's advisor, as is the case for other matters related to a student's preparation for research.

9. Time Limits

Students must select an advisor and a Ph.D. advisory committee by the end of the semester in which all preliminary exams have been passed. Students must pass the comprehensive examination by the end of the fourth year in the Ph.D. program. All requirements for the Ph.D. degree must be completed within four years of passing the comprehensive examination and within eight years of entering the Ph.D. program.

It is recognized that flexibility is necessary, especially for transfer and part-time students; hence petitions for exceptions will be considered by the Graduate Committee. The four year deadline for passing the comprehensive exam and the eight-year deadline for completing the Ph.D. is imposed by the Graduate School and exceptions require approval of the Dean of the Graduate School.

10. Leave of Absence

A student may request up to a one-year leave of absence from the Ph.D. program. The student must be in good standing, indicate the return date, give justification for the leave of absence, and agree to contact his/her advisor and the Graduate Committee at least once per semester. Each petition must be approved by the Graduate Committee.

A leave of absence pauses the clock, but does not extend deadlines automatically; extension of deadlines requires a separate petition to the Graduate Committee. A leave of absence does allow the student to interrupt registration for thesis hours following the comprehensive exam. Students who leave a graduate program for more than three consecutive semesters must reapply for admission.

Transitional Rules

All current M.S. and Ph.D. students have the option of graduating under the current rules or under the rules in effect when they were admitted. See the Graduate Handbook Archive for earlier versions of the rules.

Exceptions

Unless otherwise stated, exceptions to these rules must be approved by the graduate committee. In cases where an exception can be made while still satisfying all requirements of the graduate school, the graduate committee may approve the request with consultation of the students advisory committee. In cases involving exceptions to graduate school rules, the graduate committee, if it approves the exception, will submit a petition to the graduate school, which will then either approve or deny the exception.

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