Graduate Student Handbook
Mathematics and Applied Mathematics
2004

Contents

1. Introduction
2. Graduate Program of Study
3. Requirements for MS and PhD degrees in Mathematics
1. MS program in Mathematics
2. PhD program in Mathematics
3. Co-major PhD degrees
4. Core course requirements
5. Qualifying examinations
6. Oral preliminary and final examinations
7. Graduate English requirements
8. Teaching requirement
4. Requirements for MS and PhD degrees in Applied Mathematics
1. MS program in Applied Mathematics
2. PhD program in Applied Mathematics
3. Co-major PhD degrees
4. Core course requirements
5. Qualifying examinations
6. Oral preliminary and final examinations
7. Graduate English requirements
8. Teaching requirement
5. Satisfactory progress towards the degree
1. MS degree students
2. PhD degree students
1. Students admitted to the PhD program on entering with an M.S.
2. Students admitted to the PhD program on entering without an M.S.
3. Students admitted to the PhD program from the MS program
3. Admission into the PhD program from the MS program
4. Failure to maintain academic standing
5. Grievance procedures
6. Minor requirements for students from other departments
1. Minors in Mathematics
2. Minors in Applied Mathematics

1. Introduction

Graduate degree students in mathematics at Iowa State University must meet requirements specified by the Graduate College, the Department of Mathematics, and the student's program of study (POS) committee. The Graduate College requirements are published in the Graduate College Handbook (GCH). Each graduate student should become familiar with its contents. The requirements specified by the Mathematics Department are described in this document. Requirements specified by the student's POS committee are defined at the time the student's POS committee is formed and the program of study formulated.

The Mathematics Department offers programs leading to M.S. and Ph.D. degrees in both mathematics and applied mathematics. In addition, the Department grants an M.S.M. (Master of School Mathematics) degree which is intended for secondary school mathematics teachers. This document does not address the requirements for the M.S.M. degree.

Listed below is a summary of the most significant requirements of the Graduate College and the Mathematics Department.

1. Graduate English requirement (applies to all international students; see GCH).
2. Core course requirements (see this document).
3. Major professor and POS committee (see GCH).
4. Program of study (see GCH and this document).
5. Written qualifying examination(s) for Ph.D. students (see this document).
6. Supervised teaching requirement for Ph.D. students (see this document).
7. Oral preliminary examination for Ph.D. students (see this document and GCH).
8. Doctoral dissertation, Master's thesis or creative component.
9. Final oral examination (see this document and GCH).

These requirements are imposed to establish certain minimum standards for normal situations. However, some situations may be unusual and require special consideration. Students who believe their circumstances warrant modification of these requirements should petition the Departmental Graduate Committee in writing.

The following sections describe the requirements for graduate degrees in mathematics and applied mathematics. Continuation in the graduate program and financial support is contingent upon satisfactory progress toward a degree. General guidelines for a student making satisfactory progress are outlined in this document.

2. Graduate Program of Study

The Graduate Coordinator (GC) of the Mathematics Department serves as Director of Graduate Education (DOGE) for both the mathematics program and the applied mathematics program. The GC designates a temporary advisor (normally the GC) for all new graduate students in the Mathematics Department. The temporary advisor guides the student in the selection of a field of study and in the development of a graduate program until the major professor and the POS committee are selected. The major professor serves as permanent advisor and as chair of the POS committee. A list of the duties of the POS committee may be found in the GCH.

Timely selection of a major professor, appointment of a POS committee, and development of a program of study are essential requirements. The Graduate College recommends that the committee be formed as early as the beginning of the third semester of graduate study. It should be formed no later than the beginning of the fourth semester for a student in the M.S. program, and the beginning of the fifth semester for a student in the Ph.D. program. The major professor will be selected by the student with the aid of the temporary advisor. The POS committee is selected by the student with the aid of the major professor. Failure to select a major professor impedes progress towards the degree and leads to dismissal from the program. If for any reason the major professor resigns or is removed from their position, and the student is in good academic standing, then the above procedure will be used to select a new major professor and reconstitute the POS committee.

3. Requirements for MS and PhD degrees in Mathematics

The Mathematics Department offers programs leading to both M.S. and Ph.D. degrees in Mathematics.

3(i). M.S. program in Mathematics

For the M.S. program a minimum of 30 acceptable credits is required, with at least 22 of these earned in residence. The total of 30 credits must include 21 hours of 500-600 level mathematics courses, and these 21 hours must include at least 12 hours of core courses subject to the conditions in 3(iv) below. Each student must elect a thesis or non-thesis master's program. For the thesis program, 6 credits of Math 699 may be included in the 30 hours. The non-thesis program requires a creative component including a formal mathematics paper. Three credits of Math 599 may be included in the 30 credits for the creative component; these credits must be identified on the program of study.

Although cognate study (as described in 3(ii) below ) is not required at the M.S. level, it is strongly recommended. When cognate study is in the form of a minor, it consists of 6--9 credits (from the 30 credit total) in a department other than Mathematics. These credits must be acceptable to the representative of the minor department on the student's POS committee.

In addition to the course work, the M.S. student must pass an oral, comprehensive final examination.

A grade of B or better, in the course or on the final examination, must be earned in each core course on the POS (see 3(iv) and 4(iv) below). A grade of C or better must be earned in all other courses on the POS. The student must maintain a cumulative grade point average of at least 3.0 in all course work, exclusive of research credit.

3(ii). Ph.D. program in Mathematics

For the Ph.D. program, a minimum of 72 acceptable credits is required, with at least 36 of these earned in residence. (See the GCH for details regarding credit requirements.) At least 54 credits must be in formal courses (not research); 18 of the 54 must be in the core courses listed in 3(iv) below. In addition, at least 42 must be in 500--600 level mathematics courses excluding Math 590 and Math 699. These 42 credits must include development of mathematical breadth beyond that represented by other specific requirements.

Included in the 54 credits of formal courses is a cognate study requirement. A cognate course is defined to be a course which is (i) acceptable for graduate credit, (ii) taught in another department (a course cross-listed with Mathematics is acceptable if registered as a course in another department), and (iii) relevant to the major. Ph.D. students in Mathematics may satisfy the cognate study requirement by earning 12 credits in cognate courses. The course work for the cognate study requirement must be approved by the student's POS committee. A student may satisfy the requirement by electing a minor in another department.

In addition to the course work, the Ph.D. student must pass two written qualifying examinations and an oral preliminary examination, prepare a dissertation, and pass an oral final examination which is usually limited to the defense of the dissertation. These requirements are described in subsequent sections.

A grade of B or better, in the course or on the final examination, must be earned in each core course on the POS (see 3(iv) and 4(iv) below). A grade of C or better must be earned in all other courses on the POS. The student must maintain a cumulative grade point average of at least 3.33 in graduate level mathematics courses and of at least 3.0 in all course work, exclusive of research credit.

3(iii). Co-major Ph.D. degrees

Well-qualified students are encouraged to consider a Ph.D. program having a co-major in Mathematics and some other appropriate program. Such programs are to be initiated by a written proposal from the student to the Mathematics Department Graduate Committee. The proposal must contain an outline of how all requirements are to be met. Authorization by the Graduate Committee to embark on a co-major program will be based on this proposal, and on the academic history of the student. The POS committee is to be directed by co-chairmen, one from each of the co-major departments. The dissertation must have significant content in both fields. Co-major programs are subject to the following minimum standards.

• Co-major Ph.D. students are required to earn at least 30 credits in 500--600 level mathematics courses other than Math 590 and 699. They are required to take a total of four courses from the mathematics core including at least one one-year sequence (Math 504--505 or Math 515--516). They are also required to pass one of the qualifying examinations described in 3(v) below.
• Co-major Ph.D. students are required to have two years of professional experience including at least one year of supervised teaching. The other year may be supervised research as a research assistant or associate.

3(iv). Core course requirements

The core course requirements are satisfied by taking courses in two areas. The areas and the core courses are

• Algebra -- Math 504, 505 and 510
• Analysis -- Math 515, 516 and 511

• M.S. students must take at least two of the three courses in algebra and at least two of the three courses in analysis
• Ph.D. students must take all six core courses.

In order to maintain flexibility for students to change from Applied Mathematics to Mathematics, core course requirements for the Applied Mathematics degree (see 4(iv) below ) may be substituted for the core course requirements listed above in one of the two areas of algebra or analysis.

A grade of B or better must be earned in each core course. A deficiency may be made up by taking a final examination during a subsequent offering of the course and receiving a grade of B or better, or by passing the corresponding written qualifying examination.

3(v). Qualifying examinations

A Ph.D. student in the Mathematics Program must pass two written qualifying examinations. The student must take a written qualifying examination covering material in two of the following four areas.

• Algebra (see the Algebra Qualifying Examination Syllabus )
• Real and Complex Analysis (see the Analysis Qualifying Examination Syllabus )
• Methods of Applied Mathematics (see the Applied Mathematics Qualifying Examination Syllabus )
• Numerical Analysis (see the Numerical Analysis Qualifying Examination Syllabus )

Students are strongly encouraged to consult their major professor prior to deciding which examinations to take, since certain examination combinations may not be suitable for certain areas of research.

A student taking an examination will be responsible for the topics listed in the appropriate syllabus. These topics are normally covered in the appropriate core courses as listed below:

• Algebra: Math 504--505 and Math 510.
• Real and Complex Analysis: Math 515--16 and Math 511.
• Methods of Applied Mathematics: Math 519--520.
• Numerical Analysis: Math 502--503.

However, the qualifying examination syllabi are definitive, and not all topics on the syllabi are covered each year in the appropriate courses. It is the student's responsibility to be prepared to answer questions about any topic on the appropriate syllabus.

A student will be allowed two attempts to pass a given qualifying examination. A student who fails the same qualifying examination twice may appeal in writing to the Graduate Committee to take it a third time if supported by a majority of the appropriate Qualifying Examination Committee. More than two failures on any combination of qualifying exams constitute grounds for dismissal from the Ph.D. program.

Students must request the examination in advance via the GC. This is usually done the semester before the scheduled examination so that a committee may be formed to write and grade the examination. Requests can be canceled before 4pm on the day preceding the day of the exam. If an examination is requested and not canceled, it counts as one attempt (whether or not the examination is actually written). The examinations are usually given twice a year: in August before or at the beginning of the Fall semester, and in January before or at the beginning of the Spring semester.

3(vi). Oral preliminary and final examinations

The oral preliminary examination tests a student's knowledge of the major, minor and supporting fields of their research area. The examination is taken after a student has passed both written qualifying examinations, satisfied the graduate English requirement, formed a POS committee, and has an approved POS form. A student who fails the preliminary oral examination is allowed to retake it one additional time. Six months must elapse between the first attempt and the second. The preliminary oral examination must be passed at least six months prior to the final defense, unless an exception is allowed by the Dean of the Graduate College. A form requesting scheduling of the examination must be submitted to the Graduate College at least two weeks before the proposed date of the examination.

The final examination of an M.S. candidate is oral and comprehensive. It normally consists of a defense of the thesis or creative component and an examination of the candidate's knowledge of the topics covered in the program of study.

The final examination of a Ph.D. candidate is oral, and is usually limited to a defense of the dissertation.

3(vii). Graduate English requirements

Graduate students whose native language is English are no longer required to take an English diagnostic test. See http://www.grad-college.iastate.edu/about/englishexamination.html.

Graduate students whose native language is not English, and who do not have a bachelor's degree from ISU, must take the English Placement Test at the beginning of their first semester of enrollment. A student who does not pass this examination is assigned to one or more courses in the English 101 series. This course work must be completed during the first year of study. (See the GCH for details.)

Graduate students whose native language is not English, but who do have a bachelor's degree from a U.S. institution, are no longer required to take the Graduate English Examination for International Students.

3(viii). Teaching requirement

Each Ph.D. student is required to have one year of supervised teaching. However, if approved by the student's POS committee, equivalent supervised experience in oral mathematics communication may be substituted for teaching. In that case the POS committee must specify in writing what the equivalent experience will be.

Every teaching assistant must demonstrate an ability to teach effectively. To assure this, before the beginning of the first semester they assumes their duties, teaching assistants are required to give a short, prepared lecture to a panel of experienced teaching assistants and/or faculty that is suitable for an algebra, trigonometry, or similar class. In addition, each teaching assistant whose native language is not English must take the SPEAK/TEACH test (the test administered by the University to screen applicants for classroom duties). They must pass it at the first or second level before they are assigned a class or recitation section, and they must pass it at the first or second level within their first year of residence to guarantee continued financial support.

4. Requirements for MS and PhD degrees in Applied Mathematics

The Mathematics Department offers programs leading to both M.S. and Ph.D. degrees in Applied Mathematics.

4(i). M.S. program in Applied Mathematics

For the M.S. program a minimum of 30 acceptable credits is required, with at least 22 of these earned in residence. The total of 30 credits must include 21 hours of 500-600 level mathematics courses, and these 21 hours must include at least 12 hours of core courses subject to the conditions in 4(iv) below. Each student must elect a thesis or non-thesis master's program. For the thesis program, 6 credits of Math 699 may be included in the 30 hours. The non-thesis program requires a creative component including a formal mathematics paper. Three credits of Math 599 may be included in the 30 credits for the creative component; these credits must be identified on the program of study.

Although cognate study (as described in 4(ii) below ) is not required at the M.S. level, it is strongly recommended. When cognate study is in the form of a minor, it consists of 6--9 credits (from the 30 credit total) in a department other than Mathematics. These credits must be acceptable to the representative of the minor department on the student's POS committee.

In addition to the course work, the M.S. student must pass an oral, comprehensive final examination.

A grade of B or better, in the course or on the final examination, must be earned in each core course on the POS (see 4(iv) below). A grade of C or better must be earned in all other courses on the POS. The student must maintain a cumulative grade point average of at least 3.0 in all course work, exclusive of research credit.

4(ii). Ph.D. program in Applied Mathematics

For the Ph.D. program, a minimum of 72 acceptable credits is required, with at least 36 of these earned in residence. (See the GCH for details regarding credit requirements.) At least 54 credits must be in formal courses (not research); 18 of the 54 must be in the core courses listed in 4(iv) below. In addition, at least 42 must be in 500--600 level mathematics courses excluding Math 590 and Math 699. These 42 credits must include development of mathematical breadth beyond that represented by other specific requirements.

Included in the 54 credits of formal courses is a cognate study requirement. A cognate course is defined to be a course which is (i) acceptable for graduate credit, (ii) taught in another department (a course cross-listed with Mathematics is acceptable if registered as a course in another department), and (iii) relevant to the major. Ph.D. students in Applied Mathematics may satisfy the cognate study requirement by earning 12 credits in cognate courses. The course work for the cognate study requirement must be approved by the student's POS committee. A student may satisfy the requirement by electing a minor in another department.

In addition to the course work, the Ph.D. student must pass two written qualifying examinations, pass an oral preliminary examination, prepare a dissertation, and pass an oral final examination which is usually limited to the defense of the dissertation. These requirements are described in subsequent sections.

A grade of B or better must be earned in each core course, and a grade of C or better in all other courses of the POS. The student must maintain a cumulative grade point average of at least 3.33 in graduate level mathematics courses and of at least 3.0 in all course work, exclusive of research credit.

4(iii). Co-major Ph.D. degrees

Well-qualified students are encouraged to consider a Ph.D. program having a co-major in Applied Mathematics and some other appropriate program. Such programs are to be initiated by a written proposal from the student to the Mathematics Department Graduate Committee. The proposal must contain an outline of how all requirements are to be met. Authorization by the Graduate Committee to embark on a co-major program will be based on this proposal, and on the academic history of the student. The POS committee is to be directed by co-chairmen, one from each of the co-major departments. The dissertation must have significant content in both fields. Co-major programs are subject to the following minimum standards.

• Co-major Ph.D. students are required to earn at least 30 credits in 500--600 level mathematics courses other than Math 590 and 699. They are required to take a total of four courses from the applied mathematics core including at least one one-year sequence (Math 502--503 or Math 519--520). They are also required to pass one of the qualifying examinations described in 4(v) below.
• Co-major Ph.D. students are required to have two years of professional experience including at least one year of supervised teaching. The other year may be supervised research as a research assistant or associate.

4(iv). Core course requirements

The core course requirements are satisfied by taking courses from the following list:

• Numerical Analysis -- Math 502 and 503
• Real Analysis -- Math 515
• Methods of Applied Mathematics -- Math 519 and 520
• Functions of a Single Complex Variable -- Math 511
• Ordinary Differential Equations -- Math 557

• M.S. students must take at least four courses including either the Math 502--503 sequence or the Math 519--520 sequence.
• Ph.D. students must take all core courses in Numerical Analysis, Real Analysis, and Methods of Applied Mathematics, and either Math 511 or Math 557.

A grade of B or better must be earned in each core course. A deficiency may be made up by taking a final examination during a subsequent offering of the course and receiving a grade of B or better, or by passing the corresponding written qualifying examination.

4(v). Qualifying examinations

Ph.D. students in the Applied Mathematics Program must pass two written qualifying examinations. They must take a written qualifying examination covering material in two of the following four areas.

• Methods of Applied Mathematics (see the Applied Mathematics Qualifying Examination Syllabus )
• Numerical Analysis (see the Numerical Analysis Qualifying Examination Syllabus )
• Algebra (see the Algebra Qualifying Examination Syllabus )
• Real and Complex Analysis (see the Analysis Qualifying Examination Syllabus )

Students are strongly encouraged to consult their major professor prior to deciding which examinations to take, since certain examination combinations may not be suitable for certain areas of research.

A student taking an examination will be responsible for the topics listed in the appropriate syllabus. These topics are normally covered in the appropriate core courses as listed below:

• Methods of Applied Mathematics: Math 519--520.
• Numerical Analysis: Math 502--503.
• Algebra: Math 504--505 and Math 510.
• Real and Complex Analysis: Math 515--16 and Math 511.

However, the qualifying examination syllabi are definitive, and not all topics on the syllabi are covered each year in the appropriate courses. It is the student's responsibility to be prepared to answer questions about any topic on the appropriate syllabus.

A student will be allowed two attempts to pass a given qualifying examination. A student who fails the same qualifying examination twice may appeal in writing to the Graduate Committee to take it a third time if supported by a majority of the appropriate Qualifying Examination Committee. More than two failures on any combination of qualifying exams constitute grounds for dismissal from the Ph.D. program.

Students must request the examination in advance via the GC. This is usually done the semester before the scheduled examination so that a committee may be formed to write and grade the examination. Requests can be canceled before 4pm on the day preceding the day of the exam. If an examination is requested and not canceled, it counts as one attempt (whether or not the examination is actually written). The examinations are usually given twice a year: in August before or at the beginning of the Fall semester, and in January before or at the beginning of the Spring semester.

4(vi). Oral preliminary and final examinations

The oral preliminary examination tests a student's knowledge of the major, minor and supporting fields of their research area. The examination is taken after a student has passed both written qualifying examinations, satisfied the graduate English requirement, formed a POS committee, and has an approved POS form. A student who fails the preliminary oral examination is allowed to retake it one additional time. Six months must elapse between the first attempt and the second. The preliminary oral examination must be passed at least six months prior to the final defense, unless an exception is allowed by the Dean of the Graduate College. A form requesting scheduling of the examination must be submitted to the Graduate College at least two weeks before the proposed date of the examination.

The final examination of an M.S. candidate is oral and comprehensive. It normally consists of a defense of the thesis or creative component and an examination of the candidate's knowledge of the topics covered in the program of study.

The final examination of a Ph.D. candidate is oral, and is usually limited to a defense of the dissertation.

4(vii). Graduate English requirements

Graduate students whose native language is English are no longer required to take an English diagnostic test. See http://www.grad-college.iastate.edu/about/englishexamination.html.

Graduate students whose native language is not English, and who do not have a bachelor's degree from ISU, must take the English Placement Test at the beginning of their first semester of enrollment. A student who does not pass this examination is assigned to one or more courses in the English 101 series. This course work must be completed during the first year of study. (See the GCH for details.)

Graduate students whose native language is not English, but who do have a bachelor's degree from a U.S. institution, are no longer required to take the Graduate English Examination for International Students.

4(viii). Teaching requirement

Each Ph.D. student is required to have one year of supervised teaching. However, if approved by the student's POS committee, equivalent supervised experience in oral mathematics communication may be substituted for teaching. In that case the POS committee must specify in writing what the equivalent experience will be.

Every teaching assistant must demonstrate an ability to teach effectively. To assure this, before the beginning of the first semester they assumes their duties, teaching assistants are required to give a short, prepared lecture to a panel of experienced teaching assistants and/or faculty that is suitable for an algebra, trigonometry, or similar class. In addition, each teaching assistant whose native language is not English must take the SPEAK/TEACH test (the test administered by the University to screen applicants for classroom duties). They must pass it at the first or second level before they are assigned a class or recitation section, and they must pass it at the first or second level within their first year of residence to guarantee continued financial support.

5. Satisfactory progress towards the degree

Every Spring each graduate student, with assistance from their advisor, is required to complete a Graduate Student Activities Report for the previous calendar year. In addition, instructors are requested to prepare brief evaluations of each mathematics graduate student's performance in each course; these are placed in the student's file. The Graduate Committee uses this information to assess each student's progress and make recommendations to the Department Chair for financial support in the next academic year. Financial support is contingent upon satisfaction of the requirements outlined in this section.

The Committee uses the following general guidelines as criteria to assess progress toward the degree. International students with teaching assistantships should pass the SPEAK/TEACH test within their first year. The Graduate English requirement must be satisfied by all students during their first year.

5(i). M.S. degree students

Students in the M.S. program should complete all requirements for the M.S. degree in two years. Under special circumstances, the student and their advisor may request an additional semester of support. A POS committee must be formed before the end of the third semester in the M.S. program.

The student must maintain a cumulative grade point average of at least 3.0 in all course work, exclusive of research credit.

5(ii). Ph.D. degree students

The student must maintain a cumulative grade point average of at least 3.33 in graduate level mathematics courses and of at least 3.0 in all course work, exclusive of research credit.

If a graduate student does not maintain a cumulative 3.0 grade point average on all course work taken, exclusive of research credit, they may be placed on probation by the Dean of the Graduate College. The Graduate College places a hold on future registrations by a student on probation; see the GCH for more details. Before a student on probation registers for each term, there must be a review of their record by the POS committee. Further registration will not then be permitted without recommendation in writing by the GC to the Graduate College.

It is the purpose of the yearly review to anticipate any problems that a student may have in making satisfactory progress toward a degree. Generally, failure to meet the time limits or maintain the grade point averages specified in 5(i) above and 5(ii) above is considered the main evidence of unsatisfactory academic progress. If the student fails to meet any of the time limits under extenuating circumstances, they may petition the Graduate Committee for extension of one or more of those limits.

Under certain circumstances it may be necessary to terminate a graduate student's enrollment in a program because of lack of satisfactory academic progress, or for other reasons as specified in the GCH. In particular, a Ph.D. candidate who fails any combination of three qualifying examinations is liable for dismissal. The procedures of dismissal are spelled out in the GCH.

If dismissal is based on failure to make satisfactory progress, the graduate student may appeal to an ad hoc grievance committee that is appointed for this purpose by the Chair of the Mathematics Department. Details of the constitution of the grievance committee, and the procedures it will follow, are given in the GCH.

6. Minor requirements for students from other departments