columbia phd in math

• Mathematics Education

Leading with Skill and Purpose

Master the skills you need to advance in the field of Mathematics Education. Take the next step and start your application today!

Welcome to the Mathematics Education program

The Mathematics Education program places a strong emphasis on mathematics content and the role of mathematical thinking in the teaching and learning of math. Our M.A. degrees offering both initial and professional certification while our advanced Ed.M. and doctoral degrees are geared toward teaching, supervision, and research roles which span from elementary through college levels of instruction. Our graduate students become leaders in mathematics education at all levels.

Choose Your Degree

Our program offers a variety of degrees for pre-professional and professional teachers as well as advanced degrees for students interested in tackling the teaching of mathematics in-depth. 

• I want initial certification to teach in grades 7-12
• I want an advanced masters for teaching in grades 7-12
• I'm interested in a degree, but I don't need certification
• I'm interested in doctoral study or teaching educators at the college level

Our M.A. programs are geared towards pre-professional teachers who are just starting out in the field.

• M.A. with Initial Certification (36-credit)
• M.A. with Transitional B Certification (36-credit)
• M.A. through Teaching Residents at Teachers College (36-credit)

We offer two degrees for graduate students who are pursuing advanced masters degrees.

• M.S. degree (60-credits) — emphasizes preparation in mathematics content.
• Ed.M. degree (60-credits) — places emphasis on preparation in professional education. 
• M.A. in Mathematics Education (non-certification) - 32-credits
• Doctor of Education, Ed.D. (90-credits)
• Doctor of Education in the College Teaching of Mathematics, Ed.D.C.T. (90-credits)
• Doctor of Philosophy in Mathematics Education, Ph.D. (75-credits)

Program News

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Program Research

Journal of Mathematics Education at Teachers College

JMETC is affiliated with the Teachers College Program in Mathematics Education. Over its long and distinguished history, the Program in Mathematics Education has stressed the preparation of leaders in education. Faculty and staff are committed to leadership training through a variety of courses, workshops, and research experiences, domestic and through international study offerings.

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Admissions Information

Application requirements.

• Mathematics Education NY State Initial: Mathematics 7-12
• Mathematics Education NY State Professional: Mathematics 7-12
• Mathematics Education (Peace Corps) NY State Transitional B: Mathematics 7-12
• Mathematics Education (Teaching Residents) NY State Initial: Mathematics 7-12 [Program is not accepting applications for the 2024 cycle.]

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• Tuition & Fees
• Financial Aid
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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

Graduate Student Handbook (Coming Soon: New Graduate Student Handbook)

Phd program overview.

The PhD program prepares students for research careers in probability and statistics in academia and industry. Students admitted to the PhD program earn the MA and MPhil along the way. The first year of the program is spent on foundational courses in theoretical statistics, applied statistics, and probability. In the following years, students take advanced topics courses. Research toward the dissertation typically begins in the second year. Students also have opportunities to take part in a wide variety of projects involving applied probability or applications of statistics.

Students are expected to register continuously until they distribute and successfully defend their dissertation. Our core required and elective curricula in Statistics, Probability, and Machine Learning aim to provide our doctoral students with advanced learning that is both broad and focused. We expect our students to make Satisfactory Academic Progress in their advanced learning and research training by meeting the following program milestones through courseworks, independent research, and dissertation research:

By the end of year 1: passing the qualifying exams;

By the end of year 2: fulfilling all course requirements for the MA degree and finding a dissertation advisor;

By the end of year 3: passing the oral exam (dissertation prospectus) and fulfilling all requirements for the MPhil degree

By the end of year 5: distributing and defending the dissertation.

We believe in the Professional Development value of active participation in intellectual exchange and pedagogical practices for future statistical faculty and researchers. Students are required to serve as teaching assistants and present research during their training. In addition, each student is expected to attend seminars regularly and participate in Statistical Practicum activities before graduation.

We provide in the following sections a comprehensive collection of the PhD program requirements and milestones. Also included are policies that outline how these requirements will be enforced with ample flexibility. Questions on these requirements should be directed to ADAA Cindy Meekins at [email protected] and the DGS, Professor John Cunningham at [email protected] .

Applications for Admission

• Our students receive very solid training in all aspects of modern statistics. See Graduate Student Handbook for more information.
• Our students receive Fellowship and full financial support for the entire duration of their PhD. See more details here .
• Our students receive job offers from top academic and non-academic institutions .
• Our students can work with world-class faculty members from Statistics Department or the Data Science Institute .
• Our students have access to high-speed computer clusters for their ambitious, computationally demanding research.
• Our students benefit from a wide range of seminars, workshops, and Boot Camps organized by our department and the data science institute .
• Suggested Prerequisites: A student admitted to the PhD program normally has a background in linear algebra and real analysis, and has taken a few courses in statistics, probability, and programming. Students who are quantitatively trained or have substantial background/experience in other scientific disciplines are also encouraged to apply for admission.
• GRE requirement: Waived for Fall 2024.
• Language requirement: The English Proficiency Test requirement (TOEFL) is a Provost's requirement that cannot be waived.
• The Columbia GSAS minimum requirements for TOEFL and IELTS are: 100 (IBT), 600 (PBT) TOEFL, or 7.5 IELTS. To see if this requirement can be waived for you, please check the frequently asked questions below.
• Deadline: Jan 8, 2024 .
• Application process: Please apply by completing the Application for Admission to the Columbia University Graduate School of Arts & Sciences .
• Timeline: P.hD students begin the program in September only.  Admissions decisions are made in mid-March of each year for the Fall semester.

Frequently Asked Questions

• What is the application deadline? What is the deadline for financial aid? Our application deadline is January 5, 2024 .
• Can I meet with you in person or talk to you on the phone? Unfortunately given the high number of applications we receive, we are unable to meet or speak with our applicants.
• What are the required application materials? Specific admission requirements for our programs can be found here .
• Due to financial hardship, I cannot pay the application fee, can I still apply to your program? Yes. Many of our prospective students are eligible for fee waivers. The Graduate School of Arts and Sciences offers a variety of application fee waivers . If you have further questions regarding the waiver please contact  gsas-admissions@ columbia.edu .
• How many students do you admit each year? It varies year to year. We finalize our numbers between December - early February.
• What is the distribution of students currently enrolled in your program? (their background, GPA, standard tests, etc)? Unfortunately, we are unable to share this information.
• How many accepted students receive financial aid? All students in the PhD program receive, for up to five years, a funding package consisting of tuition, fees, and a stipend. These fellowships are awarded in recognition of academic achievement and in expectation of scholarly success; they are contingent upon the student remaining in good academic standing. Summer support, while not guaranteed, is generally provided. Teaching and research experience are considered important aspects of the training of graduate students. Thus, graduate fellowships include some teaching and research apprenticeship. PhD students are given funds to purchase a laptop PC, and additional computing resources are supplied for research projects as necessary. The Department also subsidizes travel expenses for up to two scientific meetings and/or conferences per year for those students selected to present. Additional matching funds from the Graduate School Arts and Sciences are available to students who have passed the oral qualifying exam.
• Can I contact the department with specific scores and get feedback on my competitiveness for the program? We receive more than 450 applications a year and there are many students in our applicant pool who are qualified for our program. However, we can only admit a few top students. Before seeing the entire applicant pool, we cannot comment on admission probabilities.
• What is the minimum GPA for admissions? While we don’t have a GPA threshold, we will carefully review applicants’ transcripts and grades obtained in individual courses.
• Is there a minimum GRE requirement? No. The general GRE exam is waived for the Fall 2024 admissions cycle. 
• Can I upload a copy of my GRE score to the application? Yes, but make sure you arrange for ETS to send the official score to the Graduate School of Arts and Sciences.
• Is the GRE math subject exam required? No, we do not require the GRE math subject exam.
• What is the minimum TOEFL or IELTS  requirement? The Columbia Graduate School of Arts and Sciences minimum requirements for TOEFL and IELTS are: 100 (IBT), 600 (PBT) TOEFL, or 7.5 IELTS
•  I took the TOEFL and IELTS more than two years ago; is my score valid? Scores more than two years old are not accepted. Applicants are strongly urged to make arrangements to take these examinations early in the fall and before completing their application.
• I am an international student and earned a master’s degree from a US university. Can I obtain a TOEFL or IELTS waiver? You may only request a waiver of the English proficiency requirement from the Graduate School of Arts and Sciences by submitting the English Proficiency Waiver Request form and if you meet any of the criteria described here . If you have further questions regarding the waiver please contact  gsas-admissions@ columbia.edu .
• My transcript is not in English. What should I do? You have to submit a notarized translated copy along with the original transcript.

Can I apply to more than one PhD program? You may not submit more than one PhD application to the Graduate School of Arts and Sciences. However, you may elect to have your application reviewed by a second program or department within the Graduate School of Arts and Sciences if you are not offered admission by your first-choice program. Please see the application instructions for a more detailed explanation of this policy and the various restrictions that apply to a second choice. You may apply concurrently to a program housed at the Graduate School of Arts and Sciences and to programs housed at other divisions of the University. However, since the Graduate School of Arts and Sciences does not share application materials with other divisions, you must complete the application requirements for each school.

How do I apply to a dual- or joint-degree program? The Graduate School of Arts and Sciences refers to these programs as dual-degree programs. Applicants must complete the application requirements for both schools. Application materials are not shared between schools. Students can only apply to an established dual-degree program and may not create their own.

With the sole exception of approved dual-degree programs , students may not pursue a degree in more than one Columbia program concurrently, and may not be registered in more than one degree program at any institution in the same semester. Enrollment in another degree program at Columbia or elsewhere while enrolled in a Graduate School of Arts and Sciences master's or doctoral program is strictly prohibited by the Graduate School. Violation of this policy will lead to the rescission of an offer of admission, or termination for a current student.

When will I receive a decision on my application? Notification of decisions for all PhD applicants generally takes place by the end of March.

Notification of MA decisions varies by department and application deadlines. Some MA decisions are sent out in early spring; others may be released as late as mid-August.

Can I apply to both MA Statistics and PhD statistics simultaneously?  For any given entry term, applicants may elect to apply to up to two programs—either one PhD program and one MA program, or two MA programs—by submitting a single (combined) application to the Graduate School of Arts and Sciences.  Applicants who attempt to submit more than one Graduate School of Arts and Sciences application for the same entry term will be required to withdraw one of the applications.

The Graduate School of Arts and Sciences permits applicants to be reviewed by a second program if they do not receive an offer of admission from their first-choice program, with the following restrictions:

• This option is only available for fall-term applicants.
• Applicants will be able to view and opt for a second choice (if applicable) after selecting their first choice. Applicants should not submit a second application. (Note: Selecting a second choice will not affect the consideration of your application by your first choice.)
• Applicants must upload a separate Statement of Purpose and submit any additional supporting materials required by the second program. Transcripts, letters, and test scores should only be submitted once.
• An application will be forwarded to the second-choice program only after the first-choice program has completed its review and rendered its decision. An application file will not be reviewed concurrently by both programs.
• Programs may stop considering second-choice applications at any time during the season; Graduate School of Arts and Sciences cannot guarantee that your application will receive a second review.
• What is the mailing address for your PhD admission office? Students are encouraged to apply online . Please note: Materials should not be mailed to the Graduate School of Arts and Sciences unless specifically requested by the Office of Admissions. Unofficial transcripts and other supplemental application materials should be uploaded through the online application system. Graduate School of Arts and Sciences Office of Admissions Columbia University  107 Low Library, MC 4303 535 West 116th Street  New York, NY 10027
• How many years does it take to pursue a PhD degree in your program? Our students usually graduate in 4‐6 years.
• Can the PhD be pursued part-time? No, all of our students are full-time students. We do not offer a part-time option.
• One of the requirements is to have knowledge of linear algebra (through the level of MATH V2020 at Columbia) and advanced calculus (through the level of MATH V1201). I studied these topics; how do I know if I meet the knowledge content requirement? We interview our top candidates and based on the information on your transcripts and your grades, if we are not sure about what you covered in your courses we will ask you during the interview.
• Can I contact faculty members to learn more about their research and hopefully gain their support? Yes, you are more than welcome to contact faculty members and discuss your research interests with them. However, please note that all the applications are processed by a central admission committee, and individual faculty members cannot and will not guarantee admission to our program.
• How do I find out which professors are taking on new students to mentor this year?  Applications are evaluated through a central admissions committee. Openings in individual faculty groups are not considered during the admissions process. Therefore, we suggest contacting the faculty members you would like to work with and asking if they are planning to take on new students.

For more information please contact us at [email protected] .

For more information please contact us at  [email protected]

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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

• Doctor of Philosophy in Mathematics (PhD)
• Graduate School
• Prospective Students
• Graduate Degree Programs

Canadian Immigration Updates

Applicants to Master’s and Doctoral degrees are not affected by the recently announced cap on study permits. Review more details

Go to programs search

Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics. The PhD program trains students to operate as research mathematicians. The focus of the program is on substantial mathematical research leading to the PhD dissertation. Students also develop their skills in presenting and teaching mathematics and its applications.

For specific program requirements, please refer to the departmental program website

What makes the program unique?

UBC has one of the largest and most vigorous departments of mathematics in Canada. Our faculty routinely win national and international awards for their research and teaching achievements. We have an engaged and sociable cohort of graduate students who are essential members of a broad selection of active research groups. Each group holds a variety of seminars and events that allow graduate students, postdoctoral fellows, visitors and faculty to enjoy regular interaction.

UBC is the headquarters for the Pacific Institute of Mathematical Sciences (PIMS). PIMS hosts a plethora of mathematical events such as conferences and summer schools, greatly enriching the scientific environment in the quantitative sciences at UBC. Our mathematics students are also regular participants at the nearby Banff International Research Station for Mathematical Innovation and Discovery. Finally, our Institute for Applied Mathematics provides options for interdisciplinary studies for PhD students who wish to work in applied and computational mathematics.

I chose UBC because of the reputation of the university and mathematics department, the alignment of my research interests with my advisor’s expertise, and my love for Canada!

Ethan White

Quick Facts

Program enquiries, admission information & requirements, 1) check eligibility, minimum academic requirements.

The Faculty of Graduate and Postdoctoral Studies establishes the minimum admission requirements common to all applicants, usually a minimum overall average in the B+ range (76% at UBC). The graduate program that you are applying to may have additional requirements. Please review the specific requirements for applicants with credentials from institutions in:

• Canada or the United States
• International countries other than the United States

Each program may set higher academic minimum requirements. Please review the program website carefully to understand the program requirements. Meeting the minimum requirements does not guarantee admission as it is a competitive process.

English Language Test

Applicants from a university outside Canada in which English is not the primary language of instruction must provide results of an English language proficiency examination as part of their application. Tests must have been taken within the last 24 months at the time of submission of your application.

Minimum requirements for the two most common English language proficiency tests to apply to this program are listed below:

TOEFL: Test of English as a Foreign Language - internet-based

Overall score requirement : 100

IELTS: International English Language Testing System

Overall score requirement : 7.0

Other Test Scores

Some programs require additional test scores such as the Graduate Record Examination (GRE) or the Graduate Management Test (GMAT). The requirements for this program are:

The GRE is not required.

2) Meet Deadlines

3) prepare application, transcripts.

All applicants have to submit transcripts from all past post-secondary study. Document submission requirements depend on whether your institution of study is within Canada or outside of Canada.

Letters of Reference

A minimum of three references are required for application to graduate programs at UBC. References should be requested from individuals who are prepared to provide a report on your academic ability and qualifications.

Statement of Interest

Many programs require a statement of interest , sometimes called a "statement of intent", "description of research interests" or something similar.

Supervision

Students in research-based programs usually require a faculty member to function as their thesis supervisor. Please follow the instructions provided by each program whether applicants should contact faculty members.

Instructions regarding thesis supervisor contact for Doctor of Philosophy in Mathematics (PhD)

Citizenship verification.

Permanent Residents of Canada must provide a clear photocopy of both sides of the Permanent Resident card.

4) Apply Online

All applicants must complete an online application form and pay the application fee to be considered for admission to UBC.

Tuition & Financial Support

Financial support.

Applicants to UBC have access to a variety of funding options, including merit-based (i.e. based on your academic performance) and need-based (i.e. based on your financial situation) opportunities.

Program Funding Packages

All full-time students who begin a UBC-Vancouver PhD Mathematics program in September 2018 or later will be provided with a funding package of at least $24,256 for each of the first four years of their PhD. The funding package may consist of any combination of internal or external awards, teaching-related work, research assistantships, and graduate academic assistantships.

Average Funding

• 52 students received Teaching Assistantships. Average TA funding based on 52 students was $13,784.
• 48 students received Research Assistantships. Average RA funding based on 48 students was $11,580.
• 3 students received Academic Assistantships. Average AA funding based on 3 students was $1,814.
• 54 students received internal awards. Average internal award funding based on 54 students was $13,279.
• 4 students received external awards. Average external award funding based on 4 students was $27,083.

Scholarships & awards (merit-based funding)

All applicants are encouraged to review the awards listing to identify potential opportunities to fund their graduate education. The database lists merit-based scholarships and awards and allows for filtering by various criteria, such as domestic vs. international or degree level.

Graduate Research Assistantships (GRA)

Many professors are able to provide Research Assistantships (GRA) from their research grants to support full-time graduate students studying under their supervision. The duties constitute part of the student's graduate degree requirements. A Graduate Research Assistantship is considered a form of fellowship for a period of graduate study and is therefore not covered by a collective agreement. Stipends vary widely, and are dependent on the field of study and the type of research grant from which the assistantship is being funded.

Graduate Teaching Assistantships (GTA)

Graduate programs may have Teaching Assistantships available for registered full-time graduate students. Full teaching assistantships involve 12 hours work per week in preparation, lecturing, or laboratory instruction although many graduate programs offer partial TA appointments at less than 12 hours per week. Teaching assistantship rates are set by collective bargaining between the University and the Teaching Assistants' Union .

Graduate Academic Assistantships (GAA)

Academic Assistantships are employment opportunities to perform work that is relevant to the university or to an individual faculty member, but not to support the student’s graduate research and thesis. Wages are considered regular earnings and when paid monthly, include vacation pay.

Financial aid (need-based funding)

Canadian and US applicants may qualify for governmental loans to finance their studies. Please review eligibility and types of loans .

All students may be able to access private sector or bank loans.

Foreign government scholarships

Many foreign governments provide support to their citizens in pursuing education abroad. International applicants should check the various governmental resources in their home country, such as the Department of Education, for available scholarships.

Working while studying

The possibility to pursue work to supplement income may depend on the demands the program has on students. It should be carefully weighed if work leads to prolonged program durations or whether work placements can be meaningfully embedded into a program.

International students enrolled as full-time students with a valid study permit can work on campus for unlimited hours and work off-campus for no more than 20 hours a week.

A good starting point to explore student jobs is the UBC Work Learn program or a Co-Op placement .

Tax credits and RRSP withdrawals

Students with taxable income in Canada may be able to claim federal or provincial tax credits.

Canadian residents with RRSP accounts may be able to use the Lifelong Learning Plan (LLP) which allows students to withdraw amounts from their registered retirement savings plan (RRSPs) to finance full-time training or education for themselves or their partner.

Please review Filing taxes in Canada on the student services website for more information.

Cost Estimator

Applicants have access to the cost estimator to develop a financial plan that takes into account various income sources and expenses.

Career Outcomes

88 students graduated between 2005 and 2013: 1 is in a non-salaried situation; for 19 we have no data (based on research conducted between Feb-May 2016). For the remaining 68 graduates:

Sample Employers in Higher Education

Sample employers outside higher education, sample job titles outside higher education, phd career outcome survey, career options.

A great majority of our PhD graduates move on to postdoctoral fellowships and faculty positions at universities and research institutes in North America and around the world. However, a significant fraction of students move into careers in industry. Students considering non-academic careers are encouraged to complete an industrial internship (for instance through the Mitacs Accelerate program - headquartered at UBC) during their studies.

Enrolment, Duration & Other Stats

These statistics show data for the Doctor of Philosophy in Mathematics (PhD). Data are separated for each degree program combination. You may view data for other degree options in the respective program profile.

ENROLMENT DATA

Completion rates & times, upcoming doctoral exams, friday, 5 july 2024 - 9:00am - room 200, thursday, 11 july 2024 - 10:30am - 203, mathematics building, 1984 mathematics road.

• Research Supervisors

Advice and insights from UBC Faculty on reaching out to supervisors

These videos contain some general advice from faculty across UBC on finding and reaching out to a supervisor. They are not program specific.

This list shows faculty members with full supervisory privileges who are affiliated with this program. It is not a comprehensive list of all potential supervisors as faculty from other programs or faculty members without full supervisory privileges can request approvals to supervise graduate students in this program.

• Adem, Alejandro (Cohomology of finite groups, orbifolds, stringy topology, algebra, sporadic simple group, group actions, arithmetic groups, K-theory, homotopy theory, spaces of homomorphisms)
• Angel, Omer (Probability theory, percolation, random graphs, random walks, particle processes, scaling limits)
• Bachmann, Sven (Mathematics and statistics; Mathematical Analysis; quantum phenomena; Mathematical physics; Quantum statistical physics; Topological states of matter)
• Balmforth, Neil (Fluid mechanics, nonlinear dynamics and applied partial differential equations)
• Behrend, Kai (Moduli spaces, Gromov-Witten invariants, string theory, Donaldson-Thomas invariants, Euler characteristics, categorification)
• Bennett, Michael (Number Theory, Diophantine Approximation and Classical Analysis)
• Bryan, Jim (Algebraic and differential geometry; Algebraic geometry, moduli spaces, enumerative invariants related to theoretical physics.)
• Cautis, Sabin (Mathematics and statistics; Geometry)
• Chau, Albert (Differential Geometry and Partial Differential Equations)
• Chen, Jingyi (Algebraic and differential geometry; Differential Geometry, Partial Differential Equations)
• Colliander, James (hamiltonian dynamical systems; partial differential equations; harmonic analysis)
• Coombs, Daniel (Mathematical biology; Cellular immunology; Complex physical systems; Epidemiology (except nutritional and veterinary epidemiology); Cell Signaling and Infectious and Immune Diseases; Cell biophysics; Disease models; Epidemiology; Immune cell signalling; Mathematics)
• Cytrynbaum, Eric (Bacterial cell division, Microtubule and cellular organization, Wave propagation in excitable media)
• Dao Duc, Khanh (Genomics; Mathematical biology; Neurocognitive patterns and neural networks; Agricultural spatial analysis and modelling; combine mathematical,computational and statistical tools to study fundamental biological processes; regulation and determinants of gene expression and translation; Machine Learning for Biological Imaging and Microscopy; Database development and management; Biological and Artificial Neural Networks for geometric representation)
• Doebeli, Michael Walter (Mathematical ecology and evolution, evolution of diversity, adaptive speciation, evolution of cooperation, game theory, experimental evolution in microorganisms)
• Feng, James (Chemical engineering; Mathematics and statistics; Biophysics; Complex fluids; Fluid mechanics; Mathematical biology)
• Fraser, Ailana (Differential Geometry, Geometric Analysis)
• Friedlander, Michael (numerical optimization, numerical linear algebra, scientific computing, Scientific computing)
• Frigaard, Ian (Fluid mechanics (visco-plastic fluids))
• Ghioca, Dragos (Drinfeld modules, isotrivial semiabelian varieties, Lehmer inequality)
• Gordon, Julia Yulia (Representation theory of p-adic groups and motivic integration; Trace Formula and its applications)
• Gustafson, Stephen James (Mathematics and statistics; Mathematical Analysis; Differential Equation; Global and Non-Linear Analysis; Mathematical physics; Nonlinear partial differential equations; Nonlinear waves; Topological solitons)
• Hauert, Christoph (Mathematics and statistics; Modelization and Simulation; Evolution and Phylogenesis; Biological Behavior; dynamical systems; evolution; game theory; social dilemmas; stochastic processes)
• Hermon, Jonathan (probability theory; Markov chains and the cutoff phenomenon; particle systems; percolation)
• Holmes-Cerfon, Miranda (Mathematical modelling and simulation; Computational methods in statistics; Numerical analysis; Thermodynamics and statistical physics)

Doctoral Citations

Sample thesis submissions.

• Free boundary minimal submanifolds in geodesic balls of simply connected space forms
• On a completion of cohomological functors generalizing Tate cohomology
• Distribution of integral points on varieties
• Effective and explicit S-unit equations with many terms
• Classifying space for commutativity and unordered flag manifolds
• Finite-size scaling of a few statistical physics models in high dimensions
• Residual supersingular Iwasawa theory and μ-invariants for Zₚ²-extensions
• Numerical methods for biological flows laden with deformable capsules and solid particles
• The construction of blow-up solutions for some evolution equations
• Topics in discrete analysis
• Inviscid damping phenomena in some fluid models
• Gibbs measures and factor codes in symbolic dynamics
• Deep reinforcement learning agents for industrial control system design
• Structure-preserving numerical schemes for phase field models
• Enumerative geometry problems for Calabi-Yau manifolds with an action

Related Programs

Same specialization.

• Master of Science in Mathematics (MSc)

At the UBC Okanagan Campus

Further information, specialization.

Mathematicians use theoretical and computational methods to solve a wide range of problems from the most abstract to the very applied. UBC's mathematics graduate students work in many branches of pure and applied mathematics.

UBC Calendar

Program website, faculty overview, academic unit, program identifier, classification, social media channels, supervisor search.

Departments/Programs may update graduate degree program details through the Faculty & Staff portal. To update contact details for application inquiries, please use this form .

Nicholas Richardson

Having grown up outside of Toronto and completed my undergrad and master's degree at the University of Waterloo, I was ready to change the scenery and go study somewhere else. I joke that is it the farthest I could move without leaving Canada, but more truthfully it was the campus that felt "right...

Gabriel Currier

I quite like the kind of math that people do here, and enjoy working with my supervisors. The campus is also a beautiful place and the graduate student community is pretty laid back and friendly.

Nathan Lawrence

Many factors contributed to my choice of UBC for graduate school. I was attracted to Vancouver’s geographical similarities to Portland in the pacific northwest. Also, I have family in the area. However, most importantly, I was intrigued and inspired by my professors and advisors to take on the...

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Columbia Economics FAQs :

Faqs for incoming phd students.

1. Who should I contact if I have questions about the department?

The PhD Program Manager, Amy Devine ([email protected]) and PhD Program Coordinator, Rosie Lourentzatos ([email protected]) are the first points of contact for questions about the department.

2. How should incoming first-year students prepare for the start of the PhD program?

The Economics Department strongly recommends that all incoming PhD students attend Math Camp. It takes place in August each year. We do not need you to do any particular preparation in the earlier part of the summer. You are all well qualified for the program.

3. Is Math Camp required?

No, Math Camp is not required but it is strongly recommended.

4. What software resources are available to Economics PhD students?

PhD students have access to licenses including Mathematica, Matlab, ArcGIS, Stata and a high-performance computing account with various other software.

5. Where do first-year students study?

First-year PhD students generally do not have individual work space in the department. Instead, they study in the Columbia Libraries, especially the Business and Economics Library in Uris Hall. Students can also reserve departmental rooms for group study when available.

6. Is there an Economics Department PhD student club? How do new students join?

Yes, the Association for Graduate Economics Students (AGES) hosts regular events and workshops. All incoming PhD students are automatically enrolled as members.

7. Who advises first-year PhD students about academic-related questions?

The Director of Graduate Studies serves as the first-year academic adviser. The current DGS is Prof. Navin Kartik.

8. Who advises first-year PhD students if they have questions about student life?

For questions about student life, first-year students can contact AGES ( [email protected] ), Rosie Lourentzatos ( [email protected] ) or The Graduate School Office of Student Affairs ( [email protected] ).

9. Can students pass out of the Math Methods (GR6410) course?

Yes, students may pass out of the Math Methods course if they successfully complete the corresponding exam and receive DGS approval.

10. Does the department require first-year PhD students to take Certifying exams?

First-year PhD students may have to take end-of-year certifying examinations in microeconomics, macroeconomics, and econometrics. These examinations are taken in the summer after the first year. They are graded pass or fail. If students receive a grade of B+ or better in both of the one-semester courses that make up the first-year sequence in microeconomics, macroeconomics, or econometrics, they are exempted from the requirement to take the certification exam in that field.

11. Does the department require second-year PhD students to take Field Exams?

In addition to courses, second-year students may have to pass a field exam in each field they have selected. (Each student must select two fields). Field exams are given in the summer after the second year. If students receive a grade of B+ or better in all of the courses taken to satisfy the requirements of a second-year field, they are exempted from the requirement to take the field exam in that field.

12. Are PhD students required to work as Teaching Fellows?

Yes, as part of their pedagogical training, all PhD students must work as Teaching Fellows for at least 2 semesters in order to obtain their degree. As part of the Columbia multi-year funding package, students generally work in years 2-4 as Teaching Fellows or Research Fellows unless they obtain funding from an external source.

13. What type of research opportunities are available to PhD students?

Research opportunities are available in the Economics Department, in the greater Columbia community and outside the University. Students begin research as early as in the summer after their first year. The Program for Economic Research (PER) supports many PhD student research initiatives. For more information, see link here .  Depending on their areas of interest, PhD students collaborate with Economics faculty and/or faculty in other schools such as the Business School, School of International and Public Affairs and Mailman School of Public Health, among others. The Graduate School of Arts and Sciences supports student research as well. For more information, see link .

14. Does the department offer funding for conference travel?

The department allocates specific funding for conference travel in PhD students’ 4 th and 5 th years. In addition, students may submit funding requests to PER at any time. Funding for conference travel at any time is also available from the Graduate School of Arts and Sciences, and frequently from individual faculty mentors or research groups/initiatives in the department. For more information, see link .

15. Does the department offer funding for data purchase?

Yes, PER supports data purchase requests. Awards are made on a case-by-case basis.

16. Does the department offer opportunities for PhD students to present their research?

PhD students have several venues to present research both in and out of the department. Starting in their second year, students present in at least one colloquium during the year. Starting in their third year, students present research in a colloquium once per semester. Additionally, students present research in workshops, lunches and breakfast meetings. Outside the department, students present their research in a variety of venues including the Business School, The Institute for Social and Economic Research Policy, and conferences around the world.

17. Can students take courses for credit in other departments such as Columbia Business School?

Yes, in lieu of one of the fields designated by the department, students may petition the DGS to take an individually-designed field. An individually-designed field consists of 3 courses, not all of which need to be offered by the Department. For more information, please see link here .

18. What is the Business Economics (BusEc) track?

For more information about the BusEc track, please see link here .

19. Can students take courses for credit at other universities such as Princeton and NYU?

Yes, as part of the Inter-College Doctoral Consortium (IUDC), Columbia PhD students can enroll in courses at participating universities. For more information, see link here .

20. How long does it typically take a PhD student to complete the program?

In recent years, most of our PhD students have completed the program in 6 years.

21. Once they graduate, where do Columbia PhD students get jobs?

For recent placement information, please see link .  

FAQs about Columbia University

22. Who should I contact if I have general questions about Columbia?

The Graduate School of Arts and Sciences has a comprehensive website that offers detailed information about graduate life. For more information, see link here . If you are unable to find the information you need, please contact Amy Devine.

23. Where can I find information about course offerings at Columbia?

Course information is listed on the Directory of Classes .

24. Where can I find information about the academic calendar?

The Office of the University Registrar maintains the academic calendar. For more information, see link here .

25. How can I find out about events happening on campus?

The Economics Department maintains an electronic announcement page and posts updates on the Economics PhD bulletin board in the International Affairs Building. PER distributes updates regarding speaker events, lectures and workshops.

26. How can I find out more information about what is covered by Columbia’s health benefits for PhD students?

For detailed information about health benefits, please consult Columbia Health’s webpage here .

27. What does a sample apartment look like?

See examples of accommodations here on Columbia Residential’s website.

28. How do I find out more about the on-campus housing registration procedure?

See detailed information about the application process here .

29. Is there a guarantee that on-campus housing will be available until I complete my PhD degree?

For students in good academic standing who make adequate progress toward their degree, guaranteed on-campus housing is available for up to 6 years provided you remain in good standing and apply by the deadline. For more information, see here .

30. Are on-campus housing units furnished?

Yes, for more information about accommodations reserved for PhD students in the Graduate School of Arts and Sciences program, please see link . (Select the school specific tab and choose Graduate School of Arts and Sciences.)

31. Does Columbia assist students who would prefer to rent off-campus apartments?

Yes, please contact Columbia’s Off-Campus Housing Assistance Office .

32. What are the fitness options?

Graduate students can work out at Dodge Fitness Center . They are not required to pay a membership fee.

33. Do I have to pay for the gym membership?

No, PhD students in Economics do not pay the Dodge Fitness membership fee during the semester. However, individual and group classes are fee-based activities.

FAQs about Morningside Heights and New York City

34. What sort of safety measures are in place to protect the Columbia community?

New York has a lower-than-average crime rate and ranks among the safest large cities in the country. Within New York City, Morningside Heights is consistently named one of the safest precincts. Furthermore, the Department of Public Safety ensures the security of Columbia’s campus and its students. For useful information from Public Safety, including current crime information and trends, please see the following link .

35. How can I find out about events happening in the community?

For upcoming events, students should consult the Arts Initiative link .

36. Are there student discounts available for arts and entertainment in New York?

Yes, the Arts Initiative webpage has numerous listings for free and discounted performances. For more information, see link .

37. How do people get around the city?

Public transportation options include the Metropolitan Transportation Authority (MTA) subway and bus system . Citibikes are available throughout the city. Many opt to walk to nearby destinations.

38. Are there discounted transportation options?

There are no discounts for the MTA bus or subway with the exception for those with qualifying disabilities. For more information, see link .

Visual Tours of Columbia :

https://www.youtube.com/watch?v=7cwUcdpUayQ

https://undergrad.admissions.columbia.edu/visit/virtual-tours

Additional Links:

https://econ.columbia.edu/phd/current-students/program-requirements/

https://econ.columbia.edu/news/

https://gsas.columbia.edu/student-guide/new-student-guide

https://gsas.columbia.edu/new-student-guide/new-student-checklist

https://gsas.columbia.edu/new-student-guide/frequently-asked-questions-new-students

https://residential.columbia.edu/content/students/accommodations#/cu_accordion_item-391

https://isso.columbia.edu/

1022 International Affairs Building (IAB)

Mail Code 3308

420 West 118th Street

New York, NY 10027

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Ph.D. Program

Students entering through the Integrated Biomedical Sciences program have the opportunity to study with research faculty from the School of Medicine and across USC.

All of our Ph.D. students enter through the Integrated Biomedical Sciences program that includes primary core courses and research rotations that allow you to decide the exact research you want to conduct.

Research Areas and Faculty Mentors

Choosing your research mentor and research area will be two of the biggest decisions you will make during your Ph.D. program. While we encourage you to have an idea of who you would like to work with before you apply, we also give you the opportunity to explore all your options. 

Admission and Application

Admission into our program is on a rolling basis with submissions opening in the Fall semester and decisions being made in the Spring semester.

Tuition and Financial Aid

Tuition and financial aid information for students applying to and entering the Biomedical Sciences Ph.D. program.

PREP Program

USC PREP seeks to increase the number of applicants to biomedical graduate programs from under-represented communities by offering the opportunity to work for a year in a biomedical research laboratory while preparing for graduate school in the biomedical sciences.

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