phd in mathematics requirements

Department of Mathematics

Requirements for the ph.d. degree.

In order to qualify for the Mathematics Ph.D., all students are required to:

• Complete eight term courses at the graduate level, at least two with Honors grades.
• Pass qualifying examinations on their general mathematical knowledge;
• Submit a dissertation prospectus;
• Participate in the instruction of undergraduates ;
• Be in residence for at least three years;
• Complete a dissertation that clearly advances understanding of the subject it considers.

All students must also complete any other  Graduate School of Arts and Sciences degree requirements  as they appear in the Programs and Policies bulletin.

The normal time for completion of the Ph.D. program is five to six years. Requirement (1) normally includes basic courses in algebra, analysis, and topology.  Students typically complete the eight-course requirement by the end of their third year.  The Honors grades of (1) must be achieved within the first two years.  A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term.  All qualifying examinations must be passed by the end of the second year.  There is no limit to the number of times that students can take the exams, and so they are encouraged to take them as soon as possible.

The dissertation prospectus should be submitted during the third year. 

The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)–(5) and obtaining an adviser.

In addition to all other requirements, students must successfully complete MATH 991a, Ethical Conduct of Research, prior to the end of their first year of study. This requirement must be met prior to registering for a second year of study.

Master’s Degrees :

The M.Phil. and M.S. degrees are conferred only en route to the Ph.D.; there is no separate master’s program in Mathematics.

M.Phil.   Please refer to the Graduate School Degree Requirements

M.S.   A student must complete six term courses with at least one Honors grade, perform adequately on the general qualifying examination, and be in residence at least one year.

Department of Mathematics

Phd requirements.

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Course Requirements

Mathematics PhD candidates must show satisfactory work in Algebra (110.601-602), Real Variables (110.605), Complex Variables (110.607), and one additional non-seminar mathematics graduate course in their first year. The first-year algebra and analysis requirement can be satisfied by passing the corresponding written qualifying exam in September of the first year; these students must complete at least two courses each semester. In addition, PhD candidates must take Algebraic Topology (110.615) and Riemannian Geometry (110.645) by their second year. Students having sufficient background can substitute an advanced topology course for 110.615, or an advanced geometry course for 110.645 with the permission of the instructor.

Candidates must show satisfactory work in at least two mathematics graduate courses each semester of their second year, and if they have not passed their oral qualifying exam, in the first semester of their third year.

Teaching Seminar

Candidates must take, attend, participate in, and pass the course 110.771 (GTA Teaching Seminar). The seminar is an important part of the preparation for classroom teaching, and thus an essential part of mathematics graduate education. The seminar is generally required in a student’s first year at JHU. A student supported by an external fellowship may delay taking the seminar until the spring before they are required to TA (but may not postpone the seminar entirely).

Candidates must pass written qualifying exams by the beginning of their second year in Analysis (Real & Complex) and in Algebra. Exams are scheduled for September and May of each academic year, and the dates are announced well in advance. More information as well as old exams and syllabi can be found on the Qualifying Exams page .

Candidates must pass an oral qualifying examination in the student’s chosen area of research by April 10th of the third year. The topics of the exam are chosen in consultation with the faculty member who has agreed (provisionally) to be the student’s thesis advisor, who will also be involved in administering the exam.

PhD Dissertation

Candidates must produce a written dissertation based upon independent and original research. After completion of the thesis research, the student will defend the dissertation by means of the  Graduate Board Oral exam . The exam must be held at least three weeks before the Graduate Board deadline the candidate wishes to meet.

Our PhD program does not have a foreign language requirement.

The MA Degree

Although the Department of Mathematics does not admit students seeking a terminal MA degree, students in the PhD program may earn an MA degree.

MA candidates must complete:

• Four graduate courses given by the Hopkins Department of Mathematics
• Two additional courses at the graduate or 400 level, other than 110.401, 110.405 and 110.415, given by the Hopkins Department of Mathematics, or with the permission of the graduate program director, graduate mathematics courses given by other departments or universities.

All courses used to satisfy the requirements must be completed with a grade of B- or better. (Advanced graduate courses completed with a grade of P can also be used to satisfy the requirements.)

Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

• Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
• Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
• Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
• Complete a seminar, giving a talk of at least one-hour duration
• Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
• Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members.  All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

Ph.D. Program Overview

Description.

The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of  interests of the faculty . The department has outstanding groups in the areas of algebra, algebraic geometry,  analysis, applied mathematics, combinatorics, dynamical systems, geometry, logic, Lie groups, number theory, probability, and topology. The field also maintains close ties with distinguished graduate programs in the fields of  applied mathematics ,  computer science ,  operations research , and  statistics .

Core Courses

A normal course load for a beginning graduate student is three courses per term. 

There are no qualifying exams, but the program requires that all students pass four courses to be selected from the six core courses. First-year students are allowed to place out of some (possibly, all) of the core courses. In order to place out of a course, students should contact the faculty member who is teaching the course during the current academic year, and that faculty member will make a decision. The minimum passing grade for the core courses is B-; no grade is assigned for placing out of a core course.

At least two core courses should be taken (or placed out) by the end of the first year. At least four core courses should be taken (or placed out) by the end of the second year (cumulative). These time requirements can be waived for students with health problems or other significant non-academic problems. They can be also waived for students who take time-consuming courses in another area (for example, CS) and who have strong support from a faculty; requests from such students should be made before the beginning of the spring semester. 

The core courses  are distributed among three main areas: analysis, algebra and topology/geometry. A student must pass at least one course from each group. All entering graduate students are encouraged to eventually take all six core courses with the option of an S/U grade for two of them. 

The six core courses are:

MATH 6110, Real Analysis

MATH 6120, Complex Analysis

MATH 6310, Algebra 1

MATH 6320, Algebra 2

MATH 6510, Introductory Algebraic Topology

MATH 6520, Differentiable Manifolds.

Students who are not ready to take some of the core courses may take MATH 4130-4140, Introduction to Analysis, and/or MATH 4330-4340, Introduction to Algebra, which are the honors versions of our core undergraduate courses.

"What is...?" Seminar

The "What Is...?" Seminar is a series of talks given by faculty in the graduate field of Mathematics. Speakers are selected by an organizing committee of graduate students. The goal of the seminar is to aid students in finding advisors.

Schedule for the "What Is...?" seminar

Special Committee

The Cornell Graduate School requires that every student selects a special committee (in particular, a thesis adviser, who is the chair or the committee) by the end of the third semester.

The emphasis in the Graduate School at Cornell is on individualized instruction and training for independent investigation. There are very few formal requirements and each student develops a program in conjunction with his or her special committee, which consists of three faculty members, some of which may be chosen from outside the field of mathematics. 

Entering students are not assigned special committees. Such students may contact any of the members on the Advising Committee if they have questions or need advice.

Current Advising Committee

Analysis / Probability / Dynamical Systems / Logic: Lionel Levine Geometry / Topology / Combinatorics: Kathryn Mann Probability / Statistics:  Philippe Sosoe Applied Mathematics Liaison: Richard Rand

Admission to Candidacy

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. Upon passing the A exam, the student will be awarded (at his/her request) an M.S. degree without thesis.

The admission to candidacy examination is given to determine if the student is “ready to begin work on a thesis.” The content and methods of examination are agreed on by the student and his/her special committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the core graduate courses. 

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the special committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes five to six years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the special committee. By the time of the oral admission to candidacy examination, the candidate should have selected as chairperson of the committee the faculty member who will supervise the research. When the thesis is completed, the student presents his/her results at the thesis defense or B Exam. All doctoral students take a Final Examination (the B Exam, which is the oral defense of the dissertation) upon completion of all requirements for the degree, no earlier than one month before completion of the minimum registration requirement.

Masters Degree in the Minor Field

Ph.D. students in the field of mathematics may earn a Special Master's of Science in Computer Science. Interested students must apply to the Graduate School using a form available for this purpose. To be eligible for this degree, the student must have a member representing the minor field on the special committee and pass the A-exam in the major field. The rules and the specific requirements for each master's program are explained on the referenced page.

Cornell will award at most one master's degree to any student. In particular, a student awarded a master's degree in a minor field will not be eligible for a master's degree in the major field.

Graduate Student Funding

Funding commitments made at the time of admission to the Ph.D. program are typically for a period of five years. Support in the sixth year is available by application, as needed. Support in the seventh year is only available by request from an advisor, and dependent on the availability of teaching lines. Following a policy from the Cornell Graduate School, students who require more than seven years to complete their degree shall not be funded as teaching assistants after the 14th semester.

Special Requests

Students who have special requests should first discuss them with their Ph.D. advisor (or with a field member with whom they work, if they don't have an advisor yet). If the advisor (or field faculty) supports the request, then it should be sent to the Director of Graduate Studies.  

Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

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Overview of Graduation Requirements

To graduate with a PhD in Mathematics, a student must satisfy all of the following requirements:

• 45 credits, including 15 doctoral dissertation research credits/GRAD 6950
• If you have a Master’s degree in mathematics at UConn, then 30 credits are required, including 15 doctoral dissertation research credits.
• Pass at least one prelim exam after each semester for the first three semesters of their graduate study.
• Finish all prelim exam requirements by the beginning of the spring semester in their second year.
• Finish all core course requirements by the end of their second year of graduate study,
• Choose a thesis advisor no later than the end of the fall semester of the third year.
• Form your advisory committee :  Major Advisor and at least two Associate Advisors or Co-Major Advisors and at least one Associate Advisor.
• Meant to further the student’s education, scholarship and professional development.
• Material should be in the broad area in which the student intends to write a dissertation, but should not focus on the actual thesis research.  Students present and answer questions about the material they have studied.
• The exam is normally taken at the end of the third year or beginning of the fourth year.
• Submit Dissertation Proposal
• Submit Plan of Study
• Apply for Graduation in Student Admin by the fourth week of the final semester.
• Dissertation Specifications under Dissertation Information
• Thesis templates (for LaTex) are available on our Thesis Formatting page
• Submit Approval Page – Step 7
• Complete Survey of Earned Doctorates – Step 7
• Add Diploma Address in Student Admin and Diploma Info.

Preliminary Examination and Core Course Requirements

Pure Mathematics

• Math 5111/Measure and Integration
• Math 5120/Complex Function Theory
• Math 5210/Abstract Algebra
• Math 5310/Introduction to Geometry and Topology I
• Math 5160/Probability Theory and Stochastic Processes I
• Math 5210/Abstract Algebra I
• Math 5211/Abstract Algebra II
• Math 5260/Mathematical Logic I
• Math 5360/Differential Geometry

Applied Mathematics

• Math 5410/Introduction to Applied Mathematics I
• Math 5510/Numerical Analysis and Approximation Theory I
• Math 5440/Partial Differential Equations
• Math 5520/Finite Element Solution Methods I

Past Prelim Exams

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PhD in Mathematics

Here are the requirements for earning the PhD degree in Mathematics offered by the School of Math. For requirements of other PhD programs housed within the School, please see their specific pages at  Doctoral Programs . The requirements for all these programs consist of three components:  coursework ,  examinations , and  dissertation  in accordance to the guidelines described in the  GT Catalogue .

Completion of required coursework, examinations, and dissertation normally takes about five years. During the first one or two years, students concentrate on coursework to acquire the background necessary for the comprehensive examinations. By the end of their third year in the program, all students are expected to have chosen a thesis topic, and begin work on the research and writing of the dissertation.

The program of study must contain at least 30 hours of graduate-level coursework (6000-level or above) in mathematics and an additional 9 hours of coursework towards a minor. The minor requirement consists of graduate or advanced undergraduate coursework taken entirely outside the School of Mathematics, or in an area of mathematics sufficiently far from the students area of specialization.

Prior to admission to candidacy for the doctoral degree, each student must satisfy the School's comprehensive examinations (comps) requirement. The first phase is a written examination which students must complete by the end of their second year in the graduate program. The second phase is an oral examination in the student's proposed area of specialization, which must be completed by the end of the third year.

Research and the writing of the dissertation represent the final phase of the student's doctoral study, and must be completed within seven years of the passing of comps. A final oral examination on the dissertation (theses defense) must be passed prior to the granting of the degree.

The Coursework

The program of study must satisfy the following  hours ,  minor , and  breadth  requirements. Students who entered before Fall 2015 should see  the old requirements , though they may opt into the current rules described below, and are advised to do so.

Hours requirements.  The students must complete 39 hours of coursework as follows:

• At least 30 hours must be in mathematics courses at the 6000-level or higher.
• At least 9 hours must form the doctoral minor field of study.
• The overall GPA for these courses must be at least 3.0.
• These courses must be taken for a letter grade and passed with a grade of at least C.

Minor requirement.  The minor field of study should consist primarily of 6000-level (or higher) coursework in a specific area outside the School of Math, or in a mathematical subject sufficiently far from the student’s thesis work. A total of 9 credit hours is required and must be passed with a grade of B or better. These courses should not include MATH 8900, and must be chosen in consultation with the PhD advisor and the Director of Graduate Studies to ensure that they form a cohesive group which best complements the students research and career goals. A student wishing to satisfy the minor requirement by mathematics courses must petition the Graduate Committee for approval.  Courses used to fulfill a Basic Understanding breadth requirement in Analysis or Algebra should not be counted towards the doctoral minor. Upon completing the minor requirement, a student should immediately complete the  Doctoral Minor form .

Breadth requirements.  The students must demonstrate:

• Basic understanding of 2 subjects must be demonstrated through passing the subjects' written comprehensive exams.  At least 1 of these 2 exams must be in Algebra or Analysis.
• Basic understanding of the third subject may be demonstrated either by completing two courses in the subject (with a grade of A or B in each course) or by passing the subject's written comprehensive exam.
• A basic understanding of both subjects in Area I (analysis and algebra) must be demonstrated.
• Earning a grade of A or B in a one-semester graduate course in a subject demonstrates exposure to the subject.
• Passing a subject's written comprehensive exam also demonstrates exposure to that subject.

The subjects.  The specific subjects, and associated courses, which can be used to satisfy the breadth requirements are as follows.

• Area I subjects:​

• Area II subjects:​

Special Topics and Reading Courses.

• Special topics courses may always be used to meet hours requirements.
• Special topics courses may be used to meet breadth requirements, subject to the discretion of the Director of Graduate Studies.
• Reading courses may be used to meet hours requirements but not breadth requirements.

Credit Transfers

Graduate courses completed at other universities may be counted towards breadth and hours requirements (courses designated as undergraduate or Bachelors' level courses are not eligible to transfer for graduate credit).  These courses do not need to be officially transferred to Georgia Tech. At a student’s request, the Director of Graduate Studies will determine which breadth and hours requirements have been satisfied by graduate-level coursework at another institution.  

Courses taken at other institutions may also be counted toward the minor requirement, subject to the approval of the Graduate Director; however, these courses must be officially transferred to Georgia Tech.

There is no limit for the transfer of credits applied toward the breadth requirements; however, a maximum of 12 hours of coursework from other institutions may be used to satisfy hours requirements. Thus at least 27 hours of coursework must be completed at Georgia Tech, including at least 18 hours of 6000-level (or higher) mathematics coursework.

Students wishing to petition for transfer of credit from previous graduate level work should send the transcripts and syllabi of these courses, together with a list of the corresponding courses in the School of Math, to the Director of Advising and Assessment for the graduate program.

Comprehensive Examinations

The comprehensive examination is in two phases. The first phase consists of passing two out of seven written examinations. The second phase is an oral specialty examination in the student's planned area of concentration. Generally, a student is expected to have studied the intended area of research but not necessarily begun dissertation research at the time of the oral examination.

Written examinations.  The written examinations will be administered twice each year, shortly after the beginning of the Fall and Spring semesters. The result of the written examination is either pass or fail. For syllabi and sample exams see the  written exams page .

All students must adhere to the following rules and timetables, which may be extended by the Director of Graduate Studies, but only at the time of matriculation and only when certified in writing. Modifications because of leaves from the program will be decided on a case-by-case basis.

After acceptance into the PhD Program in Mathematics, a student must pass the written examinations no later than their fourth administration since the student's doctoral enrollment. The students can pass each of the two written comprehensive exams in separate semesters, and are allowed multiple attempts.

The Director of Graduate Studies (DGS) will be responsible for advising each new student at matriculation of these rules and procedures and the appropriate timetable for the written portion of the examination. The DGS will also be responsible for maintaining a study guide and list of recommended texts, as well as a file of previous examinations, to be used by students preparing for this written examination.

Oral examination.  A student must pass the oral specialty examination within three years since first enrolling in the PhD program, and after having passed the written portion of the comprehensive exams. The examination will be given by a committee consisting of the student's dissertation advisor or probable advisor, two faculty members chosen by the advisor in consultation with the student, and a fourth member appointed by the School's Graduate Director. The scope of the examination will be determined by the advisor and will be approved by the graduate coordinator. The examining committee shall either (1) pass the student or (2) fail the student. Within the time constraints of which above, the oral specialty examination may be attempted multiple times, though not more than twice in any given semester. For more details and specific rules and policies see the  oral exam page .

Dissertation and Defense

A dissertation and a final oral examination are required. For details see our  Dissertation and Graduation  page, which applies to all PhD programs in the School of Math.

Guide to Graduate Studies

The PhD Program The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in one’s own way. For this reason, a Ph.D. dissertation involving some original research is a fundamental part of the program. The stages in this program may be described as follows:

• Acquiring a broad basic knowledge of mathematics on which to build a future mathematical culture and more detailed knowledge of a field of specialization.
• Choosing a field of specialization within mathematics and obtaining enough knowledge of this specialized field to arrive at the point of current thinking.
• Making a first original contribution to mathematics within this chosen special area.

Students are expected to take the initiative in pacing themselves through the Ph.D. program. In theory, a future research mathematician should be able to go through all three stages with the help of only a good library. In practice, many of the more subtle aspects of mathematics, such as a sense of taste or relative importance and feeling for a particular subject, are primarily communicated by personal contact. In addition, it is not at all trivial to find one’s way through the ever-burgeoning literature of mathematics, and one can go through the stages outlined above with much less lost motion if one has some access to a group of older and more experienced mathematicians who can guide one’s reading, supplement it with seminars and courses, and evaluate one’s first attempts at research. The presence of other graduate students of comparable ability and level of enthusiasm is also very helpful.

University Requirements

The University requires a minimum of two years of academic residence (16 half-courses) for the Ph.D. degree. On the other hand, five years in residence is the maximum usually allowed by the department. Most students complete the Ph.D. in four or five years. Please review the program requirements timeline .

There is no prescribed set of course requirements, but students are required to register and enroll in four courses each term to maintain full-time status with the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Qualifying Exam

The department gives the qualifying examination at the beginning of the fall and spring terms. The qualifying examination covers algebra, algebraic geometry, algebraic topology, complex analysis, differential geometry, and real analysis. Students are required to take the exam at the beginning of the first term. More details about the qualifying exams can be found here .

Students are expected to pass the qualifying exam before the end of their second year. After passing the qualifying exam students are expected to find a Ph.D. dissertation advisor.

Minor Thesis

The minor thesis is complementary to the qualifying exam. In the course of mathematical research, students will inevitably encounter areas in which they have gaps in knowledge. The minor thesis is an exercise in confronting those gaps to learn what is necessary to understand a specific area of math. Students choose a topic outside their area of expertise and, working independently, learns it well and produces a written exposition of the subject.

The topic is selected in consultation with a faculty member, other than the student’s Ph.D. dissertation advisor, chosen by the student. The topic should not be in the area of the student’s Ph.D. dissertation. For example, students working in number theory might do a minor thesis in analysis or geometry. At the end of three weeks time (four if teaching), students submit to the faculty member a written account of the subject and are prepared to answer questions on the topic.

The minor thesis must be completed before the start of the third year in residence.

Language Exam

Mathematics is an international subject in which the principal languages are English, French, German, and Russian. Almost all important work is published in one of these four languages. Accordingly, students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination. Students are asked to translate one page of mathematics into English with the help of a dictionary. Students may request to substitute the Italian language exam if it is relevant to their area of mathematics. The language requirement should be fulfilled by the end of the second year. For more information on the graduate program requirements, a timeline can be viewed at here .

Non-native English speakers who have received a Bachelor’s degree in mathematics from an institution where classes are taught in a language other than English may request to waive the language requirement.

Upon completion of the language exam and eight upper-level math courses, students can apply for a continuing Master’s Degree.

Teaching Requirement

Most research mathematicians are also university teachers. In preparation for this role, all students are required to participate in the department’s teaching apprenticeship program and to complete two semesters of classroom teaching experience, usually as a teaching fellow. During the teaching apprenticeship, students are paired with a member of the department’s teaching staff. Students attend some of the advisor’s classes and then prepare (with help) and present their own class, which will be videotaped. Apprentices will receive feedback both from the advisor and from members of the class.

Teaching fellows are responsible for teaching calculus to a class of about 25 undergraduates. They meet with their class three hours a week. They have a course assistant (an advanced undergraduate) to grade homework and to take a weekly problem session. Usually, there are several classes following the same syllabus and with common exams. A course head (a member of the department teaching staff) coordinates the various classes following the same syllabus and is available to advise teaching fellows. Other teaching options are available: graduate course assistantships for advanced math courses and tutorials for advanced undergraduate math concentrators.

Final Stages

How students proceed through the second and third stages of the program varies considerably among individuals. While preparing for the qualifying examination or immediately after, students should begin taking more advanced courses to help with choosing a field of specialization. Unless prepared to work independently, students should choose a field that falls within the interests of a member of the faculty who is willing to serve as dissertation advisor. Members of the faculty vary in the way that they go about dissertation supervision; some faculty members expect more initiative and independence than others and some variation in how busy they are with current advisees. Students should consider their own advising needs as well as the faculty member’s field when choosing an advisor. Students must take the initiative to ask a professor if she or he will act as a dissertation advisor. Students having difficulty deciding under whom to work, may want to spend a term reading under the direction of two or more faculty members simultaneously. The sooner students choose an advisor, the sooner they can begin research. Students should have a provisional advisor by the second year.

It is important to keep in mind that there is no technique for teaching students to have ideas. All that faculty can do is to provide an ambiance in which one’s nascent abilities and insights can blossom. Ph.D. dissertations vary enormously in quality, from hard exercises to highly original advances. Many good research mathematicians begin very slowly, and their dissertations and first few papers could be of minor interest. The ideal attitude is: (1) a love of the subject for its own sake, accompanied by inquisitiveness about things which aren’t known; and (2) a somewhat fatalistic attitude concerning “creative ability” and recognition that hard work is, in the end, much more important.

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Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements.

NYU Shanghai Ph.D. Track

The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the  NYU Shanghai Ph.D. page .

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Additional information for students interested in studying applied math is available here .

Probability

PDE/Analysis

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

The oral defense is the final examination on the student's dissertation. The defense is conducted by a panel of five faculty members (including the student's advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student's topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs  page.

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Doctoral Degree Requirements

The PhD in Mathematics requires completing at least 36 credits of graduate coursework beyond the bachelor’s degree, preliminary written and oral examinations, 24 thesis credits, and a doctoral thesis with final defense. 

PhD students in Mathematics are expected to earn an MS degree upon completion of their preliminary oral examination.

Entering students

• Required to have completed an undergraduate degree prior to matriculation into the program. 
• Some students enter with previous graduate coursework which can include having completed a Master’s degree.

Course requirements for a doctoral degree

• 36 credits of coursework — Students normally complete the coursework for the PhD at the University of Minnesota. Students may transfer up to 18 credits of previously completed graduate coursework toward their PhD in consultation with their advisor and the Director of Graduate Studies upon submitting their degree plan. 
• MATH 8001: Preparation for College Teaching — All PhD students must complete MATH 8001 in the Fall semester of their first year.
• 18 credits of core coursework — Courses in Mathematics that are the foundation for advanced doctoral work in Mathematics. 
• 18 credits supporting coursework — Mathematics coursework in your research area or that supports this research. Students may take a maximum of 12 credits outside of Mathematics. Coursework used for a formal minor can be counted towards this requirement.
• 24 thesis credits — Taken upon the completion of the preliminary oral examination. Students are expected to complete their thesis credits no more than two semesters after successfully completing their preliminary oral examination.

+ Core courses

Core courses.

• General Algebra (MATH 8201/02)
• Manifolds and Topology (MATH 8301/02)
• Mathematical Modeling and Methods of Applied Mathematics (MATH 8401/02)
• Numerical Analysis and Scientific Computing (MATH 8441/42)
• Real Analysis (MATH 8601/02)
• Theory of Probability Including Measure Theory (MATH 8651/52)
• Complex Analysis (MATH 8701/02)

Preliminary written exam

Students must demonstrate proficiency in basic areas of mathematics by passing the preliminary written exams.

Students are expected to complete their preliminary written exams by the end of the second year of study. Extension to this timing may be approved through a meeting with the academic advisor and the Director of Graduate Studies.

What’s required

Students must pass two written examinations by either:

1. Taking the written examinations.

Given Fall and Spring semester in Real Analysis, Complex Analysis, Algebra and Manifolds/Topology.

2. Passing the final examination in the second semester of any of the core courses.

What to expect.

• Students with previous graduate coursework may transfer up to 18 credits to fulfill core course credit requirements upon passing preliminary written exams.
• Students without previous graduate coursework who complete core coursework requirements by passing exams will take up to 36 credits of other major coursework.  

Preliminary oral exam

Students complete a preliminary oral examination to demonstrate proficiency in their primary area of study and supporting program or minor program. The exam also serves as a final exam for a Plan B Master’s in Mathematics. 

• Typically completed after the third year of study.
• Must be completed prior to the last day of Spring semester in the fourth year. 
• Changes to this timing may be approved by meeting with the advisor and the Director of Graduate Studies.

The preliminary oral examination concentrates on the primary area of study and the supporting program or minor. 

• Examination committee — The examination committee of four faculty members consists of the major area advisor and three additional faculty members. Preliminary Oral Exam Committees require a faculty member from outside of Mathematics OR Outside of the University of Minnesota. Students who have declared a minor in another department are required to have a committee member from the department they are minoring in.
• Advisor — The advisor recommends coursework in the basic material, as well as expository and research papers for individual study.
• Expository paper — The study, including the recommended research papers, will be summarized in an expository paper (approximately 10 pages), with a substantial bibliography. This will demonstrate a knowledge of the definitions and results in the area, and indicate open problems which may form the basis for the PhD thesis.
• Registration and credits — Students taking their preliminary oral examinations during Fall or Spring semester are expected to register for six pre-thesis credits (MATH 8666). 
• The student should choose their primary area and decide on an advisor who will support them through these exams by the end of fall semester in the second year.
• In the semester prior to the oral exam, students should work with their advisor to determine a committee and expectations for their exam. 
• Students are expected to have begun work on their expository paper by the beginning of the semester in which they are planning to complete this exam. 

See the PhD degree (steps 1-7) and the Plan B Master’s degree (the preliminary oral examination serves as a Final Exam for a Plan B Master’s in Mathematics) completion steps:

Degree completion steps

Final exam/dissertation defense

Mathematics PhD students typically complete their degree in the sixth year of their program. The examination is a defense of the thesis that is the culmination of the student’s work in the program. 

• The doctoral final exam committee consists of four members, including the advisor(s).
• The chair of this committee must be a full mathematics faculty member who is not the student's advisor.  
• If there is a formal minor, this committee member must represent that program. In the case of multiple minors, there must be a separate thesis reviewer for each minor.

The doctoral final exam must include a public presentation of the candidate’s dissertation to the doctoral final oral examination committee and the invited scholarly community, followed by a closed session for questions by the examiners. 

See the PhD degree completion steps (steps 8-15):

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Doctor of Philosophy Program

Besides satisfying the general regulations of the Graduate School for the degree of Doctor of Philosophy, the student must comply with the requirements briefly outlined below. For complete details about these requirements see section IV of the Graduate Handbook .

Pass four Qualifying Examinations . The exams are based on material that is covered in the courses listed and on material from undergraduate prerequisites. Credit for passing a similar examination at another university cannot be transferred. See sections IV and VI of the Graduate Handbook for more information.

Advanced Topics Examinations. A student becomes eligible to take the Advanced Topics Examination after passing the Qualifying Examinations.

Plan of Study. The plan of study should be submitted electronically to the Graduate School through myPurdue by each student preparing to hold their Advanced Topics. 

Preliminary Examination. The preliminary examination for most students will only require the completion of a form for the Graduate School. An oral or written examination may be required by the student's advisory committee for admission to candidacy. Graduate School regulations require that at least two sessions (including summer sessions) must elapse between the preliminary examination and the thesis defense.

Admission to Candidacy. To be admitted to candidacy for the Ph.D. degree, the student must have fulfilled the requirements above which are detailed in section IV of the Graduate Handbook .

Dissertation. A thesis must be submitted in final form presenting new results of sufficient importance to merit publication.

Recommendation for the Ph.D. Degree. If the requirements are met within the time limits detailed in section IV of the Graduate Handbook , the candidate will be recommended to the faculty to receive the degree of Doctor of Philosophy.

For information about financial support and research in absentia see section IV of the Graduate Handbook .

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Ph.D. Degree Programs

The UCSD Mathematics Department admits students into the following Ph.D. programs:

• Ph.D. in Mathematics -- Pure or Applied Mathematics.
• Ph.D. in Mathematics with a  Specialization in Computational Science .
• Ph.D. in Mathematics with a  Specialization in Statistics .

In addition, the department participates in the following Ph.D. programs:

• Ph.D. in  Bioinformatics .
• Ph.D. in  Mathematics and Science Education  (joint program between UCSD and SDSU).

For application information, go to  How to Apply (Graduate) .  

Ph.D. in Mathematics

The Ph.D. in Mathematics allows study in pure mathematics, applied mathematics and statistics. The mathematics department has over 60 faculty, approximately 100 Ph.D. students, and approximately 35 Masters students. A list of the UCSD mathematics faculty and their research interests can be found at  here . The Ph.D. in Mathematics program produces graduates with a preparation in teaching and a broad knowledge of mathematics. Our students go on to careers as university professors, as well as careers in industry or government.

In the first and second years of study, Ph.D. students take courses in preparation for three written qualifying examinations (quals). One qual must be taken in Algebra or Topology, and another in Real or Complex Analysis. A third qual may be taken in Numerical Analysis or Statistics or one of the remaining topics in the first two groups. All three quals must be passed by the start of the third year. After the qualifying exams are passed, the student is expected to choose an advisor and follow a course of study agreed on by the two of them. At this point, the student chooses a thesis topic, finds a doctoral committee and presents a talk on his or her proposed research topic. If the committee is satisfied with this talk, the student has "Advanced to Candidacy." The student will then pursue their research agenda with their advisor until they have solved an original problem. The student will submit a written dissertation and reconvene his or her committee for a Final Defense. At the Final Defense, the student gives a seminar talk that is very similar to a talk that he or she might give for a job interview.

Nearly every admitted Ph.D. student gets financial support. The financial support is most commonly in the form of a Teaching Assistantship, however, Research Assistantships and other fellowships are also available.

Because of the large faculty to student ratio, graduate students have many opportunities to interact with faculty in courses or smaller research seminars. The graduate students also run their own "Food for Thought" seminar for expository talks as well as a research seminar where they give talks about their research.

UCSD has excellent library facilities with strong collections in mathematics, science, and engineering. Ph.D. students are provided with access to computer facilities and office space.

Full-time students are required to register for a minimum of twelve (12) units every quarter, eight (8) of which must be graduate-level mathematics courses taken for a letter grade only. The remaining four (4) units can be approved upper-division or graduate-level courses in mathematics-related subjects (MATH 500 may not be used to satisfy any part of this requirement). After advancing to candidacy, Ph.D. candidates may take all course work on a Satisfactory/Unsatisfactory basis. Typically, students should not enroll in MATH 299 (Reading and Research) until they have passed at least two Qualifying Examinations at the PhD or Provisional PhD level, or obtained approval of their faculty advisor.  

Written Qualifying Examinations

Effective Fall Quarter 1998, the department made changes in their qualifying exam requirements with a view to:

• improving applied mathematics' access to students and the attractiveness of its program to applicants; and
• broadening the education of our doctoral students and leading more of them towards applied areas.

The department now offers written qualifying examinations in  SEVEN (7)  subjects. These are grouped into three areas as follows:  

• Three qualifying examinations must be passed. At least one must be passed at the Ph.D. level and a second must be passed at either the Ph.D. or Provisional Ph.D. level.
• Of the three qualifying exams, there must be at least one from each of Areas 1 and 2. 
• Students must pass at least two exams from distinct areas with a minimum grade of Provisional Ph.D. (For example, a Ph.D. pass in Real Analysis, Provisional Ph.D. pass in Complex Analysis, M.A. pass in Algebra would  NOT  satisfy this requirement, but a Ph.D. pass in Real Analysis, M.A. pass in Complex Analysis, Provisional Ph.D. pass in Algebra would, as would a Ph.D. pass in Numerical Analysis, Provisional Ph.D. pass in Applied Algebra, and M.A. pass in Real Analysis.) All exams must be passed by the September exam session prior to the beginning of the third year of graduate studies. (Thus, there is no limit on the number of attempts, encouraging new students to take exams when they arrive, without penalty.) Except for this deadline, there is no limit on the number of exams a student may attempt.

After qualifying exams are given, the faculty meet to discuss the results of the exams with the Qualifying Exam and Appeals Committee (QEAC). Exam grades are reported at one of four levels:  

Department policy stipulates that at least one of the exams must be completed with a Provisional Ph.D. pass or better by September following the end of the first year. Anyone unable to complete this schedule will be terminated from the doctoral program and transferred to one of our Master's programs. Any grievances about exams or other matters can be brought before the Qualifying Exam and Appeals Committee for consideration.

Exams are typically offered twice a year, one scheduled late in the Spring Quarter and again in early September (prior to the start of Fall Quarter). Copies of past exams are available on the  Math Graduate Student Handbook .

In choosing a program with an eye to future employment, students should seek the assistance of a faculty advisor and take a broad selection of courses including applied mathematics, such as those in Area 3.  

Master's Transferring to Ph.D.

Any student who wishes to transfer from masters to the Ph.D. program will submit their full admissions file as Ph.D. applicants by the regular closing date for all Ph.D. applicants (end of the fall quarter/beginning of winter quarter). It is the student's responsibility to submit their files in a timely fashion, no later than the closing date for Ph.D. applications at the end of the fall quarter of their second year of masters study, or earlier. The candidate is required to add any relevant materials to their original masters admissions file, such as most recent transcript showing performance in our graduate program. Letters of support from potential faculty advisors are encouraged. The admissions committee will either recommend the candidate for admission to the Ph.D. program, or decline admission. In the event of a positive recommendation, the Qualifying Exam Committee checks the qualifying exam results of candidates to determine whether they meet the appropriate Ph.D. program requirements, at the latest by the fall of the year in which the application is received. For students in the second year of the master's program, it is required that the student has secured a Ph.D. advisor before admission is finalized. An admitted student is supported in the same way as continuing Ph.D. students at the same level of advancement are supported. Transferring from the Master's program may require renewal of an I-20 for international students, and such students should make their financial plans accordingly. To be eligible for TA support, non-native English speakers must pass the English exam administered by the department in conjunction with the Teaching + Learning Commons.  

Foreign Language Requirement

There is no Foreign Language requirement for the Ph.D. in Mathematics.  

Advancement to Candidacy

It is expected that by the end of the third year (9 quarters), students should have a field of research chosen and a faculty member willing to direct and guide them. A student will advance to candidacy after successfully passing the oral qualifying examination, which deals primarily with the area of research proposed but may include the project itself. This examination is conducted by the student's appointed doctoral committee. Based on their recommendation, a student advances to candidacy and is awarded the C. Phil. degree.  

Dissertation and Final Defense

Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the Ph.D. degree is awarded. When the dissertation is substantially completed, copies must be provided to all committee members at least four weeks in advance of the proposed defense date. Two weeks before the scheduled final defense, a copy of the dissertation must be made available in the Department for public inspection.  

Time Limits

The normative time for the Ph.D. in mathematics is five (5) years. Students must be advanced to candidacy by the end of eleven (11) quarters. Total university support cannot exceed six (6) years. Total registered time at UCSD cannot exceed seven (7) years.  

It may be useful to describe what the majority of students who have successfully completed their Ph.D. and obtained an academic job have done. In the past some students have waited until the last time limit before completing their qualifying exams, finding an advisor or advancing to candidacy. We strongly discourage this, because experience suggests that such students often do not complete the program. Although these are formal time limits, the general expectation is that students pass two qualifying exams, one at the Ph.D. level and one at the masters level by the beginning of their second year. (About half of our students accomplish this.) In the second year, a student begins taking reading courses so that they become familiar with the process of doing research and familiarize themselves with a number of faculty who may serve as their advisor. In surveying our students, on average, a student takes 4 to 5 reading courses before finding an advisor. Optimally, a student advances to candidacy sometime in their third year. This allows for the fourth and fifth year to concentrate on research and produce a thesis. In contrast to coursework, research is an unpredictable endeavor, so it is in the interest of the student to have as much time as possible to produce a thesis.

A student is also a teaching assistant in a variety of courses to strengthen their resume when they apply for a teaching job. Students who excel in their TA duties and who have advanced to candidacy are selected to teach a course of their own as an Associate Instructor. Because there are a limited number of openings to become an Associate Instructor, we highly recommend that you do an outstanding job of TAing in a large variety of courses and advance to candidacy as soon as possible to optimize your chances of getting an Associate Instructorship.

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PhD Requirements

The purpose of the Doctor of Philosophy program is to prepare the student for research and teaching.

It is expected that each graduate student who is a U.S. citizen or permanent resident should begin the process of establishing North Carolina residency during the first semester of graduate study. Detailed information can be found here.

Time and residency requirements

First year courses.

Courses taken during the first year are usually chosen from the following list, which is designed to prepare students for the PhD qualifying examinations. Master’s students will typically take these courses as well in the first year before focusing in the second year on the requirements for a Master’s degree.

Qualifying Exam Requirements

There are five qualifying exams:

• Algebra: Math 676 and 677
• Analysis: Math 653 and 656
• Geometry-Topology: Math 680 and 681
• Methods of Applied Mathematics: Math 668 and 669
• Scientific Computation: Math 661 and 662

PhD qualifying exams are given twice each year, near the beginning of classes in August and January. PhD students are encouraged to take the PhD qualifying exams early and in principle would be ready to take them in August after the first year. The qualifying exams, sometimes called comps, are subject to the following rules:

• A PhD student can pass either the Pure Math option for the for the qualifying examination or the Applied Math option.
• To pass the Pure Math Option, a student is required to pass three of the five qualifying exams by the beginning of the sixth semester. Any three of the five can be passed.
• To pass the Applied Math option, a student is required to pass Methods of Applied Math and Scientific Computation by the beginning of the sixth semester.
• In each examination period a student can take any number of qualifying examinations, from one to five.
• A graduate student who passes a PhD qualifying examination, as determined by the Graduate Committee, will receive credit for that examination toward the PhD requirements.
• If a student does not pass at least one PhD exam by the beginning of the fourth semester, the department will not guarantee financial support past the end of the fourth semester. However, if such a student passes one exam by the beginning of the fifth semester, then reinstatement of financial support will be considered.
• To remain in the PhD program, a graduate student must pass the written qualifying exam, with either the Pure Math or the Applied Math option, by the beginning of the sixth semester. A student who does not do this will be out of the PhD program.
• Any exceptional cases will be decided by the graduate committee.

Course Requirements

All Ph.D. students must take and receive a grade of P or higher in at least six courses from the following two lists:

• Comprehensive courses that are not basic courses for any of the three comprehensive exams passed by the student
• Algebra: Math 641, 643, 771, 774, 775
• Analysis: Math 657, 751, 753, 754, 857
• Applied Mathematics: Math 635, 761, 762, 768, 769, 892
• Geometry-Topology: Math 781, 782, 773, 775, 776

Furthermore, of these six courses every PhD student must take and receive a grade of P or higher in three courses numbered over 700 from the second tier list

A student taking a pure math option, respectively an applied math option, may replace one, respectively one or more, course/s in the second tier requirement with other graduate level courses inside or outside of the department. For each replacement course, the student must obtain permission, prior to registration, from both the adviser and the graduate director.

Any incomplete grades must be resolved within one year (ideally within one semester).

Oral Examination Requirement

When the student is prepared and has selected a direction for the PhD dissertation, the PhD candidate must pass an oral examination on material basic to the proposed dissertation area. The examination will be conducted by the PhD committee of the student, which consists of five faculty members and is chaired by the student’s adviser. The committee will recommend action to correct any deficiencies noted during the oral examination.

After passing the oral examination the candidate continues working in the area of concentration to complete the PhD dissertation.

Dissertation Defense

Computer language requirement.

A Master’s or PhD student must pass a computer language requirement by demonstrating a certain level of programming ability. Please note the following guidelines:

• Computer language requirements are the same for PhD and Master’s students.
• Passing the following courses at UNC will be sufficient to satisfy the computer language requirement: MATH 565, MATH 566, MATH 661, MATH 662, MATH 761, MATH 762, COMP 110, COMP 116, COMP 121, COMP 401
• Any computer science course which lists one of these courses as a prerequisite is also acceptable.
• A Master’s or PhD student may also satisfy the computer language requirement by passing an approved one semester undergraduate course on computer programming at any university.
• If the course title title on the transcript is not self-explanatory, then a syllabus, text or other information may be required. In all cases where there is some question about whether a course fulfills the requirement the Graduate Director will decide in consultation with the Graduate Committee.

Teaching Requirement

Students are required to take and successfully pass the TA Teaching Seminar, a special section of Math 920, during their first fall semester of their program. Students are also required to perform a minimum of two semesters of instructional service.

A semester of instructional service can be satisfied by any of the following:

• Teach one course: 12 hours
• Lead 4 recitations (includes 110L and 231L): 3 hours each
• Lead 2 labs (383L, 528L, 529L): 6 hours each

For Additional Information Contact

Ann Van Elsue Graduate Student Services Manager Phillips Hall 331A 919-962-4178 [email protected]

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Doctor of Philosophy (PhD)

Program synopsis and training.

 The Doctor of Philosophy (PhD) in mathematics is the highest degree offered by our program. Graduates will have demonstrated their ability to conduct independent scientific research and contribute new mathematical knowledge and scholarship in their area of specialization. They will be well-supported and well prepared for research and faculty positions at academic institutions anywhere in the world. Owing to their independence, analytic abilities, and proven tenacity, our PhD graduates are also sought after by private and government employers.

Our PhD program offers two tracks, one for Theoretical Mathematics and one for Applied Mathematics . The tracks differ only in the course and  qualifying requirements during the first two years. Applicants are required to decide on one of the tracks and applications will be evaluated subject to respective criteria described below.

Once students have passed their Qualifying Requirements, the two tracks merge and there is no distinction in later examinations and research opportunities. In particular, the candidacy exam for both tracks consists of a research proposal, the graduate faculty available for advising is the same, and the final degree and thesis defense are independent of the initially chosen track.

Expected Preparations for Admission

Competitive applicants to the theoretical track are expected to have strong foundations in Real Analysis and Abstract Algebra, equivalent to our Math 5201 - 5202  and Math 5111 - 5112 sequences.

Expected preparations for the applied track include the equivalents of a rigorous Real Analysis course (such as Math 5201 ), a strong background in Linear Algebra, as well as an introductory course in Scientific Computing.

Besides these basic requirements, competitive applicants in either track submit evidence for a broad formation in mathematics at the upper-division or beginning graduate level. Relevant coursework in other mathematical or quantitative sciences may also be considered, especially for the applied track.

Prior research experiences are not required for either track, and we routinely admit students without significant research background. Nevertheless, applicants are encouraged to include accounts of research and independent project endeavors as well as letters of supervising mentors in order to be more competitive for fellowship considerations. The research component is likely to have greater weight in applications to the applied track.

These prepared documents serve to provide our admission committee with a narrative overview of the applicant's mathematical trajectory. Their primary focus should, therefore, be to enumerate and describe any evidence of mathematical ability and mathematical promise. The information included in the documents should be well-organized, comprehensive, informative, specific, and relevant. This will help our committee to properly and efficiently evaluate the high number of applications we receive each year.

Our Graduate Recruitment Committee will generally  not  consider GRE test scores for this Autumn 2024 admissions. If you have already taken the test, please do not self-report the scores to us. In exceptional circumstances students may have the option to report unofficially. 

International students whose native language is not English and are not exempt should score at least a 20 on the Speaking portion of the TOEFL or at least 6.5 on the IELTS Speaking portion.  We also recommend an overall score of at least 95 on TOEFL or at least 7.0 on IELTS.  For a list of exempt countries, please see  https://gpadmissions.osu.edu/intl/additional-requirements-to-apply.html

Qualifying Requirements by Track

The qualifying requirements for the theoretical track are fulfilled by passing our Abstract Algebra course sequence  ( Math 6111 , Math 6112 ) and  our Real Analysis course sequence ( Math 6211 , Math 6212 ), each with at least an A-, or  by passing a respective examination.

The qualifying requirements for the applied track combine a mandatory Scientific Computing course ( Math 6601 ), one of the algebra or analysis courses, and three additional courses chosen from  Math 6602 , Math 6411 ,  Math 6451 , and the courses comprising the algebra and analysis sequences.

The breadth requirements in the applied track are more flexible than in the theoretical track, but also include a mandatory graduate course in a non-math STEM department from an approved list. 

You can find more information about our PhD program requirement here .

Opportunities & Outcomes

The research opportunities and academic outcomes of our doctoral program are described in detail in the Graduate Program Prospectus  [pdf]. 

Our department has about 80 active graduate faculty on the Columbus and regional campuses. Virtually every area of mathematics is represented in our program, with a sampling displayed below.

• Commutative, Non-commutative, & Quantum Algebra
• Analytic, Algebraic, Computational Number Theory
• Algebraic Geometry, Tropical Geometry
• Applied Mathematics, Mathematical Physics
• Real and Complex Analysis
• Functional Analysis, Operator Algebras
• Combinatorics and Graph Theory
• Differential Geometry
• Dynamical Systems and Ergodic Theory
• Financial and Actuarial Mathematics
• Logic and Foundations
• Probability Theory, Statistical Mechanics
• Mathematical Biology
• Ordinary and Partial Differential Equations
• Representation theory
• Scientific Computing
• Topology, Topological Data Analysis

See also our  Applied Mathematics Topics List  [pdf].

Our program offers many support opportunities without teaching duties as well, to allow more time for scientific endeavors. These opportunities include university fellowships, external funding, and departmental fellowships and special assignments. See the  Financial Support  page for more details.

The median time to degree completion in our program is below six years but also varies significantly among our students, with as little as four years for students entering with substantial prior preparations. Funding is guaranteed for six years and can be extended to seven years with advisor support and the permission of the Graduate Studies Committee.  

Most of our graduates continue their careers in academia. Post-doctoral placements in the last two years include, for example, UCLA, Stanford, ETH-Zürich, Brown University, University of Michigan, Northwestern University, University of Vienna, EPF Lausanne, Free University at Berlin, Purdue University, and University of Utah. In recent years our graduates also went to Princeton University, IAS, University of Chicago, Yale University, University of Michigan, Cal-Tech, Northwestern University, University of Texas, Duke University, SUNY Stony Brook, Purdue University, University of North Carolina - Chapel Hill, and Indiana University. Recent non-academic placements include Google, Facebook, Amazon, NSA, and prestigious financial institutions.

Students also have access to training and networking opportunities that prepare them better for careers in private industry and teaching - for example, through the Erdős Institute  - and are regularly offered highly competitive positions in the industry. 

Nearly half of the graduate population consists of domestic students coming from both larger universities and smaller liberal arts colleges with a solid math curriculum. And as a program group member of the National Math Alliance , we are dedicated to enhancing diversity in our program and the scientific community. The International students in our program come from all parts of the world with a wide variety of educational backgrounds.

Prospective students:  [email protected]

Graduate Office Department of Mathematics The Ohio State University 231 W 18th Avenue ( MA 102 ) Columbus, Ohio 43210 United States of America                

Phone: (614) 292-6274 Fax: (614) 292-1479

[pdf] - Some links on this page are to .pdf files. If you need these files in a more accessible format, please email  [email protected] . PDF files require the use of Adobe Acrobat Reader software to open them. If you do not have Reader, you may use the following link to Adobe to download it for free at:  Adobe Acrobat Reader .

Mathematics Education PhD

Doctor of philosophy.

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Admissions Information

Displaying requirements for the Spring 2024, Summer 2024, and Fall 2024 terms.

• Points/Credits: 75
• Entry Terms: Spring, Summer, Fall

Application Deadlines

For details about rolling deadlines , visit our admission deadlines page.

Select programs remain open beyond our standard application deadlines , such as those with an extended deadline or those that are rolling (open until June or July). If your program is rolling or has an extended deadline indicated above, applications are reviewed as they are received and on a space-available basis. We recommend you complete your application as soon as possible as these programs can close earlier if full capacity has been met.

Application Requirements

Requirements from the TC Catalog (AY 2023-2024)

Displaying catalog information for the Fall 2023, Spring 2024 and Summer 2024 terms.

View Full Catalog Listing

Doctoral Degrees

All candidates for the Ed.D., Ed.D.C.T., or Ph.D. degrees are expected to demonstrate both mathematics and mathematics education competencies through a series of certification examinations taken upon the completion of 60 graduate points. Certification examinations test the student’s knowledge of current research and theory in mathematics education and mathematics content. Examinations are offered once in the fall, spring, and summer terms. Courses recommended as preparation for the examinations in mathematics education include MSTM 6037,  MSTM 4019, and other mathematics education courses; Courses recommended as preparation for the examinations in mathematics are 6000- level mathematics content courses.

Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, discrete mathematics, foundations of mathematics, geometry and topology, and probability and statistics. Students may sit for the examination in mathematics content during the regular certification examination times. Alternatively, they may register for advanced content courses and, with permission of the program, sit for the content area certification examination upon completion of the course. Incoming doctoral candidates should register for MSTM 6037 Professional Seminar in Mathematics during the first year of doctoral studies.

Doctoral students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Doctor of Philosophy in Mathematics Education

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree program requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Candidates are encouraged to develop an association with a faculty member early in their studies to identify a problem area of mutual interest to plan a course of studies that leads to the competencies needed to complete dissertation research and prepare for a professional role. Further details are available in the brochures on doctoral studies and in the general descriptions of doctoral programs available from the Office of Doctoral Studies (ODS).

A program of study for the Doctor of Philosophy degree must include at least 45 points taken under Teachers College registration. In order to permit the acquisition of broad and basic scholarship, each program of study should include at least 60 points in mathematics, mathematics education, statistics, and computing. At least 35 points should be in advanced courses – including research courses (MSTM 6500 or 6501 and MSTM 7500). (Any Teachers College course at the 6000 level or above, any Columbia University Graduate School of Arts and Sciences course with a “G” prefix, any “W” course numbered above 4000, or any transferred course with a graduate-level prerequisite will be considered an advanced course.) Further, 15 points in the philosophical, psychological, and curricular foundations of education must be included in every Ph.D. degree program. Students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Candidates for the Ph.D. degree are required to demonstrate competency in two languages chosen from among French, German, and Russian. Students who require other languages for the preparation of their dissertation may petition the program to request one substitution. Students in mathematics may not use computer languages or statistics to satisfy the language requirement.

The Ph.D. dissertation is a scholarly study contributing new theoretical knowledge to the field and should be planned early in the program when sufficient advanced courses have been completed to permit the candidate to enroll in relevant research courses. Ph.D. dissertations in mathematics education should be (1) experimental studies in learning, (2) analytical studies in policy theory in mathematics education, or (3) other scholarly investigations of problems and issues of broad significance in the field.

The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.

• View Other Degrees

Program Director : Professor Alexander Karp

Teachers College, Columbia University 323 Thompson

Phone: (212) 678-3381 Fax: (212) 678-8319

Email: tcmath@tc.edu

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	University of Southern California
	Jun 25, 2024   USC Catalogue 2024-2025     USC Catalogue 2024-2025 Application deadline: December 15 Completion of the program requires a maximum effort by the student for a minimum of four years of full-time work. Screening Procedure The screening procedure consists of written examinations covering core mathematics content. Student must pass three written exams chosen from among the following five core subjects: Probability The department offers the examinations twice a year, prior to the beginning of the Fall and Spring semesters.  Either the Algebra or Analysis examination must be successfully completed by the end of the second semester in the program. All of the examinations must be successfully completed by the end of the fourth semester.  The qualifying examination should follow one or two semesters after the successful completion of the screening procedure. Qualifying Exam Committee No later than at the end of the first semester after passing the screening procedure, the student must form a qualifying exam committee. The committee must consist of an adviser (committee chair) and four other faculty members, including at least one from another department.  Qualifying Examination The qualifying examination consists of written and oral components. The written portion of the qualifying examination consists of a PhD dissertation proposal. This document (6 pages minimum) should include: an introduction and overview of the area of research, a statement of the proposed research problem, literature survey, proposed approach including techniques or methods to be employed and references. No preliminary results are required. This research proposal should be submitted to the qualifying exam committee at least one week before the oral component of the exam.  The oral portion of the qualifying examination consists of a presentation of the PhD dissertation proposal and examination by the committee. The student must demonstrate research potential. The student must register for Math 794a in the semester immediately following successful completion of the qualifying examination. Course Requirements The student must complete, with no grade lower than B, a minimum of 60 units of courses carrying graduate credit. Courses outside of the Mathematics Department must be approved by the Graduate Committee. Required Courses The following courses must be completed with a grade of B or higher. Students may opt to pass the written screening exam, at the PhD level, in lieu of the course. MATH 510a Algebra Units: 3 MATH 525a Real Analysis Units: 3 MATH 540 Topology Units: 3 MATH 794a Doctoral Dissertation Units: 2 MATH 794b Doctoral Dissertation Units: 2 Additional courses Five additional courses from the following list must also be completed: MATH 502a Numerical Analysis Units: 3 MATH 505b Applied Probability Units: 3 MATH 507a Theory of Probability Units: 3 MATH 510b Algebra Units: 3 MATH 520 Complex Analysis Units: 3 MATH 525b Real Analysis Units: 3 MATH 532 Combinatorial Analysis Units: 3 MATH 533 Algebraic Combinatorics Units: 3 MATH 535a Differential Geometry Units: 3 MATH 535b Differential Geometry Units: 3 MATH 541a Introduction to Mathematical Statistics Units: 3 MATH 555b Partial Differential Equations Units: 3 MATH 565a Ordinary Differential Equations Units: 3 Additional Requirements Transfer of credit. No transfer of credit will be considered until the screening examination is passed. A maximum of 30 units of graduate work at another institution may be applied toward the course requirements for the PhD. A grade lower than B will not be accepted and at most one grade of B will be accepted. Dissertation and Defense Following successful completion of the screening procedure and approval of a dissertation topic by the chair of the student’s qualifying exam committee, the student proceeds with research towards the dissertation.  The student must form a dissertation committee consisting of at least three members, including the thesis advisor (committee chair) and a member outside the mathematics department. The PhD thesis, based on a substantial amount of original research conducted by the student, must be defended and approved by the dissertation committee. Request Info Browse Degrees Student Resources Faculty Resources Diversity, Equity & Inclusion Give to SLU Search & Directory Graduate Math Requirements Graduate students in the Saint Louis University Department of Mathematics and Statistics must fulfill certain academic requirements. Master’s Degree Coursework Saint Louis University’s Master of Arts in Math requires 10 courses in mathematics at the 4000-level or higher. At least seven of the courses must be at the 5000-level or higher. All master’s students must complete at least two 5000-level sequences chosen from algebra, analysis and topology. Many students build their program around a number of year-long sequences from areas including algebra, analysis and topology. The department typically offers year-long sequences in algebra, analysis, complex variables and probability and statistics at the 4000-level; algebra, analysis and topology at the 5000-level; and differential geometry at the 6000-level. The department also routinely offers a variety of electives determined by student and faculty interest. Full-time students typically take three courses a semester and complete the degree in two years. A first year master’s student usually takes two or three year-long sequences. If you have not had courses in algebra or analysis at the undergraduate level, we recommend taking the 4000-level algebra and analysis sequences. This prepares you to take the 5000-level sequences in algebra, analysis and topology your second year. For students who have had substantial coursework in algebra or analysis at the undergraduate level, some of the 5000-level sequences could be completed in the first year. Additional Requirements In addition to the 10 courses in mathematics, master’s students must take a comprehensive oral exam in the final semester of their program. This exam is administered by three faculty members. The exam consists of three parts, one for each of three assessment areas. Assessment areas are chosen by the director of graduate studies in consultation with the student. In each part, the student gives a 10-minute talk on a mathematical topic in that area. Each talk will be followed by a question-and-answer period. The duration of each of the three parts is about 30 minutes. Master’s students have the option of writing a master’s thesis. In that case, two of the courses in the second year would be devoted to research for the thesis, and the master’s oral exam is replaced by an oral defense of the thesis. Financial Support A master’s student can receive up to two years of support as a teaching assistant. Renewal of the assistantship for the second year is not guaranteed as the student needs to demonstrate sufficient progress towards the degree. A master’s student must obtain at least a 3.0 GPA overall. If after the first year the GPA is lower than a 3.0, the teaching assistantship cannot be renewed for the second year. Furthermore, a B or better must be obtained in each course comprising the two required 5000-level sequences. A master’s student who plans to pursue a Ph.D. in mathematics should maintain a GPA above a 3.0 and should include some As. Ph.D. Coursework The requirements for SLU’s Ph.D. in mathematics include written examinations, a language examination, an oral examination, and writing and defending a dissertation. In addition, there is an important procedural step called “advancement to candidacy.” Students who enter the Ph.D. program with a bachelor’s degree in mathematics must complete 48 credit hours (16 courses) in mathematics at the 4000-level or higher, in addition to 12 hours of dissertation research as part of MATH 6990: Dissertation Research. At most, nine of these 48 hours can be at the 4000-level with the remaining 39 hours at the 5000- or 6000-level. For those who enter with a master’s degree in mathematics, the requirement is 24 hours (eight courses) of coursework at the 5000 or 6000-level plus 12 hours of dissertation research. All Ph.D. students must complete the 5000-level sequences in algebra, analysis, and topology, as well as the 6000-level sequence in differential geometry. Beyond that, students choose a set of courses that provide them with a broad knowledge of mathematics and a deep understanding of their intended research area. The department routinely offers a variety of electives determined by student and faculty interest. Full-time students typically take three courses each semester, including reading courses and dissertation research. A Ph.D. student must obtain at least a 3.0 GPA overall. If the GPA is lower than a 3.0, then the teaching assistantship cannot be renewed for the next year. Ph.D. students must pass three-hour written examinations in three of the four areas covered by the 5000-level and 6000-level sequences: algebra, analysis, topology, and differential geometry. These examinations are given three times each year – at the beginning of each semester, and at the end of the spring semester. Students should take these examinations as soon as possible after completing the relevant coursework and must, in any case, attempt them within 10 months of completing the relevant coursework. However, if the sequence was completed before entering our Ph.D. program the exam must be taken within 10 months of entering the Ph.D. program. A student who fails any written examination twice ordinarily cannot continue in the Ph.D. program. Ph.D. students must pass a written examination in one of the following languages: French, German or Russian. The examination consists of translating a mathematical journal article that is written in one of those languages. After a Ph.D. student has completed the written examinations and chosen a dissertation advisor and an area of research, she or he must pass an oral examination administered by a committee of five faculty members. This oral examination involves a presentation on the student’s area of intended research, followed by questions from the examiners. After passing the written and oral Ph.D. examinations, the student is eligible to advance to candidacy. This step involves writing a prospectus for the dissertation and identifying the three faculty members who will serve as readers of the student’s dissertation. Students who want to apply for certain graduate fellowships must have advanced to candidacy. The culminating requirement for the Ph.D. degree is writing and successfully defending a dissertation that presents the results of the original and independent mathematical research that the student has carried out, with the guidance of a faculty member. A graduate student can receive total of up to five years of support from Saint Louis University as a teaching assistant, including support received while in the master’s and the doctoral program. Renewal of the assistantship from year to year is not guaranteed, as the student needs to demonstrate sufficient progress towards the degree. Students who are awarded teaching assistantships normally teach one course per semester. This allows graduate students maximum freedom to pursue graduate study while perfecting their teaching skills. The nine-month stipend amount is approximately $19,000, including full tuition remission and medical benefits. In addition, each year the department can nominate outstanding candidates for Minority Fellowships and Presidential Fellowships. --> | AA/EOE/ADAI     University of Southern Mississippi       Jun 25, 2024   Working copy 2024-2025 Graduate Bulletin     Working copy 2024-2025 Graduate Bulletin The master’s program is designed for students to develop a working background in mathematics. Moreover, students interested in applied mathematics can build the foundation to continue in a doctoral program in applied and computational mathematics. Thus, the master’s program provides flexibility to accommodate a wide range of interests, as well as the opportunity to specialize in applied mathematics. Campus:  Hattiesburg, Online 100% Admission Requirements In addition to complying with the Academic Requirements and Procedures prescribed by the Graduate School, applicants must provide a resume, statement of purpose, and three letters of recommendation. Applicants whose native language is not English must earn a TOEFL score of at least 550 (TOEFL PBT), 217 (TOEFL CBT), or 80 (TOEFL iBT), or an IELTS score of at least 6.5. Program Requirements and Academic Policies In addition to meeting the requirements stated in  General Degree Requirements    and General Academic Information   , the following requirements must be satisfied: Of the 30 required graduate hours, at least 18 hours must be in mathematics courses numbered above 600. For students choosing the thesis option, up to 6 hours of MAT 698 count toward this requirement. For students who choose the non-thesis option, MAT 698 will not count towards their degree. Subject to approval of the school director and the student’s graduate committee, up to nine (9) semester hours of non-mathematics courses may be used as a portion of the 30 required graduate hours. Said nine hours should be taken from the following list of non-mathematics courses, or should comprise a minor in another discipline. BSC 747, Multivariate Applications in Ecology (3) CSC 513, Algorithms (3 hrs) CSC 630/730, Parallel Programming Techniques (3 hrs) PHY 601, Mechanics (3 hrs) PHY 603, Statistical Physics (3 hrs) PHY 650, Quantum Mechanics I (3 hrs) PHY 710, Computational Methods for Physical Systems I (3 hrs) PHY 711, Computational Methods for Physical Systems II (3 hrs) Each candidate for the master’s degree will be expected to demonstrate subject matter mastery on the required written master’s comprehensive examination. For the non-thesis student, the comprehensive examination will consist of three written exams, with each exam covering one of the four areas indicated in the course requirements below. The areas are selected by the student. Students choosing the thesis option must satisfy the following requirements: Completion and successful defense of a thesis under the direction of a thesis director. The thesis director must be selected from the graduate faculty by the second semester. The thesis prospectus must be approved by the graduate committee by the end of the third semester. Prospectus approval and thesis defense cannot take place during the same semester. A written comprehensive examination consisting of two written exams, with each exam covering one of the four areas indicated in the course requirements below. The areas are selected by the student. Course Requirements (30 hours) The student, with the help of his or her academic adviser, must select courses from at least three of the following areas, with the option of additional electives.  MAT 536 - Theory of Functions of a Complex Variable 3 hrs. MAT 542 - Advanced Calculus II 3 hrs. MAT 636 - Functions of a Complex Variable 3 hrs. MAT 641 - Functions of a Real Variable I 3 hrs. MAT 642 - Functions of Real Variable II 3 hrs. MAT 521 - Number Theory 3 hrs. MAT 524 - Modern Algebra II 3 hrs. MAT 603 - Modern Algebra 3 hrs. Numerical and Data Analysis: MAT 520 - Probability and Mathematical Statistics II 3 hrs. MAT 561 - Numerical Analysis II 3 hrs. MAT 610 - Numerical Linear Algebra 3 hrs. Differential Equations: MAT 515 - Introduction to Differential Equations II 3 hrs. MAT 517 - Introduction to Partial Differential Equations 3 hrs. MAT 605 - Ordinary Differential Equations 3 hrs. MAT 606 - Partial Differential Equations 3 hrs. Thesis option: For students choosing the thesis option, 6 hours of the following course are required: MAT 698 - Thesis 1-6 hrs. for a total of 6 hrs. Admissions & Aid Campus Life Info For... Mathematics - M.ED. Master of education, learning format. The Master of Education (M.Ed.) with a concentration in Mathematics is designed for students who are interested in furthering their knowledge of mathematics at the graduate level, without regard to employment as teachers, as well as those who wish to meet state or district requirements for teacher licensure. The program leads to the Professional License (Grades 5-8 or Grades 8-12). Request Information Admission Requirements The applicant must: Complete the online graduate admission application Submit the $50.00 application fee Have earned a baccalaureate degree from a regionally accredited college or university. An overall undergraduate quality point average (QPA) of at least 2.80 on a 4.00 scale or QPA of 2.80 for all courses completed in the last two years of the student’s full-time undergraduate program. Mathematics preparation comparable to Framingham State University’s mathematics major including Calculus I, II, and III, Linear Algebra and Applications, Number Theory, and one (1) computer science course. A Massachusetts Initial License in Mathematics. This requirement will be waived for persons who are not using this degree in order to obtain teacher licensure in the State of Massachusetts. Provide two letters of recommendation submitted on the Framingham State University Letter of Recommendation form and sent directly to the University’s Graduate Admissions office by the recommender. One letter must be from an employer or supervisor, and the other must be from a faculty member who has taught the candidate at the collegiate level if the candidate attended classes in the last five years; Submit a typed, 300-word personal statement discussing their motivation for seeking a master’s degree in view of prior formal education, current job responsibilities, and career plans. Students whose academic background does not meet the requirements under item 5 above may still qualify for admission. In these cases, students would be asked to make up course deficiencies as part of their graduate program, in addition to the core and concentration courses. Program Requirements The program requires successful completion of ten (10) courses, which include three (3) core courses, and seven (7) concentration courses. A comprehensive examination is required as the student’s culminating experience. EFFECTIVE AS OF THE 2023-2024 GRADUATE CATALOG EDUC 991 Philosophy of Education and Teaching Practice EDUC 998 Language Developments and Communication EDUC 999 Research and Evaluation (recommended after completion of three Content/Concentration courses) MATH 901 Foundations of Mathematics MATH 999 Reading and Research in Higher Mathematics Five (5) additional courses are approved in writing by the student’s advisor. The student is expected to develop competencies in the following areas: analysis, algebra, geometry, discrete mathematics, and probability and statistics. Visit Framingham Learning Outcomes Upon completion of the program, students will: Be able to analyze, assess, and develop logical arguments in a rigorous and logical manner. Have a deeper knowledge and understanding of the nature of mathematics, its history, and its impact on civilizations. Be able to recognize, explain, and discuss the patterns and connections between the mathematics studied in each course and the world we live in. Be able to model complex situations arising in the classroom in a variety of ways to create better understanding of the mathematics. Understand and appreciate the beauty, the structure, and the relationships underlying all areas of human endeavor arising from mathematics. Be able to identify and develop a research topic based upon their teaching experiences, their course work and their readings concerning the teaching of mathematics which will culminate in thoroughly researched theses. Meet the Faculty Dr. Julie Levandosky Michael Krul Robert Page, Ph.D. Dr. Mohammad Salmassi Graduation requirements. Students must complete a Graduation and Comprehensive Examination Application and submit to the office of Graduate Studies. Framingham State University Office of Graduate Studies, Dwight Hall Rm 202 100 State Street Framingham, MA 01701 Application deadlines are strictly adhered to. The deadline for submitting the Graduate Application for December is August 15, May the deadline is January 15, and the August deadline is April 15. The Application includes both Commencement and Comprehensive Examination information. The Comprehensive Exam is conducted by a three-member panel and must be passed. A majority ruling determines the result. A student who fails the exam is given one opportunity to re-take. The repeat cannot be taken in the same semester of failure without the approval of the Dean and Program Advisor. Students must file a new application for the retake. Please see the Graduate Catalog for further details. Transfer Credit Requests for a waiver of a program prerequisite or approval of transfer credit of an equivalent graduate course completed at another accredited college or university will be considered at the time of admission based on course descriptions and documentation submitted with the student’s application. Courses accepted in transfer must meet the academic criteria established by Framingham State University. A maximum of two (2) graduate courses may be accepted in transfer and applied toward a Framingham State University degree program. Financial Aid In order to be eligible for financial aid, you must be matriculated in a degree program and enrolled in at least two courses per semester. For more information visit the Framingham State University Financial Aid Office, or call 508-626-4534. International Students Application materials such as transcripts, letters of recommendation, test score reports and copies of teaching licenses should be mailed directly to: Admissions Processing Center Framingham State University Dwight Hall, Room 209 100 State Street, PO Box 9101 Framingham, MA 01701-9101 MORE ABOUT THE PROGRAM Course Cycle Curriculum Map Contact Graduate Admissions RELATED RESOURCES Tuition and Fees STEM Scholarship Information Graduate Catalog Graduate Student Handbook Take the next step Lone Star Politics Politifact Texas Austin History More math? Oklahoma bill could change some requirements to graduate high school Oklahoma students could be required to take a fourth math credit to graduate high school, but they would have an extra year to complete it, if a new proposal becomes law. The state House overwhelmingly approved a measure on Wednesday in a 95-2 vote to add a fourth math credit to graduation requirements.  House Bill 3278  would allow students to begin taking high school credits in eighth grade. The bill would take effect in the 2025-26 school year. It now advances to the Senate for consideration. Two of the credits would have to be Algebra I and either Algebra II or geometry. The other two credits must be any math course with “content and/or rigor above Algebra I.” This could include traditional upper-level courses like Algebra II, geometry, trigonometry, calculus and statistics. Schools also could apply a math credit to a postsecondary career and technology program or to a course that teaches math through real-world application. More: Oklahoma County to begin negotiating for jail land near Crooked Oak schools In Oklahoma City Public Schools, this could mean an HVAC or construction trade class could count as a math credit, if the local school board approves it, said Superintendent Sean McDaniel during a Monday board meeting. “It would make sense because of the amount of math that kids will use in those pathways that we might be able to award credit,” McDaniel said. Bill would also change some career credit requirements for Oklahoma high school students Existing requirements to complete four credits of English language arts, three credits of laboratory science and three credits of history would be unchanged. Six high school credits would have to relate to a student’s aspirations after high school, under the bill.  Oklahoma students already have to create an Individual Career and Academic Plan (ICAP) to prepare for entering college, the military or the workforce. The bill would mandate that six courses, or “pathway units,” correspond to students’ ICAP goals. Mandatory courses in English, math, science and history would count toward these credits. Students also could fulfill the requirement by taking a world language, computer technology, fine arts, Advanced Placement credits, college concurrent enrollment or Junior Reserve Officers’ Training Corps (JROTC), among other options. The bill’s author, Rep. Rhonda Baker, R-Yukon, said the measure encourages students to take classes that are most relevant to their career goals. “We are revamping this so that their pathway will fit whatever they deem necessary and important to them,” she said during discussion on the House floor. 471 IMAGES phd maths eligibility Requirements for the Course Major :: Mathematics & Statistics PhD in Mathematics PhD In Mathematics PhD Research Proposal in Mathematics how to phd in maths VIDEO Study Continues...... #phd #maths #mathematics #cguniversity 🎓 #WhyStudy: PhD (Mathematics and Mathematics Education) by Mr Jahangeer PhD Mathematics Entrance Exam Result #exam Is Gen Z worth saving? Where have I been while rolling my hair. 💗 Hi. 💗 UTRGV PhD Mathematics and Statistics with Interdisciplinary Applications Brahmi #organicfood Brahmi #academics COMMENTS Requirements for the Ph.D. Degree Requirements for the Ph.D. Degree. In order to qualify for the Mathematics Ph.D., all students are required to: Complete eight term courses at the graduate level, at least two with Honors grades. Pass qualifying examinations on their general mathematical knowledge; Submit a dissertation prospectus; Participate in the instruction of undergraduates; Admissions Admissions. Financial Support. Graduate Program Administrator. Marjorie Bell (she/her) 617-496-5211. [email protected]. Science Center Room 331. 1 Oxford Street. Cambridge, MA 02138. PhD Requirements Course Requirements Mathematics PhD candidates must show satisfactory work in Algebra (110.601-602), Real Variables (110.605), Complex Variables (110.607), and one additional non-seminar mathematics graduate course in their first year. The first-year algebra and analysis requirement can be satisfied by passing the corresponding written qualifying exam in September of the first year; these ... Ph.D. Program In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics. Pass the six-hour written Preliminary Examination covering calculus ... Ph.D. Program Overview Description. The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of interests of the faculty. The department has outstanding groups in the areas of ... Mathematics PhD Program The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both ... Ph.D. in Mathematics Overview of Graduation Requirements. To graduate with a PhD in Mathematics, a student must satisfy all of the following requirements: If you have a Master's degree in mathematics at UConn, then 30 credits are required, including 15 doctoral dissertation research credits. Pass three preliminary exams and two core courses (details below). PhD in Mathematics Here are the requirements for earning the PhD degree in Mathematics offered by the School of Math. For requirements of other PhD programs housed within the School, please see their specific pages at Doctoral Programs.The requirements for all these programs consist of three components: coursework, examinations, and dissertation in accordance to the guidelines described in the GT Catalogue. Guide To Graduate Study Guide to Graduate Studies. The PhD Program. The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in ... Ph.D. in Mathematics The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the NYU Shanghai Ph ... Ph.D. in Mathematics Math Ph.D. Requirements. Passing four core course sequences from Algebra, Applied Mathematics, Complex Analysis, PDE, Topology, and/or Real Analysis. A sequence consists of all courses with the same course number except for an alphabetical suffix. Any course without an alphabetical suffix is not part of a sequence. Doctoral Degree Requirements The PhD in Mathematics requires completing at least 36 credits of graduate coursework beyond the bachelor's degree, preliminary written and oral examinations, 24 thesis credits, and a doctoral thesis with final defense. PhD students in Mathematics are expected to earn an MS degree upon completion of their preliminary oral examination. Ph.D. Requirements Courses Required (9 total): 800, 810. One 2-course sequence: 850/851 or 865/866 or 881/882. One of the following: 840, 850 or 950. Four additional courses at 800 level or above. The requirements for exams, research skills, enrollment hours and research component are the same for both the pure and applied tracks. Doctor of Philosophy Program Doctor of Philosophy Program. Besides satisfying the general regulations of the Graduate School for the degree of Doctor of Philosophy, the student must comply with the requirements briefly outlined below. For complete details about these requirements see section IV of the Graduate Handbook. Pass four Qualifying Examinations. Ph.D. in Mathematics The Ph.D. in Mathematics allows study in pure mathematics, applied mathematics and statistics. The mathematics department has over 60 faculty, approximately 100 Ph.D. students, and approximately 35 Masters students. A list of the UCSD mathematics faculty and their research interests can be found at here. PhD Requirements The basic requirements for the PhD degree in mathematics include demonstrating a mastery of a broad area of mathematics and writing a dissertation making an original and substantial contribution to mathematics. Specific requirements for the PhD degree in mathematics consist of: Coursework. Qualifying Exams. PhD Requirements Time and residency requirements. PhD students are required to take a minimum of 48 semester hours of course work, including at least 3 units of Math 994, PhD dissertation. PhD students must complete their degree within eight years unless special permission is given for an extension of time. Students who remain beyond 10 semesters are ... Doctor of Philosophy (PhD) The Doctor of Philosophy (PhD) in mathematics is the highest degree offered by our program. Graduates will have demonstrated their ability to conduct independent scientific research and contribute new mathematical knowledge and scholarship in their area of specialization. They will be well-supported and well prepared for research and faculty positions at academic institutions anywhere in the ... Mathematics Education PhD Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, discrete mathematics, foundations of mathematics, geometry and topology, and probability and statistics. Students may sit for the examination in mathematics content during the regular certification examination times. Degree Requirements for PhD in Mathematics PhD students are required to take 4 of 5 core courses, one of which must be MATH 675. The core courses are. MATH 675 (Linear Analysis) MATH 621 (Algebra) MATH 631 (Topology) MATH 677 (Ordinary Differential Equations) MATH 685 (Numerical Analysis) Students should also take the Graduate Seminar (1 credit) for at least six semesters (maximum nine ... Ph. D. Requirements Course Requirements. Students are required to complete 36 units of graduate credit in the major and 12 units in a supporting minor, which may be declared in Mathematics, although outside minors are encouraged. Units may not be counted towards both the major and minor. In addition, 18 units of dissertation (Math 920) must be completed. PhD Requirements PhD Requirements. Below is a summary of the requirements for the Ph.D. in Mathematics. General requirements for graduate degrees at Rutgers are governed by the rules of the Graduate School - New Brunswick and are listed in the current catalog. These include how and when credit can be transferred and how many credits can be taken each semester. PhD in Mathematics Math Course Requirement: every graduate student must pass, with a grade of B- or higher, at least 10 courses in the math department of 3+ credits each, at the 500+ level. Breadth seminar requirement: every graduate student must pass the following two seminars within their first two years at CSU. Seminar on applications of math. 1-credit. Program: Mathematics (PhD) Course Requirements. The student must complete, with no grade lower than B, a minimum of 60 units of courses carrying graduate credit. ... and a member outside the mathematics department. The PhD thesis, based on a substantial amount of original research conducted by the student, must be defended and approved by the dissertation committee. Graduate Requirements : SLU Graduate students in the Saint Louis University Department of Mathematics and Statistics must fulfill certain academic requirements. Master's Degree Coursework. Saint Louis University's Master of Arts in Math requires 10 courses in mathematics at the 4000-level or higher. Program: Mathematics MS Subject to approval of the school director and the student's graduate committee, up to nine (9) semester hours of non-mathematics courses may be used as a portion of the 30 required graduate hours. Said nine hours should be taken from the following list of non-mathematics courses, or should comprise a minor in another discipline. Mathematics The Master of Education (M.Ed.) with a concentration in Mathematics is designed for students who are interested in furthering their knowledge of mathematics at the graduate level, without regard to employment as teachers, as well as those who wish to meet state or district requirements for teacher licensure. The program leads to the Professional License (Grades 5-8 or Grades 8-12). Benefits and Duties of Graduate Teaching Assistants Coursework Requirements for Graduate Teaching Assistants. Each GTA (with 0.5 FTE) must be enrolled in a minimum of 6 and a maximum of 15 credits in graduate- level courses (two to five 3-credit courses) each semester. ... Department of Mathematics The University of Alabama Box 870350 Tuscaloosa, AL 35487-0350 (205) 348-5090 [email protected]. Oklahoma could require more math credits to graduate high school The state House overwhelmingly approved a measure on Wednesday in a 95-2 vote to add a fourth math credit to graduation requirements. 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