## 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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- The firm deadline for applications for Autumn 2025, is December 5, 2024.
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## 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.

## PhD Program

More information and a full list of requirements for the PhD program in Mathematics can be found in the University Bulletin .

During their first year in the program, students typically engage in coursework and seminars which prepare them for the Qualifying Examinations . Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis.

Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics:

- real analysis
- geometry and topology
- applied mathematics

## Course Requirements for students starting prior to Autumn 2023

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297.

Within the 27 units, students must satisfactorily complete a course sequence. This can be fulfilled in one of the following ways:

- Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry
- Math 216A, B, & C: Introduction to Algebraic Geometry
- Math 230A, B, & C: Theory of Probability
- 3 quarter course sequence in a single subject approved in advance by the Director of Graduate Studies.

## Course Requirements for students starting in Autumn 2023 and later

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297. The course sequence requirement is discontinued for students starting in Autumn 2023 and later.

By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.

During their third year, students will take their Area Examination , which must be completed by the end of Winter Quarter. This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also used as an opportunity for the student to present their committee with a summary of research conducted to date as well as a detailed plan for the remaining research.

## Years 4&5

Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

## Throughout the PhD Program

All students continue through each year of the program serving some form of Assistantship: Course, Teaching or Research, unless they have funding from outside the department.

Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest.

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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:

Year I - Fall Term | Year I - Spring Term |
---|---|

Linear Algebra | Topology II |

Differential Geometry I | Differential Geometry II |

Real Variables | Ordinary Differential Equations |

Complex Variables | Functional Analysis I |

Year II - Fall Term | Year II - Spring Term |
---|---|

Advanced Topics in Geometry: Isometric Immersions Before and After Nash | Advanced Topics in Geometry: Randomness and Complexity |

Advanced Topics in Geometry: High Dimensional Expanders and Ramanujan Complexes | Advanced Topics in Geometry: Topics in Geometric Nonlinear Functional Analysis |

Harmonic Analysis | Advanced Topics in Geometry: Analysis and Geometry of Scalar Curvature |

Advanced Topics in PDE: Resonances in PDEs | Advanced Topics in PDE: Analytic Aspects of Harmonic Maps |

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

Year I - Fall Term | Year I - Spring Term |
---|---|

Linear Algebra | Applied Stochastic Processes |

PDE I | Asymptotic Analysis |

Fluid Mechanics | Continuum mechanics |

Numerical Methods I | Numerical Methods II |

Year II - Fall Term | Year II - Spring Term |
---|---|

Neurophysiology and Neuronal Networks | Data Analysis |

Complex fluids | Mathematical Physiology |

Real Variables | Geophysical Fluid Dynamics |

Computational Fluid Dynamics | Nonlinear Optimization |

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

Probability

Year I - Fall Term | Year I - Spring Term |
---|---|

Stochastic Calculus | Probability: Limit Theorems II |

Probability: Limit Theorems I | Applied Stochastic Analysis |

Real Variables | Advanced Topics in Probability: Random Graphs |

Complex Variables | Advanced Topics in Math Biology:Stochastic Problems in Cellular Molecular and Neural Biology |

Year II - Fall Term | Year II - Spring Term |
---|---|

Advanced Topics in Probability: Ergodic Theory of Markov Processes | Advanced Topics in Geometry: Randomness and Complexity |

Advanced Topics in Probability: Motion in Random Media | Advanced Topics in Probability: Random Matrices |

Advanced Topics in Applied Math: Quantifying Uncertainty in Complex Turbulent Systems | Advanced Topics in Probability: Markov Chain Analysis |

Derivative Securities | Advanced Topics in Numerical Analysis: Monte Carlo Methods |

PDE/Analysis

Year I - Fall Term | Year I - Spring Term |
---|---|

Linear Algebra | Topology II |

PDE I | Ordinary Differential Equations |

Real Variables | PDE II |

Complex Variables | Functional Analysis I |

Year II - Fall Term | Year II - Spring Term |
---|---|

Differential Geometry I | Algebra II |

Harmonic Analysis | Advanced Topics in PDE: Extreme Problems for Elliptic Eigenvalues |

Advanced Topics in Analysis: Calculus of Variations | Advanced Topics in Analysis: Dynamics of the Nonlinear Schroedinger Equation |

Probability: Limit Theorems I | Probability: Limit Theorems II |

## 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.

## Overview of the PhD Program

For specific information on the Applied Mathematics PhD program, see the navigation links to the right.

What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the Graduate Policies pages.

## General Ph.D. Requirements

- 10 semester-long graduate courses, including at least 8 disciplinary. At least 5 of the 10 should be graduate-level SEAS "technical" courses (or FAS graduate-level technical courses taught by SEAS faculty), not including seminar/reading/project courses. Undergraduate-level courses cannot be used. For details on course requirements, see the school's overall PhD course requirements and the individual program pages linked therein.
- Program Plan (i.e., the set of courses to be used towards the degree) approval by the Committee on Higher Degrees (CHD).
- Minimum full-time academic residency of two years .
- Serve as a Teaching Fellow (TF) in one semester of the second year.
- Oral Qualifying Examination Preparation in the major field is evaluated in an oral examination by a qualifying committee. The examination has the dual purpose of verifying the adequacy of the student's preparation for undertaking research in a chosen field and of assessing the student's ability to synthesize knowledge already acquired. For details on arranging your Qualifying Exam, see the exam policies and the individual program pages linked therein.
- Committee Meetings : PhD students' research committees meet according to the guidelines in each area's "Committee Meetings" listing. For details see the "G3+ Committee Meetings" section of the Policies of the CHD and the individual program pages linked therein.
- Final Oral Examination (Defense) This public examination devoted to the field of the dissertation is conducted by the student's research committee. It includes, but is not restricted to, a defense of the dissertation itself. For details of arranging your final oral exam see the Ph.D. Timeline page.
- Dissertation Upon successful completion of the qualifying examination, a committee chaired by the research supervisor is constituted to oversee the dissertation research. The dissertation must, in the judgment of the research committee, meet the standards of significant and original research.

## Optional additions to the Ph.D. program

Harvard PhD students may choose to pursue these additional aspects:

- a Secondary Field (which is similar to a "minor" subject area). SEAS offers PhD Secondary Field programs in Data Science and in Computational Science and Engineering . GSAS lists secondary fields offered by other programs.
- a Master of Science (S.M.) degree conferred en route to the Ph.D in one of several of SEAS's subject areas. For details see here .
- a Teaching Certificate awarded by the Derek Bok Center for Teaching and Learning .

SEAS PhD students may apply to participate in the Health Sciences and Technology graduate program with Harvard Medical School and MIT. Please check with the HST program for details on eligibility (e.g., only students in their G1 year may apply) and the application process.

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## 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.

## Mathematical Sciences

Mellon college of science, ph.d. programs, doctor of philosophy in mathematical sciences.

Students seeking a Ph.D. in Mathematical Sciences are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Doctor of Philosophy in Mathematical Sciences is a traditional research degree, and its requirements are representative of all doctoral programs.

After being admitted to graduate status by the Department, a student seeking a Ph.D. must be admitted to candidacy for this degree by fulfilling the appropriate program requirements.

The most important requirement for the Ph.D. degree is timely completion and public defense of an original Ph.D. thesis. The Ph.D. thesis is expected to display depth and originality and be publishable by a refereed journal.

## Doctor of Arts in Mathematical Sciences

The Doctor of Arts degree shares all requirements and standards with the Ph.D., except with regard to the thesis. The D.A. thesis is not expected to display the sort of original research required for a Ph.D. thesis, but rather to demonstrate an ability to organize, understand, and present mathematical ideas in a scholarly way, usually with sufficient innovation and worth to produce a publishable work. Whenever practical, the department provides D.A. candidates with the opportunity to use materials developed to teach a course. While a typical Ph.D. recipient will seek a position that has a substantial research component, the D.A. recipient will usually seek a position where research is not central.

## Doctor of Philosophy in Algorithms, Combinatorics, and Optimization (ACO)

This program is administered jointly by the Department of Mathematical Sciences, the Department of Computer Science, and the Tepper School of Business. It focuses on discrete mathematics and algorithmic issues arising in computer science and operations research, particularly the mathematical analysis of these issues. The participating units evaluate applicants separately. The requirements for this degree and information on participating faculty are available at the ACO page .

## Doctor of Philosophy in Pure and Applied Logic (PAL)

This is an interdisciplinary program with faculty from the Department of Mathematical Sciences, the Department of Philosophy, and the School of Computer Science. The participating units evaluate applicants separately and set their own program requirements. Students who have been admitted to the PAL program, and who complete the requirements for the Ph.D. in Mathematical Sciences with a thesis in the area of logic, can choose to receive either a Ph.D. in Pure and Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which degree to receive is usually based on the intended career path.

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## PhD in Mathematics

The PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an adviser, and creative research culminating in a written dissertation and defense. All doctoral students must also do some teaching on the way to the PhD. There are minimal course requirements, and detailed requirements and procedures for the PhD program are outlined in the PhD Handbook .

Please note that our department alternates recruiting in-coming classes that are focused on either applied or pure mathematics. For the Fall 2024 admissions (matriculation in September 2024), we are focusing on students interested in areas of applied mathematics.

All our professors are active in research, and are devoted to teaching and mentoring of students. Thus, there are many opportunities to be involved in cutting-edge research in pure and applied mathematics. Moreover, the seven other research universities in the Boston area are all within easy reach, providing access to many more classes, seminars and colloquia in diverse areas of mathematical research.

Teaching assistantships are available for incoming PhD students, as well as a limited number of University-wide fellowships. Tufts has on-campus housing for graduate students, but many choose to live off-campus instead.

In addition to the above, PhD students often:

- Mentor undergraduates as teaching assistants and course instructors, and through graduate-student run programs like the Directed Reading Program.
- Meet with advisors and fellow students to share research and collaborate with scholars across disciplines
- Attend professional development workshops and present research at conferences

## PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

## Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

- Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
- Analysis (examples include MA 711, MA 713, and MA 717)
- PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
- Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
- Topology (examples include MA 721, MA 722, and MA 727)
- Geometry (examples include MA 725, MA 731, and MA 745)
- Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
- Applied Mathematics (examples include MA 750, MA 751, and MA 770)
- Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
- Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
- Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

## Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

## More Information

Please reach out to us directly at [email protected] if you have further questions.

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## Mathematics Graduate Program

Thinking of applying to graduate school in mathematics.

Penn was ranked 8th among all US universities in a leading national study , and our mathematics graduate program was recently highest in a study of graduate programs in arts and sciences at Penn. We have a very active and involved mathematics faculty , diverse course offerings and a broad seminar schedule , with a variety of research projects and strengths in algebra, analysis, geometry-topology, combinatorics, logic, probability, and mathematical physics. We have a supportive atmosphere, with personal attention from the faculty and extensive interaction among graduate students. Our grad students can take courses not only in the Mathematics Department but also elsewhere at Penn, and the wide resources of the university are available. Our former graduate students have gone on to mathematical careers both in academia and in industry.

Our full-time Ph.D. students receive a generous and competitive support package including

- five years of funding with a combination of fellowships and teaching assistantships;
- a stipend and a full tuition scholarship;
- no teaching responsibilities for at least two years (generally including the first and fourth year);
- health insurance coverage provided at no cost to the student.

We invite you to learn about our graduate program, our math department, our university and living in Philadelphia, a cosmopolitan city and a true mathematical hub, with easy access to nearby mathematics departments and research institutes.

We are looking for interested, mathematically talented and dedicated students to be a part of our group of excellent future mathematicians. Consider applying to Penn for your graduate education. Questions?

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## Mathematics, PhD

The Department of Mathematics of the University of Pennsylvania offers a full Graduate Program in Mathematics, conferring the degrees of Master of Arts (A.M.), Master of Philosophy (M.Phil.), and Doctor of Philosophy (Ph.D.). The educational aim of this program is to provide well-rounded mathematical training for a career of research and teaching in mathematics, as well as for other careers which use advanced mathematics in a substantial way. Students are offered the possibility of a dual Ph.D. degree in Mathematics and a Masters degree in other subjects, including physics and computer science.

This program covers a variety of areas, including analysis, geometry-topology, algebra, mathematical physics, combinatorics, logic, and probability. See our Graduate Mathematics Page and our Math Department home page for detailed information about other aspects of this program and of the Penn Math Department as a whole, including its colloquia, seminars and lecture series, and the research interests of the faculty.

Full time Ph.D. students receive financial support for five years, at least two of which are in the form of a fellowship.

In addition, Penn offers an interdisciplinary graduate program in Applied Mathematics and Computational Science , for which there is separate application process.

For more information: https://www.math.upenn.edu/graduate/

View the University’s Academic Rules for PhD Programs .

## Sample Plan of Study

A total of 20 course units are required for graduation.

Code | Title | Course Units |
---|---|---|

Year 1 | ||

Topology and Geometric Analysis | ||

Topology and Geometric Analysis | ||

Algebra | ||

Algebra | ||

Analysis | ||

Analysis | ||

Year 2 | ||

Year 3 | ||

Year 4 | ||

Year 5 | ||

The degree and major requirements displayed are intended as a guide for students entering in the Fall of 2024 and later. Students should consult with their academic program regarding final certifications and requirements for graduation.

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## Ph.D. Program

Introduction.

These guidelines are intended to help familiarize graduate students with the policies governing the graduate program leading to the degrees of Doctor of Philosophy (Ph.D.) in Applied Mathematics. This material supplements the graduate school requirements found on the Graduate Student Resources page and the Doctoral Degree Policies of the graduate school. Students are expected to be familiar with these procedures and regulations.

## The Doctor of Philosophy program

The Doctor of Philosophy (Ph.D.) Degree in Applied Mathematics is primarily a research degree, and is not conferred as a result of course work. The granting of the degree is based on proficiency in Applied Mathematics, and the ability to carry out an independent investigation as demonstrated by the completion of a doctoral dissertation. This dissertation must exhibit original mathematical contributions that are relevant to a significant area of application.

## Course requirements for the Ph.D. program

- AMATH 561, 562, 563
- AMATH 567, 568, 569
- AMATH 584, 585, 586
- AMATH 600: two, 2-credit readings, each with a different faculty member, to be completed prior to the start of the student's second year.
- Students must take a minimum of 15 numerically graded courses. At most two of these can be at the 400 level or be cross listed with courses at the 400 level. Graduate level courses previously taken at UW (e.g., during a Master's program) count toward this requirement. Graduate level courses taken outside of UW may count toward the requirement for 15 numerically graded courses with the approval of the Graduate Program Coordinator. The entire course of study of a student and all exceptions to this list must be approved by the Graduate Program Coordinator and the student’s advisor or faculty mentors.

For students who entered the doctoral program autumn 2017 or autumn 2018, please see these degree requirements. For students who entered the doctoral program prior to autumn 2017, please see these degree requirements.

## Faculty mentoring

Upon arrival, incoming students will be assigned two faculty mentors. Until a student settles on an advisor, the faculty mentors aid the student in selecting courses, and they each guide the student through a 2-credit independent reading course on material related to the student’s research interest. The faculty mentors are not necessarily faculty in the Department of Applied Mathematics.

## Faculty advisor

By the end of a student’s first summer quarter, an advisor must be determined. T he advisor provides guidance in designing a course of study appropriate for the student’s research interests, and in formulating a dissertation topic.

A full Supervisory Committee should be formed four months prior to the student’s General Exam. The full Supervisory Committee should have a minimum of three regular members plus the Graduate School Representative , and will consist of at least two faculty members from Applied Mathematics, one of whom is to be the Chair of the Committee. If the proposed dissertation advisor is a member of the Applied Mathematics faculty, then the advisor will be the Chair. The dissertation advisor may be from another department, or may have an affiliate (assistant, associate, full) professor appointment with the Applied Mathematics department and is then also a member of the Supervisory Committee.

The Dissertation Reading Committee , formed after the General Exam, is a subset of at least three members from the Supervisory Committee who are appointed to read and approve the dissertation. Two members of the Dissertation Reading Committee must be from the Applied Mathematics faculty. At least one of the committee members must be a member of the core Applied Mathematics faculty. It is required that this member is present for both the general and final examination, and is included on the reading committee.

While the principal source of guidance during the process of choosing specialization areas and a research topic is the thesis advisor, it is strongly advised that the student maintain contact with all members of the Supervisory Committee. It is suggested that the student meet with the Supervisory Committee at least once a year to discuss their progress until the doctoral thesis is completed.

## Examination requirements for the Ph.D. program

Students in the Ph.D. program must pass the following exams:

- The qualifying exam
- The general exam
- The final exam (defense)

## Satisfactory performance and progress

At all times, students need to make satisfactory progress towards finishing their degree. Satisfactory progress in course work is based on grades. Students are expected to maintain a grade point average of 3.4/4.0 or better. Satisfactory progress on the examination requirements consists of passing the different exams in a timely manner. Departmental funding is contingent on satisfactory progress. The Graduate School rules regarding satisfactory progress are detailed in Policy 3.7: Academic Performance and Progress . The Department of Applied Mathematics follows these recommended guidelines of the Graduate School including an initial warning, followed by a maximum of three quarters of probation and one quarter of final probation, then ultimately being dropped from the program. We encourage all students to explore and utilize the many available resources across campus.

## Expected academic workload

A first-year, full-time student is expected to register for a full course load, at least three numerically graded courses, typically totaling 12-18 credits. All other students are expected to consult with their advisor and register for at least 10-18 credits per quarter. Students who do not intend to register for a quarter must seek approved academic leave in order to maintain a student status. Students who do not maintain active student status through course registration or an approved leave request need to request reinstatement to rejoin the program. Reinstatement is at the discretion of the department. Students approved for reinstatement are required to follow degree requirements active at time of reinstatement.

## Annual Progress Report

Students are required to submit an Annual Progress Report to the Graduate Program Coordinator by the second week of Spring Quarter each year. The annual progress report should contain the professional information related to the student’s progress since the previous annual report. It should contain information on courses taken, presentations given, publications, thesis progress, etc., and should be discussed with the student's advisor prior to submission. Students should regard the Annual Progress Report as an opportunity to self-evaluate their progress towards completing the PhD. The content of the Annual Progress Report is used to ensure the student is making satisfactory progress towards the PhD degree.

## Financial assistance

Financial support for Doctoral studies is limited to five years after admission to the Ph.D. program in the Department of Applied Mathematics. Support for an additional period may be granted upon approval of a petition, endorsed by the student’s thesis supervisor, to the Graduate Program Coordinator.

## Master of Science program

Students in the Ph.D. program obtain an M.Sc. Degree while working towards their Ph.D. degree by satisfying the requirements for the M.Sc. degree.

## Additional Ph.D. Degree Options and Certificates

Students in the Applied Mathematics Ph.D. program are eligible to pursue additional degree options or certificates, such as the Advanced Data Science Option or the Computational Molecular Biology Certificate . Students must be admitted and matriculated to the PhD program prior to applying for these options. Option or certificate requirements are in addition to the Applied Mathematics degree requirements. Successful completion of the requirements for the option or the certificate leads to official recognition of this fact on the UW transcript.

Career resources, as well as a look at student pathways after graduation, may be found here.

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## 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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Find Graduate Programs in the Mathematical Sciences offers comparative information on graduate programs in the mathematical sciences for prospective graduate students and their advisers. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information. Currently 276 graduate programs are listed.

All listings (alpha order) All listings by state

## Institution name

Program type, masters programs (check all that apply), phd specialties (check all that apply), financial support available, gre required, online options available, number of phds awarded in the last year, enrollments, canadian province, list or edit your graduate program in the mathematical sciences.

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## Find Graduate Programs Find the right graduate program in the mathematical sciences

Find Graduate Programs (FGP) in the Mathematical Sciences offers comparative information on over 500 graduate programs in the mathematical sciences in the US and Canada. This web service provides only an overview of the programs offered; departments should be contacted directly for more detailed information. Currently 740 graduate programs are listed.

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In the wake of the pandemic, many mathematical sciences departments have made at least short-term changes in their requirements regarding the GRE for individuals applying for admission to graduate programs. The Google doc USA/Canada Math PhD Programs: GRE requirements and Qualifying Exams , curated by Brown University graduate student Emily Winn, provides a list of those current requirements.

## Department of Mathematics

Phd requirements.

- Prospective Graduate Student FAQ
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## Qualifying Exams

- Recent PhD Theses
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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.)

## Mathematics Education, PHD

On this page:, at a glance: program details.

- Location: Tempe campus
- Second Language Requirement: No

## Program Description

Degree Awarded: PHD Mathematics Education

This transdisciplinary PhD program in mathematics education accommodates students from a variety of academic backgrounds. It provides students with a solid foundation in graduate-level mathematics as well as research skills and perspectives that enable them to incorporate mathematics into such core educational areas as:

Conducting individual and collaborative research in the learning and teaching of mathematics is an integral part of the program.

## Degree Requirements

Curriculum plan options.

- 84 credit hours, a written comprehensive exam, an oral comprehensive exam, a prospectus and a dissertation

Required Core (12 credit hours) MTE 501 Research in Undergraduate Mathematics Education I (3) MTE 502 Research in Undergraduate Mathematics Education II (3) MTE 503 Research in Undergraduate Mathematics Education Ill (3) MTE 504 Research in Undergraduate Mathematics Education IV (3)

Electives (42 credit hours)

Area Courses (12 credit hours)

Research (6 credit hours) MTE 792 Research (6)

Culminating Experience (12 credit hours) MTE 799 Dissertation (12)

Additional Curriculum Information Four to five graduate-level (500 and above) elective courses from mathematics, cognitive science, psychology, educational technology, philosophy or research should be taken as approved by the advisor.

For the area courses, students are required to take four graduate-level courses from the following areas of interest: mathematics, applied mathematics or statistics. Students should see the academic unit for the approved course list.

Students should see the school's website for information about qualifier and comprehensive examinations based on math coursework.

The doctoral dissertation culminating experience consists of a dissertation prospectus, oral dissertation defense and the submission of a final revised, formatted dissertation document to the Graduate College. Dissertations are composed under chair- and committee-supervised research, including literature review, research, data collection and analysis, and writing.

When approved by the student's supervisory committee and the Graduate College, up to 30 credit hours from a previously awarded master's degree may be used for this program. If students do not have a previously awarded master's degree, the remaining coursework is made up of electives and research.

## Admission Requirements

Applicants must fulfill the requirements of both the Graduate College and The College of Liberal Arts and Sciences.

Applicants are eligible to apply to the program if they have earned a bachelor's or master's degree in mathematics or a closely related area, with exceptionally high grades in advanced coursework in mathematics, from a regionally accredited institution.

Applicants must have a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in the last 60 hours of their first bachelor's degree program or a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in an applicable master's degree program.

All applicants must submit:

- graduate admission application and application fee
- official transcripts
- statement of education and career goals
- writing sample
- three letters of recommendation
- proof of English proficiency

Additional Application Information An applicant whose native language is not English must provide proof of English proficiency regardless of their current residency.

At least two of the letters of recommendation must be from faculty.

## Next Steps to attend ASU

Learn about our programs, apply to a program, visit our campus, application deadlines, learning outcomes.

- Able to complete original research in applied mathematics.
- Able to incorporate mathematical concepts into novel teaching methods.
- Address an original research question in mathematics education.

## Career Opportunities

Graduates of the doctoral program in mathematics education have opportunities in Arizona, the U.S. and internationally. Opportunities are typically at research universities and liberal arts colleges, community colleges, and education consulting firms and in roles such as:

- faculty-track academic
- education consultant or analyst
- mathematics professor, instructor or researcher

## Program Contact Information

If you have questions related to admission, please click here to request information and an admission specialist will reach out to you directly. For questions regarding faculty or courses, please use the contact information below.

- [email protected]
- 480/965-3951

## 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 2025, Summer 2025, and Fall 2025 terms.

- Points/Credits: 75
- Entry Terms: Spring, Summer, Fall
- Enrollment Formats: Full-Time, Part-Time

## Application Deadlines

Entry Term Available | Priority Deadlines | Final Deadlines | Extended Deadlines |
---|---|---|---|

Spring | November 15, 2024 | November 15, 2024 | N/A |

Summer | December 1, 2024 | June 1, 2025 | N/A |

Fall | December 1, 2024 | July 1, 2025 | N/A |

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

Requirement | |
---|---|

, including Statement of Purpose and Resume | |

Results from an accepted (if applicable) | |

$75 Application Fee | |

Two (2) Letters of Recommendation |

## 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

- Mathematics Education

Doctor of Philosophy (PhD)

## Advance Your Career

The Ph.D. program emphasizes research and requires a written dissertation for completion. The program is individualized to meet the needs of graduate students. The student must develop, with the guidance from the major professor and committee, a program that is applicable to their background and interest. The average Ph.D. program requires 4-6 years beyond a master’s degree. The program is comprised of coursework in four major areas.

- Mathematics or a related area
- Cognate Area
- Research Core

This residential program has rolling admission . Applications must be fully complete and submitted (including all required materials) and all application fees paid prior to the deadline in order for applications to be considered and reviewed. For a list of all required materials for this program application, please see the “ Admissions ” tab.

July 1 is the deadline for Fall applications.

November 15 is the deadline for Spring applications.

March 15 is the deadline for Summer applications.

*Those applicants interested in being considered for any available PhD funding should submit completed applications by December 1 for the following Fall semester.

## Program at a Glance

- Major/Department: Curriculum and Instruction
- Research Area: Mathematics Education
- Degree Objective: Doctor of Philosophy (PhD)
- Program Delivery: Residential
- Does this program lead to licensure? * No , this is a non-licensure program
- Application Deadlines: July 1 (Fall), November 15 (Spring), March 15 (Summer)

Start Your Giant Leap with One Small Step

## Request Information

Mathematics Education Courses

15-18 credit hours

In mathematics education, students engage in courses that cover topics in the cognitive and cultural theories of learning and teaching mathematics, and the role of curriculum in mathematics education.

A three (3) course sequence is required that consists of:

- EDCI 63500 – Goals and Content in Mathematics Education
- EDCI 63600 – The Learning of Mathematics: Insights and Issues
- EDCI 63700 – The Teaching of Mathematics: Insights and Issues

In addition, students are encouraged to take (6 – 9) hours of EDCI 620: Developing as a Mathematics Education Researcher

Related Course Work

Minimum of 6 credit hours

All students should have appropriate course work in mathematics, statistics, educational technology, or a related field. Students without a master’s level background in mathematics may be required to take more courses in mathematics. This will be determined by the student’s major professor and advisory committee.

9 credit hours

Students will take three graduate courses in a self-selected cognate area. Cognate area selection should be discussed with the student’s major professor and advisory committee. Possible cognate areas include: mathematics, psychology, philosophy, sociology, technology.

Research Core Courses

15 credit hours

All doctoral students in the Department of Curriculum and Instruction must complete five (5) courses from areas in research methodology and analysis before beginning their dissertation:

- EDPS 53300 – Introduction to Research in Education
- EDCI 61500 – Qualitative Research Methods in Education
- STAT 51100 – Statistical Methods OR EDPS 55600 – Introduction to Quantitative Data Analysis
- EDPS 63000 – Research Procedures in Education
- Advance electives in either quantitative or qualitative methods

In addition to a submitted application (and any applicable application fees paid), the following materials are required for admission consideration, and all completed materials must be submitted by the application deadline in order for an application to be considered complete and forwarded on to faculty and the Purdue Graduate School for review.

A completed master’s degree is required prior to admission.

Application Requirements

Here are the materials required for this application

- Transcripts (from all universities attended)
- Minimum undergraduate GPA of 3.0 on a 4.0 scale
- 3 Recommendations
- Academic Statement of Purpose
- Personal History Statement
- Writing Sample
- International Applicants must meet English Proficiency Requirements set by the Purdue Graduate School

We encourage prospective students to submit an application early, even if not all required materials are uploaded. Applications are not forwarded on for faculty review until all required materials are uploaded.

How to Apply

When submitting your application for this program, please select the following options:

- Select a Campus: Purdue West Lafayette (PWL)
- Select your proposed graduate major: Curriculum and Instruction
- Please select an Area of Interest: Mathematics Education
- Please select a Degree Objective: Doctor of Philosophy (PhD)
- Primary Course Delivery: Residential

This program does not lead to licensure in the state of Indiana or elsewhere. Contact the College of Education Office of Teacher Education and Licensure (OTEL) at [email protected] before continuing with program application if you have questions regarding licensure or contact your state Department of Education about how this program may translate to licensure in your state of residence.

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## Laura Bofferding

Amber brown, signe kastberg, rachael kenney, jill newton, questions contact the office of graduate studies at [email protected] ..

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## Sheena Zeng selected 2024-2028 Self Graduate Fellow

Tue, 04/23/2024.

Gloria J. Prothe

Sheena Zeng, first-year doctoral student in mathematics, was selected along with fourteen doctoral students to receive the University of Kansas' prestigious Madison and Lila Self Graduate Fellowship for the 2024-2025 academic year.

The fellowship is a four-year package awarded to incoming or first-year doctoral students who demonstrate leadership, initiative and passion for achievement. The fellowship covers full tuition and fees, provides graduate research assistant support of $34,850 per year, a $5,500 professional development award, a first-year $5,000 start-up award, $1,000 textbook and technology awards (years 2-4), and a unique professional development program.

The Fellow Development Program provides general education and training in communication, management, innovation, policy and leadership to assist Self Graduate Fellows in preparation for future leadership roles. The role of the development program is to complement the specialized education and training provided in doctoral programs. The total value of the four-year doctoral fellowship exceeds $200,000.

The late Madison “Al” and Lila Self launched and permanently endowed the Self Graduate Fellowship in 1989, motivated by their strong belief in the vital importance of developing leadership for tomorrow. Madison Self was a 1943 KU graduate in chemical engineering. Lila Self attended KU with the Class of 1943.

Advice and Resources for Mathematics Graduate Students

## Qualifying Review

Students often stress a lot about the QR Exams. Here we gather some advice from students who have made it through this process. For details on the Qualifying Review Process , please see the official math department webpage. It is important to note that the Qualifying Review is not just a sequence of exams: each student is carefully discussed by the Doctoral Committee to determine readiness to pass the Qualifying Review, including their academic record at Michigan (courses, grades, comments of professors) as well as plans with a tentative advisor. The process is not just an all-or-nothing exam score above a certain number.

That being said, we acknowledge that students do stress about the QR exams, and every math PhD student must pass exams in three subjects (although it is acceptable also to “course out” of one of the subjects). The Math Department QR Exam page . has outlines of each exam’s syllabus, past QR exams and some solutions. (Beware though, some solutions might have some errors! Write to us if you think you found one!)

Qualifying Review examinations (QRs) are offered in the following four areas – Algebra, Topology, Analysis, and Applied Analysis. Exams are offered before fall term (late August/Early September), before Winter Term (early January) and after winter term (early May). There is no penalty for trying and failing: students are encouraged to try an exam as soon as they think they might be ready.

Students must pass one of these exams by January of their second year. We advise and expect students to try one in May of their first year, after spending that year preparing for the QR exam in that subject by taking the corresponding “Alpha Courses;” if needed, student can make a plan to prepare through the summer and/or fall. Of course, students who have studied the material at the graduate level already are encouraged to take the exams even earlier: your score on the QR is a good data point for choosing classes. It is usually a big mistake to skip the alpha courses without having passed the QR exam in the corresponding subjects.

All three exams should be passed by January of the third year. You can also `course out’ of one of the QR exams: instead of taking a qual, you can take two courses specific courses in that area and earn at least B’s. Please read the more detailed rules on the math department website.

The applied analysis qual is often cancelled, due to no one registering for it.

Take the alpha courses.

The alpha classes (Math 593, 594, 591, 592, 596, 597) are designed to prepare you for the quals. You might think that are not related to your field of interest, but the content of these courses is something every mathematician should be proficient in. For those with more applied interests, you can substitute Math 556, 572 for 592 and 594.

Start taking the QRs early, and try again and again.

Start early and don’t be afraid of taking a QR exam even if you are not fully prepared. Sometimes the quals are easy and you might get lucky, and there are no penalties for failing a given qual.

Don’t be afraid of coursing out.

If you only have one QR remaining and have not been able to clear it despite multiple attempts, consider coursing out.

Focus on one Exam at a time

Try to get at least one QR done at a time. You can study for multiple quals at a time, but study more for one particular area, that you feel the most confident about.

Form study groups

If you plan to study on your own, you might often not feel motivated enough to do it. In such cases, it is good to have form a study group to keep you focused. In addition, your study partners might know how to solve some problems that you don’t. You can easily find people studying for a particular exam by either asking around or sending an email to the math graduate student list. Additionally, the AWM sometimes has QR study sessions before the exams.

Take timed practice exams

Many people perform very differently under time pressure. Try to solve a past QR exam in three hours. This will simulate the time pressure that you will face during an exam and will make you better prepared for it.

- The alpha courses are designed to prepare students for the QR exams, in addition to being a great overview of the particular areas by masters in the field (and potential dissertation advisors). It is not a good idea to skip these courses unless you first pass the QR exam.
- Before taking the exam in a particular subject, you can sit in the appropriate alpha courses without registering to review, and/or as seek out course notes and problem sets from previous alpha classes. You can make a habit to work with the first year students on their problem sets, even if you are not in the course.
- Past QR Exams are probably the best resources to study for QRs for those who have already taken the courses.
- Mel Hochster made extensive study materials for the Algebra QR exam, including practice problems and solutions, over a period of time in the early 2000’s:
- Review Materials from Fall 2002
- Review Materials from Fall 2003
- Also, scroll down Mel’s website : toward the bottom are Old Algebra QR Exams with solutions from January 2004, May 2004, September 2004, and January 2005.
- Harry Richman has written out solutions to some Analysis QRs – http://www-personal.umich.edu/~hrichman/quals.html
- Eamon Quinlan’ s notes for the Analysis QR- http://www-personal.umich.edu/~equinlan/Analysis%20Notes.pdf

Sanal Shivaprasad

I took all the quals as soon as I came in. In retrospect, this was probably a bad idea. I was just settling in to a new place, and the quals were right after a tiring week of the teaching orientation. I remember that period as being one of the most stressful times at the university.

I would recommend you try to take as many of the quals as you can when you come in (maybe 1 or 2), while not stressing too much about it. And, don’t expect to get any studying done in the week right the quals before, due to the teaching orientation.

Rachel Webb

For me, the best way to study for a test is to take old versions of the test. I start doing old tests from the beginning of my study, beginning with the oldest one available. At first it may take me several weeks to get through a test, as I need to go reread relevant parts of the textbook and maybe work several easier homework problems before I can solve the test problems. But solving the tests slowly gets faster, and by the end of my study I can solve a test in one or two days.

I would definitely recommend studying for the quals through past exams. I personally went through around 4-5 past exams in Analysis and Algebra, and made sure that I understood each problem (some older Analysis exams do not have solutions, so I asked them on Stack Exchange). Taking notes on some common tricks is also useful — for instance, the density argument in Real Analysis.

Another minor aspect is that for some Analysis/PDE students, the “Applied Analysis” exam might be worth considering. My experience is that, having learnt numerical differential equations, the Applied Analysis exam was a lot easier to me than the Algebraic Topology exam. The skills tested turned out more useful as well.

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Phd student accused of killing her friend’s newborn baby could face death penalty if convicted.

A PhD student charged with killing her friend’s newborn baby and injuring his infant twin brother could face the death penalty if she’s convicted of the horrific crime, according to Pennsylvania prosecutors.

The Allegheny District Attorney’s Office revealed in court Friday it plans to seek capital punishment against Nicole Virzi , who allegedly smashed the skull of 6-week-old Leon Katz while she was baby-sitting the tot inside the family’s Pittsburgh-area home in June.

Virzi, 30, was watching the baby after Leon’s parents, Ethan Katz and his wife, Savannah Roberts, took his twin sibling, Ari, to the hospital for injuries that the California woman was later also accused of inflicting.

Prosecutors filed notice that they intend to pursue the death penalty in the June 15 homicide, citing various aggravating factors for the rare step, including allegedly committing the homicide by means of torture, the Pittsburgh Post-Gazette reported.

Virzi claimed that Leon tumbled from his bouncer chair when she stepped away, but doctors found the injuries “consistent with having been sustained as a result of child abuse, as these are inflicted injuries that are not natural and not accidental,” WTAE previously reported, citing court records and police.

The county’s medical examiner ruled Leon’s cause of death was blunt force trauma to the head. A head CT scan showed Leon suffered a severe skull fracture to the left side of the head, along with multiple brain bleeds.

She’s facing charges of homicide, aggravated assault and child endangerment.

Virzi, who was reportedly a clinical psychology student at UC San Diego’s Joint Doctoral Program, was referred to as a “trusted family friend” in a fundraising page established in the aftermath of the death.

While Virzi hails from California, she was staying in a Pittsburgh-area Airbnb at the time of the killing.

Virzi’s attorney, David Shrager, said last month that his client was devastated by Leon’s death while claiming she was innocent.

“If there was something that she would want to convey, it would just be the absolutely horrible pain that she’s feeling,” Shrager said, according to the newspaper. “These were her close friends.”

No woman is currently on death row in Pennsylvania and Gov. Josh Shapiro, a Democrat, has vowed not to sign off on any death warrant while he’s in office.

Virzi didn’t appear during her formal arraignment Friday and waived a preliminary hearing last month, the Post-Gazette reported.

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## Borong Wang awarded fellowship to IAS for 2024-2025 academic year

Associate Professor Botong Wang was awarded a fellowship at the Institute for Advanced Study (IAS) for the 2024-2025 academic year. This prestigious membership allows for focused research and the free and open exchange of ideas among an international community of scholars at one of the foremost centers for intellectual inquiry.

Each year, IAS welcomes more than 250 of the most promising post-doctoral researchers and distinguished scholars from around the world to advance fundamental discovery as part of an interdisciplinary and collaborative environment. Visiting scholars are selected through a highly competitive process for their bold ideas, innovative methods, and deep research questions by the permanent Faculty—each of whom are preeminent leaders in their fields. Past IAS Faculty include, Albert Einstein, Erwin Panofsky, John von Neumann, Hetty Goldman, George Kennan, and J. Robert Oppenheimer.

Located in Princeton, NJ, the Institute for Advanced Study was established in 1930. Today, research at IAS is conducted across four Schools—Historical Studies, Mathematics, Natural Sciences, and Social Science—to push the boundaries of human knowledge.

Among past and present scholars, there have been 35 Nobel Laureates, 44 of the 62 Fields Medalists, and 23 of the 27 Abel Prize Laureates, as well as MacArthur and Guggenheim fellows, winners of the Turing Award and the Wolf, Holberg, Kluge, and Pulitzer Prizes.

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## Sixia Chen, Ph.D.

Faculty biostatistician, associate professor.

Office: Hudson College of Public Health 801 Northeast 13th Street, Room 325 Post Office Box 26901 Oklahoma City, Oklahoma 73126-0901

(405) 271-2229, x48628

Dr. Chen has more than 13 years practical and theoretical research experience with survey sampling and missing data analysis problems. Before joining OUHSC, Dr. Chen served as the senior sampling statistician at Westat research organization (a world leading research organization in survey sampling and methods research) from 2012 to 2015. Dr. Chen has served as PI, Co-PI and Co-I for multiple local and national grants including NIH. He has extensive inter-/multi-disciplinary research experience in data integration, missing data analysis, survey sampling, biostatistics, tobacco research, and Native American health disparity. Recently, Dr. Chen has started to work on machine learning and big data research with three funded NIH grants (two as the PI) related to machine learning. He has more than 23 methodological publications in top statistical journals (20 are first author articles) and more than 32 collaborative publications in other fields. He is now serving as associate editor for the following four well-known peer reviewed journals: Journal of Korean Statistical Society, Scandinavian Journal of Statistics, Journal of Survey Statistics and Methodology (Top 2 journals in survey statistics and methodology in the world), Survey Methodology (forthcoming in September 2021), and director of Novel Methodologies Unit of Biostatistics, Epidemiology, and Research Design Core of the Oklahoma Shared Clinical and Translational Resources (OSCTR). In addition, Dr. Chen is now serving as the president of American Statistical Association Oklahoma Chapter. Dr. Chen is a Faculty Affiliate of the TSET Health Promotion Research Center. He performs as faculty biostatistician for Biomedical and Behavioral Methodology Core, Biostatistics Core for Stephenson Cancer Center and Sooner Survey Center at OUHSC. He has also served as a consultant for the Tribal Epidemiology Center of the Southern Plains Tribal Health Board of Oklahoma since 2016.

- PhD, Statistics, Iowa State University, 2012
- BA, Mathematics and Applied Mathematics, Fudan University, 2007

## Appointments:

- Associate Professor, Department of Biostatistics and Epidemiology, Hudson College of Public Health, OUHSC, 2022–Present
- Assistant Professor, Department of Biostatistics and Epidemiology, Hudson College of Public Health, OUHSC, 2015–2022
- Senior sampling statistician, Westat, 2012-2015

## Teaching

- BSE 5603 Sampling Theory and Methods
- BSE 5653 Nonparametric Methods
- BSE 5960 Directed Readings
- BSE 5980 Research for Master’s Thesis
- BSE 6553 Linear Models I

## Clinical/Research Interests:

- Survey sampling
- Missing data problems
- Machine learning and big data
- Statistical disclosure control
- Causal inference
- Empirical likelihood
- Non-parametric and semi-parametric modeling and small area estimation
- Tobacco research and Native American health disparities

## Select Publications:

- S. Chen , D. Haziza, C. Leger and Z. Mashreghi. (2019). Pseudo-population bootstrap methods for imputed survey data. Biometrika, 106 , 369-384
- S. Chen and D. Haziza. (2019). On the nonparametric multiple imputation with multiply robustness. Statistica Sinica, 29, 2035-2053
- S. Chen and D. Haziza. (2017). Multiply robust imputation procedures for the treatment of item nonresponse in surveys . Biometrika. 104, 439-45
- S. Chen and J. K. Kim. (2014). Two-phase sampling for propensity score estimation in self-selected samples. The Annals of Applied Statistics . 3, 1492-1515.
- S. Chen and J. K. Kim. (2014). Population empirical likelihood for nonparametric inference in survey sampling. Statistica Sinica . 24, 335-35

Link to Dr. Chen's current publications

## IMAGES

## COMMENTS

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 ...

Why Study Mathematics in United States. Studying Mathematics in United States is a great choice, as there are 95 universities that offer PhD degrees on our portal. Over 957,000 international students choose United States for their studies, which suggests you'll enjoy a vibrant and culturally diverse learning experience and make friends from ...

Yale University. New Haven, CT. #8 in Mathematics (tie) Save. 4.6. A graduate degree in mathematics can help students hone their skills in a specialty area, from algebra and number theory to ...

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 ...

PhD Program. More information and a full list of requirements for the PhD program in Mathematics can be found in the University Bulletin. During their first year in the program, students typically engage in coursework and seminars which prepare them for the Qualifying Examinations . Currently, these two exams test the student's breadth of ...

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 ...

a Secondary Field (which is similar to a "minor" subject area). SEAS offers PhD Secondary Field programs in Data Science and in Computational Science and Engineering. GSAS lists secondary fields offered by other programs. a Master of Science (S.M.) degree conferred en route to the Ph.D in one of several of SEAS's subject areas.

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 ...

Students who have been admitted to the PAL program, and who complete the requirements for the Ph.D. in Mathematical Sciences with a thesis in the area of logic, can choose to receive either a Ph.D. in Pure and Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which degree to receive is usually based on the intended career path.

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 in Mathematics. The PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an adviser, and creative research culminating in a written dissertation and defense. All doctoral students must also do some teaching on the way to the PhD.

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin. Courses: The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here. Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above.

Thinking of applying to graduate school in mathematics? Penn was ranked 8th among all US universities in a leading national study, and our mathematics graduate program was recently highest in a study of graduate programs in arts and sciences at Penn.We have a very active and involved mathematics faculty, diverse course offerings and a broad seminar schedule, with a variety of research projects ...

2024-25 Catalog. Mathematics, PhD. The Department of Mathematics of the University of Pennsylvania offers a full Graduate Program in Mathematics, conferring the degrees of Master of Arts (A.M.), Master of Philosophy (M.Phil.), and Doctor of Philosophy (Ph.D.). The educational aim of this program is to provide well-rounded mathematical training ...

Introduction These guidelines are intended to help familiarize graduate students with the policies governing the graduate program leading to the degrees of Doctor of Philosophy (Ph.D.) in Applied Mathematics. This material supplements the graduate school requirements found on the Graduate Student Resources page and the Doctoral Degree Policies of the graduate school.

Guide to Graduate Studies. 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.

Find Graduate Programs (FGP) in the Mathematical Sciences offers comparative information on over 500 graduate programs in the mathematical sciences in the US and Canada. ... The Google doc USA/Canada Math PhD Programs: GRE requirements and Qualifying Exams, curated by Brown University graduate student Emily Winn, provides a list of those ...

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 ...

Study mathematics as both an applied and pure discipline with the Mathematics PhD from Temple's College of Science and Technology. In this doctoral program, you will gain the necessary skills to conduct your own original research and prepare for a career in administration, higher education or industry. The Mathematics PhD program's dynamic ...

Program Contact Information. If you have questions related to admission, please click here to request information and an admission specialist will reach out to you directly. For questions regarding faculty or courses, please use the contact information below. [email protected]. 480/965-3951.

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. ... Contact Us. Program Director: Professor Alexander Karp. Box: 210-M. Teachers College, Columbia University 323 Thompson ...

This program is not admitting students for the 2025-2026 academic year at this time. Fall 2023 quarter (beginning in September) Priority deadline: February 1, 2023. Final submission deadline: June 1, 2023. Winter 2024 quarter (beginning in January) Final submission deadline: November 15, 2023. Priority deadline: Applications will be considered ...

Signe Kastberg. Professor and Mary Endres Chair in Elementary Education Mathematics Education Curriculum and Instruction. Work Phone: (765) 494-2354 Work Email: [email protected]. Categories: CnI Online Fac, Curriculum and Instruction, Mathematics Education.

Director of Graduate Studies. Mathematics Department Tulane University 6823 St. Charles Ave. New Orleans, LA 70118 phone: (504) 865-5727 fax: (504) 865-5063 ... known for its friendly atmosphere and its practice of fostering close contact and cordial relations between faculty and graduate students. To us, this is a very important aspect of life ...

Sheena Zeng, first-year doctoral student in mathematics, was selected along with fourteen doctoral students to receive the University of Kansas' prestigious Madison and Lila Self Graduate Fellowship for the 2024-2025 academic year.

Students often stress a lot about the QR Exams. Here we gather some advice from students who have made it through this process. For details on the Qualifying Review Process, please see the official math department webpage.It is important to note that the Qualifying Review is not just a sequence of exams: each student is carefully discussed by the Doctoral Committee to determine readiness to ...

A PhD student charged with killing her friend's newborn baby and injuring his infant twin brother could face the death penalty if she's convicted of the horrific crime, according to ...

Associate Professor Botong Wang was awarded a fellowship at the Institute for Advanced Study (IAS) for the 2024-2025 academic year. This prestigious membership allows for focused research and the free and open exchange of ideas among an international community of scholars at one of the foremost centers for intellectual inquiry.

Office: Hudson College of Public Health 801 Northeast 13th Street, Room 325 Post Office Box 26901 Oklahoma City, Oklahoma 73126-0901

Discover how UC PhD graduate Dr. Gerry Toft is revolutionizing artificial intelligence by applying advanced mathematics, particularly in matroid theory. With a focus on improving AI's accuracy in mathematical concepts, Dr. Toft combines his expertise with a passion for uncovering the beautiful patterns within mathematics. Now working remotely for the US platform Outlier, he shares insights on ...