## Mathematics

## Main Content

The School of Mathematical and Statistical Sciences offers graduate degree programs leading to the Master of Arts or Master of Science degree in mathematics and the Doctor of Philosophy degree in mathematics. Students in the masters program can choose from a rich assortment of courses in both pure and applied mathematics and statistics. Each masters degree candidate can either (a) work closely with a professor in writing a research paper or thesis in an area of interest to the student, or (b) elect a non-research paper/non-thesis option. A double major at the masters level between mathematics and a related discipline is also an option. At the doctoral level, a student may specialize in any one of a large number of fields such as algebra, applied mathematics, combinatorics, computational mathematics, control theory, differential equations, geometry, numerical analysis, probability, or statistics. Interdisciplinary programs are also available.

The School is committed to providing a challenging and rewarding experience for its graduate students. The School offers individual attention and mentoring, strives to establish a friendly, supportive environment, and assists students as much as possible to achieve their professional goals. Graduate students have 24-hour access to the school computer lab which has thirty state-of-the-art PCs, all with internet connections. For more computing needs, students can access the University Unix computer servers from the lab.

Students interested in the teaching of mathematics may apply up to nine credit hours in graduate level courses in the School of Education toward the 30 credit hours required for the Master of Science degree in mathematics subject to approval of the Director of Graduate Studies.

Acceptance for graduate study in mathematics and subsequent continuation in the graduate program are at the discretion of the School of Mathematical and Statistical Sciences, provided that the student has been admitted to the Graduate School and meets the retention standards of the Graduate School. All applicants for the graduate program are considered for teaching assistantships. In order to be considered for a fellowship, the applicant must take the GRE exam, and all applicants are strongly encouraged to take the GRE General Test.

Prospective students are encouraged to contact the School of Mathematical and Statistical Sciences at mathgradinfo@siu.edu or the web site at math.siu.edu for application forms or additional information.

In addition to the general rules, regulations, and requirements of the Graduate School, the following specific requirements pertain to the degrees available in mathematics.

This program requires a nonrefundable $65 application fee that must be submitted with the application for Admissions to Graduate Study in Mathematics. Applicants must pay this fee by credit card.

## Master of Arts (M.A.) in Mathematics

Students will be considered for acceptance into the M.A. in Mathematics degree program if they have completed with distinction the equivalent of a strong undergraduate major in mathematics. Once accepted, the requirements are as follows:

- The candidate must complete a total of 30 credit hours of graduate-level mathematics courses of which at least 15 must be at the 500 level.
- The candidate must complete with a grade of
*B*or better each of the courses MATH 419, MATH 421, MATH 430, MATH 452, MATH 455, and at least two of the courses MATH 501, MATH 519, MATH 530. This requirement may be met in whole or in part by means of equivalent courses taken elsewhere. - The candidate must demonstrate the ability to read mathematical literature in French, German, or Russian. This may be certified by passing with a grade of
*B*or better the research tool course 488 offered by the Languages, Cultures, and International Trade program, by passing with a score of 465 or better an examination given by the Educational Testing Service of Princeton, NJ, or by passing a suitable examination given by a faculty member from the School of Mathematical and Statistical Sciences who has been approved by the Director of Graduate Studies. - The candidate must prepare a thesis (three credit hours in MATH 599) under the supervision of a thesis adviser and two other faculty members from the school. This committee will be appointed by the Director of Graduate Studies after consultation with all those involved. Students hired as teaching assistants are required to take MATH 514. Anyone planning a career involving collegiate level teaching is encouraged to take it.

The candidate must demonstrate satisfactory performance on a final oral examination covering the graduate course work and the thesis. This examination will be given by the three members of the candidate’s committee and chaired by the thesis adviser. The student will pass the examination if the thesis adviser and at least one of the other two committee members so agree.

## Master of Science (M.S.) in Mathematics

Students will be considered for acceptance into the M.S. in Mathematics degree program if they have completed an undergraduate major in mathematics or a strong undergraduate minor in mathematics together with a major in a closely related discipline. Once accepted, the requirements are as follows:

- The candidate must complete a total of at least 30 credit hours of graduate credit approved by the Director of Graduate Studies of which 15 credit hours must be at the 500 level, only 3 credit hours of which can be for MATH 598 or MATH 599, and at least 21 credit hours must be in courses (exclusive of MATH 411, MATH 412, MATH 511, MATH 512A-G and MATH 513A-I) offered by the School of Mathematical and Statistical Sciences. A master's student can take up to 9 credit hours outside mathematics, subject to approval of the Director of Graduate studies during the student's first semester in the master's program. Students hired as teaching assistants are required to take MATH 514. Anyone planning a career involving collegiate level teaching is encouraged to take it.
- The candidate’s program must include: (a) MATH 452 and MATH 419 AND (b) at least one 400- or 500-level mathematics course from two of the following three areas: (1) algebra and analysis (excluding MATH 452 and MATH 419); (2) geometry and topology; (3) probability and statistics. These requirements may be met in whole or in part by means of equivalent courses taken here or elsewhere prior to acceptance for graduate study in the program. Students who do not receive a
*B*or better in MATH 452 on the first attempt are required to repeat it. Students who do not receive a*B*or better in MATH 419 on the first attempt are required to repeat it. - 3(a). Research Paper/Thesis Option. The candidate must prepare a research paper or thesis (3 credit hours in MATH 598 or MATH 599) under the supervision of a research adviser and two other faculty members from the School. This committee will be appointed by the Director of Graduate Studies after consultation with all those involved. --OR--

3(b). Non-Research Paper/Non-Thesis Option. The candidate must take at least 15 credit hours at the 500 level, excluding MA 595. These 15 credit hours must be approved by the Director of Graduate Studies. This option is not available for candidates who wish to continue on to a Ph.D. Candidates who are interested in pursuing a PhD should take the Research Paper/Thesis option. However, a candidate can easily move between options. - The candidate must demonstrate competence with the research tool of computer programming. This research tool requirement will be met by passing with a grade of
*B*or better in CS 202 (see Undergraduate Catalog) or the equivalent, or by passing a suitable examination given by a faculty member from the School of Mathematical and Statistical Sciences who has been appointed by the Director of Graduate Studies. - The candidate must demonstrate satisfactory performance on a final oral examination covering the graduate course work and the research paper or thesis. This examination will be conducted by the three members of the candidate’s committee and moderated by the research adviser. The student will pass the examination if the research adviser and at least one of the other two committee members so agree.

## Accelerated Master's Program

Undergraduate mathematics majors at SIUC can enter an accelerated master's program in which 9 hours of mathematics courses will satisfy requirements in both the bachelor's degree and the master's degree, allowing for completion of both degrees after 5 (4+1) years. Because the master's degree requires 30 hours of coursework, students in the accelerated master's program only need 21 graduate hours after their senior year thereby making it possible to complete the master's degree in only one year. To enter this program, students initiate their intention while an active undergraduate at SIUC and must have at least a 3.0 GPA in all coursework. Please see the Director of Graduate Studies in the School of Mathematical and Statistical Sciences for more information.

## M.S. in Mathematics Tracks

Students can get a general M.S. in Mathematics or they can choose one of the four tracks listed below. Students should make their choice when they apply or during their first year in the M.S. in Mathematics program.

**Applied Mathematics **** Track**

Entrance requirements are the same as for the M.S. Students must take both MATH 405 and 407, and both MATH 419 and 452 with a C or better. Students must take MATH 501, and two of MATH 502, 505, or 507. They should then write their thesis/research paper in the area of Applied Mathematics, unless they choose the non-thesis/non-research paper option.

**Statistics**** Track**

Entrance requirements are the same as for the M.S., and MATH 483 with a C or better, or its equivalent. Students must take MATH 484, and both MATH 419 and 452 with a C or better. Students must take MATH 580 and 584. They should then write their thesis/research paper in the area of Statistics, unless they choose the non-thesis/non-research paper option.

**Computational Mathematics Track**

Entrance requirements are the same as for the M.S. Students must take MATH 475 and CS 451, and both MATH 419 and 452 with a C or better. Students must take MATH 574 and CS 555. They should then write their thesis/research paper in the area of Computational Mathematics, unless they choose the non-thesis/non-research paper option.

**Pure Mathematics Track**

Entrance requirements are the same as for the M.S. Students must take MATH 421, 430 or 435, and 455, and both MATH 419 and 452 with a C or better. Students must take at least one of MATH 501, 519, or 530. They should then write their thesis/research paper in the area of Pure Mathematics, unless they choose the non-thesis/non-research paper option.

## Doctor of Philosophy (Ph.D.) in Mathematics

Students will be considered for acceptance into the doctoral program in Mathematics if they have completed with distinction a graduate program comparable to that required for a master’s degree in mathematics, statistics, or computer science at SIUC. Additional evidence of outstanding scholarly ability or achievement (e.g., a high score on the advanced section of the Graduate Record Examination or published research papers of high quality) will lend strength to the application. Normally students will have completed MATH 419, MATH 421, MATH 430, MATH 452, and MATH 455 or their equivalent before entering the doctoral program in Mathematics; those who have not must make up any deficiencies during their first year in the Ph.D. in Mathematics program. Once admitted, the requirements are as follows:

- The candidate must pass the school qualifying examination within four regular semesters after admission. Qualifying examinations are given twice annually, in January and in August. The student will be allowed to take qualifying exams at most three times. A student who fails to pass the qualifying examination within the allotted time will be dropped from the Ph.D. in Mathematics program at the end of the semester. The qualifying exam consists of three parts, each covering a regularly scheduled 500-level MATH course exclusive of MATH 511, MATH 512A-G, MATH 513A-I, MATH 514, MATH 516A, MATH 516B, MATH 583, MATH 585 and MATH 586. The student will decide which courses to be tested on in consultation with the Director of Graduate Studies. Two of the three must be chosen from MATH 501, MATH 519, MATH 530 and MATH 580, and must include either MATH 501 or MATH 519. All three parts must be passed, but not necessarily all at once. One of the parts may be from a related field provided, if in judgement of the Graduate Programs Committee, it has mathematically rigorous content.
- The candidate must demonstrate competence with a computer programming research tool. This requirement will be met by passing with a grade of
*B*or better in CS 202 (see Undergraduate Catalog) or its equivalent, or by passing a suitable examination given by a faculty member from the School of Mathematical and Statistical Sciences who has been appointed by the Director of Graduate Studies. - MATH 501 and MATH 519 or their equivalent with a
*B*or better are required courses for all doctoral students in the general (non-track) Ph.D. program. The candidate must complete a major area (12 credit hours) and two minor areas (six credit hours each). The course work in the major and minor areas must be at the 500-level and must be exclusive of the courses used to satisfy the qualifying examination. Normally the major and minor areas will be based on courses currently taught in the school. However, one of the minor areas may be taken outside the school, subject to the approval of the Director of Graduate Studies. With regard to the major and two minor areas, at least one of the three must be in an applied area. The final definition of “applied” will be determined by the dissertation adviser. The following courses cannot be used to satisfy requirements of the Ph.D. in Mathematics program: MATH 400, MATH 401, MATH 402, MATH 403, MATH 404, MATH 411, MATH 412, MATH 511, MATH 512A-G, MATH 513A-I, and MATH 516A, MATH 516B. - The candidate must file a request with the Director of Graduate Studies to appoint a dissertation committee to supervise the remaining doctoral work. This committee shall consist of five members with the candidate’s dissertation adviser as chair. At least one member of the committee must represent each of the minor areas, and the dissertation adviser and one other member will represent the major area. One member of the committee will be chosen from outside of the school. This committee will be appointed by the Director of Graduate Studies after consultation with the candidate, the proposed dissertation adviser, the School Director, and the other faculty members involved.
- The candidate must pass a preliminary examination which can be either (i) a written and oral examination over the major area and one minor area chosen by the candidate, or (ii) an oral presentation on their proposed research. This will normally be done after satisfying the research tools requirement and within 15 months of passing the qualifying examination. This examination will be prepared, administered, and evaluated by the dissertation committee. Any member of the graduate faculty may attend the oral portion of the preliminary examination and (at the discretion of the committee chair) question the candidate. The candidate will pass the preliminary examination provided that four members of the committee including the chair so agree. A report on the examination will be included with the candidates official academic records. In the event that the candidates performance is unsatisfactory, the committee as a whole shall decide on the time and content of an appropriate re-examination. A candidate who fails the re-examination will be dropped from the doctoral program. In unusual circumstances a candidate who has passed the preliminary examination may wish to change the major area or dissertation adviser. This will be allowed if the Director of Graduate Studies and school Director so agree, in which case the dissertation committee will be reconstituted in an appropriate manner. The revised committee may then prescribe additional course work and require the candidate to retake the preliminary examination.

In unusual circumstances a candidate who has passed the preliminary examination may wish to change the major area or dissertation adviser. This will be allowed if the Director of Graduate Studies and school Director so agree, in which case the dissertation committee will be reconstituted in an appropriate manner. The revised committee may then prescribe additional course work and require the candidate to retake the preliminary examination. - The candidate must be officially admitted to candidacy for the Ph.D. in Mathematics degree. This will be done after all of the above requirements have been met.
- The candidate must complete a dissertation (representing at least 24 credit hours in MATH 600) under the supervision of the candidate’s dissertation adviser. The dissertation adviser and the other four members of the dissertation committee will evaluate the quality of the completed work which must conform to high literary and scholastic standards and constitute an original and publishable contribution to mathematics. A final oral examination will be conducted by the dissertation committee. During this examination the candidate will first present the major results of the dissertation and then respond to questions. Any member of the University graduate faculty may attend and (at the discretion of the dissertation adviser) ask related questions. The dissertation will be accepted, provided the dissertation adviser and at least three of the other four members of the committee so agree.

### Ph.D. in Mathematics Tracks

Students can get a general Ph.D. in Mathematics or they can choose one of the four tracks listed below. Students should make their choice when they apply or during their first year in the Ph.D. in Mathematics program.

#### Applied Mathematics Track

The entrance requirements are MATH 405, MATH 407, MATH 419, MATH 421, and MATH 452, or their equivalents. Students must take two of MATH 502, MATH 505, MATH 519, or MATH 507. For their Qualifying Exam they must take MATH 501 or MATH 519 and two of MATH 502, MATH 505, MATH 507, MATH 555, MATH 574, MATH 575, or MATH 580. They should then write their dissertation in the area of Applied Mathematics.

#### Statistics Track

The entrance requirements are MATH 419, MATH 421, MATH 452, and MATH 483, or their equivalents. Students must take MATH 580 and MATH 581. For their Qualifying Exam they must take MATH 580 and at least one of MATH 501, MATH 519, or MATH 581, as well as one of MATH 584 or MATH 575 if needed. They should then write their dissertation in the area of Statistics.

#### Computational Mathematics Track

The entrance requirements are MATH 419, MATH 421, MATH 452, MATH 449, and CS 451, or their equivalents. Students must take MATH 501, MATH 519, MATH 549, and MATH 574. For their Qualifying Exam they must take CS 555, one of MATH 501 or MATH 519, and one other 500-level MATH course (preferably MATH 549, MATH 574, or MATH 575). For their preliminary examination, computer science should be a minor area. They should then write their dissertation in the area of Computational Mathematics.

#### Pure Mathematics Track

The entrance requirements are MATH 419, MATH 421, MATH 430, MATH 452, and MATH 455, or their equivalents. Students must take MATH 501, MATH 502, MATH 505, MATH 519, MATH 555, and MATH 574 and one of MATH 520, MATH 525, MATH 526, MATH 530, or MATH 549. For their Qualifying Exam they must take at least two of MATH 501, MATH 519, MATH 530, or MATH 555 and the remainder, if needed, from MATH 502, MATH 505, MATH 520, MATH 525, MATH 526, MATH 574, or MATH 549. They should then write their dissertation in the area of Pure Mathematics.

### Direct Entry into the Ph.D. in Mathematics Program

A prospective student without a masters degree can request direct entry into the Ph.D. in Mathematics program. They must meet the same coursework requirements and demonstrate that they have completed a research project in English. Students should be aware that this option reduces the amount of TA funding they can receive by 12 months.

### Accelerated Entry into the Ph.D. in Mathematics Program

A current student in our masters in Mathematics program can request accelerated entry into the Ph.D. in Mathematics program once they have completed one year. They must meet the same coursework requirements and demonstrate that they have completed a research project in English. Students should be aware that the option reduces the amount of TA funding they can receive by 12 months.

### Graduate Assistantship

University policy allows 24 months of graduate assistantships for masters students, 48 months for Ph.D. students with a masters degree, and 60 months for direct entry Ph.D. students. See the Admission Policies, Requirements, and Procedures tab for more information on financial assistance.

## Certificate in Dual Credit Mathematics

This post-baccalaureate certificate allows an Illinois high school mathematics teacher with a Master's degree (in any field) to teach certain courses for college credit to high school students. An undergraduate degree in Mathematics, Mathematics Education, or a related field is required for admission. The program requires 18 credit hours of graduate level Mathematics courses. Many courses are available online.

For more information: mathgradinfo@siu.edu