dual phd in math and physics

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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 Activities and Events

• 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).
• The MPP Graduate Colloquium includes seminars from the OCIE Seminar Series in History and Philosophy of Mathematics.  Click here for more information about the seminar series.
• 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 2023 and later. Students should consult with their academic program regarding final certifications and requirements for graduation.

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The following degrees and certificates are available in the MSU Department of Physics and Astronomy's graduate program. The detailed degree requirements can be found in the Graduate Handbook . For programs with components outside of the department, links to further resources  from the relevant departments are provided.

• M.S. in Physics
• Ph.D. in Physics
• M.S. in Astrophysics and Astronomy
• Ph.D. in Astrophysics and Astronomy
• Interdisciplinary Ph.D. in Physics
• Dual Ph.D. Degree in Physics and Mathematics
• Dual Ph.D. Degrees with Computational Mathematics Science and Engineering  (see more details below)
• Dual Ph.D. Degree in Astrophysics and Computational Mathematics Science and Engineering
• Dual Ph.D. Degree in Physics and Quantitative Biology
• Dual Ph.D. Degree in Physics and Electrical and Computer Engineering
• Graduate Certificate in Accelerator Science and Engineering

A hybrid graduate program in beam physics  is available in the Department, but follows the requirements for the M.S. and Ph.D. degrees in Physics described in the handbook. 

Graduate Certificates in other Departments that are popular by students in the Department of Physics and Astronomy are the following. Requirements can be found through the provided links.

• Certificate in Computational Math, Science, and Engineering (CMSE)
• For the corresponding CNS website with application and other instructions see here .
• Future Academic Scholars in Teaching (FAST) Fellowships

The dual Ph.D. degree with CMSE is very popular. Here is some additional information about what is required to pursue this degree in terms of research:

According to the  CMSE graduate handbook , section 5), for a dual PhD "The student’s dissertation must be composed of novel research that advances the state-of-the-art in algorithms or applications relating to computational and/or data science and must include significant intellectual contributions to both disciplines.”  It is up to the guidance committee to assess whether this condition is met when proposing the research plan for a dual degree. The committee must have at least two members who are (joint) faculty in CMSE – one of those two must be primarily appointed in CMSE. It is  not  a requirement that one of the CMSE faculty serves formally as second or co-advisor and the involvement of a CMSE faculty member in guiding your research will depend on the nature of your research. However, you need to make sure that the assessment of the research plan involves the two CMSE faculty members

So, how does one assess whether a research plan qualifies for a dual PhD in physics and CMSE? Dual PhD projects with CMSE must have a very significant computational or data science component (i.e., the student spends a substantial fraction of their time on algorithm development, implementation, etc.), which generally includes at least one of the following:

• the development of a completely new numerical or mathematical algorithm
• the transfer of algorithms used in other disciplines into physics to solve a problem that would otherwise not be tractable
• the development of substantial new open-source software package that uses computational modeling, data science, and numerical and/or mathematical algorithms to advance their area of research.  

Things that do not qualify for a dual PhD include doing modeling and/or data analysis using packages that were entirely written by other people (or making minor modifications to the same), or doing some work of the type described above that is only a minimal component of their dissertation.  Re-implementing algorithms that are already used also falls into this category (i.e., writing a Python version of something that already exists in Fortran/C++/Matlab/etc.).

The guidance committee makes an assessment on the basis of the above guidelines, which is subsequently reviewed by the physics and CMSE graduate program directors, prior to submission for approval to the university.

For questions, contact the PA Graduate Program Director or the CMSE Graduate Program Director.

Joint Math/CS PhD

In Winter 2018, the Department of Mathematics and the Department of Computer Science launched a joint program through which participating students can earn the degree

“Ph. D. in Mathematics and Computer Science.”

The basic structure is that students must gain admission to both PhD programs and satisfy both sets of course requirements. They write a single dissertation that satisfies both programs.

While the program is open to all eligible students, we expect that at least initially it will be most popular among students working in CS Theory, Discrete Mathematics, and Mathematical Logic.

Each student in this program will have a primary program (either Mathematics or Computer Science). Throughout the course of studies, the primary program will provide administrative support to the student, including in matters regarding financial support.

To be admitted to the joint program, students will have to be admitted by both departments as follows.

Application after entering the PhD program

Students enrolled in either the Mathematics or the Computer Science PhD program may apply to the joint program during the first four years in their current program. If admitted to the joint program, their current program will be primary.

Such an applicant must submit the following material to the Director of Graduate Studies/Graduate Committee Chair of the intended secondary program, while notifying the Director of Graduate Studies/Graduate Committee Chair of the primary program:

• statement of purpose, explaining why the joint program is the right program for the applicant
• statement of coursework and research done so far
• statement of a schedule how the applicant proposes to satisfy the secondary program’s requirements
• advisor’s recommendation, including endorsement of the applicant’s statements (items 2, 3, 4 above)
• if the application occurs during the first year of the primary program, the applicant needs to provide two additional letters of recommendation and their undergraduate transcript. It is permitted to reuse material from the application to the primary program.

Requirements, monitoring

Course requirements.

Students enrolling in the joint program will need to satisfy the course requirements of both departments. They will have to satisfy the course requirements of their primary program on the schedule of that program, and satisfy the course requirements of their secondary program by the end of their fifth year in the primary program.

According to current rules, two of the CS electives can be courses offered by the Mathematics department. These courses are permitted to overlap with the Mathematics course requirements.

Exam Requirements

Students in the joint program shall fulfill the examination requirements of the primary program; the current list of requirements can be found at

• Computer Science Requirements
• Mathematics Requirements

For students participating in the joint program, the deadlines for these exams can be relaxed by petitioning the Director of Graduate Studies/Graduate Committee Chair of the primary program.

Monitoring student progress

Students’ annual progress reports go to both departments’ Director of Graduate Studies/Graduate Committee Chair in accordance with each department’s format.

PhD dissertation and defense

Subject of the dissertation.

The dissertation is expected to be in an area relevant to both fields.

PhD thesis defense

The scheduling of the PhD Thesis defense follows the Mathematics Department’s custom as follows.

• A nearly final draft of the thesis is made accessible to faculty at least two weeks prior to the defense, either in hard copy in the departmental office or, preferably, by posting on the internet.
• The dissertation is reviewed in writing by two readers, one of whom is typically the thesis advisor.
• The reports by the first and the second readers are circulated among faculty of both departments, along with the Thesis abstract and the following information: the location (physical or virtual) where the thesis can be viewed, the planned time and location of the defense, and the names and affiliations of the thesis committee members.
• There is a two-week period for comments by faculty before the admission of the thesis for defense.

The thesis defense itself consist of a 50-minute public presentation of the main results and methods of the dissertation, followed by a public question-answer period, followed by a closed-session question-answer period.

Oversight, committees

The program proceeds under joint Math-CS oversight, exercised by the Director of Graduate Studies/Graduate Committee Chair of each department.

Examination committees

The following rules apply to all examination committees (Qualifying/Topic Exam, Master’s, Candidacy, and PhD). The committee will consist of at least three members, including the student’s advisor(s). It will include at least one member of each department, and will either be chaired by a joint appointee of the two departments or co-chaired by a member of each department. Each department shall publicize these exams in accordance with its established customs.

Ph.D. in Scientific Computing

This program is intended for University of Michigan Ph.D. students who will make extensive use of large-scale computation, computational methods, or algorithms for advanced computer architectures in their doctoral studies. A firm knowledge of the scientific discipline is essential.

This is not a stand-alone degree; it is a joint degree program . Students must be accepted into the Ph.D. program of a home department at the University of Michigan. The actual degree name will have “…and Scientific Computing” appended to the the normal title, e.g., “Ph.D. Degree in Aerospace Engineering and Scientific Computing.”

Students in the Scientific Computing degree program come from many different disciplines. Our current enrollment exemplifies the breadth of departments, schools, and colleges represented by our Ph.D. students.

Students may enroll in the program after having completed one term in their home Ph.D. department. We recommend applying prior to being promoted to candidacy status, but can often accommodate students later in their degree progress.

Please contact MICDE at [email protected] if you have any questions about the Ph.D. in Scientific Computing.

Academic Requirements

Application procedures.

Current Students

Tracking Progress

Funding Resources

Current Enrollment

Students must complete the normal doctoral requirements of their home departments, as well as additional requirements in scientific computing. The specific requirements are:

Non-exhaustive examples of course selections for various departments can be seen on our  Example Course Choices page.

Group I Courses

Twenty-four (24) credit hours of coursework toward your home degree. You must complete your home degree requirements in order to receive the Ph.D. in Scientific Computing. It cannot be earned on its own. Group I may overlap with groups II or III. 

Group II Courses

Nine (9) credit hours of approved courses in scientific computing methodologies.

Group III Courses

Nine (9) credit hours of approved courses in computational science and applications in scientific computing outside the home department  (this typically includes courses in computer science, parallel algorithms, advanced computer architectures, computational fluid dynamics, or other courses in scientific computation not offered by a student’s home department).

Committee Composition

An emphasis on scientific computing reflected in doctoral thesis and doctoral committee composition. At least one faculty member on your committee should be an expert in scientific computing, affiliated with MICDE  or  MIDAS .

Demonstration of Understanding

Preliminary/Qualifying Exam Question: You must answer at least one question related to scientific computing during your department’s preliminary or qualifying examination.  If you join the program after having completed your qual/prelim, you can still use this option if you were asked a question related to computational methods or applications during your qual/prelim.  The student’s advisor or a MICDE  or  MIDAS -affiliated member of the committee must then email MICDE to confirm that this requirement is complete.

If the format of your PhD program’s preliminary/qualifying examination cannot accommodate this requirement, or if you are beyond this stage at the point of joining the program and were not asked a question on your prelim/qual, you have the following option to complete the Demonstration of Understanding requirement:

Literature Review: A 3-5 page critical assessment of previous research that has been done in your research area, specifically the scientific computing/computational aspect of your research problem.  This must be submitted to [email protected]  for review 2-4 semesters before your dissertation defense.

If you have any questions about fulfilling the Demonstration of Understanding requirement, please email [email protected] .

For Faculty:

Please send an email to [email protected] describing the scientific computing-related question that was asked during the examination and acknowledging that the student answered the question satisfactorily.

Ph.D. Seminar

If you enrolled in the Ph.D. in Scientific Computing in or after January 2022 , you are required to present at least once before graduation in the Ph.D. Student Seminar Series . Before presenting, you are strongly encouraged to attend as many sessions of the the Ph.D. Seminar Series as you can, from students in your department and outside it. The Ph.D. Student Seminar Series is an opportunity to learn how to simplify your explanation of your research problems and methods in order to talk about them to colleagues outside of your lab or your home department, which will help you prepare for future job searches.

Sign up to present in 2023-2024 on the MICDE Ph.D. Student Seminar Sign-Up form .

Students are expected to work closely with their academic advisors and with MICDE to develop a plan to meet these requirements.

• Talk to your academic advisor about your interest in the Ph.D. in Scientific Computing. Your department must approve your enrollment in the program.
• Submit the Course Audit form . You don’t have to have a full plan in place before filling out the Course Audit form, but please spend some time considering each of the questions and put your answers in the formats requested.
• After the MICDE program administrator checks your Audit Form and transcript, they will contact you to schedule an advising session with an MICDE Management & Education Committee faculty member. During the session, you, the faculty member, and the MICDE program administrator will finalize your plan to meet the requirements of the Ph.D. in Scientific Computing.
• After your advising session, you can apply to the Ph.D. in Scientific Computing . In order to apply, you must complete the Rackham Application Form , have it signed by your department, and submit it to [email protected] . You are not enrolled in the program unless you have completed this step.

Questions? Contact the Program Administrator at [email protected] .

Eligibility

This is not a stand-alone degree; it is a   joint degree program . Students must be accepted into the Ph.D. program of a home department at the University of Michigan-Ann Arbor.

Enrollment Deadlines

Students are enrolled on a rolling basis as they apply.

Information for Current Students

Please contact the program administrator ( [email protected] ) for all questions related to the Ph.D. in Scientific Computing.

We track students’ progress through the Ph.D. in Scientific Computing Web Progress Form . Your Web Progress Form is created after the advising session, and is accessible by prospective students as well as those who are enrolled. Every summer we will reach out to students to update their Web Progress Form with anything that has changed since the previous summer.

Updating the Web Progress Form

Please plan to update your Web Progress Form each summer with new information, including:

• If you answered questions about scientific computing in your quals/prelims and your Web Progress Form does not reflect this, please describe the questions in the Candidacy Status section.
• If you have formed your doctoral committee, please list the members in the Committee Information section.
• If you have made any changes to the courses you took or plan to take to fulfill requirements for the Ph.D. in Scientific Computing (including changing courses from “planned” to “completed” once you’ve taken them) please update the Course requirements section.
• If you have made progress in your research that is not yet reflected on your WPF (awards, fellowships, conference presentations, publications, etc.) please update the Research Progress section.
• Please make sure that your current estimated graduation term is listed in the  Future Plans section. This is not set in stone, but helps us to understand where you are in your degree process.

Enrollment Status

Note that each student has one of the following 5 statuses on the Web Progress Form . If you believe the enrollment status listed on your Web Progress Form is incorrect, please email [email protected] .

• Enrolled  ( had an advising session, turned in their application form to MICDE and Rackham has processed the application )
• Prospective  ( had an advising session, but has not yet enrolled ) Please let us know if you are still interested in enrolling in the program so we can finish your enrollment. You can log in to the Web Progress Form to see what courses were discussed in your original advising appointment.
• Leave of Absence  ( you are enrolled in the program, and currently in a leave of absence from your home program ) Please let us know when you return from a leave of absence.
• Graduated  ( you graduated from the program in 2015 or later)
• Discontinued  (you discontinued the Ph.D. in Scientific Computing and/or your home program)

You can view your Web Progress Form at any time. If you want to make any changes to your Web Progress Form outside of the summer window, or if you have any problems with accessing the form, please email [email protected] .

• Confirm that your transcript shows you are enrolled in the PhD in Scientific Computing.  If your transcript doesn’t show your enrollment in the program, please contact the program administrator ( [email protected] ) to find out your status within the program.
• If your transcript shows your enrollment in the Scientific Computing program, please review all the information we have on file for you on the Web Progress Form . In particular, check the Graduation requirements summary section at the top. If any of the boxes are blank or incomplete, please ask the program administrator ( [email protected] ) to review your requirements and confirm that they are complete.
• During the term you want to graduate, please contact the program administrator ( [email protected] ) to let them know so they can process your information.

Don’t forget to add the PhD in Scientific Computing program to the title page of your dissertation! For example:  (Physics and Scientific Computing)

A1: Please see  this list for examples. Note that they are only samples of what other students have done, but they are not the only choices. This degree is extremely individualized, so please email the program administrator ( [email protected] ) for more course information.

Q2: I met with the program director, but I get an error when I try to access the Web Progress Form. What can I do?

A2: Please contact the program administrator ( [email protected] ) to inquire about your status.

Q3: Can I change the courses listed on my form?

A3: Yes, but note that any course changes must be approved by MICDE. Email the program administrator ( [email protected] ) if you have any questions.

Q4: How often are students required to complete the Web Progress Form

A4: We ask students to fill out the form annually, by the end of summer each year.

Q5: What if I want to know if a course is approved before the Annual Form is due?

A5: Please contact the program administrator ( [email protected] ) to initiate the approval process. Once approved, they will record it in your form.

Q6: The form lists my status as “PROSPECTIVE” but I think I should be enrolled. What should I do?

This bar graph represents the numbers of students from different departments at U-M enrolled in the program. Students come from the College of Engineering, School of Kinesiology, College of LSA, Michigan Medicine, College of Pharmacy, Ross Business School, School for Environment and Sustainability, School of Information and the School of Public Health.

Departments include: Aerospace Engineering, Civil and Environmental Engineering, Biomedical Engineering, Chemical Engineering, Climate and Space Sciences and Engineering, Electrical Engineering and Computer Science, Industrial & Operations Engineering, Macromolecular Science & Engineering, Mechanical Engineering, Materials Science & Engineering, Naval Architecture & Marine Engineering, Nuclear Engineering & Radiological Sciences, Applied Physics, Chemistry, Chemical Biology, Earth and Environmental Sciences, Linguistics, Mathematics, Physics, Political Science, Psychology, Biostatistics, Environmental Health Sciences, Epidemiology, Health Behavior & Health Education, Kinesiology, Health Infrastructures & Learning Systems, Neuroscience, Pharmaceutical Sciences, Business and School for Environment and Sustainability.

This list is not exhaustive, and continues to grow.

Ph.D. in Scientific Computing years in existence

Current Ph.D. in Scientific Computing students

Alumni since 1992

History of the Ph.D. in Scientific Computing

Text Version

Faculty Leadership

For all questions about the Ph.D. in Scientific Computing, please email [email protected] .

Karthik Duraisamy

2022 – present

2004 – 2022

Bill Martin

1988 – 2004

Mark your calendar for the MICDE SciFM 2024 Conference on April 2nd & 3rd, 2024!

Thank you for submitting the form

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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.

Prerequisites

Many students in DAMTP are admitted after taking the Cambridge Part III (MMath/MASt) course and others will have completed a comparable Master-level course. Some may already have carried out a small-scale research project. All of our students, therefore, begin their PhD work with a good grasp of advanced material, on which they can build as their research progresses.

Research Areas

Research in DAMTP can be divided into the following broad areas: Applied and Computational Analysis, Astrophysics, Geophysics, Fluid and Solid Mechanics, Mathematical Biology, Quantum Information, Soft and Quantum Matter, High Energy Physics, and General Relativity and Cosmology. The boundaries between such areas are not rigid, however, and many members of staff will contribute to more than one area (this is regarded as a key factor in the continuing success of DAMTP). There are active seminar programmes across all subject areas, attendance at which is an important part of PhD student training.

PhD Supervision

Each PhD student in DAMTP has a supervisor who is responsible for guiding their research and monitoring their progress. Each student is admitted to work within a particular subject area, and often with a specific supervisor. Some students will work in close collaboration with their supervisor, or as part of a larger research group, while others may work more independently (with their supervisor's approval). Collaborative projects may involve other researchers or groups outside Cambridge, in the UK or worldwide.

Progress during the course

Students in DAMTP are admitted on a probationary basis in the first instance and are assessed for registration after roughly one year of work. A review of progress starts before the end of the third term of research when students are asked to submit a short report.  A more detailed appraisal and interview are conducted during the fourth term of their research.  For the fourth term assessment, two assessors are assigned to consider the academic progress of each student, including a record of their attendance at seminars and other related activities. Progress continues to be monitored throughout their PhD through regular online supervision reports.

Students are encouraged to give talks and seminars within the department, and to present their findings at conferences or meetings, once the time is right. Many students submit a prize essay at the beginning of their fifth term and the best essays each year meet the standards expected of publishable work. We regard it as particularly important that our students submit their work for publication in leading journals, as well as to web-based archives, and many will already have several papers in circulation when they come to write their thesis. Additional support and advice for students is available at any stage of their PhD through a system of designated departmental advisors, as well as from members of the DAMTP Postgraduate Education Committee.

Working Environment

DAMTP is part of the Centre for Mathematical Sciences or CMS. The site is shared with the Department of Pure Mathematics and Mathematical Statistics and also with the Isaac Newton Institute and the Betty and Gordon Moore Library (the main university mathematical science library). CMS provides a modern, comfortable and well-equipped working environment for PhD students, facilitating day-to-day contact with academic staff and other students.

Additional training and opportunities

All students in DAMTP can benefit from a wide variety of additional courses and training opportunities.  In addition to the wide range of lectures and seminars on offer in DAMTP and CMS, the Department actively promotes and encourages researcher development and transferable skills training (e.g. sessions on improving communication skills, organisational and leadership skills, presenting work at seminars or conferences, and applying for postdoctoral positions). Some of these workshops are coordinated with the centrally-run Researcher Development Programme which is open to all students of the University; others are run by the Faculty of Mathematics.

There is no requirement for PhD students to teach but there are plenty of opportunities to do so, such as offering problem-solving classes (college supervisions) for small groups of undergraduate students or offering help with running examples classes for Part III students.

Please note: part-time study may not always be viable 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.

The Postgraduate Virtual Open Day usually takes place at the end of October. It’s a great opportunity to ask questions to admissions staff and academics, explore the Colleges virtually, and to find out more about courses, the application process and funding opportunities. Visit the  Postgraduate Open Day  page for more details.

See further the  Postgraduate Admissions Events  pages for other events relating to Postgraduate study, including study fairs, visits and international events.

Departments

This course is advertised in the following departments:

• Faculty of Mathematics
• Department of Applied Mathematics and Theoretical Physics

Key Information

3-4 years full-time, 4-7 years part-time, study mode : research, doctor of philosophy, department of applied mathematics and theoretical physics this course is advertised in multiple departments. please see the overview tab for more details., course - related enquiries, application - related enquiries, course on department website, dates and deadlines:, lent 2024 (closed).

Some courses can close early. See the Deadlines page for guidance on when to apply.

Easter 2024 (Closed)

Michaelmas 2024, easter 2025, funding deadlines.

These deadlines apply to applications for courses starting in Michaelmas 2024, Lent 2025 and Easter 2025.

Similar Courses

• Mathematics MPhil
• Mathematics (Applied Mathematics) MASt
• Mathematics (Theoretical Physics) MASt
• Mathematics (Mathematical Statistics) MASt
• Mathematics (Pure Mathematics) MASt

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The University of Chicago is renowned for its interdisciplinary culture, and doctoral students can pursue a variety of joint or dual degree programs. Opportunities to create a specific combination can be discussed with one’s Director of Graduate Study.

Existing programs include:

PhD in Political Economy

Offered jointly between the Department of Political Science and the Harris School of Public Policy , the PhD program in Political Economy provides accelerated training in formal theory and statistical methods alongside deep engagement with political science. 

Joint PhD in Anthropology and Linguistics

In addition to linguistic anthropology as a sub-field within the Department of Anthropology , a joint Ph.D. program is available to students who are admitted to both the Department of Anthropology and the  Department of Linguistics . Administratively, the student is admitted to, and remains registered in, the primary, or “home” department, and subsequently seeks admission to the second department in joint residence status. Students approved to pursue the joint degree program must complete the requirements of both departments, including the distinct introductory and advanced courses stipulated by each, the departmental qualifying examination in appropriate special fields, and the language requirements, including additional foreign languages for the Linguistics Ph.D. Students should declare interest in the Joint Degree Program on the initial graduate application to the Department, and should discuss this interest personally with linguistic anthropology faculty soon after arrival on campus.

Joint PhD in Psychology and Linguistics

Students in the Department of Linguistics in the Division of the Humanities who wish to work toward a joint PhD in Psychology's Cognition Program and in Linguistics must be admitted to the Department of Psychology .

Joint PhD in Financial Economics

Established in 2006, the Joint PhD Program in Financial Economics is offered jointly by the Kenneth C. Griffin Department of Economics and the Finance dissertation area at  Chicago Booth . The aim of this program is to leverage the strengths of both sponsors in training PhD students interested in financial economics. Students must satisfy program requirements for the PhD in both departments.

Joint PhD in Psychology and Business

Established in 2009, the Joint Program in Psychology and Business is overseen jointly by the  Department of Psychology  and the  Behavioral Science dissertation area  at Chicago Booth. The aim of this program is to connect the large number of social, cognitive, and organizational psychologists at Chicago Booth and within the Department of Psychology. To qualify for the joint program, a student must be admitted into either the Psychology or the Business graduate program.

JD/PhD Programs

Doctoral students in Social Sciences who are also admitted to the University of Chicago Law School may pursue a concurrent PhD/JD program , where there is an explicit and authorized close association between legal education and doctoral training. Students in the concurrent degree program alternate registration sites between the two units. Students complete all requirements for both degrees. Applicants must apply to both programs separately. The University of Chicago Law School has established a fellowship program to support students pursuing a concurrent JD/PhD at the University of Chicago, which may grant fellowship aid during the Law School years.

MD/PhD in Medicine, the Social Sciences, and Humanities

The program in  Medicine, the Social Sciences and Humanities (MeSH)  at the University of Chicago trains medical students to become innovative physician-scholars at the critical interface of medicine and society. The MeSH program is an opportunity for students interested in obtaining an MD and a PhD in a field outside of the traditional biological and physical sciences. Students interested in MeSH may pursue a doctoral degree among any of the graduate programs relevant to the social sciences and humanities at the University of Chicago.

Joint PhD in Social Thought & Classics

The  Joint Ph.D. Program in Social Thought and Classics  is intended for students whose study of a particular issue or text from the ancient Greek and Roman world requires a broadly inter-disciplinary approach alongside a professional mastery of philological skills. Those interested in pursuing this joint degree program must first be admitted in EITHER the  Committee on Social Thought  OR the  Department of Classics  and complete at minimum the two quarter language survey (Greek or Latin), offered by the Department of Classics, with an average grade of B or higher. Application shall then be made to the second department and, provided that the standards of admission to that department are met, students will be admitted to joint degree status. 

Joint PhD Social Thought & Philosophy

The  Joint Ph.D. Program in Social Thought and Philosophy  is designed to provide students with equal in-depth training, simultaneously provided by the Committee on Social Thought and the Department of Philosophy . Those interested in pursuing this joint degree program must first be admitted in EITHER the Committee on Social Thought OR the Department of Philosophy. After commencing the program of study, application shall then be made to the second department and, provided that the standards of admission to that department are met, students will be admitted to joint degree status. 

Other Joint and Ad Hoc Degree Possibilities

Students admitted to any doctoral program in Social Sciences may subsequently petition the University to create a joint program with another department. Such individually-created joint degree programs begin in the second year of graduate studies or later. In all cases, students complete the separate program requirements for each degree, with no additional residence requirement, and write one Ph.D. dissertation that separately meets the dissertation requirements of each department.

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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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Program Information

Students currently enrolled in a University of Michigan Ph.D. or Master's program outside of the Mathematics Department who have completed at least one term of coursework and are in good academic standing are eligible to apply for a Master's of Mathematics dual degree.  (If you are interested in doing a dual degree with the Quantitative Finance & Risk Management Master's, visit the  Quant Dual Degree page ).

The Mathematics Dual Degree program has the following expectations:

• The Mathematics Department expects you to complete the Mathematics Master’s Degree either before or at the same time as the degree in your home department.
• Usually only a grade of “B” or higher in a course is allowed to be counted towards the Mathematics Master’s degree. You are expected to achieve an average of “B+” or higher for the overall GPA of the courses counted towards your Math Master’s dual degree.
• Students must have any changes to their course plan approved by an advisor prior to taking any course(s) that are not on the original course plan.

If you are in the dual degree program, and you anticipate not being able to meet any of these expectations, you must contact the department via email ([email protected]). Students who fail to meet the above expectations may be discontinued from the Mathematics Master’s program.

Students who have just graduated from a graduate program are not eligible to apply for a dual degree program.

Rackham Dual Degree Requirements

Please be sure to read Rackham's dual degree policies here .

Current Students can find Rackham's dual admission eligibility requirements and application instructions here .

Eligibility Requirements

• Must be a current Rackham Master’s or Doctoral student to apply.
• Must have completed at least one academic term in the current Rackham program with a cumulative GPA equal to or above a 3.0. As a first term graduate student, you are not eligible to apply until your grades are posted indicating a minimum GPA of 3.0.
• Must meet with your current program advisor or graduate coordinator prior to submitting the application to add a degree or certificate.
• Must complete the  Pre-Approval Form for Dual Admission  and obtain a signature of approval from the authorized signer in your current graduate program before you apply. Without approval and an authorized signature on the form, your application will not be processed and the application fee of $10 will not be refunded. You will be required to upload the completed and signed Pre-Approval Form in the online application.

Applying for a Dual Degree

Applying to pursue a dual degree is a different application process than the online admissions system used for external applicants.

First, click on the program(s) you are interested in below and sketch possible course plans.

• Actuarial MS Math - Email Professor Virginia Young at [email protected]
• Applied MS Math  - Email Professor Divakar Viswanath at [email protected]
• Applied & Interdisciplinary Mathematics MS - Email Professor Alben at [email protected]
• General MS Math - Email Professor Divakar Viswanath at [email protected]

Second, email or make an advising appointment with the corresponding advisor listed above to discuss your plans and verify that they will meet the requirements.  Also, sign this Mathematics Master's Dual Degree Program Expectations Contract explained above and submit to the Grad Office at [email protected].

Third, complete this  Rackham Pre-approval Form for Dual Admission , submit it to the Grad Office at [email protected] for a signature, then apply online to the Rackham Dual Degree program.

Lastly, when your coursework is mostly completed, fill out this Rackham Graduate School Dual/Joint Degree Election Form , make an appointment with the corresponding advisor to have it signed, and submit it to submit to the Grad Office at [email protected].

Questions about the Dual Degree Program should be directed to [email protected].

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MSci in Mathematics and Physics within the Natural Sciences programme (FGC0): 2023-2024

For more information about the Natural Sciences degree programme, please contact:

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(updated on September 9, 2021)

In contrast to an applied mathematics degree or the B.S. in Physics with a Mathematical Physics Concentration, the B.S. in Mathematics and Physics is a synergistic, coherent, and parallel education in mathematics and physics.  A graduate in this program will understand theory and applications in both mathematics and physics and may endeavor to work in either field.  The challenging coursework is similar to combining the mathematics and physics cores, with the physics laboratory cluster replaced by a single advanced laboratory course.

The College’s General Education Requirements, a computer science course, a chemistry sequence plus open electives round out the curriculum.  A student in this program may use either of two academic advisors, one from each department, who would also constitute a committee for the administration of the degree and the approval of curriculum petitions. The B.S. in Mathematics and Physics is not only an excellent preparation for either mathematics or physics graduate schools, it is also suitable for careers in industry and government.  The breadth of training, from pure mathematical analysis to a hands-on laboratory experience, is uniquely attractive. It is appropriate for computational science and professional and graduate schools where an excellent education in logical thinking and an in-depth, broad technical problem-solving ability are prized.

The total number of required credits is 120 (29 MATH, 32 PHYS, 11-13 ENGR and CHEM, with 6 of the normal GER credits satisfied by MATH and PHYS courses).  There are 50 credits of electives of various types.  The table below lists the required courses for students entering in the class of fall 2021*. Students who matriculated to CWRU before fall 2021 should consult the General Bulletin for the year they started at CWRU for program requirements that apply for them.

*A student’s Academic requirement page in SIS and the University’s General Bulletin, https://case.edu/bulletin/ , are the definitive sources for course and degree information.

* course usually taken in this year, ‘F’ or ‘S’ indicates the course is usually offered only in fall or spring. Other courses are either offered both semesters (100 & 200 level) or on no fixed schedule.

** An advanced physics course to be selected from the following list: PHYS 315, 316, 320, 326, 327, 328, 336, 365.

*** The ‘MP group’ of four courses corresponds to two physics courses and two mathematics courses. The physics courses are chosen from PHYS 250, 349, and 350. The mathematics courses are subject to approval by the advisory committee and are thereby referred to as `approved electives. These courses may be chosen from the general list of mathematics courses at the 300 level or higher. It may also be possible to choose a course outside the mathematics and physics departments as a substitute in the MP group, subject to approval by the advisory committee.

**** If approved by the M&P committee, other science sequence courses may be substituted.

***** Students are encouraged to take either the Math or Physics SAGES departmental seminar and capstone courses but should then take both courses from the same department. The physics departmental seminar consists of 1 credit of PHYS 303 plus two credits of PHYS 352.

****** The breadth requirements include 6 hours of Social Sciences and 6 hours of Arts and Humanities. This may increase by 3 credits if the required Global and Cultural Diversity course is not also one of the breadth requirement courses. Courses required for the B.S. in Mathematics and Physics satisfy the 6 credit GER for Natural Sciences and Mathematics as well as the Quantitative Reasoning course requirement.

******* The number of open electives may vary depending on course choices made by the student, as determined by the degree requirement that the total number of credits be at least 120.

Typical Schedule

(* indicates options, 4-5 of the Open Elective courses are normally used to satisfy GER Breadth Requirements.)

For more information, contact Prof. Harsh Mathur, [email protected] or Prof. Gary Chottiner, [email protected] in the Department of Physics or contact the academic representative of the Department of Mathematics.

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Bachelor of Science in Physics and Mathematics, Dual Major

Deactivated program.

Please note: Effective Fall 2024, this program will be deactivated. Admission of new students is suspended. Students currently enrolled can complete their degree without disruption.

Academics and Curriculum

Since the physics major requires 34 hours of mathematics, and the mathematics component of the major requires 45 hours, 11 additional hours of mathematics need to be taken. 

View the Bachelor of Science in Physics and Mathematics, Dual Major program information and degree requirements in the Academic Catalog.

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University of Colorado Denver | Anschutz Denver | Anschutz Medical Campus

2024-2025 academic catalog, economics ma/applied mathematics ms dual degree, with a focus in applied statistics, introduction.

Graduate Advisors:   Economics - Andrea Velasquez, Chloe East, and Barton Willage Applied Mathematics - Click here.

The fields of mathematics and economics are inextricably linked. In economics, mathematics and statistics are used extensively in theory construction, tests of existing theories and discovery of regularities to inform new theories. Economics also gives mathematicians/statisticians new challenges, new outlets and new ideas to incorporate in mathematics. These complementarities have long been recognized and economics graduate students have always been advised to take advanced courses in statistics.

A "dual" degree means that students who complete the program earn two master's degrees: MA in economics and MS in applied mathematics. Students interested in completing the dual degree in economics and applied mathematics must apply separately to each program, meet the admission requirements of each program, and be accepted by each program. If one program accepts a student for the dual degree but the other program does not, then the student may not graduate under the dual degree program. Students may apply to both programs at the same time or apply to the economics program first, and then to the applied math program after their first semester, or vice versa. Both programs must be completed in the same semester to take advantage of the dual degree program. Further information about this program can be obtained from either the Department of Economics or the Math Department.

Click here for admissions requirements for the MA program in Economics

Click here for admissions requirements for the MS program in Applied Mathematics

There are an increasing number of economics MA students wishing to obtain graduate training and a degree in statistics. Having an MA degree in economics and an MS degree in Applied Mathematics will make a student highly employable in the job market and provide them an edge in applying for elite PhD programs.

Graduate Education Policies and Procedures apply to this program.

Program requirements.

• The requirements for the dual degree in economics and applied mathematics include completing 21 credit hours in ECON and 21 credit hours in MATH (42 total credit hours).
• Students are expected to meet all course prerequisites. ECON 5803 Mathematical Economics is a prerequisite for ECON 5073 Microeconomic Theory and ECON 5813 Econometrics I . This prerequisite requirement is waived for students who are currently admitted to the MS Applied Mathematics program.
• Students must complete all ECON and MATH credits at the graduate level (5000-level or higher).
• Students must earn a minimum grade of B- (2.7) in all courses  that apply to the degree  and must achieve a minimum cumulative GPA of 3.0. Courses taken using P+/P/F or S/U  grading cannot apply to program requirements.  No course may be taken more than twice and only one attempt will retain the credit.
• Students must complete all coursework with CU Denver faculty.

To learn more about the Student Learning Outcomes for the MS program in Applied Mathematics, please visit our website .  

To learn more about the Student Learning Outcomes for the  MA program in Economics , please visit our   website .

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Georgia Institute of Technology College of Sciences

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Sciences in the Spotlight: Georgia Tech Student Honors Celebration

Students from all six College of Sciences schools were recognized for excellence at this year's celebration.

As the academic year nears its end, a season of celebration begins. Students from across the Institute were recognized for excellence this year at the annual Student Honors Celebration on Wednesday, April 10. Several College of Sciences students were recognized.

See the full list of student awardees from across the Institute. View photos from the Student Honors Celebration — and more spring events around the College of Sciences.

Institute Awards

Provost’s academic excellence award.

Hope Hazelton Psychology Major

Zikang Leng Physics and Computer Science Dual Major

Outstanding Tutor Award

Harrison Banks Physics Major

Outstanding Learning Assistant Award

Ellia Kelso Biology Major (Pre-Med)

College of Sciences Awards

A. joyce nickelson and john c. sutherland prize.

Lance Lampert Mathematics and Physics Dual Major

The Joyce Nickelson and John C. Sutherland Undergraduate Research Award is presented by the College of Sciences to a student who has engaged in scholarship at the interface of physics and mathematics. 

Lance Lampert entered Georgia Tech as a graduate of Syosset High School, in Syosset, New York. This May, he will graduate with dual degrees in Physics and in Mathematics. Lampert has research experience in the School of Physics with both Professor Dragomir Davidovic and Professor Colin Parker, and with the GTRI Quantum Systems Division.

In summer 2022, Lampert participated in the National Science Foundation Research Experience for Undergraduates program at the University of Michigan, and he spent last summer as a researcher at the CERN in Switzerland where he worked on advancing the measurement of the gravitational acceleration of antimatter. Lampert will embark on graduate study in physics this fall, and is currently deciding between multiple offers of positions.  

Roger M. Wartell, Ph.D., and Stephen E. Brossette, M.D., Ph.D. Award for Multidisciplinary Studies in Biology, Physics, and Mathematics

Brittany Ahn Neuroscience Major, Mathematics Minor

The Roger M. Wartell and Stephen E. Brossette Award is presented to a student who has engaged in scholarship at the interface of the life sciences with physics or mathematics. 

This May, Brittany Ahn will graduate with a degree in Neuroscience and a minor in Mathematics. At Georgia Tech, Ahn engaged in research in the Computational Industrial Design Lab, the GTRI Electrical-Optical Lab, and the Mathematical Neuroscience Lab with Professor Hannah Choi. 

Last summer, Ahn participated in the NSF-Simons Center for Quantitative Biology Research Experience for Undergraduates program at Northwestern University, during which she modeled the effect of temperature on neuronal action potential dynamics. 

Ahn has served as a teaching assistant in both industrial systems engineering and the neuroscience program, a math tutor, and as a volunteer with the Atlanta Science Festival and the Special Olympics. This fall, Ahn will enroll in the doctoral program in Computational Neuroscience at Boston University.  

Robert A. Pierotti Memorial Scholarship

• Callie Goins Chemistry Major, Materials Science and Engineering Minor

Emily Melvin Atmospheric and Oceanic Sciences Major

Michelle Seeler Biology Major, Spanish Minor

The College of Sciences presents the Robert A. Pierotti Memorial Scholarship to top graduating seniors. This year there are three recipients.

Callie Goins will graduate with a degree in Chemistry and a minor in Materials Science and Engineering. Prior to attending Georgia Tech, Goins attended River Ridge High School in Woodstock, Georgia, and dual enrolled at Kennesaw State University.

For the last three years, she has conducted research in the laboratory of Professor John Reynolds, leading to her undergraduate thesis titled “Investigating IR Switching of Dioxythiophene-Based Conjugated Polymers.”

Goins has also completed summer internships with Alcon and with Parker Lord, and served as a teaching assistant in the School of Chemistry and Biochemistry. Goins appears as a co-author on peer reviewed articles in the journals Materials Advances and ACS Materials Letters and on a number of conference presentations. She is the recipient of the American Chemical Society Undergraduate Award in Organic Chemistry.

Professor Reynolds shares that “Callie has always demonstrated a tremendous enthusiasm for learning … She is a student who loves scientific discourse and takes advantage of every opportunity that she gets to share her research.” This fall, Goins will embark on graduate studies; she is currently choosing between a number of opportunities.

Emily Melvin will be among the first graduates of the new Atmospheric and Oceanic Sciences B.S. degree (AOS). Melvin’s degree will include the AOS research option, also offered through the School of Earth and Atmospheric Sciences.

Melvin hails from Marstons Mills, Massachusetts. She has served as an intern with Brookhaven National Laboratory and at the Naval Research Laboratory where she worked on simulations of the proposed flight plans to explore the marine atmospheric boundary layer. Beyond academic work, Melvin has volunteered as treasurer and marketing manager of The Dance Company at Georgia Tech, a group of Tech students who love to dance and perform.

Melvin plans to attend graduate school in atmospheric sciences and is currently selecting a program of study.

Michelle Seeler grew up in Lawrenceville, Georgia. She is graduating with a degree in Biology, a minor in Spanish, and completion of the research option. For the last two years, Seeler has worked with Professor Julia Champion on the targeted delivery of therapeutics.

In summer 2022, Seeler conducted research at the Jackson Laboratory (JAX) biomedical research institution, and she spent the summer of 2023 at Harvard Medical School. She served as the founding president of the March of Dimes at Georgia Tech, and as president of the Support Health and Education for Women initiative at Georgia Tech.

Professor Champion notes that “Michelle is an intelligent, motivated, a dedicated researcher and effective communicator, and she has an innate desire to use her talents to help patients in the future — especially women who have been underserved by current research efforts and spending.” After graduation, Michelle plans to enroll in the Ph.D. program in Biomedical Sciences at University of California, San Francisco.

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Title: a dual concept of the angle in mathematics and practice.

Abstract: We consider the angle in mathematics and arrive at a conclusion that there are two concepts on the issue. One is a descriptive geometrical one, while the other is from functional analysis. They are somewhat different, allow for different options, and both are legitimate and in use. Their difference may cause certain confusions. While the `geometrical angle' allows for different choice of units, the `functional angle' is a purely dimensionless one, being related to the angle in radians. We consider possible options to resolve the problem as it concerns the units.

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Faculty Respond to Recent Earthquake

Our Earth and Environmental Studies faculty talked to local news about the 4.8 magnitude earthquake that shook NJ and the surrounding area on Friday April 5

Posted in: Earth & Environmental Studies

Dr. Matt Gorring speaks with ABC Eyewitness News

Dr. Greg Pope spoke with NJ Spotlight News