phd in mathematical finance

Department of Mathematics

Financial mathematics.

A pioneer in its field, the Financial Mathematics Program offers 15 months of accelerated, integrated coursework that explores the deep-rooted relationship that exists between theoretical and applied mathematics and the ever-evolving world of finance. Their mission is to equip students with a solid foundation in mathematics, and in doing so provide them with practical knowledge that they can successfully apply to complicated financial models. Financial Mathematics students become leaders in their field; program alumni have gone forth to find success at companies like JP Morgan, UBS, and Goldman Sachs. Read more

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• PhD in Mathematical Finance

The PhD in Mathematical Finance is for students seeking careers in research and academia. Doctoral candidates will have a strong affinity for quantitative reasoning and the ability to connect advanced mathematical theories with real-world phenomena. They will have an interest in the creation of complex models and financial instruments as well as a passion for in-depth analysis.

Learning Outcomes

The PhD curriculum has the following learning goals. Students will:

• Demonstrate advanced knowledge of literature, theory, and methods in their field.
• Be prepared to teach at the undergraduate, master’s, and/or doctoral level in a business school or mathematics department.
• Produce original research of quality appropriate for publication in scholarly journals.

After matriculation into the PhD program, a candidate for the degree must register for and satisfactorily complete a minimum of 16 graduate-level courses at Boston University. More courses may be needed, depending on departmental requirements.

PhD in Mathematical Finance Curriculum

The curriculum for the PhD in Mathematical Finance is tailored to each incoming student, based on their academic background. Students will begin the program with a full course load to build a solid foundation in not only math and finance but also the interplay between them in the financial world. As technology plays an increasingly larger role in financial models, computer programming is also a part of the core coursework.

Once a foundation has been established, students work toward a dissertation. Working closely with a faculty advisor in a mutual area of interest, students will embark on in-depth research. It is also expected that doctoral students will perform teaching assistant duties, which may include lectures to master’s-level classes.

Course Requirements

The minimum course requirement is 16 courses (between 48 and 64 credits, depending on whether the courses are 3 or 4 credits each). Students’ course choices must be approved by the Mathematical Finance Director prior to registration each semester. The following is a typical program of courses.

• GRS EC 701 Microeconomic Theory
• GRS MA 711 Real Analysis
• GRS MA 779 Probability Theory I
• QST FE 918 Doctoral Seminar in Finance
• GRS EC 703 Advanced Microeconomic Theory
• GRS MA 776 Partial Differential Equations
• GRS MA 781 Probability Theory 2
• QST FE 920 Advanced Capital Market Theory
• GRS EC 702 Macroeconomic Theory
• GRS MA 783 Advanced Stochastic Processes
• QST MF 850 Advanced Computational Methods
• QST MF 922 Advanced Mathematical Finance
• GRS EC 704 Advanced Microeconomic Theory
• GRS MA 751 Statistical Machine Learning
• QST MF 810 FinTech Programming
• QST MF 921 Topics in Dynamic Asset Pricing

Additional Requirements

Qualifying examination.

Students must appear for a qualifying examination after completion of all coursework to demonstrate that they have:

• acquired advanced knowledge of literature and theory in their area of specialization;
• acquired advanced knowledge of research techniques; and
• developed adequate ability to craft a research proposal.

Guidelines for the examination are available from the departments. Students who do not pass either the written and/or oral comprehensive examination upon first try will be given a second opportunity to pass the exam. Should the student fail a second time, the student’s case will be reviewed by the Mathematical Finance Program Development Committee (MF PDC), which will determine if the student will be withdrawn from the PhD program. In addition, the PhD fellowship (if applicable) of any student who does not pass either the written and/or oral comprehensive examination after two attempts will be suspended the semester after the exam was attempted.

Dissertation

Following successful completion of the qualifying examination, the student will develop a research proposal for the dissertation. The final phase of the doctoral program is the completion of an approved dissertation. The dissertation must be based on an original investigation that makes a substantive contribution to knowledge and demonstrates capacity for independent, scholarly research.

Doctoral candidates must register as continuing students for DS 999 Dissertation, a 2-credit course, for each subsequent regular semester until all requirements for the degree have been completed. PhD students graduating in September are required to register for Dissertation in Summer Session II preceding graduation.

Academic Standards

Time limit for degree completion.

After matriculation into the PhD program, a candidate for the degree must meet certain milestones within specified time periods (as noted in the table below) and complete all degree requirements within six years of the date of first registration. Those who fail to meet the milestones within the specified time, or who do not complete all requirements within six years, will be reviewed by the PhD PDC and may be dismissed from the program. A Leave of Absence does not extend the six-year time limit for degree completion.

Performance Review

The Mathematical Finance Program Development Committee will review the progress of each doctoral candidate. Students must maintain a 3.30 cumulative grade point average in all courses to remain in good academic standing. Students who are not in good academic standing will be allowed one semester to correct their status. Prior to the start of the semester, the student must submit a letter to the Faculty Director (who will forward it to the PDC) explaining why the student has fallen short of the CGPA requirement and how the student plans to correct the situation. Failure to increase the CGPA to acceptable levels may result in probation or withdrawal from the program, at the discretion of the PhD Program Development Committee (PDC).

Graduation Application

Students must submit a graduation application at least seven months before the date they expect to complete degree requirements. It is the student’s responsibility to initiate the process for graduation. The application is available online and should be submitted through the Specialty Master’s & PhD Center website for graduation in January, May, or August.

If graduation must be postponed beyond the semester for which the application is submitted, students should contact the Specialty Master’s & PhD Center to defer the date. If students wish to postpone their graduation date past the six-year time limit for completion, they must formally petition the PhD Program Development Committee (PDC) for an extension. The petition, which must include the reason(s) for the extension as well as a detailed timetable for completion, is subject to departmental and PDC approval.

PhD degree requirements are complete only when copies of the dissertation have been certified as meeting the standards of Questrom School of Business and have been accepted by Mugar Memorial Library.

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The Mathematical and Computational Finance Program at Stanford University (“MCF”) is one of the oldest and most established programs of its kind in the world. Starting out in the late 1990’s as an interdisciplinary financial mathematics research group, at a time when “quants” started having a greater impact on finance in particular, the program formally admitted masters students starting in 1999. The current MCF program was relaunched under the auspices of the Institute for Computational and Mathematical Engineering in the Stanford School of Engineering in 2014 to better align with changes in industry and to broaden into areas of financial technology in particular. We are excited to remain at the cutting edge of innovation in finance while carrying on our long tradition of excellence.

The MCF Program is designed to have smaller cohorts of exceptional students with diverse interests and viewpoints, and prepare them for impactful roles in finance. We are characterized by our cutting edge curriculum marrying traditional financial mathematics and core fundamentals, with an innovative technical spirit unique to Stanford with preparation in software engineering, data science and machine learning as well as the hands-on practical coursework which is the hallmark skill-set for leaders in present day finance.

About / Departments

Finance Department | PhD Program

Phd program.

Our faculty, ranked #1 worldwide based on publications in top finance journals (ASU Finance Rankings), consists of more than 30 researchers who study all major areas of finance, making it one of the largest finance faculty in the country. Stern’s finance faculty is highly rated in terms of research output, and faculty members sit on the editorial boards of all major finance journals.

The finance department offers an exceptionally large range of courses devoted exclusively to PhD students. Apart from core PhD courses in asset pricing and corporate finance, students can choose from a range of electives such as household finance, macro-finance, and financial intermediation. PhD students also enjoy the benefits of Stern’s economics department, NYU’s economics department in the Graduate School of Arts and Science (GSAS), and the Courant Institute of Mathematics.

Graduates of Stern’s Finance PhD program have been placed at leading research institutions such as Harvard, MIT, Chicago, Stanford, Wharton, Yale, and UCLA.

Holger Mueller , Finance PhD coordinator

More information on the Finance PhD

Download the Finance PhD poster (PDF)

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The field of finance covers the economics of claims on resources. Financial economists study the valuation of these claims, the markets in which they are traded, and their use by individuals, corporations, and the society at large.

At Stanford GSB, finance faculty and doctoral students study a wide spectrum of financial topics, including the pricing and valuation of assets, the behavior of financial markets, and the structure and financial decision-making of firms and financial intermediaries.

Investigation of issues arising in these areas is pursued both through the development of theoretical models and through the empirical testing of those models. The PhD Program is designed to give students a good understanding of the methods used in theoretical modeling and empirical testing.

Preparation and Qualifications

All students are required to have, or to obtain during their first year, mathematical skills at the level of one year of calculus and one course each in linear algebra and matrix theory, theory of probability, and statistical inference.

Students are expected to have familiarity with programming and data analysis using tools and software such as MATLAB, Stata, R, Python, or Julia, or to correct any deficiencies before enrolling at Stanford.

The PhD program in finance involves a great deal of very hard work, and there is keen competition for admission. For both these reasons, the faculty is selective in offering admission. Prospective applicants must have an aptitude for quantitative work and be at ease in handling formal models. A strong background in economics and college-level mathematics is desirable.

It is particularly important to realize that a PhD in finance is not a higher-level MBA, but an advanced, academically oriented degree in financial economics, with a reflective and analytical, rather than operational, viewpoint.

Faculty in Finance

Anat r. admati, juliane begenau, jonathan b. berk, greg buchak, antonio coppola, peter m. demarzo, darrell duffie, steven grenadier, benjamin hébert, arvind krishnamurthy, hanno lustig, matteo maggiori, paul pfleiderer, joshua d. rauh, claudia robles-garcia, ilya a. strebulaev, vikrant vig, jeffrey zwiebel, emeriti faculty, robert l. joss, george g.c. parker, myron s. scholes, william f. sharpe, kenneth j. singleton, james c. van horne, recent publications in finance, make decisions with a vc mindset, behavioral responses to state income taxation of high earners: evidence from california, beyond the balance sheet model of banking: implications for bank regulation and monetary policy, recent insights by stanford business, how to: reject pitches like a venture capitalist, when the export-import bank closed up, u.s. companies saw global sales plummet, cashless: is digital currency the future of finance.

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Why Study for a Mathematical Finance PhD?

I was emailed by a reader recently asking about mathematical finance PhD programs and the benefits of such a course. If you are considering gaining a PhD in mathematical finance, this article will be of interest to you.

If you are currently near the end of your undergraduate studies or are returning to study after some time in industry, you might consider starting a PhD in mathematical finance. This is an alternative to undertaking a Masters in Financial Engineering (MFE), which is another route into a quantitative role. This article will discuss exactly what you will be studying and what you are likely to get out of a PhD program. Clearly there will be differences between studying in the US, UK or elsewhere. I personally went to grad school in the UK, but I will discuss both UK and US programs.

Mathematical finance PhD programs exist because the techniques within the derivatives pricing industry are becoming more mathematical and rigourous with each passing year. In order to develop new exotic derivatives instruments, as well as price and hedge them, the financial industry has turned to academia. This has lead to the formation of mathematical finance research groups - academics who specialise in derivatives pricing models, risk analysis and quantitative trading.

Graduate school, for those unfamiliar with it, is a very different experience to undergraduate. The idea of grad school is to teach you how to effectively research a concept without any guidance and use that research as a basis for developing your own models. Grad school really consists of a transition from the "spoon fed" undergraduate lecture system to independent study and presentation of material. The taught component of grad school is smaller and the thesis component is far larger. In the US, it is not uncommon to have two years of taught courses before embarking on a thesis (and thus finding a supervisor). In the UK, a PhD program is generally 3-4 years long with either a year of taught courses, or none, and then 3 years of research.

A good mathematical finance PhD program will make extensive use of your undergraduate knowledge and put you through graduate level courses on stochastic analysis, statistical theory and financial engineering. It will also allow you to take courses on general finance, particularly on corporate finance and derivative securities. When you finish the program you will have gained a broad knowledge in most areas of mathematical finance, while specialising in one particular area for your thesis. This "broad and deep" level of knowledge is the hallmark of a good PhD program.

Mathematical Finance research groups study a wide variety of topics. Some of the more common areas include:

• Derivative Securities Pricing/Hedging: The technical term for this is "financial engineering", as "quantitative analysis" now encompasses a wide variety of financial areas. Some of the latest research topics include sophisticated models of options including stochastic volatility models, jump-diffusion models, asymptotic methods as well as investment strategies.
• Stochastic Calculus/Analysis: This is more of a theoretical area, where the basic motivation stems from the need to solve stochastic differential equations. Research groups may look at path-dependent PDEs, functional Ito calculus, measure theory and probability theory.
• Fixed Income Modeling: Research in this area centres on effectively modelling interest rates - such as multi-factor models, multi-curve term structure models as well as interest rate derivatives such as swaptions.
• Numerical Methods: Although not always strictly related to mathematical finance, there is a vast amount of university research carried out to try and develop more effective means of solving equations numerically (i.e. on the computer!). Recent developments include GPU-based Monte Carlo solvers, more efficient matrix solvers as well as Finite Differences on GPUs. These groups will almost certainly possess substantial programming expertise.
• Market Microstructure/High-Frequency Modeling: This type of research is extremely applied and highly valued by funds engaged in this activity. You will find many academics consulting, if not contracting, for specialised hedge funds. Research areas include creating limit order market models, high frequency data statistical modelling, market stability analysis and volatility analysis.
• Credit Risk: Credit risk was a huge concern in the 2007-2008 financial crisis and many research groups are engaged in determining such "counterparty risks". Credit derivatives are still a huge business and so a lot of research goes into collateralisation of securities as well as pricing of exotic credit derivatives.

These are only a fraction of the total areas that are studied within mathematical finance. The best place to find out more about research topics is to visit the websites of all the universities which have a mathematical finance research group, which is typically found within the mathematics, statistics or economics faculty.

The benefits of undertaking a PhD program are numerous:

• Employment Prospects: A PhD program sets you apart from candidates who only possess an undergraduate or Masters level ability. By successfully defending a thesis, you have shown independence in your research ability, a skill highly valued by numerate employers. Many funds (and to a lesser extent, banks) will only hire PhD level candidates for their mathematical finance positions, so in a pragmatic sense it is often a necessary "rubber stamp". In investment banks, this is not the case so much anymore, as programming ability is generally prized more. However, in funds, it is still often a requirement. Upon being hired you will likely be at "associate" level rather than "analyst" level, which is common of undergraduates. Your starting salary will reflect this too.
• Knowledge: You will spend a large amount of time becoming familiar with many aspects of mathematical finance and derivatives theory. This will give you a holistic view into the industry and a more transferable skill set than an undergraduate degree as you progress up the career ladder. In addition, you will have a great deal of time to learn how to program models effectively (without the day-to-day pressure to get something implemented any way possible!), so by the time you're employed, you will be "ahead of the game" and will know best practices. This aspect is down to you, however!
• Intellectual Prospects: You are far more likely to gain a position at a fund after completing a PhD than without one. Funds are often better environments to work in. There is usually less stress and a more relaxed "collegiate" environment. Compare this to working on a noisy trading floor, where research might be harder to carry out and be perceived as less important.

I would highly recommend a mathematical finance PhD, so long as you are extremely sure that a career in quantitative finance is for you. If you are still unsure of your potential career options, then a more general mathematics, physics or engineering PhD might be a better choice.

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PhD Program in Finance

2023-24 curriculum outline.

The MIT Sloan Finance Group offers a doctoral program specialization in Finance for students interested in research careers in academic finance. The requirements of the program may be loosely divided into five categories: coursework, the Finance Seminar, the general examination, the research paper, and the dissertation. Attendance at the weekly Finance Seminar is mandatory in the second year and beyond and is encouraged in the first year.  During the first two years, students are engaged primarily in coursework, taking both required and elective courses in preparation for their general examination at the end of the second year.  Students are required to complete a research paper by the end of their fifth semester, present it in front of the faculty committee and receive a passing grade.  After that, students are required to find a formal thesis advisor and form a thesis committee by the end of their eighth semester. The Thesis Committee should consist of at least one tenured faculty from the MIT Sloan Finance Group.

Required Courses

The following set of required courses is designed to furnish each student with a sound and well-rounded understanding of the theoretical and empirical foundations of finance, as well as the tools necessary to make original contributions in each of these areas. Finance PhD courses (15.470, 15.471, 15.472, 15.473, 15.474) in which the student does not receive a grade of B or higher must be retaken.

First Year - Summer

Math Camp begins on the second Monday in August. 

First Year - Fall Semester

14.121/14.122 Micro Theory I/II

14.451/14.452 Macro Theory I/II ( strongly recommended)

14.380/14.381 — Statistics/Applied Econometrics

15.470 — Asset Pricing

First Year - Spring Semester

14.123/14.124 Micro Theory III/IV

14.453/14.454 Macro Theory III/IV (strongly recommended)

14.382 – Econometrics

15.471 – Corporate Finance

Second Year - Fall Semester

15.472 — Advanced Asset Pricing

  14.384 — Time-Series Analysis or  14.385 — Nonlinear Econometric Analysis  (Enrolled students receive a one-semester waiver from attending the Finance Seminar due to a scheduling conflict)

15.475 — Current Research in Financial Economics

Second Year - Spring Semester

15.473 — Advanced Corporate Finance

 15.474 — Current Topics in Finance (strongly encouraged to take multiple times)

15.475 — Current Research in Financial Economics

Recommended Elective Courses

Beyond these required courses, students are expected to enroll in elective courses determined by their primary area of interest. There are two informal “tracks” in Financial Economics: Corporate Finance and Asset Pricing. Recommended electives are designed to deepen the student's grasp of material that will be central to the writing of his/her dissertation. Students also have the opportunity to take courses at Harvard University. There is no formal requirement to select one track or another, and students are free to take any of the electives.

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• Mathematical and Computational Finance @ Oxford
• Study with us

DPhil (PhD) studies in Mathematical Finance @ Oxford

The Mathematical and Computational Finance Group (MCFG) at Oxford is one of the largest and most dynamic research environments in mathematical finance in the world.

We combine core mathematical expertise with interdisciplinary approach. We foster lively interactions between researchers coming from different backgrounds and a truly impressive seminar programme, all this within one of the world's top universities, singular through its tradition and unique environment.

If you are passionate about mathematics and research and want to pursue a DPhil in Financial Mathematics, Oxford simply offers one of the best and most exciting places to do it!

 Research Topic and Supervisor Allocation

We welcome students with their own particular ideas of research topic as well as students with a broad interest in the field of Mathematical Finance. You have an opportunity to tell us about your research passions, and indicate potential supervisors, in your application form. This will be followed up during the interview.

In light of this, if you are offered a place, an appropriate supervisor will be proposed prior to your arrival in Oxford. However, there can be some flexibility over this once you arrive.  Keeping with the Oxford tradition, we offer our students independence and respect as early researchers, and always aim to match students with the most appropriate supervisors.

Outstanding students with a strong background in analysis, probability and data science are welcome to apply for our DPhil program. Each year we receive a large number of excellent applications. The selection process is extremely competitive and we can only admit a handful of candidates each year.

In order to apply for DPhil studies in Mathematical & Computational Finance, please indicate your interest in Mathematical and Computational Finance on your application form. Selected applicants will be invited for an interview -- either in person or by video call.

For general information on DPhil please consult our  Doctor of Philosophy (DPhil) admissions pages .

For the CDT Mathematics of Random Systems please consult our  the CDT website .

Or please contact  @email .

Funding for DPhil students is available from a variety of sources. Please note that some funding opportunities have deadlines: it is advised to apply before the deadline in order to maximise your chances of receiving funding.

Funding is also available through the  Centre for Doctoral Training in Mathematics of Random Systems . To apply for this program please How to Apply .

Email:  @email Phone:  +44 (0)1865 615234

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DPhil Graduates

Mathematics (PHD) – Financial Mathematics Track

Program at a glance.

• In State Tuition
• Out of State Tuition

Learn more about the cost to attend UCF.

The Financial Mathematics track in the Mathematics PhD program is designed to prepare students for research and leadership positions in industry, government, non-governmental organizations, and academia requiring employment of financial mathematics.

The Mathematics PhD program consists of at least 75 credit hours of course work beyond the bachelor's degree, of which a minimum of 48 hours of formal course work, exclusive of independent study, are required. The program requires 36 credit hours of core courses and 15 credit hours of dissertation research (7980).

Total Credit Hours Required: 75 Credit Hours Minimum beyond the Bachelor's Degree

Application Deadlines

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Enter your information below to receive more information about the Mathematics (PHD) – Financial Mathematics Track program offered at UCF.

Track Prerequisites

Bachelor's degree in related field.

Students entering the graduate program with regular status are assumed to have a working knowledge of undergraduate calculus, differential equations, linear algebra (or matrix theory), boundary value problems, statistics, computer programming, and maturity in the language of advanced calculus (at the level of MAA 4226).

Degree Requirements

Required courses.

• All students are required to complete the following courses with grade of "B" or better.
• MAA5237 - Mathematical Analysis (3)
• MAS5145 - Advanced Linear Algebra and Matrix Theory (3)
• MAP5641 - Financial Mathematics I (3)
• MAP6642 - Financial Mathematics II (3)
• MAP5612 - Computational Methods for Financial Mathematics I (3)
• MAP6616 - Computational Methods for Financial Mathematics II (3)
• MAP6646 - Risk Management for Financial Mathematics (3)
• MAP5606 - Differential Equations for Financial Mathematics (3)
• MAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3)
• MAP6207 - Optimization Theory (3)
• STA6857 - Applied Time Series Analysis (3)
• MAP5931 - Proseminar for Financial Mathematics (1)
• MAP5933 - Seminar in Financial Mathematics (2)
• The remaining credit hours consist of additional dissertation research (7980 or 7919), at least 15 credit hours of regular classroom elective courses, and at most 12 credit hours of independent study or independent directed research. Students who pass the qualifying examination may substitute some of the core courses with the approval of the adviser and the graduate program director.

Elective Courses

• Earn at least 24 credits from the following types of courses: Elective courses require the approval of the adviser and the graduate program director; up to 12 credit hours of elective courses may be taken outside the department. At least one-half of the program courses must be taken at the 6000 level. At least 12 hours of elective course work must be formal course work, exclusive of independent study. Electives are chosen in consultation with the student's advisory committee and may be chosen from the suggested options: Discrete Mathematics, General Applied Mathematics, Mathematical Computer Tomography, Image Processing and Computer Graphics, Mathematical Finance, Mathematical Physics, Pure Mathematics, Data Science, and Mathematical Statistics. A list of elective course options can be obtained from the graduate program director. Courses that are taken outside the Mathematics department must be approved by both the adviser and graduate program director. These courses are selected in consultation with the student's advisory committee.

Dissertation

• Earn at least 15 credits from the following types of courses: MAP 7980 - Dissertation Research 15 Credit Hours (minimum) After passing the candidacy examination and meeting the other requirements that are required for admission to candidacy, the student can register for Doctoral Dissertation (MAP 7980). A minimum of 15 Doctoral Dissertation credit hours are required for the degree.

Examinations

Qualifying examination.

• The qualifying/comprehensive examination is based on the core course work. To continue in the PhD program, students must pass the examination at the PhD level. Two attempts are permitted. The examination will be administered twice a year: one in the Fall semester and the other in the Spring semester. To take the examination, students must have earned a "B" or better in each core course, must have a minimum grade point average of 3.0 (out of 4.0) in the program, or must obtain permission from the graduate program director. Students will normally take the examination after the first year and are expected to have passed it by the end of the second year of study, unless a written request for a postponement has been approved by the Graduate Committee at least two months before the examination date. The student must pass the Qualifying Examination in at most two attempts. It is strongly recommended that the student select a dissertation adviser by the completion of 18 credit hours of course work, and it is strongly recommended that the student works with the dissertation adviser to form a dissertation committee within two semesters of passing the Qualifying Examination.

Candidacy Examination

• The Candidacy Examination consists of a written examination based on the materials from two selected two-semester sequence courses taken by the students. A committee formed or selected by the Graduate Committee or the graduate program director is responsible for preparing and grading the written examinations. Each sequence that is selected for the candidacy examination must be approved by the dissertation adviser, the dissertation committee, and the graduate program director. Students in the Financial Mathematics Track will ordinarily select one of the sequences for their candidacy examination to be MAP 5641/MAP6642 Financial Mathematics I and II, and MAP5612/MAP6616 Computational Methods for Financial Mathematics I and II. The Candidacy Examination can be attempted after passing the qualifying examination. The Candidacy Examination must be completed within three years after passing the qualifying examination. A student must successfully pass the Candidacy Examination within at most two attempts.

Admission to Candidacy

• The following are required to be admitted to candidacy and enroll in dissertation hours: Completion of all course work, except for dissertation hours. Successful completion of the candidacy examination. The dissertation advisory committee is formed, consisting of approved graduate faculty and graduate faculty scholars. Submittal of an approved program of study.

Dissertation Proposal Examination

• After passing the candidacy examination, the student will prepare a dissertation proposal and orally present it to the dissertation advisory committee for approval. The proposal will include a description of the research performed to date and an agenda for the research planned to be completed for the dissertation. In addition to standards of correctness, indicating a suitable level of mastery of the material of the area of the dissertation, and suitability of the proposed dissertation topic, the presentation must meet current standards for professional presentations within the discipline of mathematics. For the successful completion of the Dissertation Proposal Examination, the presentation must be judged as passing the requirements for the examination by the majority of the dissertation committee. This exam must be passed within 18 months of passing the candidacy examination and not later than the end of the sixth year of graduate study. A candidate must pass this examination within at most two attempts.

Dissertation Defense

• Upon completion of a student's research, the student's committee schedules an oral defense of the dissertation. Most students complete the program within five years after obtaining their bachelor's degree. Students are expected to complete the dissertation in no more than seven years from the date of admission to the program.

Independent Learning

• The required 15 credit hours of dissertation will provide ample opportunities for students to gain the independent learning experience through studying published research papers and deriving, on their own, new and meaningful research results.

Grand Total Credits: 75

Application requirements, financial information.

Graduate students may receive financial assistance through fellowships, assistantships, tuition support, or loans. For more information, see the College of Graduate Studies Funding website, which describes the types of financial assistance available at UCF and provides general guidance in planning your graduate finances. The Financial Information section of the Graduate Catalog is another key resource.

Fellowship Information

Fellowships are awarded based on academic merit to highly qualified students. They are paid to students through the Office of Student Financial Assistance, based on instructions provided by the College of Graduate Studies. Fellowships are given to support a student's graduate study and do not have a work obligation. For more information, see UCF Graduate Fellowships, which includes descriptions of university fellowships and what you should do to be considered for a fellowship.

The department offers over 20 Graduate Teaching Assistantships every year on a competitive basis. A few Graduate Research Assistantships are also available for qualified students.

Financial Mathematics Graduate Programs in America

1-25 of 68 results

MIT Sloan School of Management

Cambridge, MA •

Massachusetts Institute of Technology •

Graduate School

• • Rating 4.9 out of 5   10 reviews

Master's Student: I am an incoming MBA student to MIT Sloan. The application and enrollment process has been incredibly informative. I’ve been able to network with numerous current students and have worked on mapping out my future career post-MBA. I am excited for my 2 years at MIT Sloan! ... Read 10 reviews

Massachusetts Institute of Technology ,

Graduate School ,

CAMBRIDGE, MA ,

10 Niche users give it an average review of 4.9 stars.

Featured Review: Master's Student says I am an incoming MBA student to MIT Sloan. The application and enrollment process has been incredibly informative. I’ve been able to network with numerous current students and have worked on mapping... .

Read 10 reviews.

Princeton University

Princeton, NJ •

• • Rating 4.33 out of 5   3 reviews

Master's Student: The best part of the Princeton University mechanical engineering graduate degree is the excellent faculty that teach the courses. They are incredibly knowledgeable and also very willing to help students in office hours or in sponsorship of projects. The worst part of the Princeton University mechanical engineering graduate degree is the lack of structure for the graduate research program which can leave you feeling unsure on the direction of your research. ... Read 3 reviews

PRINCETON, NJ ,

3 Niche users give it an average review of 4.3 stars.

Featured Review: Master's Student says The best part of the Princeton University mechanical engineering graduate degree is the excellent faculty that teach the courses. They are incredibly knowledgeable and also very willing to help... .

Read 3 reviews.

Owen Graduate School of Management

Nashville, TN •

Vanderbilt University •

• • Rating 4.4 out of 5   5 reviews

Master's Student: I attend my first semester in the fall of 2024. My experience so far has been amazing. I cannot wait until I start my experience. ... Read 5 reviews

Vanderbilt University ,

NASHVILLE, TN ,

5 Niche users give it an average review of 4.4 stars.

Featured Review: Master's Student says I attend my first semester in the fall of 2024. My experience so far has been amazing. I cannot wait until I start my experience. .

Read 5 reviews.

Jack Welch College of Business and Technology

Sacred Heart University •

Graduate School •

FAIRFIELD, CT

• • Rating 5 out of 5   2

University of North Texas

• • Rating 4.61 out of 5   129

Lehigh University

BETHLEHEM, PA

• • Rating 4.42 out of 5   19

Olin Business School

St. Louis, MO •

Washington University in St. Louis •

• • Rating 4 out of 5   7 reviews

Master's Student: The enrolment process was an absolute pleasure. Being able to sit in on classes and interact with faculty and students was a fantastic opportunity. It gave me a real feel for the academic dynamic and the supportive community. This firsthand experience greatly influenced my decision, and I'm eagerly looking forward to becoming a part of the institution. ... Read 7 reviews

Washington University in St. Louis ,

ST. LOUIS, MO ,

7 Niche users give it an average review of 4 stars.

Featured Review: Master's Student says The enrolment process was an absolute pleasure. Being able to sit in on classes and interact with faculty and students was a fantastic opportunity. It gave me a real feel for the academic dynamic and... .

Read 7 reviews.

Chicago Booth School of Business

Chicago, IL •

University of Chicago •

• • Rating 4.86 out of 5   14 reviews

Master's Student: My academic experience at the Chicago Booth Executive MBA program has been exceptionally enriching. The program's rigorous curriculum, combined with interactive class discussions and real-world case studies, has provided invaluable insights into business strategy and leadership. The best part has been the opportunity to learn from distinguished faculty and collaborate with talented peers from diverse backgrounds. As for the worst parts, I can honestly say there haven't been any significant drawbacks to my experience. ... Read 14 reviews

University of Chicago ,

CHICAGO, IL ,

14 Niche users give it an average review of 4.9 stars.

Featured Review: Master's Student says My academic experience at the Chicago Booth Executive MBA program has been exceptionally enriching. The program's rigorous curriculum, combined with interactive class discussions and real-world case... .

Read 14 reviews.

Marshall School of Business

Los Angeles, CA •

University of Southern California •

• • Rating 4.71 out of 5   17 reviews

Current Master's student: Marshall is a fantastic business program. So far, my academic experience has been nothing short of fantastic. I have never enjoyed school before, but almost every class I have learned new, applicable, and incredibly helpful techniques that I apply in my job every day. Most of the professors are very helpful, and passionate about their subjects. Marshall has clubs for almost every industry, so depending on your industry of interest, Marshall has clubs to prepare you for interviews and get you great exposure, and they're a great way to network as well. If your industry is not represented, you have the opportunity to create one. Marshall is still relatively underrepresented in minority categories like women and people of color, but from my understanding, they are working to improve those numbers. ... Read 17 reviews

University of Southern California ,

LOS ANGELES, CA ,

17 Niche users give it an average review of 4.7 stars.

Featured Review: Current Master's student says Marshall is a fantastic business program. So far, my academic experience has been nothing short of fantastic. I have never enjoyed school before, but almost every class I have learned new,... Marshall has clubs for almost every industry, so depending on your industry of interest, Marshall has clubs to prepare you for interviews and get you great exposure, and they're a great way to... Marshall is still relatively underrepresented in minority categories like women and people of color, but from my understanding, they are working to improve those numbers. .

Read 17 reviews.

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Whiting School of Engineering

Baltimore, MD •

Johns Hopkins University •

• • Rating 4.83 out of 5   12 reviews

Master's Student: Just starting now but the onboarding process is great! The student orientation was very helpful and the school has an amazing network. ... Read 12 reviews

Johns Hopkins University ,

BALTIMORE, MD ,

12 Niche users give it an average review of 4.8 stars.

Featured Review: Master's Student says Just starting now but the onboarding process is great! The student orientation was very helpful and the school has an amazing network. .

Read 12 reviews.

The Graduate School of Arts & Sciences - University of Virginia

Charlottesville, VA •

University of Virginia •

• • Rating 4 out of 5   1 review

Alum: Very good in some areas, excellent in other areas, many academic choices available in all areas of study ... Read 1 review

University of Virginia ,

CHARLOTTESVILLE, VA ,

1 Niche users give it an average review of 4 stars.

Featured Review: Alum says Very good in some areas, excellent in other areas, many academic choices available in all areas of study .

Read 1 reviews.

College of Sciences - Georgia Institute of Technology

Atlanta, GA •

Georgia Institute of Technology •

• • Rating 5 out of 5   1 review

Other: Georgia Tech is among the top colleges you can attend. My journey there had its highs and lows, but looking back, every experience contributed significantly to my growth. A piece of advice I'd offer to newcomers is to prioritize building friendships early on. One regret I have as I reflect on my year is not connecting with more people. I initially thought I should always work independently, but that was a misstep in my academic journey. Remember, it's essential to strike a balance between learning and having fun. ... Read 1 review

Georgia Institute of Technology ,

ATLANTA, GA ,

1 Niche users give it an average review of 5 stars.

Featured Review: Other says Georgia Tech is among the top colleges you can attend. My journey there had its highs and lows, but looking back, every experience contributed significantly to my growth. A piece of advice I'd offer... .

Haas School of Business

Berkeley, CA •

University of California - Berkeley •

• • Rating 5 out of 5   3 reviews

Master's Student: I am a new EWMBA admit at Haas and so far the experience has been fantastic! It's a close-knit community of intellectual, humble, and talented working professionals. The entire team of program directors, admissions officers, etc. are SO willing to help! ... Read 3 reviews

Blue checkmark.

University of California - Berkeley ,

BERKELEY, CA ,

3 Niche users give it an average review of 5 stars.

Featured Review: Master's Student says I am a new EWMBA admit at Haas and so far the experience has been fantastic! It's a close-knit community of intellectual, humble, and talented working professionals. The entire team of program directors, admissions officers, etc. are SO willing to help! .

Tandon School of Engineering

Brooklyn, NY •

New York University •

• • Rating 4.73 out of 5   15 reviews

Master's Student: As a bioinformatics master's student at the NYU Tandon School of Engineering, I've had the opportunity to explore the fascinating intersection of biology and computer science. The program has provided a robust curriculum, covering topics such as proteomics, transcriptomics, NGS, and data analysis, which have equipped me with the skills needed to analyze and interpret complex biological data. The faculty at Tandon are experienced and supportive, and I've had the chance to collaborate with fellow students on exciting research projects. The interdisciplinary nature of bioinformatics has allowed me to gain insights into cutting-edge technologies and methodologies that are shaping the future of the field. Overall, my experience at NYU Tandon has been enriching, and I look forward to applying the knowledge and skills acquired during my master's program to contribute meaningfully to the field of bioinformatics. ... Read 15 reviews

New York University ,

BROOKLYN, NY ,

15 Niche users give it an average review of 4.7 stars.

Featured Review: Master's Student says As a bioinformatics master's student at the NYU Tandon School of Engineering, I've had the opportunity to explore the fascinating intersection of biology and computer science. The program has... The faculty at Tandon are experienced and supportive, and I've had the chance to collaborate with fellow students on exciting research projects. The interdisciplinary nature of bioinformatics has... Overall, my experience at NYU Tandon has been enriching, and I look forward to applying the knowledge and skills acquired during my master's program to contribute meaningfully to the field of... .

Read 15 reviews.

Leonard N. Stern School of Business

New York, NY •

• • Rating 4.82 out of 5   28 reviews

Master's Student: As a part-time MBA candidate at NYU Stern, I'm deeply impressed by the program's blend of academic rigor and practical application. The faculty, industry leaders in their own right, provide invaluable insights, fostering a rich learning environment. The diversity among my peers enhances our discussions, offering varied perspectives on business challenges. Stern's location in NYC is ideal for networking and accessing career opportunities, which is crucial for a working professional like me. The flexibility of evening and weekend classes allows me to balance my professional and academic commitments effectively. Stern equips students with advanced business knowledge and fosters personal and professional growth, making it an exceptional choice for anyone aspiring to excel in the business world. ... Read 28 reviews

NEW YORK, NY ,

28 Niche users give it an average review of 4.8 stars.

Featured Review: Master's Student says As a part-time MBA candidate at NYU Stern, I'm deeply impressed by the program's blend of academic rigor and practical application. The faculty, industry leaders in their own right, provide... .

Read 28 reviews.

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Carroll School of Management

Chestnut Hill, MA •

Boston College •

• • Rating 5 out of 5   2 reviews

Master's Student: I am currently enrolled in the part time, professional evening MBA program. So far it has brought me to communicate with like minded individuals and the professors truly want to see you succeed so they will go out of their way to connect with you and help you. ... Read 2 reviews

Boston College ,

CHESTNUT HILL, MA ,

2 Niche users give it an average review of 5 stars.

Featured Review: Master's Student says I am currently enrolled in the part time, professional evening MBA program. So far it has brought me to communicate with like minded individuals and the professors truly want to see you succeed so... .

Read 2 reviews.

College of Natural Sciences

Austin, TX •

University of Texas - Austin •

University of Texas - Austin ,

AUSTIN, TX ,

Questrom School of Business

Boston, MA •

Boston University •

• • Rating 4.29 out of 5   7 reviews

Master's Student: Boston University's MBA program transformed me. Faculty, experts in their fields, nurtured my learning. A diverse student body broadened my perspective. Experiential learning honed skills and purpose. BU's strong alumni network opened doors. The sense of community is invaluable. BU has equipped me for success and instilled a passion for growth. Grateful for this transformative journey. ... Read 7 reviews

Boston University ,

BOSTON, MA ,

7 Niche users give it an average review of 4.3 stars.

Featured Review: Master's Student says Boston University's MBA program transformed me. Faculty, experts in their fields, nurtured my learning. A diverse student body broadened my perspective. Experiential learning honed skills and... .

College of Liberal Arts & Sciences - University of Illinois

Urbana, IL •

University of Illinois Urbana-Champaign •

University of Illinois Urbana-Champaign ,

URBANA, IL ,

Lally School of Management

Rensselaer Polytechnic Institute •

Rensselaer Polytechnic Institute ,

College of Arts and Sciences - University of Miami

Coral Gables, FL •

University of Miami •

• • Rating 4.67 out of 5   6 reviews

Master's Student: I am in graduate school and needed something online but also wanted something that was going to challenge me and provide me with a step further than my undergrad school provided. I compared many MPA programs and chose the University of Miami because the program was so similar to the in-person MPA program, taught by the same professors, and included the same courses. While entirely online, I have come to know my fellow graduate students and come to know the faculty in each of the courses I have taken. I'm currently half-way through the program and cannot wait to complete this degree! ... Read 6 reviews

University of Miami ,

CORAL GABLES, FL ,

6 Niche users give it an average review of 4.7 stars.

Featured Review: Master's Student says I am in graduate school and needed something online but also wanted something that was going to challenge me and provide me with a step further than my undergrad school provided. I compared many MPA... .

Read 6 reviews.

Dedman College of Humanities and Sciences

Dallas, TX •

Southern Methodist University •

Southern Methodist University ,

DALLAS, TX ,

Tulane University School of Science and Engineering

New Orleans, LA •

Tulane University •

Master's Student: I am currently in the materials science and engineering 4+1 program which will allow me to earn my MS in one year instead of two. There are some really amazing professors here despite the department being pretty small. I can think of only one professor that made the class unnecessarily difficult. There are opportunities for research and extracurriculars too. ... Read 3 reviews

Tulane University ,

NEW ORLEANS, LA ,

Featured Review: Master's Student says I am currently in the materials science and engineering 4+1 program which will allow me to earn my MS in one year instead of two. There are some really amazing professors here despite the department... .

Babson College

Babson Park, MA •

• • Rating 4.54 out of 5   13 reviews

Master's Student: So far my academic experience has been good at Babson college. The instructors are available and willing to go out of their way to answer any questions you have and make sure that you are comfortable with the classroom content. They will also share resources with you and introduce you to the people that you need to meet your goals. ... Read 13 reviews

BABSON PARK, MA ,

13 Niche users give it an average review of 4.5 stars.

Featured Review: Master's Student says So far my academic experience has been good at Babson college. The instructors are available and willing to go out of their way to answer any questions you have and make sure that you are comfortable... .

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College of Science and Engineering - University of Minnesota Twin Cities

Minneapolis, MN •

University of Minnesota Twin Cities •

• • Rating 4 out of 5   2 reviews

Doctoral Student: I started graduate school at UMN during the height of the COVID pandemic. Despite not being able to go to classes in person or get into the lab, the UMN community has been very inclusive and I have felt very supported and welcome. I would recommend UMN to any STEM graduate student because of this great community. ... Read 2 reviews

University of Minnesota Twin Cities ,

MINNEAPOLIS, MN ,

2 Niche users give it an average review of 4 stars.

Featured Review: Doctoral Student says I started graduate school at UMN during the height of the COVID pandemic. Despite not being able to go to classes in person or get into the lab, the UMN community has been very inclusive and I have... .

The Ohio State University College of Arts and Sciences

Columbus, OH •

The Ohio State University •

Graduate Student: Not a bad place, good reputation but the College is cutting funds every year. Cutting funds within sociales sciences and humanities has been a problem that the college face every year. ... Read 1 review

The Ohio State University ,

COLUMBUS, OH ,

Featured Review: Graduate Student says Not a bad place, good reputation but the College is cutting funds every year. Cutting funds within sociales sciences and humanities has been a problem that the college face every year. .

NC State College of Sciences

Raleigh, NC •

North Carolina State University •

North Carolina State University ,

RALEIGH, NC ,

Charles V. Schaefer, Jr. School of Engineering & Science

Hoboken, NJ •

Stevens Institute of Technology •

Stevens Institute of Technology ,

HOBOKEN, NJ ,

Sacred Heart University

• • Rating 4.4 out of 5   45

Bentley University McCallum Graduate School of Business

WALTHAM, MA

• • Rating 4.71 out of 5   21

Illinois Institute of Technology

CHICAGO, IL

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Mathematical Finance

A rapidly growing area of mathematical finance is quantitative behavioral finance. The high-tech boom and bust of the late 1990s followed by the housing and financial upheavals of 2008 have made a convincing case for the necessity of adopting broader assumptions in finance. These include considering motivations beyond valuation considerations, and an asset base that is not infinite. The asset flow system of ordinary differential equations developed by Prof. Caginalp and collaborators in the 1990s has been an active part of this research at Pitt. These equations are being used to understand the dynamics and stability. A related component involves large scale studies (e.g. over 100,000 data points) of market data that can be used to deduce underlying motivational effects. By extracting the valuation, recent studies have shown that momentum trading (buying on uptrend) plays a strong role, as do money supply, changes in volume and several other variable. Furthermore, with suitable modeling, one can deduce nonlinear effects. In particular, a recent uptrend that is too steep has a negative influence on prices. These topics have been the focus of the PhD thesis of Mark DeSantis at the University of Pittsburgh.

View a list of papers »

Alternatively, use our A–Z index

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Discover more about postgraduate research

PhD Financial Mathematics / Overview

Year of entry: 2024

• View full page

The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent).

Other combinations of qualifications and research or work experience may also be considered. Please contact the admissions team to check.

Full entry requirements

Apply online

In your application you’ll need to include:

• The name of this programme
• Your research project title (i.e. the advertised project name or proposed project name) or area of research
• Your proposed supervisor’s name
• If you already have funding or you wish to be considered for any of the available funding
• A supporting statement (see 'Advice to Applicants for what to include)
• Details of your previous university level study
• Names and contact details of your two referees.

Programme options

Programme description.

Opportunities for PhD research are available in a range of Financial Mathematics research topics or Mathemathics research areas . For more information, please see advice on choosing a project or find out more about specific projects . Please contact the relevant individual members of staff for information about a specific project, or get in touch with the  Postgraduate Admissions Tutor .

Students may enter our graduate programme in Mathematical Finance by initially taking our taught M.Sc. course over 1 year. This, subject to satisfactory progress, can lead to admission to the PhD programme.

For entry in the academic year beginning September 2024, the tuition fees are as follows:

• PhD (full-time) UK students (per annum): Band A £4,786; Band B £7,000; Band C £10,000; Band D £14,500; Band E £24,500 International, including EU, students (per annum): Band A £28,000; Band B £30,000; Band C £35,500; Band D £43,000; Band E £57,000
• PhD (part-time) UK students (per annum): Band A £2393; Band B £3,500; Band C £5,000; Band D £7,250; Band E 12,250 International, including EU, students (per annum): Band A £14,000; Band B £15,000; Band C £17,750; Band D £21,500; Band E £28,500

Further information for EU students can be found on our dedicated EU page.

The programme fee will vary depending on the cost of running the project. Fees quoted are fully inclusive and, therefore, you will not be required to pay any additional bench fees or administration costs.

All fees for entry will be subject to yearly review and incremental rises per annum are also likely over the duration of the course for Home students (fees are typically fixed for International students, for the course duration at the year of entry). For general fees information please visit the postgraduate fees page .

Always contact the Admissions team if you are unsure which fees apply to your project.

Scholarships/sponsorships

There are a range of scholarships, studentships and awards at university, faculty and department level to support both UK and overseas postgraduate researchers.

To be considered for many of our scholarships, you’ll need to be nominated by your proposed supervisor. Therefore, we’d highly recommend you discuss potential sources of funding with your supervisor first, so they can advise on your suitability and make sure you meet nomination deadlines.

For more information about our scholarships, visit our funding page or use our funding database to search for scholarships, studentships and awards you may be eligible for.

Contact details

Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality.  Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .

Programmes in related subject areas

Use the links below to view lists of programmes in related subject areas.

• Mathematics

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You can find regulations and policies relating to student life at The University of Manchester, including our Degree Regulations and Complaints Procedure, on our regulations website .

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MPhil/PhD Mathematics

• Graduate research
• Department of Mathematics
• Application code G1ZM
• Starting 2024
• Home full-time: Open
• Overseas full-time: Open
• Location: Houghton Street, London

This programme offers the chance to undertake a substantial piece of work that is worthy of publication and which makes an original contribution to the field of mathematics within our four broad disciplines – discrete mathematics and algorithms, financial mathematics and control theory, game theory, and operations research. You will begin on the MPhil, and will need to meet certain requirements to be upgraded to PhD status.

You have a plethora of topics to choose from including combinatorics, combinatorial optimisation, computational learning theory, control theory, financial mathematics, game theory, graph theory, integer programming, mechanism design, polyhedral combinatorics, probabilistic analysis, theory of computation and algorithms, and in the applications of mathematics in areas such as inspections, network optimisation, telecommunications, transportation, and economics.

Over the course of the years, the Department organises a number of personal development workshops for PhD students, designed to provide tailored support for specific areas of interest, such as careers, impact, and final year processes. Crucially, we have close ties with other departments at LSE, such as Statistics, Finance, Economics and Management, and we are an integral part of the mathematical community of the University of London.

All research students in the Department are provided with some funding each year to encourage and support their research activities, such as conference attendance and purchasing books and technology. Additional research funds are also available, upon application.

Programme details

For more information about tuition fees and entry requirements, see the fees and funding and assessing your application sections.

Entry requirements

Minimum entry requirements for mphil/phd mathematics.

Merit in a taught master's degree (or equivalent) in a related discipline and a 2:1 degree or equivalent in mathematics. 

Competition for places at the School is high. This means that even if you meet our minimum entry requirement, this does not guarantee you an offer of admission. 

If you have studied or are studying outside of the UK then have a look at our  Information for International Students  to find out the entry requirements that apply to you.

LSE values diversity and strives to promote equality at all levels. We strongly encourage applications from women, ethnic minorities, and members of other groups under-represented in higher education.

Assessing your application

Making an application.

We carefully consider each application on an individual basis, taking into account all the information presented on your application form, including your:

- academic achievement (including existing and pending qualifications) - CV - statement of academic purpose - outline research proposal - sample of written work - references

In addition to the general guidelines on application documents available  here , you can find specific guidelines for some of the application documents required as part of your application for the MPhil/PhD Mathematics programme below.  

Academic Achievement Provide detailed transcripts, with individual marks for all courses on your undergraduate and postgraduate degree programmes you have completed, and any available/provisional marks obtained in your current degree programme.

CV - Provide details of your education history. - Provide details of any employment history or other professional experience, including internships or volunteering activities. - Mention any relevant prior research experience, such as thesis work, research projects.    - If relevant, mention any career breaks or career changes, for example due to caring responsibilities.

Statement of Academic Purpose (1 page) - Explain your motivation for doing a PhD. - Explain your current career goals and aspirations and clarify how the PhD programme might help you realise them.  

Outline Research Proposal (1-2 pages) Many applicants will have little or no prior experience of research and therefore we do not expect a fully developed research proposal. The following is a recommendation of what to address, in a concise manner, in the research proposal. - Explain which overall research area you are interested in and explain why.  - Provide an example of one or two research papers that you have read or open problems you have heard about (in your proposed research area) and explain why you found them interesting. - Clarify who you see as potential supervisors and explain why.  - Explain how your training and skills are suitable for conducting research in your area of interest. For example, provide specific examples of related courses you have taken, and any research, internship, or work experiences that are relevant to your research area of interest. - If applicable, describe how any dissertation work from your BSc or MSc is relevant to your planned PhD research (be aware that this research will most likely be different).

Sample of Written Work (at least 5 pages) Submit something that showcases your mathematical writing. This could for example be a thesis, a project report, or some detailed exercise solutions. We like to see a writing sample that contains both mathematical details and plain text in which you discuss/interpret/explain the mathematical results. You can submit more than one writing sample if you only have short pieces of written work.

References You will need to nominate two referees. Academic referees are preferred, i.e., people who have taught you at university level.

If you can find a referee who can specifically comment on your research potential and your academic background in your chosen research area, that would be helpful. If you have any previous research experience, you could ask supervisors/project partners for a reference letter. An academic reference from your current degree programme where you already took exams are usually most helpful. If you have not taken any exams in your current programme yet, you can also ask for reference letters from previous degrees.

The referees will be asked to provide a reference letter and answer a selection of multiple-choice questions in which they will need to provide an assessment of your academic performance/potential etc. and research potential. --------------

Completed applications are sent to the Department after they are processed by the Graduate Admissions Office. In the Department, the numbers and quality of competing applications and the availability of an appropriate supervisor are considered. If your application is shortlisted for consideration, an interview will be arranged with the appropriate members of staff by telephone or video conferencing software. Once all interviews have been conducted, the Department will decide on who to accept and who to offer funding. If your application is received before the deadline, we aim to notify you about the outcome by the end of Winter Term.

You may also have to provide evidence of your English proficiency. You do not need to provide this at the time of your application to LSE, but we recommend that you do see our  English language requirements  for further information.

When to apply

The application deadline for this programme is 23 May 2024 . However, to be considered for any LSE funding opportunity, you must have submitted your application and all supporting documents by the funding deadline. See the fees and funding section for more details.

Fees and funding

Every research student is charged a fee in line with the fee structure for their programme. The fee covers registration and examination fees payable to the School, lectures, classes and individual supervision, lectures given at other colleges under intercollegiate arrangements and, under current arrangements, membership of the Students' Union. It does not cover living costs or travel or fieldwork.

Tuition fees 2024/25 for MPhil/PhD Mathematics

Home students: £4,829 for the first year (provisional) Overseas students: £22,632 for the first year

The fee is likely to rise over subsequent years of the programme. The School charges home research students in line with the level of fee that the Research Councils recommend. The fees for overseas students are likely to rise in line with the assumed percentage increase in pay costs (ie, 4 per cent per annum).

The Table of Fees shows the latest tuition amounts for all programmes offered by the School.

The amount of tuition fees you will need to pay, and any financial support you are eligible for, will depend on whether you are classified as a home or overseas student, otherwise known as your fee status. LSE assesses your fee status based on guidelines provided by the Department of Education.

Further information about fee status classification.

Scholarships, studentships and other funding

The School recognises that the  cost of living in London  may be higher than in your home town or country, and we provide generous scholarships each year to home and overseas students.

This programme is eligible for  LSE PhD Studentships and  Economic and Social Research Council (ESRC) funding . Selection for the PhD Studentships and ESRC funding is based on receipt of an application for a place – including all ancillary documents, before the funding deadline.

Funding deadline for LSE PhD Studentships: 15 January 2024

In addition to our needs-based awards, LSE also makes available scholarships for students from specific regions of the world and awards for students studying specific subject areas.  Find out more about financial support.

In addition, students on this programme are eligible for the Department of Mathematics' PhD Prize for Outstanding Academic Performance , which is an annual award for the best PhD performance from a student completing in the previous academic year.

External funding 

There may be other funding opportunities available through other organisations or governments and we recommend you investigate these options as well. 

Further information

Fees and funding opportunities

Information for international students

LSE is an international community, with over 140 nationalities represented amongst its student body. We celebrate this diversity through everything we do.  

If you are applying to LSE from outside of the UK then take a look at our Information for International students . 

1) Take a note of the UK qualifications we require for your programme of interest (found in the ‘Entry requirements’ section of this page). 

2) Go to the International Students section of our website. 

3) Select your country. 

4) Select ‘Graduate entry requirements’ and scroll until you arrive at the information about your local/national qualification. Compare the stated UK entry requirements listed on this page with the local/national entry requirement listed on your country specific page.

Programme structure and courses

In addition to progressing with your research, you are expected to take the listed training and transferable skills courses. You may take courses in addition to those listed and should discuss this with your supervisor. At the end of your second year (full-time), you will need to satisfy certain requirements, and if you meet these, will be retroactively upgraded to PhD status.

Training courses – Compulsory (not examined) Courses designed for research in Mathematics need to be chosen in consultation with your lead supervisor. Discrete Mathematics and Algorithms, Operations Research and Game Theory students will attend four courses organised by the London Taught Course Centre .

There are separate arrangements for students in Financial Mathematics, where courses are provided by the London Graduate School in Mathematical Finance . You also have the option of attending or auditing LSE Taught Masters modules, where appropriate.

Transferable skills courses – Compulsory (not examined) Mathematics: Seminar on Combinatorics, Games and Optimisation Research Student Seminar – you must attend and make presentations

Second year

Transferable skills courses – Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

Transferable skills courses – Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

Fourth year

Transferable skills courses– Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

For the most up-to-date list of optional courses please visit the relevant School Calendar page .  

You must note, however, that while care has been taken to ensure that this information is up to date and correct, a change of circumstances since publication may cause the School to change, suspend or withdraw a course or programme of study, or change the fees that apply to it. The School will always notify the affected parties as early as practicably possible and propose any viable and relevant alternative options. Note that the School will neither be liable for information that after publication becomes inaccurate or irrelevant, nor for changing, suspending or withdrawing a course or programme of study due to events outside of its control, which includes but is not limited to a lack of demand for a course or programme of study, industrial action, fire, flood or other environmental or physical damage to premises.  

You must also note that places are limited on some courses and/or subject to specific entry requirements. The School cannot therefore guarantee you a place. Please note that changes to programmes and courses can sometimes occur after you have accepted your offer of a place. These changes are normally made in light of developments in the discipline or path-breaking research, or on the basis of student feedback. Changes can take the form of altered course content, teaching formats or assessment modes. Any such changes are intended to enhance the student learning experience. You should visit the School’s  Calendar , or contact the relevant academic department, for information on the availability and/or content of courses and programmes of study. Certain substantive changes will be listed on the  updated graduate course and programme information page.

Supervision, progression and assessment

Supervision.

Supervisors are selected during the application process, where we take into account the information and preferences you mention in your application. You will be assigned to:

-  One or two principal supervisor(s) with requisite knowledge in your chosen field. Most of your day-to-day supervision will be with the principal supervisor(s). If the research project or your interests shift during your time in the Department, it is possible to change principal supervisor(s). - If there is only one principal supervisor, an appropriate second supervisor will be appointed. There will always be a principal supervisor from the Mathematics Department. Where appropriate, a second or joint supervisor may be appointed from another department or institution.

Progression and assessment

You are initially registered for the MPhil, and will be able to upgrade to PhD registration during your second year, dependent on satisfactory progress. Progress is assessed regularly by your supervisors, in consultation with the Doctoral Programme Director, on the basis of the extent to which the agreed research goals have been achieved. Any upgrade is dependent on the successful completion of a Major Review, the date of which is determined by the Doctoral Programme Director in consultation with the lead supervisor.

By the end of your first year you will be required to present a more detailed project proposal. The proposal, which should illustrate your command of the theoretical and empirical literature related to your topic, will be a clear statement of the theoretical and methodological approach you will take. It will include a draft outline and work plan, which should identify any periods of fieldwork necessary to your research. This should demonstrate the coherence and feasibility of the proposed research and thesis.

Study facilities

Students are provided with their own workspace and Windows PC within the Department of Mathematics’ PhD study room.  This area was recently renovated, and has been modernised to become a professional, purposeful, and relaxed work environment. Students are thus offered a supportive environment within a community of scholars and are well-placed to pursue a career building on their research accomplishments. 

In addition to the space provided in Columbia House, a dedicated Postgraduate Common Room is available to students in 32 Lincoln's Inn Fields.  Students will also find the  PhD Academy  useful, a dedicated space and services hub for doctoral candidates.

Students will have access to the comprehensive facilities of the  LSE Library  and to the libraries of other colleges of the University of London. They will also benefit from the IT and other facilities available at the School.

Student support and resources

We’re here to help and support you throughout your time at LSE, whether you need help with your academic studies, support with your welfare and wellbeing or simply to develop on a personal and professional level.

Whatever your query, big or small, there are a range of people you can speak to who will be happy to help.  

Department librarians   – they will be able to help you navigate the library and maximise its resources during your studies. 

Accommodation service  – they can offer advice on living in halls and offer guidance on private accommodation related queries.

Class teachers and seminar leaders  – they will be able to assist with queries relating to specific courses. 

Disability and Wellbeing Service  – they are experts in long-term health conditions, sensory impairments, mental health and specific learning difficulties. They offer confidential and free services such as  student counselling,  a  peer support scheme  and arranging  exam adjustments.  They run groups and workshops.  

IT help  – support is available 24 hours a day to assist with all your technology queries.   

LSE Faith Centre  – this is home to LSE's diverse religious activities and transformational interfaith leadership programmes, as well as a space for worship, prayer and quiet reflection. It includes Islamic prayer rooms and a main space for worship. It is also a space for wellbeing classes on campus and is open to all students and staff from all faiths and none.   

Language Centre  – the Centre specialises in offering language courses targeted to the needs of students and practitioners in the social sciences. We offer pre-course English for Academic Purposes programmes; English language support during your studies; modern language courses in nine languages; proofreading, translation and document authentication; and language learning community activities.

LSE Careers  ­ – with the help of LSE Careers, you can make the most of the opportunities that London has to offer. Whatever your career plans, LSE Careers will work with you, connecting you to opportunities and experiences from internships and volunteering to networking events and employer and alumni insights. 

LSE Library   –   founded in 1896, the British Library of Political and Economic Science is the major international library of the social sciences. It stays open late, has lots of excellent resources and is a great place to study. As an LSE student, you’ll have access to a number of other academic libraries in Greater London and nationwide. 

LSE LIFE  – this is where you should go to develop skills you’ll use as a student and beyond. The centre runs talks and workshops on skills you’ll find useful in the classroom; offers one-to-one sessions with study advisers who can help you with reading, making notes, writing, research and exam revision; and provides drop-in sessions for academic and personal support. (See ‘Teaching and assessment’). 

LSE Students’ Union (LSESU)  – they offer academic, personal and financial advice and funding.  

PhD Academy   – this is available for PhD students, wherever they are, to take part in interdisciplinary events and other professional development activities and access all the services related to their registration. 

Sardinia House Dental Practice   – this   offers discounted private dental services to LSE students.  

St Philips Medical Centre  – based in Pethwick-Lawrence House, the Centre provides NHS Primary Care services to registered patients.

Student Services Centre  – our staff here can answer general queries and can point you in the direction of other LSE services.  

Student advisers   – we have a  Deputy Head of Student Services (Advice and Policy)  and an  Adviser to Women Students  who can help with academic and pastoral matters.

Student life

As a student at LSE you’ll be based at our central London campus. Find out what our campus and London have to offer you on academic, social and career perspective. 

Student societies and activities

Your time at LSE is not just about studying, there are plenty of ways to get involved in  extracurricular activities . From joining one of over 200 societies, or starting your own society, to volunteering for a local charity, or attending a public lecture by a world-leading figure, there is a lot to choose from. 

The campus 

LSE is based on one  campus  in the centre of London. Despite the busy feel of the surrounding area, many of the streets around campus are pedestrianised, meaning the campus feels like a real community. 

Life in London 

London is an exciting, vibrant and colourful city. It's also an academic city, with more than 400,000 university students. Whatever your interests or appetite you will find something to suit your palate and pocket in this truly international capital. Make the most of career opportunities and social activities, theatre, museums, music and more. 

Want to find out more? Read why we think  London is a fantastic student city , find out about  key sights, places and experiences for new Londoners . Don't fear, London doesn't have to be super expensive: hear about  London on a budget . 

Student stories

To read all our Alumni Stories,  see our webpage here .

Quick Careers Facts for the Department of Mathematics

Median salary of our PG students 15 months after graduating: £39,500

• Financial and Professional Services              
• Information, Digital Technology and Data            
• Accounting and Auditing              
• Real Estate, Environment and Energy 
• Advertising, Marketing, PR, Media, Entertainment, Publishing and Journalism

Top 5 sectors our students work in:

The data was collected as part of the Graduate Outcomes survey, which is administered by the Higher Education Statistics Agency (HESA). Graduates from 2020-21 were the fourth group to be asked to respond to Graduate Outcomes. Median salaries are calculated for respondents who are paid in UK pounds sterling and who were working in full-time employment.

Students who successfully complete the programme often embark on an academic career. 

Further information on graduate destinations for this programme

Support for your career

Many leading organisations give careers presentations at the School during the year, and LSE Careers has a wide range of resources available to assist students in their job search. Find out more about the  support available to students through LSE Careers .

Frequently Asked Questions

Can i or must i teach as a mphil/phd student in the department.

All mathematics MPhil/PhD students are usually expected to undertake some class teaching for the Department. You will be paid separately for this. Further details will be provided on your arrival. 

Will I receive any additional funding to support conference attendance, book purchases, etc.?

Each registered PhD student in the Department is entitled to claim up to £500 per academic year towards their research expenses relating directly to your studies, such as the purchase of books or conference attendance. All claims must be accompanied by full receipts. 

Can I apply to start in the Winter Term (January) or Spring Term (April)?

Under execptional circumstances, starting in January may be permissable.  Starting in the Spring Term is not permitted.

I am already enrolled in a PhD programme at another university and I would like to transfer to your PhD programme. How do I do that?

LSE does not accept transfer of credits. All MPhil/PhD applicants, regardless of previous academic experience, are required to complete a formal application. Previous research will be considered, but all students are initially registered as MPhil students by the School, are upgraded to PhD status according to the Department's standard policy and are required to fulfil the School's minimum registration requirements.

Can I apply to study part-time?

We will consider applications for part-time registrations in the PhD programme, subject to visa regulations. Applicants with personal circumstances such as caring responsibilities who may otherwise not pursue a PhD may consider this route. We emphasise that studying for a PhD requires a serious commitment of regular periods of time and concentration. Pursuing a PhD while holding full-time employment is discouraged.

We would need to see evidence that an applicant:

• Would be available to participate in activities that are essential to becoming an independent researcher (e.g. attend seminars, go to conferences, follow taught courses in their first year(s), etc.)
• Can find mutual times to work with their proposed supervisor
• Can spend sufficient time on their PhD research

Find out more about LSE

Discover more about being an LSE student - meet us in a city near you, visit our campus or experience LSE from home. 

Experience LSE from home

Webinars, videos, student blogs and student video diaries will help you gain an insight into what it's like to study at LSE for those that aren't able to make it to our campus.  Experience LSE from home . 

Come on a guided campus tour, attend an undergraduate open day, drop into our office or go on a self-guided tour.  Find out about opportunities to visit LSE . 

LSE visits you

Student Marketing, Recruitment and Study Abroad travels throughout the UK and around the world to meet with prospective students. We visit schools, attend education fairs and also hold Destination LSE events: pre-departure events for offer holders.  Find details on LSE's upcoming visits . 

How to apply

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Imperial College London Imperial College London

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Mathematical Finance

• Faculty of Natural Sciences
• Departments, institutes and centres
• Department of Mathematics

The  Mathematical Finance Section  of the  Department of Mathematics  at Imperial College London , is devoted to  research  on mathematical modeling and computational methods in finance. It is the largest research group in Mathematical Finance in the UK and is recognized as one of the world's leading research groups in this field.

Maths Finance homepage

Research conducted in the Mathematical Finance section focuses on the quantitative modeling of financial markets and mathematical tools and theories - probability, statistics, partial differential equations, optimization, simulation - which underpin this modeling process. Recent research efforts have also focused on issues relevant to industry and regulatory issues such as counterparty credit risk, funding valuation, collateral modeling, central clearing of over-the-counter (OTC) derivatives, liquidity risk management, collateral transformation, the impact of new regulations on risk, multiple-curve term structure models and novel, holistic approaches to the modeling of financial risks and systemic risk.

Our research is disseminated through the  Imperial College Mathematical Finance Working Paper Series .

Postgraduate Opportunities

The Mathematical Finance section offers PhD research opportunities , which trains highly skilled candidates towards research careers in academia and industry. PhD students are supported by public or private sources of funding and  work on a wide range of topics in stochastic analysis, mathematical modeling of finance and computational finance. Some PhD projects are carried out in collaboration with industry sponsors. We are a founding partner of the London Graduate School in Mathematical Finance which provides an array of research-oriented courses for PhD students at participating institutions.

The Mathematical Finance section also offers an  MSc , designed to prepare graduates with a prior training in mathematics, science or engineering for careers as quantitative analysts in the financial services industry.

Mathematical Sciences

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Students seeking a Ph.D. in Mathematical Sciences are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Doctor of Philosophy in Mathematical Sciences is a traditional research degree, and its requirements are representative of all doctoral programs.

After being admitted to graduate status by the Department, a student seeking a Ph.D. must be admitted to candidacy for this degree by fulfilling the appropriate program requirements.

The most important requirement for the Ph.D. degree is timely completion and public defense of an original Ph.D. thesis. The Ph.D. thesis is expected to display depth and originality and be publishable by a refereed journal.

Doctor of Arts in Mathematical Sciences

The Doctor of Arts degree shares all requirements and standards with the Ph.D., except with regard to the thesis. The D.A. thesis is not expected to display the sort of original research required for a Ph.D. thesis, but rather to demonstrate an ability to organize, understand, and present mathematical ideas in a scholarly way, usually with sufficient innovation and worth to produce a publishable work. Whenever practical, the department provides D.A. candidates with the opportunity to use materials developed to teach a course. While a typical Ph.D. recipient will seek a position that has a substantial research component, the D.A. recipient will usually seek a position where research is not central.

Doctor of Philosophy in Algorithms, Combinatorics, and Optimization (ACO)

This program is administered jointly by the Department of Mathematical Sciences, the Department of Computer Science, and the Tepper School of Business. It focuses on discrete mathematics and algorithmic issues arising in computer science and operations research, particularly the mathematical analysis of these issues. The participating units evaluate applicants separately. The requirements for this degree and information on participating faculty are available at the ACO page .

Doctor of Philosophy in Pure and Applied Logic (PAL)

This is an interdisciplinary program with faculty from the Department of Mathematical Sciences, the Department of Philosophy, and the School of Computer Science. The participating units evaluate applicants separately and set their own program requirements. Students who have been admitted to the PAL program, and who complete the requirements for the Ph.D. in Mathematical Sciences with a thesis in the area of logic, can choose to receive either a Ph.D. in Pure and Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which degree to receive is usually based on the intended career path.

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Intellectual Rationale for the MSMF

Two remarkable changes in the last thirty years have led to the demand for a new kind of scientific skill. Globalization has led to greater interdependence of markets: more distant information from many parts of the world intervenes to determine the prices of commodities and securities on US markets. Markets move faster and are much more volatile. As a result many corporations and financial institutions have found themselves exposed to greatly increased risks that traditional financial instruments were ill equipped to handle.

During the same period the theoretical modeling of financial markets underwent a major revolution. A mathematical theory of finance was developed, which led to a new understanding of risk diversification and hedging, and to remarkable pricing formulas for derivative securities which have proved to be of great practical utility for reducing risks. It is now possible to design and price sophisticated, tailor-made securities for controlling the exposure to risk of corporations and financial institutions. The explosion in the growth and calculating power of computers has also made it possible to better evaluate risks and implement highly effective hedging strategies.

Traditional programs at universities have proved ill suited to train a new generation of students, to equip them with the requisite skills. A program that can meet the needs of the new environment is indeed demanding: students must acquire a good mathematical knowledge of stochastic processes, a good knowledge of numerical analysis and computation, plus a good understanding of the structure, functioning and modeling of financial markets. It is with this in mind that the MS degree in Mathematical Finance was created as a joint Program between the Economics and Mathematics Departments at USC. The objective of the Program is to produce graduates with a rigorous foundation in the economic theory and mathematical modeling of financial markets.

Program Objective

The objective of this Master of Science program is to produce graduates with a rigorous foundation in the economic theory and mathematical modeling of financial markets. The program creates an integrated curriculum spanning four disciplines: economics, mathematics, econometrics/statistics and computational/numerical analysis. The program is designed for recent graduates in the fields of applied mathematics, physics and engineering – or for graduates in economics, business and finance with strong mathematical backgrounds – who wish to pursue quantitatively-oriented careers in financial institutions, industry, or government.

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Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements.

NYU Shanghai Ph.D. Track

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

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Additional information for students interested in studying applied math is available here .

Probability

PDE/Analysis

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

The oral defense is the final examination on the student's dissertation. The defense is conducted by a panel of five faculty members (including the student's advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student's topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs  page.