phd in math and physics

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Mathematical Physics Ph.D. Degree

Doctor of philosophy (ph.d.) in mathematical physics.

This program offers advanced graduate training in the overlapping areas of mathematics, theoretical physics, and their applications from a unified point of view and promotes research in this field.

General supervision of the program is controlled by the Interdepartmental Graduate Committee on Mathematical Physics. While no master’s degree is offered, you may qualify for a master’s degree in mathematics or physics during the course of study. Our students usually enter the program at the beginning of the second year of graduate study in Mathematics or Physics.

 Learn more in our Student Portal Learn how to apply

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Ph.D. program

The Applied Physics Department offers a Ph.D. degree program; see  Admissions Overview  for how to apply.  

1.  Courses . Current listings of Applied Physics (and Physics) courses are available via  Explore Courses . Courses are available in Physics and Mathematics to overcome deficiencies, if any, in undergraduate preparation. It is expected the specific course requirements are completed by the  end of the 3rd year  at Stanford.

Required Basic Graduate Courses.   30 units (quarter hours) including:

• Basic graduate courses in advanced mechanics, statistical physics, electrodynamics, quantum mechanics, and an advanced laboratory course. In cases where students feel they have already covered the materials in one of the required basic graduate courses, a petition for waiver of the course may be submitted and is subject to approval by a faculty committee.
• 18 units of advanced coursework in science and/or engineering to fit the particular interests of the individual student. Such courses typically are in Applied Physics, Physics, or Electrical Engineering, but courses may also be taken in other departments, e.g., Biology, Materials Science and Engineering, Mathematics, Chemistry. The purpose of this requirement is to provide training in a specialized field of research and to encourage students to cover material beyond their own special research interests.​

​ Required Additional Courses .  Additional courses needed to meet the minimum residency requirement of 135 units of completed course work. Directed study and research units as well as 1-unit seminar courses can be included. Courses are sometimes given on special topics, and there are several seminars that meet weekly to discuss current research activities at Stanford and elsewhere. All graduate students are encouraged to participate in the special topics courses and seminars. A limited number of courses are offered during the Summer Quarter. Most students stay in residence during the summer and engage in independent study or research programs.

The list of the PhD degree core coursework is listed in the bulletin here:  https://bulletin.stanford.edu/programs/APLPH-PHD .

3.  Dissertation Research.   Research is frequently supervised by an Applied Physics faculty member, but an approved program of research may be supervised by a faculty member from another department.

4.  Research Progress Report.   Students give an oral research progress report to their dissertation reading committee during the winter quarter of the 4th year.

5.  Dissertation.

6.  University Oral Examination .  The examination includes a public seminar in defense of the dissertation and questioning by a faculty committee on the research and related fields.

Most students continue their studies and research during the summer quarter, principally in independent study projects or dissertation research. The length of time required for the completion of the dissertation depends upon the student and upon the dissertation advisor. In addition, the University residency requirement of 135 graded units must be met.

Rotation Program

We offer an optional rotation program for 1st-year Ph.D. students where students may spend one quarter (10 weeks) each in up to three research groups in the first year. This helps students gain research experience and exposure to various labs, fields, and/or projects before determining a permanent group to complete their dissertation work. 

Sponsoring faculty members may be in the Applied Physics department, SLAC, or any other science or engineering department, as long as they are members of the Academic Council (including all tenure-line faculty). Rotations are optional and students may join a group without the rotation system by making an arrangement directly with the faculty advisor. 

During the first year, research assistantships (RAs) are fully funded by the department for the fall quarter; in the winter and spring quarters, RAs are funded 50/50 by the department and the research group hosting the student. RAs after the third quarter are, in general, not subsidized by the rotation program or the department and should be arranged directly by the student with their research advisor.

How to arrange a rotation

Rotation positions in faculty members’ groups are secured by the student by directly contacting and coordinating with faculty some time between the student’s acceptance into the Ph.D. program and the start of the rotation quarter. It is recommended that the student’s fall quarter rotation be finalized no later than Orientation Week before the academic year begins. A rotation with a different faculty member can be arranged for the subsequent quarters at any time. Most students join a permanent lab by the spring quarter of their first year after one or two rotations.  When coordinating a rotation, the student and the sponsoring faculty should discuss expectations for the rotation (e.g. project timeline or deliverables) and the availability of continued funding and permanent positions in the group. It is very important that the student and the faculty advisor have a clear understanding about expectations going forward.

What do current students say about rotations?

Advice from current ap students, setting up a rotation:.

• If you have a specific professor or group in mind, you should contact them as early as possible, as they may have a limited number of rotation spots.
• You can prepare a 1-page CV or resume to send to professors to summarize your research experiences and interest.
• Try to tour the lab/working areas, talk to senior graduate students, or attend group meeting to get a feel for how the group operates.
• If you don't receive a response from a professor, you can send a polite reminder, stop by their office, or contact their administrative assistant. If you receive a negative response, you shouldn't take it personally as rotation availability can depend year-to-year on funding and personnel availability.
• Don't feel limited to subfields that you have prior experience in. Rotations are for learning and for discovering what type of work and work environment suit you best, and you will have several years to develop into a fully-formed researcher!

You and your rotation advisor should coordinate early on about things like: 

• What project will you be working on and who will you be working with?
• What resources (e.g. equipment access and training, coursework) will you need to enable this work?
• How closely will you work with other members of the group? 
• How frequently will you and your rotation advisor meet?
• What other obligations (e.g. coursework, TAing) are you balancing alongside research?
• How will your progress be evaluated?
• Is there funding available to support you and this project beyond the rotation quarter?
• Will the rotation advisor take on new students into the group in the quarter following the rotation?

About a month before the end of the quarter, you should have a conversation with your advisor about things like:

• Will you remain in the current group or will you rotate elsewhere?
• If you choose to rotate elsewhere, does the option remain open to return to the present group later?
• If you choose to rotate elsewhere, will another rotation student be taken on for the same project?
• You don't have to rotate just for the sake of rotating! If you've found a group that suits you well in many aspects, it makes sense to continue your research momentum with that group.

Application process

View Admissions Overview View the Required Online Ph.D. Program Application  

Contact the Applied Physics Department Office at  [email protected]  if additional information on any of the above is needed.

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Doctor of Philosophy (PhD)

Program synopsis and training.

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

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

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

Expected Preparations for Admission

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

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

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

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

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

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

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

Qualifying Requirements by Track

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

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

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

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

Opportunities & Outcomes

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

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

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

See also our  Applied Mathematics Topics List  [pdf].

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

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

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

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

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

Prospective students:  [email protected]

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

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

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

PhD in Applied Mathematics

Phd in applied mathematics degree.

Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities. The program has focuses on understanding nature through the fusion of Artificial Intelligence, Computing (classical to quantum), and Mathematics. We value foundational contributions, societal impact, and ethics in our work. Our program uniquely interfaces with diverse fields, including physics, neuroscience, materials science, economics, biology and fluid mechanics, to tackle some of the most pressing challenges of our time, such as sustainability, responsible digital transformations, and health and well-being.

Working individually and as part of teams collaborating across the University and beyond, you will partner with faculty to quantitatively describe, predict, design and control phenomena in a range of fields. Projects current and past students have worked on include collaborations with mechanical engineers to uncover some of the fundamental properties of artificial muscle fibers for soft robotics and developing new ways to simulate tens of thousands of bubbles in foamy flows for industrial applications such as food and drug production.

Our core mission is to provide students with individualized programs tailored to their interests, needs, and background. We welcome students from diverse technical backgrounds. Our program is dedicated to the principles of diversity, equity, and inclusion. We celebrate and value differences among our members, and we strive to create an equitable and inclusive environment for people of all backgrounds.

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Applied Mathematics PhD Degree

Harvard School of Engineering offers a  Doctor of Philosophy (Ph.D.) degree in Applied Mathematics conferred through the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences . Doctoral students may earn the masters degree en route to the Ph.D. Prospective students apply through Harvard Griffin GSAS; in the online application, select  “Engineering and Applied Sciences” as your program choice and select “PhD Applied Math” in the Area of Study menu.

The Applied Mathematics program does not offer an independent Masters Degree.

Applied Mathematics PhD Career Paths

Our graduates have gone on to careers such as start-up pioneers, social innovators, and a range of careers in industry in organizations like the Kingdom of Morocco, Meta, and Bloomberg. Others have secured faculty positions at Dartmouth, Imperial College in London, and UCLA. More generally, students with a PhD in Applied Mathematics can go on to careers in academia, banking, data science, bioinformatics, management consulting, government/military research, and more. Also, r ead about some of our Applied Mathematics alumni .

Admissions & Academic Requirements

Please review the  admissions requirements and other information  before applying. Our website also provides  admissions guidance ,   program-specific requirements , and a PhD program academic timeline .

Academic Background

Applicants typically have bachelor’s degrees in the natural sciences, mathematics, computer science, or engineering. 

Standardized Tests

GRE General: Not Accepted

Applied Mathematics Faculty & Research Areas

View a list of our  Applied Mathematics faculty and applied mathematics  affiliated research areas , Please note that faculty members listed as “Affiliates" or "Lecturers" cannot serve as the primary research advisor.  

Applied Mathematics Centers & Initiatives

View a list of the research centers & initiatives at SEAS and the Applied Mathematics faculty engagement with these entities .

Graduate Student Clubs

Graduate student clubs and organizations bring students together to share topics of mutual interest. These clubs often serve as an important adjunct to course work by sponsoring social events and lectures. Graduate student clubs are supported by the Harvard Kenneth C. Griffin School of Arts and Sciences. Explore the list of active clubs and organizations .

Funding and Scholarship

Learn more about financial support for PhD students.

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Learn more about how to apply  or review frequently asked questions for prospective graduate students.

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Graduate studies, commencement 2019.

The Harvard Department of Physics offers students innovative educational and research opportunities with renowned faculty in state-of-the-art facilities, exploring fundamental problems involving physics at all scales. Our primary areas of experimental and theoretical research are atomic and molecular physics, astrophysics and cosmology, biophysics, chemical physics, computational physics, condensed-matter physics, materials science, mathematical physics, particle physics, quantum optics, quantum field theory, quantum information, string theory, and relativity.

Our talented and hardworking students participate in exciting discoveries and cutting-edge inventions such as the ATLAS experiment, which discovered the Higgs boson; building the first 51-cubit quantum computer; measuring entanglement entropy; discovering new phases of matter; and peering into the ‘soft hair’ of black holes.

Our students come from all over the world and from varied educational backgrounds. We are committed to fostering an inclusive environment and attracting the widest possible range of talents.

We have a flexible and highly responsive advising structure for our PhD students that shepherds them through every stage of their education, providing assistance and counseling along the way, helping resolve problems and academic impasses, and making sure that everyone has the most enriching experience possible.The graduate advising team also sponsors alumni talks, panels, and advice sessions to help students along their academic and career paths in physics and beyond, such as “Getting Started in Research,” “Applying to Fellowships,” “Preparing for Qualifying Exams,” “Securing a Post-Doc Position,” and other career events (both academic and industry-related).

We offer many resources, services, and on-site facilities to the physics community, including our electronic instrument design lab and our fabrication machine shop. Our historic Jefferson Laboratory, the first physics laboratory of its kind in the nation and the heart of the physics department, has been redesigned and renovated to facilitate study and collaboration among our students.

Members of the Harvard Physics community participate in initiatives that bring together scientists from institutions across the world and from different fields of inquiry. For example, the Harvard-MIT Center for Ultracold Atoms unites a community of scientists from both institutions to pursue research in the new fields opened up by the creation of ultracold atoms and quantum gases. The Center for Integrated Quantum Materials , a collaboration between Harvard University, Howard University, MIT, and the Museum of Science, Boston, is dedicated to the study of extraordinary new quantum materials that hold promise for transforming signal processing and computation. The Harvard Materials Science and Engineering Center is home to an interdisciplinary group of physicists, chemists, and researchers from the School of Engineering and Applied Sciences working on fundamental questions in materials science and applications such as soft robotics and 3D printing.  The Black Hole Initiative , the first center worldwide to focus on the study of black holes, is an interdisciplinary collaboration between principal investigators from the fields of astronomy, physics, mathematics, and philosophy. The quantitative biology initiative https://quantbio.harvard.edu/  aims to bring together physicists, biologists, engineers, and applied mathematicians to understand life itself. And, most recently, the new program in  Quantum Science and Engineering (QSE) , which lies at the interface of physics, chemistry, and engineering, will admit its first cohort of PhD students in Fall 2022.

We support and encourage interdisciplinary research and simultaneous applications to two departments is permissible. Prospective students may thus wish to apply to the following departments and programs in addition to Physics:

• Department of Astronomy
• Department of Chemistry
• Department of Mathematics
• John A. Paulson School of Engineering and Applied Sciences (SEAS)
• Biophysics Program
• Molecules, Cells and Organisms Program (MCO)

If you are a prospective graduate student and have questions for us, or if you’re interested in visiting our department, please contact  [email protected] .

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Admissions Information for Prospective Graduate Students

Thank you for considering the PhD program in Physics at MIT. Information regarding our graduate program and our application process can be found below and through the following webpages and other links on this page. If your questions are not answered after reviewing this information, please contact us at [email protected] .

Here are some links to pages relevant to prospective students:

• Material Required for a Complete Application , and information about When/How to Apply can be found below on this page.
• We have an FAQ which should help to answer many questions, and we provide Application Assistance from staff and students if you don’t find what you need in the FAQ.
• Additional Guidance about the application itself, along with examples, can be found on a separate page. The graduate application is available at https://apply.mit.edu/apply/ .
• General information about the graduate program and research areas in the physics department may also be of use.
• MSRP (MIT Summer Research Program) is designed to give underrepresented and underserved students access to an MIT research experience, pairing each student with a faculty member who will oversee the student conducting a research project at MIT.

Statement regarding admissions process during COVID Pandemic (Updated Summer 2023)

MIT has adopted the following principle: MIT’s admissions committees and offices for graduate and professional schools will take the significant disruptions of the COVID-19 outbreak in 2020 into account when reviewing students’ transcripts and other admissions materials as part of their regular practice of performing individualized, holistic reviews of each applicant.

In particular, as we review applications now and in the future, we will respect decisions regarding the adoption of Pass/No Record (or Credit/No Credit or Pass/Fail) and other grading options during the unprecedented period of COVID-19 disruptions, whether those decisions were made by institutions or by individual students. We also expect that the individual experiences of applicants will richly inform applications and, as such, they will be considered with the entirety of a student’s record.

Ultimately, even in these challenging times, our goal remains to form graduate student cohorts that are collectively excellent and composed of outstanding individuals who will challenge and support one another.

Questions or concerns about this statement should be directed to the Physics Department ( [email protected] ).

Applying to the MIT Department of Physics

We know that the application process can be time-consuming, stressful, and costly. We are committed to reducing these barriers and to helping all applicants receive a full and fair assessment by our faculty reviewers. Help is available from the Physics Graduate Admissions Office at [email protected] and additional assistance from current students is offered during the admissions season. Further details are described at the end of this page in our Assistance for Prospective Applicants section.

The list below describes the important elements of a complete application. Please reach out to us at [email protected] if you have a concern or logistical difficulty that could prevent you from providing your strongest application.

Required for a Complete Application

1. online application and application fee.

• MIT Graduate Admissions Online Graduate Application
• Application Fee: $90 NOTE: Applicants who feel that this fee may prevent them from applying should send a short email to [email protected] to describe their general reasons for requesting a waiver. We will follow up with information about how to apply for a formal ‘application fee waiver’. Additional documents may be required, so additional time will be necessary to process requests. Either the fee or a formal fee waiver is required with a submitted application.

2. University Transcript(s)

Unofficial transcripts are sufficient for our initial review, with final transcripts required as a condition of matriculation for successful applicants. Applicants should include a scan of their transcript(s) and, if a degree is in progress, should include a list of the class subjects being taken in the current semester. The GradApply portal will allow applicants to log back into the application after the deadline to add their Fall term grades when they are available.

Note: We will respect decisions regarding the adoption of Pass/No Record (or Credit/No Credit or Pass/Fail) and other grading options during the unprecedented period of COVID-19 disruptions, whether those decisions were made by institutions or by individual students.

3. Standardized Test Results

• GRE Tests : The Physics GRE (PGRE) is recommended but not required for graduate applications. All applications will be given full consideration with or without GRE scores.
• TOEFL or IELTS Test or a waiver is required for non-native English speakers. MIT’s TOEFL school code is 3514; the code for the Department of Physics is 76. IELTS does not require a code. Eligibility for TOEFL/IELTS waivers is in our FAQ section .
• Self-reported scores are sufficient for our initial application screening, with official scores required for admitted students as a condition of their offer. Applicants should attach a scanned copy of their test score report.

4. Letters of Recommendation

Letters should include any individual work applicants have done and/or areas where they have special strengths. It is possible to submit up to 6 total letters, but 3 are sufficient for a complete application and committee members may evaluate applications based on the first three letters that they read.

5. Statement of Objectives

Research is central to graduate study in physics. The Statement of Objectives/Purpose should include descriptions of research projects, aptitude and achievements as completely as possible. This important part of the application provides an opportunity to describe any interests, skills, and background relative to the research areas selected on the application form. Applicants should share anything that prepares them for graduate studies and describe their proudest achievements.

Additional Application Materials

• Research, Teaching, and Community Engagement – Any special background or achievement that prepares the applicant for Physics graduate studies at MIT. This may include research at their undergraduate school as part of their Bachelor or Master degree, or summer research at another program or school.  We also value our student’s contributions to their community on a variety of scales (from institutional to societal) and we encourage applicants to tell us about their teaching and community engagement activities.  The “experience” questions are intended to provide a CV-like listing of achievements, some of which may be elaborated on in the “Statement of Objectives” and/or the optional “Personal Statement”.
• Publications, Talks, and Merit Based Recognition – Recognition of success in research, academics, and outreach can take many forms, including publications, talks, honors, prizes, awards, fellowships, etc.  This may include current nominations for scholarships or papers submitted for publication.
• Optional Personal Statement – Members of our community come from a wide variety of backgrounds and experiences. We welcome any personal information that will help us to evaluate applications holistically and will provide context for the applicant’s academic achievements. This statement may include extenuating circumstances, significant challenges that were overcome, a non-traditional educational background, description of any advocacy or values work, or other information that may be relevant.
• Detailed instructions for each application section, and many examples , can be found on the “ Additional Guidance ” page.  The detailed instructions are lengthy, and are intended to be read only “as needed” while you work on your application (i.e., you don’t need to go read the whole thing before you start).

When/How to Apply

When : Applications can be submitted between September 15 and December 15 by 11:59pm EST for the following year.

How : The application is online at https://apply.mit.edu/apply/

Application Assistance

Faculty, students, and staff have collaborated to provide extensive guidance to prospective applicants to our graduate degree program. Resources include several department webpages to inform prospective applicants about our PhD degree requirements and to help applicants as they assemble and submit their materials. In addition to staff responses to emails, current graduate students will answer specific individual questions, give one admissions-related webinar, and provide a mentorship program for selected prospective applicants.

During the application season, prospective students may request additional information from current students about the admissions process, graduate student life, or department culture, either as a response to a specific individual email question or for more in-depth assistance. Applicants will benefit most from contacting us early in the process, when current students and staff will be available to respond to questions and mentor selected applicants. After mid-November, department staff will continue to field questions through the admission process.

Here are some resources for prospective applicants:

• Our website provides answers to many frequently-asked admissions questions .
• Admissions staff are available for questions at [email protected] .
• Current students collaborate with staff to answer specific questions emailed to [email protected] .
• PhysGAAP Webinars are designed to provide student perspectives on the application and admissions processes in an interactive format. This year’s webinar will take place on Wednesday, Nov 1st, 2023 from 10am to 12pm EDT. Sign up here: https://mit.co1.qualtrics.com/jfe/form/SV_ah13eCcEh0cKW7I
• PhysGAAP Mentoring provides in-depth guidance through the application process.

Student-led Q&A Service

A team of our current graduate students is available to share their experience and perspectives in response to individual questions which may fall under any of the following categories:

• Coursework/research (e.g., How do I choose between two research areas and how do I find a potential research advisor?)
• Culture (e.g., What is it like to be a student of a particular identity at MIT?)
• Student life (e.g., What clubs or extracurriculars do graduate students at MIT take part in?)

To request a response from the current students, please send an email to [email protected] and indicate clearly in the subject line or first sentence that you would like your email forwarded to the PhysGAAP student team. Depending on the scope of your question, department staff will send your email to current students.

We encourage you to reach out as early as you can to maximize the benefit that this help can provide to you. While the admissions office staff will continue to field your questions throughout the admissions season, current students may not be available to respond to questions sent after November 15.

This student email resource is designed for individual basic questions. More in-depth guidance, especially about the application itself, will be available through the PhysGAAP Webinars and/or PhysGAAP Mentorship Program described below.

Student-led Webinar

A panel of our graduate students hosted a 2-hour long Zoom webinar in late October of 2022 to present information about the application and admissions processes, and to respond to questions on these topics. The webinar addressed general questions about preparing, completing, and submitting the application; what the Admissions Committee is looking for; and the general timeline for the admissions process.

Below is video from our latest webinar that took place on Wednesday, Nov 1st, 2023. Check back here in Fall 2024 for information on our next webinar.

Note: We have  compiled a document  containing supplementary material for previous PhysGAAP webinars.

Webinar Recordings

Past PhysGAAP Webinars

Please note that the two webinars below are from prior years and may contain outdated information about some topics, such as GRE requirements.

• October 2022
• December 2021
• September 2021

Mentorship for Prospective Applicants

In addition to the materials available through this website, answers to emails sent to the department, or from our graduate student webinars, we also offer one-on-one mentoring for students who desire more in-depth individual assistance. Prospective applicants may apply to the PhysGAAP Mentoring program,, which pairs prospective graduate school applicants with current graduate students who can assist them through the application process, provide feedback on their application materials and insight into graduate school and the MIT Physics Department.

We welcome interest in the PhysGAAP Mentorship program and mentorship applications are open to any prospective applicant. However, our capacity is limited, so we will give preferential consideration to PhysGAAP Mentorship applicants who would most benefit from the program and can demonstrate that they are a good fit.

PhysGAAP Mentoring may a good fit for you if you

• feel like you lack other resources to help you navigate the graduate school application process,
• find the other forms of assistance (online webinars, email at [email protected] ) insufficient to address your needs, and
• think you could benefit from one-on-one application mentorship.

PhysGAAP Mentoring may not be a good fit for you if you

• only have one or two questions that could be answered elsewhere (online webinars, email at [email protected] , or online FAQs), or
• feel like you already have sufficient resources to complete your application (e.g., the PhysGAAP webinars, access to other mentoring services or workshops)

Please note that:

• PhysGAAP Mentoring is only open to students who are planning to apply to graduate schools in Fall 2024 .
• Participation in PhysGAAP is not considered during admissions review. It helps applicants put forward their strongest materials, but does not guarantee admission into our graduate program.
• Any information you submit in the PhysGAAP Mentoring application will only be seen by the PhysGAAP team and your matched mentor.

Admissions/Application FAQs

Our Frequently Asked Questions provide further information about degree requirements, funding, educational background, application deadlines, English language proficiency, program duration, start dates and deferrals, and fee waiver requests.

The MOST Frequently Asked Question…

What is included in a strong graduate application for physics at mit.

Applications are assessed holistically and many variables are considered in the application review process. The following four main factors are required for a complete application.

• the applicant’s statement of objectives or purpose,
• transcripts of past grades,
• score reports of any required standardized tests,
• three letters of reference.

In addition, any past research experience, publications, awards, and honors are extremely helpful, particularly if they are in the area(s) of the applicant’s interest(s). Applicants may also include a personal statement in their application to provide context as the materials are assessed.

Applications are routed to admission committee members and other faculty readers using the “areas of interest” and any faculty names selected from the menu as well as based on the research interests included in the statement of objectives. Please select the areas of interest that best reflect your goals.

Instructions are available in the application itself , with further guidance on our Additional Guidance page. The Physics Admissions Office will respond to questions sent to [email protected] .

General Questions Regarding the PhD Program in Physics

Must i have a degree in physics in order to apply to this graduate program.

Our successful applicants generally hold a Bachelor of Science degree in Physics, or have taken many Physics classes if they have majored in another discipline. The most common other majors are astronomy, engineering, mathematics, and chemistry. Bachelor of Science degrees may be 3-year or 4-year degrees, depending on the education structure of the country in which they are earned.

What are the requirements to complete a PhD?

The requirements for a PhD in Physics at MIT are the doctoral examination, a few required subject classes, and a research-based thesis. The doctoral examination consists of a written and an oral examination. The written component may be satisfied either by passing the 4 subject exams or by passing designated classes related to each topic with a qualifying grade; the oral exam will be given in a student’s chosen research area. The Physics Department also requires that each student take two classes in the field of specialization and two physics-related courses in fields outside the specialty. Research for the thesis is conducted throughout the student’s time in the program, culminating in a thesis defense and submission of the final thesis.

Can I take courses at other schools nearby?

Yes. Cross-registration is available at Harvard University and Wellesley College.

How many years does it take to complete the PhD requirements?

From 3 to 7 years, averaging 5.6 years.

How will I pay for my studies?

Our students are fully supported financially throughout the duration of their program, provided that they make satisfactory progress. Funding is provided from Fellowships (internal and external) and/or Assistantships (research and teaching) and covers tuition, health insurance, and a living stipend. Read more about funding .

Note: For more detailed information regarding the cost of attendance, including specific costs for tuition and fees, books and supplies, housing and food as well as transportation, please visit the Student Financial Services (SFS) website .

How many applications are submitted each year? How many students are accepted?

Although the number varies each year, the Department of Physics usually welcomes approximately 45 incoming graduate students each year. Last year we received more than 1,700 applications and extended fewer than 90 offers of admission.

What are the minimum grades and exam scores for admitted applicants?

There are no minimum standards for overall grade point averages/GPAs. Grades from physics and other related classes will be carefully assessed. Under a special COVID-19 policy, MIT will accept transcripts with a variety of grading conventions, including any special grading given during the COVID-19 pandemic. PGREs (Physics subject GRE) is not required for graduate applications but is recommended.

Our program is conducted in English and all applicants must demonstrate their English language proficiency. Non-native English speakers should review our policy carefully before waiving the TOEFL/IELTS requirements. We do not set a minimum requirement on TOEFL/IELTS scores; however, students who are admitted to our program typically score above the following values:

• IELTS – 7
• TOEFL (computer based) – 200
• TOEFL (iBT) – 100
• TOEFL (standard) – 600

The Application Process

When is the deadline for applying to the phd program in physics.

Applications for enrollment in the fall are due each year by 11:59pm EST on December 15 of the preceding year. There is no admission cycle for spring-term enrollment.

The COVID-19 pandemic has made it difficult for me to take tests in person. Can I still apply?

PGRE (Physics subject GRE) is not required for graduate applications but is recommended. Non-native English speakers who are not eligible for a test waiver should include their results from either an in-person or online version of the TOEFL or IELTS test.

Does the Department of Physics provide waivers for the English language exam (TOEFL/IELTS)?

An English language exam (IELTS, TOEFL, TOEFL iBT, or the C2 Cambridge English Proficiency exam) is required of all applicants who are from a country in which English is not the primary language. Exceptions to this policy will be considered for candidates who, at the start of their graduate studies in 2025, will have been in the US or in a country whose official language is English for three years or longer and who will have received a degree from a college or university in a country where the language of education instruction is English. An interview via telephone, Zoom, or Skype may be arranged at the discretion of the Admissions Committee. More information on a possible English Language Waiver Decision (PDF).

Does the Department of Physics provide application fee waivers?

Although we do not want the MIT application fee to be a barrier to admission, we cannot provide application fee waivers to all who request one.  Under-resourced applicants, and applicants who have participated in the MIT Summer Research Program (MSRP), Converge, or another MIT program or an official MIT recruiting visit are eligible for a fee waiver from the MIT Office of Graduate Education (OGE). Please check MIT Graduate Diversity Programs for further details.  Departmentally, we have allotted a small number of waivers for applicants who have completed an application (including transcript uploads, and requests for letters of recommendation), but do not qualify for a waiver from the OGE. Fee waiver requests will be considered on a first-come-first-served basis, and not after December 1. Furthermore, applications lacking the paid fee or a fee waiver by 11:59pm EST on December 15 will not be reviewed or considered for admission. Please complete the  MIT Physics Departmental Fee Waiver Application Form  when you are ready to apply for a departmental waiver. Waivers are not awarded until the application is complete.

Can I arrange a visit to the Physics Department or a specific research area?

We are not currently hosting or meeting with outside visitors in person, nor are we facilitating visits to our classrooms. Current graduate students and prospective applicants should direct any questions by email to [email protected] .

Applicants are invited to send specific questions to the Physics Admissions Office and some questions may be forwarded to current students for further information. Admitted students will be invited to attend an in-person open house.

Can I receive an update on the status of my application?

Candidates can check on the status of their application at apply.mit.edu/apply at any time. It is the applicant’s responsibility to ensure that all items are sent.

When will I be notified of a final decision?

Applicants will be notified via email of decisions by the end of February. If you have not heard from us by March 1, please send email to [email protected] .

We do not provide results by phone.

Can admitted students start in a term other than the next Fall semester?

Applications submitted between September 15 and December 15 by 11:59pm EST are assessed for the following Fall semester. We do not provide a separate admission review cycle for the Spring semester. Individual research supervisors may invite incoming students to start their research during the summer term a few months earlier than their studies would normally begin. All other incoming students start their studies in late August for the Fall term.

Once admitted, applicants may request a one-year deferral to attend a specific academic program or for another approved reason, with single semester deferrals for the following Spring term granted only rarely.

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.

Physics, PHD

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

• Location: Tempe campus
• Second Language Requirement: No

Program Description

Degree Awarded: PHD Physics

The PhD program in physics is intended for highly capable students who have the interest and ability to follow a career in independent research.

The recent advent of the graduate faculty initiative at ASU extends the spectrum of potential physics doctoral topics and advisors to include highly transdisciplinary projects that draw upon:

• biochemistry
• electrical engineering
• materials science
• other related fields

Consequently, students and doctoral advisors can craft novel doctoral projects that transcend the classical palette of physics subjects. Transdisciplinary expertise of this nature is increasingly vital to modern science and technology.

Current areas of particular emphasis within the department include:

• biological physics
• electron diffraction and imaging
• nanoscale and materials physics
• particle physics and astrophysics

The department has more than 90 doctoral students and more than 40 faculty members.

Degree Requirements

Curriculum plan options.

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

Required Core (18 credit hours) PHY 500 Research Methods (6) PHY 521 Classical and Continuum Mechanics (3) PHY 531 Electrodynamics (3) PHY 541 Statistical Physics (3) PHY 576 Quantum Theory (3)

Electives or Research (54 credit hours)

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

Additional Curriculum Information Of particular note within the core courses are the PHY 500 Research Methods rotations, which are specifically designed to engage doctoral students in genuine, faculty-guided research starting in their first semester. Students complete three credit hours of PHY 500 in both their fall and spring semesters of their first year, for a total of six credit hours.

Coursework beyond the core courses is established by the student's doctoral advisor and supervisory committee, working in partnership with the student. The intent is to tailor the doctoral training to the specific research interests and aptitudes of the student while ensuring that each graduating student emerges with the expertise, core knowledge and problem-solving skills that define having a successful doctoral degree in physics.

When approved by the student's supervisory committee and the Graduate College, this program allows 30 credit hours from a previously awarded master's degree to be used for this degree. If students do not have a previously awarded master's degree, the 30 credit hours of coursework are made up of electives to reach the required 84 credit hours.

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 physics or a closely related area from a regionally accredited institution. Applicants must have had adequate undergraduate preparation equivalent to an undergraduate major of 30 credit hours in physics and 20 credit hours in mathematics. Courses in analytic mechanics, electromagnetism and modern physics, including quantum mechanics, are particularly important.

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 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
• personal statement
• 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.

Applicants requesting credit for prior graduate courses, taken either at ASU or elsewhere, must demonstrate mastery of the relevant course material to the graduate-level standards of the Department of Physics.

Next Steps to attend ASU

Learn about our programs, apply to a program, visit our campus, career opportunities.

As professional physicists, graduates can advance the frontiers of physics by generating new knowledge in their subfields while working on the most challenging scientific problems at the forefront of human understanding. Graduates find positions in a variety of settings, such as administration, government labs, industrial labs and management, and as academic faculty.

Physicists are valued for their analytical, technical and mathematical skills and find employment in a vast array of employment sectors, including:

• engineering

Program Contact Information

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

• [email protected]
• 480/965-3561

Mathematical Physics (Physics)

Doctor of Philosophy

Offered at IU Bloomington by College of Arts and Sciences .

Students pursuing a Ph.D. in Mathematical Physics can be in residence in either the Department of Physics or the Department of Mathematics.

The Mathematical Physics Ph.D. degree curriculum focuses on using techniques from mathematics to formulate and solve problems in physics as well as applying insights from physics to the solution of problems in mathematics. The program offers advanced training for students in the overlapping areas of mathematics, theoretical physics, and their applications from a unified point of view and promotes research in the field.

Indiana University's Department of Physics is known for conducting world-leading research across a wide portfolio of subdisciplines in physics while also cultivating knowledge in both graduate and undergraduate students. The department pays close attention to mentoring, advising, and professional development. And while research involves inquiry into vast and intractable problems, the faculty are interactive, friendly, and personable.

IU's Department of Mathematics has been expanding the frontiers of mathematical understanding on a wide range of topics for over 100 years. It is a nationally recognized and vibrant center for high-quality research and training with faculty who conduct world-class research.

The department enjoys the vast resources and opportunities for interdepartmental collaboration offered by Indiana University, a Research 1 institution, striving to maintain representation in most major areas of mathematics research. Within the department, an atmosphere of inquiry and dedication to teaching make for a collegial atmosphere where abundant seminars offer the opportunity to engage with members of the department and their work.

• Department of Physics website Visit the Physics website for more information.
• Department of Mathematics website Visit the Mathematics website for more information.
• Requirements Read the requirements in the Academic Bulletin.

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» Doctor of Science in Mathematics, Philosophy and Physics

The MPP program encourages strong and authentic interdisciplinary collaboration with a vibrant intellectual culture. The successful student will be awarded a D.Sc. degree with an emphasis in one of the primary foundational disciplines and will also develop a deeper understanding of how their primary discipline interacts with and is informed by cross-disciplinary connections to the other disciplines. As a post-master's-level doctoral program, the program consists of 54 credits completed over a three-year research-focused curriculum leading to a D.Sc. degree. The curriculum contains few didactic courses, which serve to train students in research and communication skills common to all three disciplines. The remaining research credits are personalized to each student’s background in close collaboration with their primary adviser and interdisciplinary thesis committee, with the goal of enabling the student to produce high-quality and competitive doctoral research in their primary discipline. 

Students will graduate well-prepared for their future career goals, with a D.Sc. degree that is recognized as fully equivalent to a Ph.D. in both the academic and industrial job sectors.

The Doctor of Science MPP program offers up to three funded fellowship positions per academic year in addition to grant-funded positions that may be arranged in consultation with specific advisers. 

Our Faculty

• Interdisciplinary Fellows
• Daniel Alpay
• Polona Durcik
• Jose Gil-Ferez
• Oghenetega Ighedo
• Peter Jipsen
• Alexander Kurz
• Andrew Moshier
• Cyril Rakovski
• Ahmed Sebbar
• Daniele Struppa
• Mihaela Vajiac
• Adrian Vajiac
• Yakir Aharonov
• Roman Buniy
• Justin Dressel
• Nooshin M. Estakhri
• Armen Gulian
• John Howell
• Andrew Jordan
• Jerry LaRue
• Matthew Leifer
• Jeff Tollaksen
• Emily Adlam
• Keith Hankins
• Brennan McDavid
• Kelvin McQueen
• Michael Valdez Moses
• Michael Pace
• Marco Panza
• Carmichael Peters
• Michael Robinson
• John Thrasher
• Bas Van der Vossen
• Virginia Warren
• Menas Kafatos
• Aaron Schurger
• Hillard Kaplan

Prerequisites

A master's degree in math, philosophy, physics or related discipline is required prior to the start of the program.

Course Curriculum

The 54-credit curriculum consists of

• 12 credits of didactic interdisciplinary coursework
• 15 credits of colloquia
• 24 credits of research
• 3 credits for viva (dissertation defense)
• Students should maintain a full-time load of 9 credits per semester to complete their dissertation and graduate in 3 years
• M.S. Food Science
• MS Computational and Data Sciences (CADS)
• Ph.D. Computational and Data Sciences
• Doctor of Science in Mathematics, Philosophy and Physics
• Luigi Maierù’s International School in the History of Mathematics
• MPP Seminar Calendar

MPP Activities and Events

• The MPP Seminar (Graduate Colloquium) consists of the sessions on the MPP Seminar Calendar here .
• Chapman University and the Topos Institute have formed a partnership that will include joint initiatives with the MPP program, including organization of MPP Seminar events, collaborative research projects, and the opportunity for MPP graduate students to engage with Topos representatives. See the announcements of the partnership on the Schmid College Blog  and the Topos website for more information.
• Luigi Maierù’s International School in the History of Mathematics will take place on May 24-26, 2024. Please see more information about the School and the Call for Applications here (deadline: March 31, 2024).
• In celebration of the first year of the MPP program , a conference on the utility of philosophy for the sciences took place on January 30 - February 2, 2024. For information on the conference and to watch video recordings of the presentations, please see the conference webpage:  "Is Philosophy Useful for Science, and/or Vice Versa?"

For program-specific details or questions, please contact:

Lisa Beesley Graduate Program Coordinator – Math, Philosophy, and Physics [email protected] Marco Panza  Provisional Program Director [email protected] (714) 997-5021

For questions on application process or requirements, please contact: Sharnique Dow Graduate Admissions Counselor [email protected]   (714) 997-6770

Graduate Financial Aid [email protected] (714) 628-2730

• Graduate Application
• Fellowship Opportunities
• Off-Campus Housing

Application Deadlines

• Priority submission deadline: January 15
• Regular submission deadline: April 15

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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.

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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Graduate School

Mathematics

General information, program offerings:, director of graduate studies:, graduate program administrator:.

The Department of Mathematics graduate program has minimal requirements and maximal research and educational opportunities. It differentiates itself from other top mathematics institutions in the U.S. in that the curriculum emphasizes, from the start, independent research. Our students are extremely motivated and come from a wide variety of backgrounds. While we urge independent work and research, a real sense of camaraderie exists among our graduate students. As a result, the atmosphere created is one of excitement and stimulation and mentoring and support. There also exists a strong scholarly relationship between the department and the Institute for Advanced Study (IAS), located a short distance from campus. Students can contact IAS members as well as attend the IAS seminar series.

Students are expected to write a dissertation in four years but may be provided an additional year to complete their work if deemed necessary. Each year, our graduates are successfully launched into academic positions at premier mathematical institutions and industry.

Program Offerings

Program offering: ph.d..

The department offers a broad variety of research-related courses as well as introductory (or “bridge”) courses in several areas, which help first-year students strengthen their mathematical background. Students also acquire standard beginning graduate material primarily through independent study and consultations with the faculty and fellow students.

Language(s)

Students must satisfy the language requirement by demonstrating to a member of the mathematics faculty a reasonable ability to read ordinary mathematical texts in one of the following three languages: French, German, or Russian. Students must pass the language test by the end of the first year and before standing for the general exam.

Additional pre-generals requirements

Seminars The department offers numerous seminars on diverse topics in mathematics. Some seminars consist of systematic lectures in a specialized topic; others present reports by students or faculty on recent developments within broader areas. There are regular seminars on topics in algebra, algebraic geometry, analysis, combinatorial group theory, dynamical systems, fluid mechanics, logic, mathematical physics, number theory, topology, and other applied and computational mathematics. Without fees or formalities, students may also attend seminars in the School of Mathematics at the IAS.

The department also facilitates several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the department colloquium will give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students and helps in creating a vibrant mathematical interaction among the graduate students; and, (3) What’s Happening in Fine Hall (WHIFH) seminar, where faculty members present talks in their own research areas specifically geared towards graduate students. Reading seminars are also organized and run by graduate students.

General exam

Beyond needing a strong knowledge of three more general subjects (algebra, and real and complex analysis), first-year students are set on the fast track of research by choosing two advanced research topics as part of their general exam. The two advanced topics are expected to come from distinct major areas of mathematics, and the student’s choice is subject to the approval of the department. Usually, by the second year, students will begin investigations of their own that lead to the doctoral dissertation.

General Exam in Mathematical Physics For a mathematics student interested in mathematical physics, the general exam is adjusted to include mathematical physics as one of the two special topics.

Qualifying for the M.A.

The Master of Arts (M.A.) degree is considered an incidental degree on the way to full Ph.D. candidacy. It is earned once a student successfully passes the language requirement and the general exam, and the faculty recommends it. It may also be awarded to students who, for various reasons, may leave the Ph.D. program, provided that the following requirements are met: passing the language requirement as well as the three general subjects (algebra, and real and complex analysis) of the general exam, and receiving department approval.

During the second, third, and fourth years, graduate students are expected to either grade or teach two sections of an undergraduate course, or the equivalent, each semester. Although students are not required to teach to fulfill department Ph.D. requirements, they are strongly encouraged to do so at least once before graduating. Teaching letters of recommendation are necessary for most postdoctoral applications.

Post-Generals requirements

Selection of a Research Adviser Upon completion of the general exam, the student is expected to choose a thesis adviser.

Dissertation and FPO

Two to three years is usually necessary for the completion of a suitable dissertation. Upon completion and acceptance of the dissertation by the department and Graduate School, the candidate is admitted to the final public oral examination. The dissertation is presented and defended by the candidate.

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.

• Igor Rodnianski

Associate Chair

• János Kollár

Director of Graduate Studies

• Lue Pan (associate)
• Chenyang Xu

Director of Undergraduate Studies

• Jennifer M. Johnson (associate)
• Michael Aizenman
• Noga M. Alon
• Manjul Bhargava
• Sun-Yung A. Chang
• Maria Chudnovsky
• Fernando Codá Marques
• Peter Constantin
• Mihalis Dafermos
• Charles L. Fefferman
• David Gabai
• June E. Huh
• Alexandru D. Ionescu
• Nicholas M. Katz
• Sergiu Klainerman
• Peter Steven Ozsváth
• Peter C. Sarnak
• Paul Seymour
• Amit Singer
• Christopher M. Skinner
• Allan M. Sly
• Zoltán Szabó
• Paul C. Yang
• Shou-Wu Zhang

Assistant Professor

• Bjoern Bringmann
• Matija Bucic
• Marc Aurèle Tiberius Gilles
• Jonathan Hanselman
• Susanna Haziot
• Ana Menezes
• Ravi Shankar
• Jacob Shapiro
• Jakub Witaszek
• Ruobing Zhang

Associated Faculty

• John P. Burgess, Philosophy
• René A. Carmona, Oper Res and Financial Eng
• Bernard Chazelle, Computer Science
• Hans P. Halvorson, Philosophy
• William A. Massey, Oper Res and Financial Eng
• Frans Pretorius, Physics
• Robert E. Tarjan, Computer Science
• Ramon van Handel, Oper Res and Financial Eng
• Louis Esser
• Sepehr Hajebi
• Kimoi Kemboi
• Dmitry Krachun
• Anubhav Mukherjee
• Sung Gi Park
• Semon Rezchikov
• Joshua X. Wang
• Mingjia Zhang

University Lecturer

• Jennifer M. Johnson

Senior Lecturer

• Jonathan M. Fickenscher
• Mark W. McConnell
• Tatyana Chmutova
• Tatiana K. Howard
• John T. Sheridan
• David Villalobos

Visiting Professor

• Bhargav B. Bhatt

Visiting Lecturer with Rank of Professor

• Camillo De Lellis
• Helmut H. Hofer
• Akshay Venkatesh

For a full list of faculty members and fellows please visit the department or program website.

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

COS 522 - Computational Complexity (also MAT 578)

Mat 500 - effective mathematical communication, mat 515 - topics in number theory and related analysis, mat 516 - topics in algebraic number theory, mat 517 - topics in arithmetic geometry, mat 518 - topics in automorphic forms, mat 519 - topics in number theory, mat 520 - functional analysis, mat 522 - introduction to pde (also apc 522), mat 525 - topics in harmonic analysis, mat 526 - topics in geometric analysis, mat 527 - topics in differential equations, mat 528 - topics in nonlinear analysis, mat 529 - topics in analysis, mat 531 - introduction to riemann surfaces, mat 547 - topics in algebraic geometry, mat 549 - topics in algebra, mat 550 - differential geometry, mat 555 - topics in differential geometry, mat 558 - topics in conformal and cauchy-rieman (cr) geometry, mat 559 - topics in geometry, mat 560 - algebraic topology, mat 566 - topics in differential topology, mat 567 - topics in low dimensional topology, mat 568 - topics in knot theory, mat 569 - topics in topology, mat 572 - topics in combinatorial optimization (also apc 572), mat 577 - topics in combinatorics, mat 579 - topics in discrete mathematics, mat 585 - mathematical analysis of massive data sets (also apc 520), mat 586 - computational methods in cryo-electron microscopy (also apc 511/mol 511/qcb 513), mat 587 - topics in ergodic theory, mat 589 - topics in probability, statistics and dynamics, mat 595 - topics in mathematical physics (also phy 508), mat 599 - extramural summer research project, phy 521 - introduction to mathematical physics (also mat 597).

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Department of Applied Mathematics and Theoretical Physics

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About the Department of Applied Mathematics and Theoretical Physics

The Department of Applied Mathematics and Theoretical Physics (DAMTP) is one of two Mathematics Departments at the University of Cambridge, the other being the Department of Pure Mathematics and Mathematical Statistics (DPMMS). The two Departments together constitute the Faculty of Mathematics , and are responsible for the teaching of Mathematics and its applications within the Mathematical Tripos.

5 courses offered in the Department of Applied Mathematics and Theoretical Physics

Applied mathematics and theoretical physics - phd.

This is a three to four-year research programme culminating in submission and examination of a thesis containing substantial original work. PhD students carry out their research under the guidance of a supervisor, and research projects are available from a wide range of subjects studied within the Department. Students admitted for a PhD will normally have completed preparatory study at a level comparable to the Cambridge Part III (MMath/MASt) course. A significant number of our PhD students secure post-doctoral positions at institutions around the world and become leading researchers in their fields.

More Information

Mathematics - MPhil - Closed

The MPhil is offered by the Faculty of Mathematics as a full-time period of research and introduces students to research skills and specialist knowledge. Its main aims are:

• to give students with relevant experience at first-degree level the opportunity to carry out focused research in the discipline under supervision; and
• to give students the opportunity to acquire or develop skills and expertise relevant to their research interests. 

Mathematics (Applied Mathematics) - MASt - Closed

This course is an application stream for the Master of Advanced Study (MASt) in Mathematics; students should apply to only one of the application streams for this course.

This course, commonly referred to as Part III, is a nine-month taught masters course in mathematics. It is excellent preparation for mathematical research and it is also a valuable course in mathematics and its applications for those who want further training before taking posts in industry, teaching, or research establishments.

Students admitted from outside Cambridge to Part III study towards the Master of Advanced Study (MASt). Students continuing from the Cambridge Mathematical Tripos for a fourth-year study towards the Master of Mathematics (MMath). The requirements and course structure for Part III are the same for all students irrespective of whether they are studying for the MASt or MMath degree, or whether they applied through the Applied Mathematics (MASA), Pure Mathematics (MASP), Mathematical Statistics (MASS), or Theoretical Physics (MASTH) application stream.

Mathematics (Theoretical Physics) - MASt - Closed

Quantitative climate and environmental science - mphil - closed.

The MPhil in Quantitative Climate and Environmental Sciences is a 10-month cross-departmental programme in the School of the Physical Sciences which aims to provide education of the highest quality in the analysis and modelling of Earth's climate and environment at a master’s level. The programme covers a range of skills required for the acquisition and assessment of laboratory and field data, and for the understanding through quantitative modelling of climate and environmental processes. 

6 courses also advertised in the Department of Applied Mathematics and Theoretical Physics

Antarctic studies - phd.

From the British Antarctic Survey

This PhD course takes place under the joint supervision of a research scientist at the British Antarctic Survey (BAS) and a University supervisor. Students may be based at BAS but will be registered for their degree with one of the partnering departments: Archaeology & Anthropology, Land Economy, Plant Sciences, Zoology, Earth Sciences, Geography and Scott Polar Research Institute, Applied Mathematics & Theoretical Physics, Chemistry, Engineering, Computer Science and Technology.

Biological Sciences BBSRC DTP - PhD - Closed

From the School of the Biological Sciences

The Cambridge Biosciences DTP is a four year fully-funded PhD programme that aims to create highly skilled and employable people. The programme offers training across 23 University Departments/Institutes and 3 Partner Institutes providing access to a wide range of research areas related to the strategic themes of the BBSRC. We offer three types of DTP studentships:

• DTP Standard

During the programme, DTP Standard and Targeted students will undertake two ten-week rotations in different labs before commencing their PhD. They will receive training in a variety of areas including but not limited to statistics, programming, ethics, data analysis, scientific writing and public engagement. Students will also undertake a 12-week internship (PIPS).

iCase students are not required to undertake rotations but may do so if they feel that this training would be useful. They must undertake a placement with their Industrial Partner for a minimum of three months and a maximum of 18 months.

Students will be expected to submit their thesis at the end of the fourth year.

Part-time study, whilst not the norm, may be viable, depending on the project, and will be considered on a case by case basis so please discuss this option with your proposed supervisor before making an application for this mode of study.

Computational Methods for Materials Science CDT - MPhil + PhD - Closed

From the Department of Physics

The development of new materials lies at the heart of many of the technological challenges we currently face, for example creating advanced materials for energy generation. Computational modelling plays an increasingly important role in the understanding, development and optimisation of new materials.

This four-year doctoral training programme on computational methods for material modelling aims to train scientists not only in the use of existing modelling methods but also in the underlying computational and mathematical techniques. This will allow students to develop and enhance existing methods, for instance by introducing new capabilities and functionalities, and also to create innovative new software tools for materials modelling in industrial and academic research.

The first year of the doctoral training programme is provided by the existing MPhil course in Scientific Computing, which has research and taught elements, as well as additional training elements. The final three years consist of a PhD research project, with a student-led choice of projects offered by researchers closely associated with the CDT. ( https://ljc.group.cam.ac.uk ) 

Data Intensive Science - MPhil - Closed

The MPhil in Data Intensive Science is a 10-month cross-departmental programme in the School of the Physical Sciences which aims to provide education of the highest quality at the master’s level. The programme covers the full range of skills required for modern data-driven science. The course covers material from the fields of machine learning and AI, statistical data analysis, research and high performance computing, and the application of these topics to scientific research frontiers.  

The course structure has been designed in collaboration with our leading researchers and industrial partners to provide students with the theoretical knowledge, practical experience, and transferable skills required to undertake world-leading data-intensive scientific research. Students will gain the broad set of skills required for scientific data analysis, covering traditional statistical techniques as well as modern machine learning approaches.  Both the theoretical underpinnings and practical implementation of these techniques will be taught, with the later aspect including training on software development best practice and the principles of Open Science. The course also aims to provide students with direct experience applying these methods to current research problems in specific scientific fields. Students who have completed the course will be equipped to undertake research on data-intensive scientific projects. Beyond academic disciplines, students will be well prepared for a career as a data science professional in a broad range of commercial sectors.

This course will equip students with all the skills required for modern scientific data analysis, enabling them to participate in large experimental or observational programmes using the latest statistical and machine learning tools deployed on leading-edge computer architectures. These computational and statistical skills will also be directly applicable to data-driven problem-solving in industry.

Planetary Science and Life in the Universe - MPhil - Closed

From the Institute of Astronomy

The MPhil in Planetary Sciences and Life in the Universe is a 10-month cross-departmental programme designed to deliver outstanding postgraduate level training in the search for life’s origins on Earth and its discovery on planets beyond Earth.

The course structure has been designed by leading scientists to provide students with the theoretical knowledge, practical experience, and transferable skills required to undertake world-leading research in Planetary Sciences and Life in the Universe. Graduating students will be equipped with the discipline specific-specialisations and skills of a masters course, whilst gaining understanding in how the core areas that bridge PSLU fields form the cross-disciplinary foundation of this exciting new frontier.

Graduates of the course will gain valuable skills rooted in the study of the physics, chemistry, mathematics, and biology of planetary science and life in the universe. Transferrable skills training is delivered through the three group-based projects running over the year: these provide a unique opportunity for students to gain experience of leadership, collaboration, and written and oral communication.  The training provided will be an outstanding foundation for PhD research in planetary science, exoplanetary science, Earth system science, planetary astrophysics, astrobiology and allied disciplines, or for the wide range of careers where analytical skills, excellent communication, and experience of leading collaborations are key.

Scientific Computing - MPhil - Closed

The MPhil programme in Scientific Computing provides world-class education on high performance computing and advanced algorithms for numerical simulation at continuum and atomic-scale levels. The course trains early-career scientists in the use of existing computational software and in the underlying components of the simulation pipeline, from mathematical models of physical systems and advanced numerical algorithms for their discretisation, to object-oriented programming and methods for high-performance computing for deployment in contemporary massively parallel computers.  As a result, course graduates have rigorous research skills and are formidably well-equipped to proceed to doctoral research or directly into employment. The highly transferable skills in algorithm development and high-performance computing make our graduates extremely employable in all sectors of industry, commerce and finance.

The MPhil in Scientific Computing is suitable for graduates from any discipline of natural sciences, technology or engineering, who have good mathematical and computational skills.  

Department Members

Professor colm-cille caulfield head of department.

• 55 Academic Staff
• 90 Postdoctoral Researchers
• 315 Graduate Students

http://www.damtp.cam.ac.uk/

Research areas.

• General Relativity and Cosmology
• High Energy Physics
• Quantum Information
• Mathematical Biology
• Fluid and Solid Mechanics
• Astrophysics
• Applied and Computational Analysis

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Requirements for a Doctorate in Physics

An advanced degree in physics at Caltech is contingent upon an extensive research achievement. Students in the program are expected to join a research group, carry out independent research, and write publications for peer-reviewed journals as well as a thesis. The thesis work proposed to a Caltech candidacy committee then presented and evaluated by a Caltech thesis committee in a public defense. Initially, students are required to consolidate their knowledge by taking advanced courses in at least three subfields of physics. Students must also pass a written candidacy exam in both classical physics and quantum mechanics in order to progress into the research phase of the degree.

Graduates of our program are expected to have extensive experience with modern research methods, a broad knowledge of contemporary physics, and the ability to perform as independent researchers at the highest intellectual and technical levels.

The PhD requirements are below and are also available in the Caltech Catalog, Section 4: Information for Graduate Students .

Plan of Study

The plan of study is the set of courses that a student will take to complete the Advance Physics Requirement and any courses needed as preparation to pass the Written Candidacy Exams (see below). Any additional courses the student plans to take as part of their graduate curriculum may be included in the plan of study but are not required. Students should consult with their Academic Advisor on their Plan of Study and discuss any exception or special considerations with the Option Representative. 

Log in to REGIS and navigate to the Ph. D. Candidacy Tab of your Graduate Degree Progress page. Add you courses into the Plan of Study section. When complete, click the "Submit Plan of Study to Option Rep" button. This will generate a notice to the Option Rep to approve your plan of study. Once you complete the courses in the Plan of Study, the Advanced Physics Requirement is completed.

Written Candidacy Exams

Physics students must demonstrate proficiency in all areas of basic physics, including classical mechanics (including continuum mechanics), electricity and magnetism, quantum mechanics, statistical physics, optics, basic mathematical methods of physics, and the physical origin of everyday phenomena. A solid understanding of these fundamental areas of physics is considered essential, so proficiency will be tested by written candidacy examinations.

No specific course work is required for the basic physics requirement, but some students may benefit from taking several of the basic graduate courses, such as Ph 106 and Ph 125. In addition, the class Ph 201 will provide additional problem solving training that matches the basic physics requirement.

Exam I: Classical Mechanics and Electromagnetism       Topics include: TBA

Exam 2: Quantum Mechanics, Statistical Mechanics and Thermodynamics      Topics include: TBA

Both exams are offered twice each year (July and October) Email  [email protected]  to sign up

Nothing additional. Sign up for the exam by emailing Mika Walton. The Student Programs Office will update your REGIS record once you pass the exams.

Advanced Physics Requirement

Students must establish a broad understanding of modern physics through study in six graduate courses. The courses must be spread over at least three of the following four areas of advanced physics. Many courses in physics and related areas may be allowed to count toward the Advanced Physics requirements.  Below are some popular examples.  Contact the Physics Option Representative to find out if any particular course not listed here can be used for this requirement. 

Physics of elementary particles and fields (Nuclear Physics, High Energy Physics, String Theory)

                 Ph 139 Intro to Particle Physics                 Ph 205abc Relativistic Quantum Field Theory                 Ph 217 Intro to the Standard Model                 Ph 230 Elementary Particle Theory (offered every two years)                 Ph 250 Intro to String Theory (offered every two years)

Quantum Information and Matter (Atomic/Molecular/Optical Physics, Condensed-Matter Physics, Quantum Information)   

                Ph 127ab Statistical Physics                 Ph 135a Intro to Condensed Matter Physics                 Ph 136a Applications of Classical Physics (Stat Mech, Optics) (offered every two years)                 Ph 137abc Atoms and Photons                 Ph 219abc Quantum Computation                 Ph 223ab Advanced Condensed Matter Physics

Physics of the Universe (Gravitational Physics, Astrophysics, Cosmology)             

                Ph 136b Applications of Classical Physics (Elasticity, Fluid Dynamics) (offered every two years)                 Ph 136c Applications of Classical Physics (Plasma, GR) (offered every two years)                 Ph 236ab Relativity                 Ph 237 Gravitational Waves (offered every two years)                 Ay 121 Radiative Processes

Interdisciplinary Physics (e.g. Biophysics, Applied Physics, Chemical Physics, Mathematical Physics, Experimental Physics)

                Ph 77 Advanced Physics Lab                   Ph 101 Order of magnitude (offered every two years)                 Ph 118 Physics of measurement                 Ph 129 Mathematical Methods of Physics                 Ph 136a Applications of Classical Physics (Stat Mech, Optics) (offered every two years)                 Ph 136b Applications of Classical Physics (Elasticity, Fluid Dynamics) (offered every two years)                 Ph 229 Advanced Mathematical Methods of Physics

Nothing additional. Once you complete the courses in your approved Plan of Study, the Advanced Physics Requirement is complete.

Oral Candidacy Exam

The Oral Candidacy Exam is primarily a test of the candidate's suitability for research in his or her chosen field. Students should consult with the executive officer to assemble their oral candidacy committee. The chair of the committee should be someone other than the research adviser.

The candidacy committee will examine the student's knowledge of his or her chosen field and will consider the appropriateness and scope of the proposed thesis research during the oral candidacy exam. This exam represents the formal commitment of both student and adviser to a research program.

See also the Physics Candidacy FAQs

After the exam, your committee members will enter their result and any comments they may have. Non-Caltech committee members are instructed to send their results and comments to the physics graduate office who will enter the information on their behalf. Once all "pass" results have been entered, the Option Rep will be prompted to recommend you for admission to candidacy. The recommendation goes to the Dean of Graduate Studies who has the final approval to formally admit you to candidacy.

Teaching Requirement

Thesis advisory committee (tac).

After the oral candidacy exam, students will hold annual meetings with their Thesis Advisory Committee (TAC). The TAC will review the research progress and provide feedback and guidance towards completion of the degree. Students should consult with the executive officer to assemble their oral candidacy committee and TAC by the end of their third year. The TAC is normally constituted from the candidacy examiners, but students may propose variations or changes at any time to the option representative. The TAC chair should be someone other than the research Adviser. The TAC chair will typically also serve as the thesis defense chair, but changes may be made in consultation with the Executive Officer and the Option Rep.

What to do in REGIS?

Login to Regis, navigate to the Ph. D. Examination Tab of your Graduate Degree Progress page, and scroll down to the Examination Committee section. Enter the names of your Thesis Advisory Committee members. Click the "Submit Examination Committee for Approval" button and this will automatically generate notifications for the Option Rep and the Dean of Graduate Studies to approve your committee. Enter the date, time and location of your TAC meeting and click "Submit Details." Your committee members will automatically be sent email reminders with the meeting details.

PhD Defense

The final thesis examination will cover the thesis topic and its relation to the general body of knowledge of physics. The candidate should send the thesis document to the defense committee and graduate office at least two weeks prior to the defense date. The defense must take place at least three weeks before the degree is to be conferred. Please refer to the  Graduate Office  and  Library  webpages for thesis guidelines, procedures, and deadlines.

• Date, time, and location of your exam and click the "Submit Examination Details" button. You committee members will automatically be sent email reminders with the exam details. 
• Commencement Information and click the "Submit Commencement Information" button (at least 2 weeks prior to defense)
• Marching Information and click the "Submit your Marching Information" button (at least 2 weeks prior to commencement)

School of Mathematical and Statistical Sciences College of Sciences

Applying to the ph.d in mathematics and statistics with interdisciplinary applications program.

Admission is available for either Fall or Spring semesters. The deadline for Fall admission is February 15 and the deadline for Spring admission is October 15.

The Doctor of Philosophy (PhD)   in Mathematics and Statistics with Interdisciplinary Applications is designed to provide a strong mathematics and statistics background to support intense quantitative work in diverse disciplines. The curriculum will prepare scholars to work on problems at the intersection of mathematics, science, engineering, medicine, finance, computer science, and other quantitative disciplines. The program aims to be the most inclusive and broadly interdisciplinary in Texas.

Admissions Requirements

To apply:  Submit a UTRGV Graduate Application at  www.utrgv.edu/gradapply . There is no application fee.

The minimum admissions criteria for this program are:

• B.S. or B.A. in a STEM field or related field, with at least 3 advanced undergraduate courses in  Mathematics from the following: Linear Algebra, Differential Equations, Modern Algebra I, Real Analysis I, Probability and Statistics I, Complex Variables OR  Earned a Master's degree in Mathematics or a related field from a regionally accredited institution in the United States or a recognized international equivalent in a similar or related field with at least 3 undergraduate classes as given above;
• Official transcripts from each institution attended (must be submitted directly to UTRGV).
• Personal Statement.
• Curriculum Vita.
• Three letters of recommendation. 

Note: GRE is no longer required.

Applicants whose native language is not English or who studied at a university outside the U.S. have the following additional requirements:

Foreign Credential Evaluation

International credentials (transcripts) must be evaluated through an approved evaluation service. The evaluation is the sole responsibility of the applicant and must be submitted for evaluation to one of the following credential evaluation services:   World Education Services   (WES),  Foreign Credential Service of America  (FCSA),  SPANTRAN  or  International Education Evaluations  (IEE).  Applicants are required to select the course-by-course report option. General reports are not sufficient

English Proficiency Exam Scores

Students whose native language is not English will be expected to provide test scores for either the Test of English as a Foreign Language (TOEFL), International English Language Testing System (IELTS) or Duolingo.  The minimum scores are given below:

TOEFL Minimum Scores

• 550 Paper-Based
• 213 Computer-based
• 79 Internet-Based

TOEFL Essentials Minimum Scores

IELTS Minimum Score

To find out if your country is exempt from the English Proficiency requirement, please check here .

Other requirements for international students

For further details on international admissions, please see International Admissions .

PhD GTA/GRA positions

SMSS offers a limited number of highly-competitive Graduate Teaching Assistantships (GTAs). Graduate Research Assistantships (GRA) may also be available. Generally, these positions offer tuition support and a monthly stipend of up to $2,400 per month during the academic year. Additional summer support may also be available. All full-time applicants will be considered for any available opportunities.

King's College London

Applied mathematics research: theoretical physics mphil/phd.

Key information

The Theoretical Physics Group in the Department of Mathematics is at the international forefront of research and offers PhD's in string and M-theory, black holes, conformal field theory, supersymmetry, integrability, and other fundamental branches of modern theoretical physics.

You can explore potential supervisors and topics on our  research group pages .

For other Applied Mathematics Research opportunities please visit this page: Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability - King's College London (kcl.ac.uk)

Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The Theoretical Physics Group organises regular seminars, where leading scientists from around the world present new results and discuss current topics. The students also organise their own informal seminars and discussion groups. The department provides funding for PhD students to attend suitable schools and conferences during their studies.

The Group actively participates in the London Theory Institute ( LonTI ). LonTI provides pedagogical lectures for PhD students on a variety of topics and is open to all students in London. Furthermore there are regular London-wide seminars and events .

Course intake

PhD: 4-8 FT per year.

Almost all of our students receive studentships from grant-awarding bodies such as ERC, EPSRC, Royal Society and STFC and also directly from the NMES Faculty. Students are automatically considered for these studentships when they apply. The number of these positions vary from year to year and are allocated by the group following an interview.

For Chinese nationals there is a possibility of a King’s-China-Scholarship . These require students to apply to King’s in early January, stating that they want to be considered for K-CSC funding. Following an interview and section students then make a separate application for funding.

We also are part of the Martingale Foundation Programme . This scheme is open to UK students with financially challenged backgrounds and funds both MSc and PhD. In particular students must first enter on our MSc programme .

• How to apply
• Fees or Funding

For funding opportunities please explore these pages:

• List of funding opportunities
• External funding opportunities for International students
• King’s-China Scholarship Council PhD Scholarship programme (K-CSC)

UK Tuition 2023/24

Full time tuition fees:

£6,540 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees:

£3,270 per year (MPhil/PhD, Mathematics Research)

International Tuition Fees 2023/24

£24,360 per year (MPhil/PhD, Mathematics Research)

£12,180 per year (MPhil/PhD, Mathematics Research)

UK Tuition 2024/25

£6,936 per year (MPhil/PhD, Mathematics Research)

£3,468 per year (MPhil/PhD, Mathematics Research)

International Tuition Fees 2024/25

£26,070 per year (MPhil/PhD, Mathematics Research)

£13,035 per year (MPhil/PhD, Mathematics Research)

Mathematics Research with University of Hong Kong or Humboldt-Universität Zu Berlin

£24,360 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)

£24,360 per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

Part time tuition fees: £12,180 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

£26,070 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)

£26,070 per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

Part time tuition fees: £13,035 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

All of these fees may be subject to additional increases in subsequent years of study, in line with King's terms and conditions.

Bench fees will be applicable to the non-award research programme for visiting students.

• Study environment

Base campus

Strand Campus

Located on the north bank of the River Thames, the Strand Campus houses King's College London's arts and sciences faculties.

You will be assigned a supervisor with whom you will work closely. You will also attend research seminars and take part in other research related activities in your research group, the department and more widely in the University of London. We do not specify fixed attendance hours, but we expect a good level of attendance, and our research students benefit from informal interaction with each other. You will be provided with access to working and storage space, as well as a laptop. On arrival you will discuss your research programme with your supervisor, and you will attend general induction sessions.

Postgraduate training

Students carry out research under the guidance of a supervisor. Our PhD students receive various forms of training during their period of research, eg attending courses in the London Taught Courses Centre, attendance at EPSRC summer schools; provision of advanced lecture courses; College training courses for graduates who will give tutorial teaching to undergraduates; weekly seminars in the area of your research; frequent research group meetings; attendance at national and international conferences and research meetings.

Communication skills are developed by preparing and presenting seminars in the department, assisted by your supervisor; apprenticeship in writing papers and, in due course, the PhD thesis.

To build your teaching skills and experience, you are strongly encouraged to apply to become a Graduate Teaching Assistant, giving tutorials to our undergraduates (training is provided)

• Entry requirements

Theoretical Physics PhD

Centre for Doctoral Studies

NMES Graduate School

A supportive and engaging environment for PhD students

Funding & Scholarships for PhD students

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Columbia Engineering

Columbia engineering bulletin 2024-2025.

Photo Credit: Columbia University ROAM Lab

Highly dexterous robotic hand from Columbia Engineering researchers led by Associate Professor of Mechanical Engineering and Computer Science Matei Ciocarlie.

500 West 120th Street New York, NY 10027

Undergraduate Admissions

Office of Undergraduate Admissions 212 Hamilton Hall, Mail Code 2807 1130 Amsterdam Avenue New York, NY 10027 Phone: 212-854-2522 Fax: 212-854-3393 [email protected] undergrad.admissions.columbia.edu

Graduate Admissions

Graduate Admissions 1220 S. W. Mudd, Mail Code 4708 500 West 120th Street New York, NY 10027 212-854-4688 [email protected] gradengineering.columbia.edu

Financial Aid

Office of Financial Aid and Educational Financing Office: 618 Lerner Hall Mailing: 100 Hamilton Hall, Mail Code 2802 1130 Amsterdam Avenue New York, NY 10027 Phone: 212-854-3711 Fax: 212-854-5353 [email protected] cc-seas.financialaid.columbia.edu

Need More Information?

You can find the contact information in the Columbia University Resource List or visit the Columbia Engineering website, engineering.columbia.edu .

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• Schools & departments

Mathematical Physics PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Programme website: Mathematical Physics

Introduction to Postgraduate Study at the University of Edinburgh

Join us online on 25 September to learn more about Scotland, the city of Edinburgh and postgraduate study at the University.

Find out more and register

Research profile

We are a multidisciplinary research group with close connections with the School’s Algebra and Geometry & Topology groups.

You’ll benefit from being not only in one of the largest mathematics research groups in the UK but also part of the Edinburgh Mathematical Physics Group – a joint research collective formed in 1999 with Heriot- Watt University and now part of the Maxwell Institute.

The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.

Our group pursues wide-ranging interests spanning a number of disciplines. A central goal is to understand the principles behind quantum gravity, through the study of black holes, cosmologies and spacetime singularities, and via the use of holography and the interplay with quantum gauge field theory through the gauge/gravity correspondence.

Particularly fruitful areas of research are the geometry of higher-dimensional black holes and their near-horizon geometries in the context of higher-dimensional generalisations of general relativity.

We’re fascinated by the various manifestations of supersymmetry: in string theory, supergravity and gauge theory. This has led us to several classification results on supersymmetric supergravity backgrounds, including a recent proof of the homogeneity conjecture. In addition we study gauge theoretic moduli spaces using supersymmetry and via integrable systems techniques, displaying an interplay between the algebraic geometry of curves and their associated function theory. This research has led to computer implementations of various algebro-geometric constructions.

Recently we have made progress in some purely mathematical problems suggested by the gauge/gravity correspondence: namely, the classification of certain exotic algebraic structures related to superconformal field theories, as well as that of certain types of homogeneous supergravity backgrounds.

Training and support

Mathematics is a discipline of high intellect with connections stretching across all the scientific disciplines and beyond, and in Edinburgh you can be certain of thriving in a rich academic setting. Our School is one of the country’s largest mathematics research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.

Research students will have a primary and secondary supervisor and the opportunity to network with a large and varied peer group. You will be carrying out your research in the company of eminent figures and be exposed to a steady stream of distinguished researchers from all over the world.

Our status as one of the most prestigious schools in the UK for mathematics attracts highly respected staff. Many of our 60 current academics are leaders in their fields and have been recognised with international awards.

Researchers are encouraged to travel and participate in conferences and seminars. You’ll also be in the right place in Edinburgh to meet distinguished researchers from all over the world who are attracted to conferences held at the School and the various collaborative centres based here. You’ll find opportunities for networking that could have far-reaching effects on your career in mathematics.

As well as experiencing a vibrant research environment that brings you into contact with a broad group of your peers, your membership of the Edinburgh Mathematical Physics Group will give you access to a dynamic programme of seminars, lecture courses and conferences. There is a dedicated website and blog, and a comprehensive range of graduate activities:

• Edinburgh Mathematical Physics Group

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to libraries for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across our University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have access to dedicated desk space with monitors and a laptop computer.

We provide all our mathematics postgraduates with access to software packages such as:

• Mathematica

Research students are allocated parallel computing time on ‘Eddie’, the Edinburgh Compute and Data Facility. You can also request use of the BlueGene/Q supercomputer facility for your research.

Entry requirements

These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

• Entry requirements by country
• English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 169 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 62 with at least 59 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS , TOEFL, Trinity ISE or PTE , in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

• UKVI list of majority English speaking countries

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

• Approved universities in non-MESC

If you are not a national of a majority English speaking country, then your degree must be no more than five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

Find out more about our language requirements:

• Academic Technology Approval Scheme

If you are not an EU , EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

Fees and costs

Tuition fees.

Scholarships and funding

Featured funding.

• School of Mathematics funding opportunities

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

• your programme
• the duration of your studies
• your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

• UK government and other external funding

Other funding opportunities

Search for scholarships and funding opportunities:

• Search for funding

Further information

• Graduate School Administrator
• Phone: +44 (0)131 650 5085
• Contact: [email protected]
• School of Mathematics
• James Clerk Maxwell Building
• Peter Guthrie Tait Road
• The King's Buildings Campus
• Programme: Mathematical Physics
• School: Mathematics
• College: Science & Engineering

Select your programme and preferred start date to begin your application.

PhD Mathematical Physics - 3 Years (Full-time)

Phd mathematical physics - 6 years (part-time), application deadlines.

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 22 January 2024 will receive full consideration for funding. Later applications will be considered until all positions are filled.

• How to apply

You must submit two references with your application.

Find out more about the general application process for postgraduate programmes:

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• Perspective
• Published: 05 August 2024

AI-driven research in pure mathematics and theoretical physics

• Yang-Hui He  ( 何楊輝 )   ORCID: orcid.org/0000-0002-0787-8380 1 , 2  

Nature Reviews Physics ( 2024 ) Cite this article

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• Computer science
• Pure mathematics
• Theoretical particle physics

The past five years have seen a dramatic increase in the usage of artificial intelligence (AI) algorithms in pure mathematics and theoretical sciences. This might appear counter-intuitive as mathematical sciences require rigorous definitions, derivations and proofs, in contrast to the experimental sciences, which rely on the modelling of data with error bars. In this Perspective, we categorize the approaches to mathematical and theoretical discovery as ‘top-down’, ‘bottom-up’ and ‘meta-mathematics’. We review the progress over the past few years, comparing and contrasting both the advances and the shortcomings of each approach. We believe that although the theorist is not in danger of being replaced by AI systems in the near future, the combination of human expertise and AI algorithms will become an integral part of theoretical research.

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Acknowledgements

The author is most grateful to A. Bhattacharya, A. Kosyak and M. Duncan for many valuable comments on the draft. The author thanks many collaborators over the past few years on AI-assisted mathematics, for the great fun and friendship: D. Aggarwal, L. Alessandretti, G. Arias-Tamargo, A. Ashmore, J. Bao, A. Baronchelli, P. Berglund, D. Berman, K. Bull, L. Calmon, H. Chen, S. Chen, A. Constantin, P.-P. Dechant, R. Deen, S. Garoufalidis, E. Heyes, E. Hirst, J. Hofscheier, J. Ipiña, V. Jejjala, A. Kasprzyk, M. Kim, S. Lal, K.-H. Lee, S.-J. Lee, J. Li, A. Lukas, S. Majumder, C. Mishra, G. Musiker, B. Nelson, A. Nestor, T. Oliver, B. Ovrut, T. Peterken, S. Pietromonaco, A. Pozdnyakov, D. Riabchenko, D. Rodriguez-Gomez, H. Sá Earp, M. Sharnoff, T. Silva, E. Sultanow, Y. Xiao, S.-T. Yau and Z. Zaz. The research is funded in part by STFC grant ST/J00037X/2 and the Leverhulme Trust for a project grant.

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Kennesaw State physics major pursues life-changing research

KENNESAW, Ga. | Aug 19, 2024

The junior from Smyrna said classes in astronomy and physics taught her how physical forces effect everything around her, and she wanted to immerse herself in them. So, she came to Kennesaw State University for the opportunity to conduct research right away as a freshman.

“Honestly, the research opportunities drew me to KSU,” said Manqueros, who is pursuing a bachelor’s degree in physics in Kennesaw State’s College of Science and Mathematics . “Other colleges mainly take graduate students for their research, and I knew that at KSU I could do meaningful research even if I was an undergraduate student.”

That desire for meaningful research drew her to the lab of associate professor Kisa Ranasinghe, who creates bioactive glass that can transport nanoparticles that treat various ailments. Manqueros approached Ranasinghe at an early-semester meeting for physics majors after hearing the professor discuss her work; Manqueros was hooked, and Ranasinghe was impressed.

“When someone stops me to say they’re interested in my research and want to learn more, that’s an indicator, right?” Ranasinghe said. “For a freshman to take that initiative and show that amount of enthusiasm is truly impressive. Very quickly I found out she has great potential.”

From that day forward, Manqueros poured herself into the life-changing research into bioglass, which isn’t really glass but a conduit that acts like glass to bring therapeutic nanoparticles into the body. Manqueros said cerium oxide nanoparticles within the bioglass can interact to treat Alzheimer’s disease, cancer, diabetes, and other physical and neurological conditions. The first part of her explanation, though, involves demystifying the idea of glass in the body.

“A lot of times when we say we're doing research on glass that we can put into your body, people freak out because they imagine the glass breaking—it’s not like that,” she explained. “The simple fact that we work with glass to better people's health—that's something that I really want to get across to people. What we do from the physics point of view is study those nanoparticles and how they interact within the glass.”

Manqueros will investigate these problems as a Birla Carbon Scholar this summer. She has also been the lead author on an abstract for a poster presentation that published earlier this year in the Georgia Journal of Science, and she presented findings at the Georgia Academy of Science conference in March, where she won first prize for undergraduate oral presentations in the division that covers physics, mathematics, computer science, and engineering.

Ranasinghe said Manqueros’ future is wide-open, though Manqueros said the future will involve more physics, either a master’s degree or a doctorate while continuing the research into bioglass. Life-changing research with societal impact will keep her engaged for a long time to come, she said.

“I actually enjoy what I do,” she said. “Oftentimes when you're doing work as a physicist, people don't see the meaning in what you do because they wonder why we need to study this. This research is impacting anyone who has some sort of disease or wants to improve their health or their body. I like that I have a direct impact on people's lives through the research that I do here at KSU.”

– Story by Dave Shelles

Photos by Matt Yung

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