columbia phd programs education

Mathematics Education PhD

Doctor of philosophy.

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

Admissions Information

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

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

Application Deadlines

• Spring: November 15
• Summer/Fall (Priority): December 1
• Summer/Fall (Final): Rolling

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

Supplemental Application Requirements/Comments

• Online Degree Application , including Statement of Purpose and Resume
• Transcripts and/or Course-by-Course Evaluations for all Undergraduate/Graduate Coursework Completed
• Results from an accepted English Proficiency Exam (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

The primary focus of the doctoral program is research, with the philosophy that students learn best by doing—beginning as apprentices and becoming junior colleagues working with faculty on scholarly research projects. The faculty in the department conduct research in all areas of computer science. The degree of Doctor of Philosophy requires a dissertation based on the candidate’s original research, which is supervised by a faculty member, and all students in the Ph.D. program are actively engaged in research throughout the program. Ph.D. students spend at least half of their time on research under the direction of their faculty adviser from their first day in the program and devote themselves full time to research after coursework and other preliminaries have been completed. Ph.D. students are also expected to participate in departmental and laboratory activities full time throughout the program, except possibly for summer internships elsewhere, and the department does not consider admission of part-time Ph.D. students.

DEPARTMENTAL INFORMATION FOR DOCTORAL STUDENTS

• Program Requirements
• MS leading to PhD
• Milestones Chart
• Milestones Registration Form: Candidacy, Thesis Proposal, Thesis Defense
• PhD course Import Forms
• PhD Algorithms Prerequisite Form
• Data Science Specialization Option  (further details here )

SCHOOL/UNIVERSITY INFORMATION FOR DOCTORAL STUDENTS

• Registration
• SEAS Doctoral Fieldwork (CPT) Policy
• Time-Off Policy for Doctoral Students on Appointment in the Sciences and Related Research Fields

GENERAL PHD INFORMATION AND ADVICE

• CAREER Club
• Computer Science Open Data
• Computer Science Graduate Job and Interview Guide
• Background in case you ever need to teach online with two days notice
• The Definitive ‘what do I ask/look for’ in a PhD Advisor Guide
• The Thesis Whisperer
• Prem Devanbu’s Review Anti-Patterns
• Computer Science Rankings
• Michael Ernst’s Compilation of Great Advice
• Productivity Tips for PhD Students
• Getting Admitted to a Top PhD Program
• Tips on the Interview Process
• Networking on the network
• Advice on research and writing
• More advice on writing
• Corporate Lab or Academic Department, Which Fits?
• How To Survive A Thesis Defense
• 10 easy ways to fail a PhD
• Dealing with plagiarism
• Academic job site
• Computing Research Association
• IEEE Computer Society

(link suggestions appreciated; send email to [email protected] )

Last updated on March 13, 2024.

Find open faculty positions here .

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Sunday 3:00 pm

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Monday 11:45 am

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Monday 1:00 pm

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Press mentions, dean boyce's statement on amicus brief filed by president bollinger.

President Bollinger announced that Columbia University along with many other academic institutions (sixteen, including all Ivy League universities) filed an amicus brief in the U.S. District Court for the Eastern District of New York challenging the Executive Order regarding immigrants from seven designated countries and refugees. Among other things, the brief asserts that “safety and security concerns can be addressed in a manner that is consistent with the values America has always stood for, including the free flow of ideas and people across borders and the welcoming of immigrants to our universities.”

This recent action provides a moment for us to collectively reflect on our community within Columbia Engineering and the importance of our commitment to maintaining an open and welcoming community for all students, faculty, researchers and administrative staff. As a School of Engineering and Applied Science, we are fortunate to attract students and faculty from diverse backgrounds, from across the country, and from around the world. It is a great benefit to be able to gather engineers and scientists of so many different perspectives and talents – all with a commitment to learning, a focus on pushing the frontiers of knowledge and discovery, and with a passion for translating our work to impact humanity.

I am proud of our community, and wish to take this opportunity to reinforce our collective commitment to maintaining an open and collegial environment. We are fortunate to have the privilege to learn from one another, and to study, work, and live together in such a dynamic and vibrant place as Columbia.

Mary C. Boyce Dean of Engineering Morris A. and Alma Schapiro Professor

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Doctoral Program

• Ph.D. Fields
• Language Exams
• Fellowships and Financial Aid
• Dissertations-in-Progress
• Award Announcements
• Graduate Handbook
• Annual Newsletter
• Doctoral Students
• Graduate History Association
• Masters Programs
• Classical Studies

The Graduate Program

Columbia has been one of the most important centers of graduate education in history since modern Ph.D. programs began in America over a century ago. Recipients of our degrees hold distinguished positions in virtually every major university in the United States, and in many abroad. Our program offers a broad education in most areas of historical scholarship and attempts to train students for a discipline and a profession in the midst of considerable change. That includes not simply assisting students in acquiring the knowledge and skills essential to becoming contributing scholars, but also helping them to become effective teachers and to exist comfortably within a demanding and complicated professional world.

The members of our faculty represent many different approaches to the study of the past, and we strive to attract students of similarly diverse interests and commitments. No one should feel that being at Columbia requires accepting any one approach to the study of history.

This part of our website is designed to provide both prospective and current students with answers to some of the many questions they may have about the department.

Admissions answers commonly-asked questions about our admissions process.

Under Ph.D. Fields you will find information about the separate fields of study available in our program and the relationship among them.

Fellowships and Financial Aid explains the various ways we provide our students with fellowships and financial aid.

Dissertations-in-Progress summarizes the course of study towards the Ph.D and highlights the work of our students.

Research awards and recent honors are showcased in Award Announcements .

The section entitled Placement sketches how we prepare our students for the academic job market and reports on how our students have done in that market in recent years.

In the Graduate Handbook , we explain our curriculum and our academic requirements and provide more detailed information about aspects of the program such as the MA, Orals, M.Phil., Dissertations, etc.

Our FAQs are useful for students seeking admission as well as for current students seeking quick information.

The Annual Newsletter keeps us informed about our students.

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We integrate an innovative skills-based curriculum, research collaborations, and hands-on field experience to prepare students.

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Doctoral Programs

The Mailman School's public health doctoral degree programs provide tremendous access to renowned researchers and thought leaders. Through their course of study, doctoral students obtain the tools they need to create knowledge in the field and advance the practice of public health.

The School offers two doctoral degrees, the Doctor of Philosophy (PhD) and the Doctor of Public Health (DrPH). Both train candidates to create new knowledge and research, apply them to important public health issues, and identify and implement potential solutions. They differ only in emphasis:

• The DrPH programs place greater emphasis on the application of science to public health leadership, practice, and program development.
• The PhD programs place greater emphasis on creating new knowledge, with PhD recipients pursuing research and/or teaching as their career goal.

The DrPH can be obtained in:

• Biostatistics
• Environmental Health Sciences
• Epidemiology
• Population and Family Health

The PhD can be obtained in:

• Sociomedical Sciences

Degree Requirements

Graduates of the DrPH degree complete a minimum of 30 credit hours beyond the course work for the MPH degree or equivalent professional degree in public health.

The PhD degree is conferred by the Graduate School of Arts and Sciences , as are all PhD degrees at Columbia University. Graduates of a Mailman PhD degree program complete a minimum of 60 credit hours that constitute the combined requirements for the MA and PhD degree. Students entering the PhD degree program with MA degrees from other universities may receive up to 30 credits of advanced standing.

To learn more about degree competencies, curriculum plans, and student handbooks, visit our  Academics  page. Academic directors in each department are available to provide additional guidance on which program best fits particular academic and career goals. Applicants are also encouraged to review faculty profiles —including their research interests—to identify common interests with their discipline of choice.

For more information, visit these pages:

• Open Houses
• Application Process

Ph.D. Specialization in Data Science

The ph.d. specialization in data science is an option within the applied mathematics, computer science, electrical engineering, industrial engineering and operations research, and statistics departments..

Only students already enrolled in one of these doctoral programs at Columbia are eligible to participate in this specialization. Students should fulfill the requirements below in addition to those of their respective department's Ph.D. program. Students should discuss this specialization option with their Ph.D. advisor and their department's director for graduate studies.

Applied Mathematics Doctoral Program

Computer Science Doctoral Program

Decision, Risk, and Operations (DRO) Program

Electrical Engineering Doctoral Program

Industrial Engineering and Operations Research Doctoral Program

Statistics Doctoral Program

The specialization consists of either five (5) courses from the lists below, or four (4) courses plus one (1) additional course approved by the curriculum committee. All courses must be taken for a letter grade and students must pass with a B+ or above. At least three (3) of the courses should come from outside the student’s home department. At least one (1) course has to come from each of the three (3) thematic areas listed below.

Specialization Requirements

• COMS 4231 Analysis of Algorithms I
• COMS 6232 Analysis of Algorithms II
• COMS 4111 Introduction to Databases
• COMS 4113 Distributed Systems Fundamentals
• EECS 6720 Bayesian Models for Machine Learning
• COMS 4771 Machine Learning
• COMS 4772 Advanced Machine Learning
• IEOR E6613 Optimization I
• IEOR E6614 Optimization II
• IEOR E6711 Stochastic Modeling I
• EEOR E6616 Convex Optimization
• STAT 6301 Probability Theory I
• STAT 6201 Theoretical Statistics I
• STAT 6101 Applied Statistics I
• STAT 6104 Computational Statistics
• STAT 5224 Bayesian Statistics
• STCS 6701 Foundations of Graphical Models (joint with Computer Science) 

Information Request Form

Ph.d. specialization committee.

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• Faculty of Arts and Sciences Professor of Statistics
• The Fu Foundation School of Engineering and Applied Science Professor of Computer Science

Richard A. Davis

• Faculty of Arts and Sciences Howard Levene Professor of Statistics

Vineet Goyal

• The Fu Foundation School of Engineering and Applied Science Associate Professor of Industrial Engineering and Operations Research

Garud N. Iyengar

• The Fu Foundation School of Engineering and Applied Science Vice Dean of Research
• Tang Family Professor of Industrial Engineering and Operations Research

Gail Kaiser

Rocco a. servedio, clifford stein.

• Data Science Institute Interim Director
• The Fu Foundation School of Engineering and Applied Science Wai T. Chang Professor of Industrial Engineering and Operations Research and Professor of Computer Science

John Wright

• The Fu Foundation School of Engineering and Applied Science Associate Professor of Electrical Engineering
• Data Science Institute Associate Director for Academic Affairs

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PhDs in Biomedical Sciences

The Coordinated Doctoral Programs in Biomedical Sciences are part of the medical school and the Columbia University Graduate School of Arts and Sciences. The programs are located at the Columbia University Irving Medical Center campus. PhD students have access to more than 250 training faculty when selecting their research direction, ensuring that each student receives optimal training and research experience. We also provide a supportive environment which goes beyond academics. 

Programs include:

• Biomedical Informatics
• Genetics and Development
• Integrated Program in Cellular, Molecular, and Biomedical Studies
• Microbiology and Immunology
• Neurobiology and Behavior
• Nutritional and Metabolic Biology
• Pathology and Molecular Medicine
• Pharmacology and Molecular Signaling
• Physiology and Cellular Biophysics

Best Global Universities for Mechanical Engineering in Russia

These are the top universities in Russia for mechanical engineering, based on their reputation and research in the field. Read the methodology »

To unlock more data and access tools to help you get into your dream school, sign up for the  U.S. News College Compass !

Here are the best global universities for mechanical engineering in Russia

Tomsk polytechnic university.

See the full rankings

• Clear Filters
• # 74 in Best Universities for Mechanical Engineering
• # 879 in Best Global Universities  (tie)

30 Best universities for Mechanical Engineering in Moscow, Russia

Updated: February 29, 2024

• Art & Design
• Computer Science
• Engineering
• Environmental Science
• Liberal Arts & Social Sciences
• Mathematics

Below is a list of best universities in Moscow ranked based on their research performance in Mechanical Engineering. A graph of 269K citations received by 45.8K academic papers made by 30 universities in Moscow was used to calculate publications' ratings, which then were adjusted for release dates and added to final scores.

We don't distinguish between undergraduate and graduate programs nor do we adjust for current majors offered. You can find information about granted degrees on a university page but always double-check with the university website.

1. Moscow State University

For Mechanical Engineering

2. Bauman Moscow State Technical University

3. National Research University Higher School of Economics

4. Moscow Aviation Institute

5. N.R.U. Moscow Power Engineering Institute

6. National Research Nuclear University MEPI

7. National University of Science and Technology "MISIS"

8. Moscow Institute of Physics and Technology

9. Moscow State Technological University "Stankin"

10. RUDN University

11. Moscow Polytech

12. Moscow State University of Railway Engineering

13. Finance Academy under the Government of the Russian Federation

14. Moscow Medical Academy

15. Russian State University of Oil and Gas

16. mendeleev university of chemical technology of russia.

17. Russian National Research Medical University

18. Plekhanov Russian University of Economics

19. National Research University of Electronic Technology

20. Moscow State Pedagogical University

21. Russian Presidential Academy of National Economy and Public Administration

22. State University of Management

23. Moscow State Institute of International Relations

24. Russian State Geological Prospecting University

25. russian state agricultural university.

26. New Economic School

27. Moscow State Technical University of Civil Aviation

28. Russian State University for the Humanities

29. Russian State Social University

30. Moscow State Linguistic University

Universities for Mechanical Engineering near Moscow

Engineering subfields in moscow.