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.
  • The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

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.

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 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
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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.

Course List
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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Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Learn more about Harvard’s Math community and our statement on diversity and inclusion.

The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers student affinity groups for graduate students and many other resources.

The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.

open. The application deadline is December 15, 2021. -->

The application deadline for fall 2024 admission has passed. Applications for fall 2025 admission will open in September 2024.

For information on admissions and financial support, please visit the Harvard Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.

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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.

FAQs |  Contact the Graduate Program  |  Apply Now

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COLLEGE OF LIBERAL ARTS AND SCIENCES

Department of Mathematics

  • Ph.D. in Mathematics
  • General Information
  • Financial Aid
  • Answers to FAQ
  • M.S. in Mathematics
  • Ph.D. in Mathematics with Thesis in Actuarial Science
  • M.S. in Actuarial Science
  • M.S. in Applied Financial Mathematics
  • M.S. in Applied Financial Mathematics – Actuarial Science
  • Course Schedule
  • Preliminary Exams

Overview of Graduation Requirements

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

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

Preliminary Examination and Core Course Requirements

Pure Mathematics

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

Applied Mathematics

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

Past Prelim Exams

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 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.

Ph.D. Degree Programs

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

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

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

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

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

Ph.D. in Mathematics

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

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

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

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

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

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

Written Qualifying Examinations

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

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

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

Qualifying Examination Subject Areas
Complex Analysis
(MATH 220A-B-C)
Real Analysis
(MATH 240A-B-C)
 
Algebra
(MATH 200A-B-C)
Applied Algebra
(MATH 202A-B-C)
Topology
(MATH 290A-B-C)
Numerical Analysis
(MATH 270A-B-C)
Statistics
(MATH 281A-B-C)
 
  • Three qualifying examinations must be passed. At least one must be passed at the Ph.D. level and a second must be passed at either the Ph.D. or Provisional Ph.D. level.
  • Of the three qualifying exams, there must be at least one from each of Areas 1 and 2. 
  • Students must pass at least two exams from distinct areas with a minimum grade of Provisional Ph.D. (For example, a Ph.D. pass in Real Analysis, Provisional Ph.D. pass in Complex Analysis, M.A. pass in Algebra would  NOT  satisfy this requirement, but a Ph.D. pass in Real Analysis, M.A. pass in Complex Analysis, Provisional Ph.D. pass in Algebra would, as would a Ph.D. pass in Numerical Analysis, Provisional Ph.D. pass in Applied Algebra, and M.A. pass in Real Analysis.) All exams must be passed by the September exam session prior to the beginning of the third year of graduate studies. (Thus, there is no limit on the number of attempts, encouraging new students to take exams when they arrive, without penalty.) Except for this deadline, there is no limit on the number of exams a student may attempt.

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

Qualifying Examination Pass Levels
Excellent performance, suitable for continuing towards doctoral work
Marginal performance at doctoral level
Not suitable for continuing towards doctoral work, but satisfactory for terminal M.A. or M.S.
Unsatisfactory for Master's level work

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

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

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

Master's Transferring to Ph.D.

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

Foreign Language Requirement

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

Advancement to Candidacy

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

Dissertation and Final Defense

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

Time Limits

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

Ph.D. Program Time Limits
Pass Qualifying Exams
Find thesis advisor
Advance to Candidacy
Final Defense

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

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

phd in mathematics usa

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Department of Mathematics

Requirements for the ph.d. degree.

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

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

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

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

The dissertation prospectus should be submitted during the third year. 

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

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

Master’s Degrees :

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

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

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

Department of Mathematics

Phd requirements.

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Course Requirements

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

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

Teaching Seminar

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

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

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

PhD Dissertation

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

Our PhD program does not have a foreign language requirement.

The MA Degree

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

MA candidates must complete:

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

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

NYU Courant Department of Mathematics

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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.

UCI Mathematics

UCI Mathematics

Ph.d program, doctor of philosophy (phd) in mathematics.

To earn a PhD in Mathematics one must satisfy the following requirements:

  • Completion of all required coursework
  • Completion of required written examinations
  • Completion of Advancement to Candidacy Oral Examination & Graduate Division paperwork
  • Completion of Teaching Experience
  • Submission of Doctoral Dissertation & Graduate Division paperwork

When accepted into the doctoral program, the student embarks on a program of formal courses, seminars, and individual study courses to prepare for the Ph.D. written examinations, advancement to candidacy oral examination, and dissertation.

Upon entering the program, students are expected to take Math 210 (Real Analysis), Math 220 (Complex Analysis) and Math 230 (Algebra), which must be passed with a grade of B or better.  Students must complete these sequences by the end of the second year.

By the start of the second year , students must achieve at least two passes at the M.S. level among four exams in Real Analysis, Complex Analysis, Algebra and Applied Mathematics.  

By the start of the third year , students must achieve at least two passes at the Ph.D. level among four exams in Real Analysis, Complex Analysis, Algebra and Applied Mathematics.

To satisfy the exam requirements, students may take the Comprehensive Exam (offered in the Spring of every year) or the Qualifying Exams (offered before the start of the fall quarter) in these areas. Students may not attempt to take an exam in a particular subject area more than 3 times .  A student who passes a Qualifying examination prior to taking the corresponding course will be exempted from taking the course.

Please Note: Corresponding qualifying exam coursework, MATH 210,220, & 230 cannot be used to satisfy both exam and coursework requirements (i.e. you can’t ‘double dip’).

Some students may require additional background prior to entering Math 210.  This will be determined by assessment prior to the start of the students’ first year by the Vice Chair for Graduate Studies, upon consultation with the graduate studies committee.  Such students will be directed into Math 205 during their first year.  These students may pass one Comprehensive Exam in the area of Analysis in lieu of achieving a M.S. pass on the Qualifying Exam, which must be satisfied prior to the start of the students’ second year. The Comprehensive Exam in Analysis will be offered once per year in the Spring quarter.

By the end of the second year, students must declare a major specialization from the following areas:

  • Applied & Computational Mathematics
  • Geometry & Topology
  • Probability

Students are required to take two series of courses from their chosen area (students who later decide to change their area must also take two series of courses from the new area).  Additionally, all students must take two series of courses outside their declared major area of specialization.  Special topics courses within certain areas of specialization and courses counted toward the M.S. degree, (other than MATH 205), will count toward the fulfillment of the major specialization requirement.

By the beginning of their third year, students must have an advisor specializing in their major area.  With the advisor's aid, one should begin to form a committee for the Advancement to Candidacy PhD oral examination.  This committee will be approved by the Department on behalf of the Dean of Graduate Studies and the Graduate Council and will have five faculty members.  At least one (and at most two), of the committee members must be faculty from outside the Department.  Before the end of the third year, students must have a written proposal, approved by their committee, for the Advancement to Candidacy oral examination.  The proposal should explain the role of at least two series of courses from the student's major area of specialization that will be used to satisfy the Advancement to Candidacy requirements.  The proposal should also explain the role of additional research reading material as well as providing a plan for investigating specific topics under the direction of the student's advisor(s).  Only one of the core courses, MATH 210ABC, 220ABC, and 230ABC may count for the course requirement for Advancement to Candidacy Examinations.

After one meets these requirements, the Graduate Studies Committee recommends to the Dean of Graduate Studies the advancement to candidacy for the PhD. degree.  Students should advance to candidacy by the beginning of their fourth year .  After advancing to candidacy, a student is expected to be fully involved in research toward writing his or her PhD dissertation.  Ideally, a student should keep in steady contact/interaction with their doctoral committee.  Teaching experience and training is an integral part of the PhD program.  All doctoral students are expected to participate in the Department's teaching program, unless otherwise communicated during the admissions process.

The candidate must demonstrate independent, creative research in Mathematics by writing and defending a dissertation that makes a new and valuable contribution to mathematics in the candidate's area of concentration.  Upon advancement to candidacy a student must form a thesis committee, a subcommittee of the advancement examination committee, consisting of at least three total faculty members, chaired by the student's advisor.  The committee guides and supervises the candidate's research, study, and writing of the dissertation; participates in or attends the oral defense of the dissertation; and recommends that the PhD be conferred upon approval of the doctoral dissertation.

The normal time for completion of the PhD is six years , and the maximum time permitted is seven years (please note the department may only provide financial support for a maximum of six years ). 

Completion of the PhD degree must occur within 9 quarters of Advancement to PhD candidacy.

Areas of Specialization and Their Corresponding Advancement to Candidacy Courses

PhD students will choose one specialization from the following six areas, as offered by the Mathematics Department, which determines coursework requirements.  Each area of specialization will have a core course, which the Department will do its best to offer each year.  The department will offer other courses every other year, or more frequently depending on student demands and other department priorities.

Algebra : Math 230ABC (core), Math 232ABC, Math 233ABC, 234ABC, 235ABC, 239ABC

Analysis : Math 210ABC (core), Math 220ABC (core), Math 211ABC, Math 260ABC, Math 295ABC, Math 296

Applied & Computational Mathematics: Math 290ABC (core), Math 225ABC, Math 226ABC, Math 227AB, Math 291ABC, Math 295ABC

Geometry & Topology: Math 218ABC (core), Math 222ABC, Math 240ABC, Math 245ABC, Math 250ABC

Logic : Math 280ABC (core), Math 281ABC, Math 282ABC, Math 285ABC

Probability : Math 210ABC, Math 211ABC, Math 270ABC, Math 271ABC, Math 272ABC, Math 274

*PhD Requirements Summarized*

By the beginning of the 2nd year: Pass at the MS level two exams in real analysis, complex analysis, algebra or applied math.

By end of the 2nd year: (1) Declare a major specialization; (2) complete the course series 210ABC, 220ABC, 230ABC.

By the beginning of the 3rd year : (1) Pass at the PhD level two qualifying exams in real analysis, complex analysis, algebra or applied math; (2) Select an advisor specialist in the major area and form a committee for the Advancement to Candidacy oral exam.

Before the end of the 3rd year: (1) Have a written proposal, approved by the committee, for the PhD Advancement to Candidacy examination.

By the beginning of the 4th year: (1) Advanced to Candidacy at the PhD level; (2) form a thesis committee (that is, a subcommittee of the advancement examination committee)

Completion of the PhD:  Average completion time is 5.8 years ; maximum time permitted is seven years . The Department will not financially support students past their sixth year in the PhD program.  Completion of the PhD degree must occur within 9 quarters (three years) of advancement to PhD candidacy.

Graduate Program in Mathematical and Computation Biology (MCSB)

The graduate program in Mathematical, Computational Systems Biology (MCSB) is designed to meet to meet the interdisciplinary training challenges of modern biology and function in concert with selected department programs, including the Ph.D. in Mathematics.

http://mcsb.uci.edu/

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.

Two students in conversation outside of Teachers College

Admissions Information

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

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

Application Deadlines

Entry Term AvailablePriority DeadlinesFinal DeadlinesExtended Deadlines
SpringNovember 15, 2023November 15, 2023N/A
SummerDecember 1, 2023June 1, 2024N/A
FallDecember 1, 2023July 1, 2024N/A

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

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

Application Requirements

 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.

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Program Director : Professor Alexander Karp

Teachers College, Columbia University 323 Thompson

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

Email: tcmath@tc.edu

Doctor of Philosophy (PhD) in Mathematics Education

Graduate Programs

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 Education
  • 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” section below.

  • July 1 is the deadline for Fall applications.
  • November 15 is the deadline for Spring applications.
  • March 15 is the deadline for Summer applications.

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.

APPLICATION PROCEDURE

Application Instructions for the Mathematics Education PhD program from the Office of Graduate Studies:

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

Here are the materials required for this application:

  • Transcripts (from all universities attended, including an earned bachelor’s degree from a college or university of recognized standing)
  • A completed master’s degree is required prior to admission to this program.
  • 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.

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

Program Requirements

I. mathematics education courses (15 – 18 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

II. Related Course Work (minimum 6 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.

III. Cognate (9 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.

IV. Research Core Courses (15 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
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Doctorate in Mathematics Education

Program Code:  PH6245

Doctoral students Reuben Asempapa, Derek Sturgill, and Ahmad Alhammouri.

The PhD in Mathematics Education develops scholars who study teaching, learning, and assessment in mathematics—kindergarten through college. The program prepares these scholars to act as stewards of the field of mathematics education, with all its complexity and diversity. The program participants conduct research in curriculum, instruction, learning, assessment, professional development, teacher beliefs, and student attitudes. Students in the PhD program not only learn how to conduct such research but also serve in apprenticeship roles in teacher preparation and professional development to prepare them for university faculty positions and other leadership roles in mathematics education. The program in is built on a common foundation of learning theory, the social and cultural contexts of education, curriculum and instruction theory, the moral and ethical dimensions of leadership, and quantitative and qualitative research methods.

It is expected that all students completing a doctoral degree in Mathematics Education will demonstrate knowledge and skills in a common core of competencies plus an area of specialization and successfully complete a dissertation. For each individual scholar, coursework serves as the basis for investigating a significant educational issue that will advance the field of Mathematics Education and prepare the student for future research. Every student in the PhD program in Mathematics Education has the opportunity to construct a highly individualized program based on each scholar’s career goals. Specializations are available based on the expertise of doctoral faculty. This program can be completed on a full- or part-time basis. As a full-time program, degree completion in 4–5 years is typical.

Application Process

Request Info

Greg Foley Program Coordinator Patton Hall 321D 740.593.4430

Frans Doppen Graduate Doctoral Coordinator Patton Hall 309EE 740.593.0254

Program Overview

Learning outcomes.

  • Demonstrate a strong foundation in mathematics subject matter.
  • Use their understanding of how PK–16 students learn and engage with mathematics to develop, evaluate, and investigate rigorous and equitable mathematics education curriculum, teaching, assessment, and technology.
  • Describe and evaluate research methodologies appropriate to the study of mathematics education.
  • Use equitable and inclusive teaching and assessment practices that are responsive to diverse learners and incorporate appropriate use of technology.
  • Discuss, evaluate, and synthesize the body of literature central to mathematics education, professional preparation standards for mathematics teachers, and PK–16 mathematics learning standards.
  • Develop skills in teaching college mathematics, mathematics courses for PK–12 teachers, mathematics methods courses for PK–12 teachers, or facilitating professional development for PK–12 teachers.
  • Analyzing, evaluate, and synthesize research theories in mathematics education, apply research theories in PK–16 contexts, and support others in applying them in PK–16 contexts.
  • Conduct independent research in mathematics education that relies on quantitative, qualitative, or mixed research design and methodology suitable for professional publications and presentations.
  • Develop awareness of current trends and issues in education broadly, and mathematics education specifically, that leads to advocacy for learners and teachers.
  • Be prepared to accept a university faculty position or other leadership roles in the field of mathematics education.

Required Courses

Minimum Total Credits: 76 semester credit hours including the dissertation Students completing the program full-time (12 hours per semester), typically complete the program in 4–5 years and are typically in residence at the Athens campus of Ohio University at least 2 years.

Foundations Core:  minimum 5 semester hours

  • EDTE 8900 First-Year Doctoral Seminar (1 credit)
  • A graduate-level course (5000 level or above) focused on critical studies chosen in consultation with a doctoral committee

Teaching & Learning Core: minimum 15 semester hours

  • EDTE 7150 Theories of Curriculum Change (3 credits)
  • EDTE 7160 Theories of Instructional Change (3 credits)
  • EDTE 7920 Curriculum and Instruction Practicum (6 credits)
  • EDTE 8000 Advanced Dynamics of Human Learning (3 credits)

Research Core: minimum 22 semester hours

  • EDRE 7200 Educational Statistics (4 credits)
  • EDRE 7210 Regression Analysis in Education (4 credits)
  • EDRE 7330 Research Design in Education (4 credits)
  • EDRE 7500 Introduction to Qualitative Methods in Education (4 credits)
  • EDTE 8040 Writing for Professional Publication in Education (3 credits)
  • One additional graduate-level research course is chosen in consultation with the student’s doctoral committee

Mathematics Education Specialization: minimum 24 semester hours

  • At least 9 semester hours of graduate-level mathematics courses are chosen in consultation with the doctoral committee to extend the depth and breadth of prior mathematical proficiency.
  • EDTE 7300 Curriculum in Mathematics Education (3 credits)
  • EDTE 8900 Research in Teacher Education: Assessments in Educational Contexts (3 credits)
  • EDTE 8940 Mathematics Education Through the Lens of Technology (3 credits)
  • One additional graduate-level mathematics education course is chosen in consultation with the doctoral committee
  • At least one additional graduate-level mathematics or mathematics education course is chosen in consultation with the doctoral committee

Dissertation: minimum 10 semester hours

It is expected that all candidates completing a doctoral degree in the Department of Teacher Education will propose, conduct, and prepare a comprehensive written report of an individually designed research study addressing a significant educational issue that will advance the field of mathematics education and will prepare the scholar for future research.

Funding Information

  • Departmental funding opportunities
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Program Faculty

Mathew Felton-Koestler

Allyson Hallman-Thrasher

Courtney Koestler

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Education Rankings by Country 2024

There is a correlation between a country's educational system quality and its economic status, with developed nations offering higher quality education.

The U.S., despite ranking high in educational system surveys, falls behind in math and science scores compared to many other countries.

Educational system adequacy varies globally, with some countries struggling due to internal conflicts, economic challenges, or underfunded programs.

While education levels vary from country to country, there is a clear correlation between the quality of a country's educational system and its general economic status and overall well-being. In general, developing nations tend to offer their citizens a higher quality of education than the least developed nations do, and fully developed nations offer the best quality of education of all. Education is clearly a vital contributor to any country's overall health.

According to the Global Partnership for Education , education is considered to be a human right and plays a crucial role in human, social, and economic development . Education promotes gender equality, fosters peace, and increases a person's chances of having more and better life and career opportunities.

"Education is the most powerful weapon which you can use to change the world." — Nelson Mandela

The annual Best Countries Report , conducted by US News and World Report, BAV Group, and the Wharton School of the University of Pennsylvania , reserves an entire section for education. The report surveys thousands of people across 78 countries, then ranks those countries based upon the survey's responses. The education portion of the survey compiles scores from three equally-weighted attributes: a well-developed public education system, would consider attending university there, and provides top-quality education. As of 2023, the top ten countries based on education rankings are:

1
2
3
4
5
6
7
8
9
10

Countries with the Best Educational Systems - 2021 Best Countries Report*

Ironically, despite the United States having the best-surveyed education system on the globe, U.S students consistently score lower in math and science than students from many other countries. According to a Business Insider report in 2018, the U.S. ranked 38th in math scores and 24th in science. Discussions about why the United States' education rankings have fallen by international standards over the past three decades frequently point out that government spending on education has failed to keep up with inflation.

It's also worthwhile to note that while the Best Countries study is certainly respectable, other studies use different methodologies or emphasize different criteria, which often leads to different results. For example, the Global Citizens for Human Rights' annual study measures ten levels of education from early childhood enrollment rates to adult literacy. Its final 2020 rankings look a bit different:

Education Rates of Children Around the World

Most findings and ranking regarding education worldwide involve adult literacy rates and levels of education completed. However, some studies look at current students and their abilities in different subjects.

One of the most-reviewed studies regarding education around the world involved 470,000 fifteen-year-old students. Each student was administered tests in math, science, and reading similar to the SAT or ACT exams (standardized tests used for college admissions in the U.S.) These exam scores were later compiled to determine each country's average score for each of the three subjects. Based on this study, China received the highest scores , followed by Korea, Finland , Hong Kong , Singapore , Canada , New Zealand , Japan , Australia and the Netherlands .

On the down side, there are many nations whose educational systems are considered inadequate. This could be due to internal conflict, economic problems, or underfunded programs. The United Nations Educational, Scientific, and Cultural Organization's Education for All Global Monitoring Report ranks the following countries as having the world's worst educational systems:

Countries with the Lowest Adult Literacy Rates

27%
31%
34%
35%
37%
37%
38%
41%
45%
47%
  • Education rankings are sourced from both the annual UN News Best Countries report and the nonprofit organization World Top 20

Download Table Data

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41%2022203
35%2018202
100%2016201
81%2022200
88%2020198
86%2015197
72%2022196
54%2022195
86%2022194
62%2016193
90%202219287
62%2018191
0%190
83%2015189
0%18877
91%2015187
95%2015186
89%2015185
81%2021184
0%183
99%2021182
0%181
95%2020180
52%2017179
89%2021178
92%2021177
68%2022176
98%2022175
95%201917471597069
97%2015173
92%2021172
90%2022171
98%2000170
99%2005169
0%168
98%2012167
100%202116648434038
98%2020165
98%202216428282728
99%202116347
45%2021162
37%2020161
27%2022160
63%2021159
59%2022158
0%157
81%2022156
31%2020155
58%2022154
98%2011153
62%2022152
76%2022151
48%2017150
82%2022149
77%2022148
38%2022147
37%2021146
94%202114532353630
100%2021144
34%2022143
77%2018142
78%20201418578
100%2014140
67%2021139
61%2018138
0%137
58%2019136
90%2019135
98%202113451574943
76%2021133
89%201913276
70%2015131
47%2022130
82%2022129
95%2021128
98%202112753545853
84%202212686857873
49%2022125
0%124
64%2015123
75%20201228480
67%2019121
84%2022120837375
94%2022119
91%2022118
77%1999117
96%201911675766056
89%2015115
90%202111441363332
77%202211356585757
90%20201128274
98%2022111
0%110
89%201910974797671
100%2021108
94%202110744484648
80%20201067769
89%2020105
84%202210472756763
99%2019103616656
88%2022102
74%201810134343234
0%100
99%20219943454740
100%202098
0%97
95%20219669726960
94%202095
0%94
96%202093
0%92
94%20179133394137
83%20229070716868
95%20198939403839
72%202288
100%201087
100%20198666616561
81%200185
75%20228437373942
0%83
98%2018825960
89%2021818174
99%202180
0%79
92%202178
94%20207768646459
99%20217646444333
99%200175
96%20207454565149
81%2018736767
0%72
96%20197152505552
100%202270
70%202069
99%20196857686358
96%20206758525455
99%202266
97%198065
100%201964
100%202263808472
0%62
0%6179816667
98%202160
0%59
97%20225863706262
100%20195764535251
71%202156
95%202155
94%20225473657365
96%20195365625964
99%202052
96%202051
99%202150
99%201849
100%201848
98%202147
99%201446
98%20204538323546
98%20214462636154
100%20204378827170
0%422221
0%4150474544
97%20224049514835
95%20203940413736
99%20183835333429
97%20193730313131
99%20183614131416
0%3516171613
99%2011343130
98%20183329292826
99%201432
0%311111
99%202130363830
100%20212960464245
0%287666
0%2715141114
100%20212642424447
100%20212555495050
97%20212424242520
100%20212325272623
100%20212227252321
92%19832126262425
99%20202017181718
0%194443
0%18
0%178987
0%165555
0%159898
0%14
97%20201323232224
0%122222
97%20201120222119
0%10212020
0%913121312
0%812151515
0%73334
0%667711
100%2001545555341
0%4181618
0%31110109
0%210111210
0%119191922
97%2006
100%2000
99%2021
100%2015
97%1980
73.12%

Which country ranks first in education?

Which country ranks last in education, frequently asked questions.

  • Best Countries for Education - 2023 - US News
  • Literacy rate, adult total (% of people ages 15 and above) - World Bank
  • World Best Education Systems - Global Citizens for Human Rights
  • UNESCO - Global Education Monitoring Reports
  • World’s 10 Worst Countries for Education - Global Citizen
  • International Education Database - World Top 20

Undergraduate Program Overview

The field of mathematics.

Mathematics begins with simple questions in arithmetic. This has led to harder and harder questions involving a huge array of techniques. Perhaps the best way of understanding the scope of mathematics is to look at some examples of questions that mathematicians have worked on and are working on.

A prime number is an integer that cannot be factored into the product of two smaller integers. Every number can be written as the product of primes. Thus, primes are the building blocks of the integers. It is easy to tell if you have a prime number, but can you give a method for deciding whether a number, say one with 200 digits, is prime that works quickly? Can you give a method that works quickly for factoring a number into prime factors? These are simple questions but efforts to answer them have led to much elegant and deep mathematics. And the answers to these questions are useful. Many of the encryption devices we use every day are based on the fact that we  can  quickly tell if a number is prime and we  cannot  quickly factor numbers.

Is the planetary system stable? In other words, taking only gravity into account, will the planets keep revolving around the sun, or will they fall into the sun, or will they move farther and farther away from the sun? We assume that the sun does not change and that there are no visitors to the planetary system. Efforts to answer this question have led to the study of chaos and fractals.

Diseases sometimes appear in geographical clusters. When do these clusters indicate that the disease is caused by something in the environment near the cluster? More generally, one can ask how does exposure to a certain substance affect the probability of an individual developing a certain kind of cancer? Often one can find two explanations that describe a data set equally well. Which is the better explanation? These are examples of a broad array of questions having to do with using imperfect and incomplete data to understand the behavior of complicated systems.

The rapid advance in genetics has led to a plethora of problems that have a large mathematical component. We describe one technique and a pair of problems arising from this technique. A micro-array tells us which genes in an organism are being expressed at a single instant. This tells us roughly what proteins are being manufactured at that time. For example, from a single yeast cell, we obtain information about the productions of 5,000 kinds of protein. If we repeat this experiment 12 times, we seem to have the information needed to get a picture of the biochemical pathways of the organism. This knowledge will help us understand, for example, how undifferentiated stem cells become blood cells or muscle cells, or how diseases harm an organism.

But there are several challenges to overcome. First micro-array readings are prone to noise, which could come from tiny differences in the measurement methods or initial conditions (for example, ambient temperature). One needs to mathematically model this noise in order to compensate for it. The second challenge is to develop methods of handling the huge amount of data produced by micro-arrays. How does one find patterns in this set of data. This is called "data mining." Clearly techniques for analyzing a huge data base can be used in many endeavors—for example, ecology.

Mathematics Majors

The goal of the mathematics program at the University of Massachusetts Amherst has three aspects. First, students learn basic material, such as linear algebra, differential equations, and statistics, that are needed to successfully attack a wide range of problems. Second, they learn to think with rigor. Lastly, they learn to approach apparently unsolvable problems by studying simpler problems, doing experiments, and bringing together different concepts.

All majors must complete a calculus sequence and courses in linear algebra, modern algebra, and analysis. Each major has wide freedom of choice in upper-division courses and can, with the assistance of a faculty advisor, tailor a program to their interests and career goals. For example, one can prepare for a career in actuarial work, statistical analysis, computer programming, data processing, industry, government, or secondary school teaching. One can also prepare for graduate study in mathematics, statistics, computer science, and other fields or professional programs in business, law, medicine, and education.

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Award-winning teaching, research opportunities, and interdisciplinary programs in a diverse, inclusive community of excellence.

Lederle Graduate Research Tower, 1654 University of Massachusetts Amherst 710 N. Pleasant Street Amherst, MA 01003-9305, USA

Department Phone: (413) 545-2762 Department Fax: (413) 545-1801 Department Office: LGRT 1622

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phd in mathematics usa

" I chose to come to SFU for the opportunities to learn about and research topics in math that are interesting to me, as well as to inspire young students through math and science outreach."

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Mathematics master's student in the Faculty of Science

Tell us a little about yourself, including what inspires you to learn and continue in your chosen field.

As a teacher myself, I love discovering new things that I think could be taught to others in fun and interesting ways. Math is full of these!

Why did you choose to come to SFU?

I chose to come to SFU for the opportunities to learn about and research topics in math that are interesting to me, as well as to inspire young students through math and science outreach.

How would you describe your research or your program to a family member?

Searching for beauty in numbers.

What three (3) keywords would you use to describe your research?

Number Theory, Elliptic Curves, Fermat Equations

How have your courses, RA-ships, TA-ships, or non-academic school experiences contributed to your academic and/or professional development?

Discovering new areas of math gives me inspiration in my own teaching. It has allowed me to teach the same topics in new, unique ways, or to bring new topics to a wider audience for the first time.

Have you been the recipient of any major or donor-funded awards? If so, please tell us which ones and a little about how the awards have impacted your studies and/or research

British Columbia Graduate Scholarship

How do you approach networking and building connections in and outside of your academic community?

Talk to (almost) everyone. There are opportunities waiting to be found if you are open to them.

What are some tips for balancing your academic and personal life?

Two more hours obsessing over details in an assignment or studying are almost never as productive as socializing for an hour and then studying for one hour. Get outside every once in a while and have some fun, your academics will be fine.

Contact James: [email protected]

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Carlos Lamarche named 2024-25 University Research Professors

phd in mathematics usa

Carlos Lamarche, Ph.D. , director of graduate studies and Gatton Endowed Professor of Economics in the University of Kentucky Gatton College of Business and Economics, has been honored as a 2024-25 University Research Professor.

Lamarche studies econometrics — a combination of economics, statistics and mathematics that aims to give empirical content to economic relationships. He focuses on the development of estimation methods for a more informative and robust analysis of microeconomic data.

He also holds a joint appointment as a professor of statistics in the  College of Arts and Sciences. His work since joining UK in 2012 has gained national and international recognition.

Lamarche is currently a co-editor at the Southern Economic Journal and associate editor of Empirical Economics.

Read Carlos' Q+A Session with UKPR here

Read about the award and the other 2024-2025 honorees here

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United states and the oecd.

The United States was one of the 20 founding member countries that signed the Convention of the OECD in 1960. Today it is one of 38 OECD Members.

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  1. Mathematics PhD Program

    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 ...

  2. Mathematics in United States: 2024 PhD's Guide

    Everything about PhD's in Mathematics in United States: Explore top universities, costs, scholarships, and admission requirements for all study formats.

  3. PhD Program

    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 ...

  4. Ph.D. Program

    In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics. Pass the six-hour written Preliminary Examination covering calculus ...

  5. 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.

  6. Admissions

    To apply for admissions, financial aid, or for additional information on admissions requirements for the PhD program in pure mathematics, visit this page.

  7. Best Mathematics Graduate Programs

    A graduate degree in mathematics can help students hone their skills in a specialty area, from algebra and number theory to discrete mathematics and combinatorics. These are the best graduate ...

  8. Applied Mathematics Doctoral Program

    The Applied Mathematics PhD Program has a very strong track record in research and training. Placement of PhD students has been outstanding, with recent PhD students taking tenure-track/tenured faculty jobs at institutions such as Carnegie Mellon, Columbia, Drexel, Purdue, Tsinghua, UC Santa Cruz, Utah, Washington and alike, as well as private sector jobs in leading financial and high-tech ...

  9. Mathematics, PhD

    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 ...

  10. Harvard Mathematics Department Graduate Information

    Welcome to Harvard Mathematics Department Graduate program! You can get the latest Harvard Mathematics Department Graduate Information here.

  11. 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.

  12. Ph.D. in Mathematics

    To graduate with a PhD in Mathematics, a student must satisfy all of the following requirements: Course Credits : 45 credits, including 15 doctoral dissertation research credits/GRAD 6950. If you have a Master's degree in mathematics at UConn, then 30 credits are required, including 15 doctoral dissertation research credits.

  13. 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.

  14. PhD programmes in Mathematics in United States

    Find the best PhD programmes in the field of Mathematics from top universities in United States. Check all 119 programmes.

  15. Mathematics Education, PHD

    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:

  16. Ph.D. in Mathematics

    Ph.D. in Mathematics. The Ph.D. in Mathematics allows study in pure mathematics, applied mathematics and statistics. The mathematics department has over 60 faculty, approximately 100 Ph.D. students, and approximately 35 Masters students. A list of the UCSD mathematics faculty and their research interests can be found at here.

  17. Requirements for the Ph.D. Degree

    In order to qualify for the Mathematics Ph.D., all students are required to: Complete eight term courses at the graduate level, at least two with Honors grades. Pass qualifying examinations on their general mathematical knowledge; Submit a dissertation prospectus; Participate in the instruction of undergraduates;

  18. PhD Requirements

    Course Requirements Mathematics PhD candidates must show satisfactory work in Algebra (110.601-602), Real Variables (110.605), Complex Variables (110.607), and one additional non-seminar mathematics graduate course in their first year. The first-year algebra and analysis requirement can be satisfied by passing the corresponding written qualifying exam in September of the first year; these ...

  19. Ph.D. in Mathematics

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

  20. Ph.D Program

    When accepted into the doctoral program, the student embarks on a program of formal courses, seminars, and individual study courses to prepare for the Ph.D. written examinations, advancement to candidacy oral examination, and dissertation.

  21. Mathematics Education PhD

    Teachers College, Columbia University, is the first and largest graduate school of education in the United States, and also perennially ranked among the nation's best.

  22. Doctor of Philosophy (PhD) in Mathematics Education

    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.

  23. Doctorate in Mathematics Education

    The PhD in Mathematics Education develops scholars who study teaching, learning, and assessment in mathematics—kindergarten through college. The program prepares these scholars to act as stewards of the field of mathematics education, with all its complexity and diversity. The program participants conduct research in curriculum, instruction, learning, assessment, professional development ...

  24. Education Rankings by Country 2024

    Ironically, despite the United States having the best-surveyed education system on the globe, U.S students consistently score lower in math and science than students from many other countries. According to a Business Insider report in 2018, the U.S. ranked 38th in math scores and 24th in science.

  25. Undergraduate Program Overview : Department of Mathematics and

    For example, one can prepare for a career in actuarial work, statistical analysis, computer programming, data processing, industry, government, or secondary school teaching. One can also prepare for graduate study in mathematics, statistics, computer science, and other fields or professional programs in business, law, medicine, and education.

  26. James Houle

    James is a Mathematics master student in the Faculty of Science. Three research keywords: Number Theory, Elliptic Curves, Fermat Equations (British Columbia Graduate Scholarship)

  27. Carlos Lamarche named 2024-25 University Research Professors

    Carlos Lamarche, Ph.D., director of graduate studies and Gatton Endowed Professor of Economics in the University of Kentucky Gatton College of Business and Economics, has been honored as a 2024-25 University Research Professor. Lamarche studies econometrics — a combination of economics, statistics and mathematics that aims to give empirical content to economic relationships.

  28. 12-year-old Suborno Isaac Bari, from New York, heads to college ...

    Recent high school graduate Suborno Isaac Bari, 12, plans to start studying math and physics at New York University in the fall, but he's already got his ambitious sights set on beginning a ...

  29. The Fuzzy Math Behind Scale AI's Valuation

    Scale AI's 27-year-old CEO, Alexandr Wang, used to compete in national high school math competitions. His latest math-related victory may have been convincing investors in Silicon Valley to stretch his own company's numbers. The startup's $13.8 billion valuation, from a billion-dollar round it ...

  30. United States

    The United States was one of the 20 founding member countries that signed the Convention of the OECD in 1960. Today it is one of 38 OECD Members.