phd positions in mathematical finance

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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 units, depending on whether the courses are 3 or 4 units each). Students’ course choices must be approved by the Mathematical Finance Director prior to registration each term. The following is a typical program of courses.

• CAS EC 701 Microeconomic Theory
• CAS MA 711 Real Analysis
• CAS MA 779 Probability Theory I
• QST FE 918 Doctoral Seminar in Finance
• CAS EC 703 Advanced Microeconomic Theory
• CAS MA 776 Partial Differential Equations
• CAS MA 781 Probability Theory 2
• QST FE 920 Advanced Capital Market Theory
• CAS EC 702 Macroeconomic Theory
• CAS MA 783 Advanced Stochastic Processes
• QST MF 850 Advanced Computational Methods
• QST MF 922 Advanced Mathematical Finance
• CAS EC 704 Advanced Microeconomic Theory
• CAS 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 term 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-unit course, for each subsequent regular term 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 term to correct their status. Prior to the start of the term, 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 five 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 term 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 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, michael blank, greg buchak, antonio coppola, darrell duffie, steven grenadier, benjamin hébert, arvind krishnamurthy, hanno lustig, matteo maggiori, paul pfleiderer, joshua d. rauh, 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, reserves were not so ample after all, agency mbs as safe assets, dollar safety and the global financial cycle, recent insights by stanford business, is the united states’ borrowing binge about to burst, a “grumpy economist” weighs in on inflation’s causes — and its cures, the surprising economic upside to money in u.s. politics.

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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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• 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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PhD Program in Finance

2024-25 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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Wharton’s PhD program in Finance provides students with a solid foundation in the theoretical and empirical tools of modern finance, drawing heavily on the discipline of economics.

The department prepares students for careers in research and teaching at the world’s leading academic institutions, focusing on Asset Pricing and Portfolio Management, Corporate Finance, International Finance, Financial Institutions and Macroeconomics.

Wharton’s Finance faculty, widely recognized as the finest in the world, has been at the forefront of several areas of research. For example, members of the faculty have led modern innovations in theories of portfolio choice and savings behavior, which have significantly impacted the asset pricing techniques used by researchers, practitioners, and policymakers. Another example is the contribution by faculty members to the analysis of financial institutions and markets, which is fundamental to our understanding of the trade-offs between economic systems and their implications for financial fragility and crises.

Faculty research, both empirical and theoretical, includes such areas as:

• Structure of financial markets
• Formation and behavior of financial asset prices
• Banking and monetary systems
• Corporate control and capital structure
• Saving and capital formation
• International financial markets

Candidates with undergraduate training in economics, mathematics, engineering, statistics, and other quantitative disciplines have an ideal background for doctoral studies in this field.

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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.

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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Financial Mathematics

Career paths in quantitative finance, quantitative research and analysis.

Professionals in this area use statistical and quantitative methods to analyze and predict the markets, and apply programming tools to produce robust investment strategies. Their work revolves around creating mathematical models that are used to assess and manage financial systems, potential risk, and timing of trades. 

Necessary Skills : a strong command of programming languages, such as Python, C#, and SQL, as well as statistical analysis tools, such as R, Matlab, and SAS. Some roles will also require knowledge of machine learning and natural language processing techniques.  Good understanding of a variety of mathematical and statistical models used in finance. 

Sample of Employer Partners in this area :

Portfolio Management

Portfolio managers engage in portfolio construction, monitoring asset exposures and allocations, managing client requests, tax management, monitoring pre-trade client guideline compliance and exception resolution. They initiate trades, and monitor the portfolios on an ongoing basis.  They also develop a deep understanding of investment products and operational policies and procedures. With career progression, they can manage a team of analysts and researchers.

Necessary Skills : in addition to effective communication skills and knowledge of asset classes, professionals in this area also require strong quantitative and mathematical modeling, coding, and analytical thinking skills. This role often prefer a financial analyst certification, like the Chartered Financial Analyst (CFA), and previous experience.  Most portfolio managers will start their careers as portfolio analysts.

Programming and Software Development

Quantitative engineers or quantitative developers work in the FinTech space. They are responsible for designing, developing, testing and deploying sophisticated software solutions to facilitate the work of various financial institutions.

Necessary Skills : excellent coding skills in Python, C++, and Java, and knowledge in probability, linear regression and time series data analysis.  In addition, interest in financial markets and knowledge of various financial products give quant developers a distinct advantage, since they work on a variety of projects with teams across an organization.

Risk Management

Professionals in this area empower the decision making process for investments and trades by providing risk analysis, and developing/enhancing risk model frameworks across various markets and assets. They use various techniques, including "value at risk" (VaR), Monte Carlo simulation, and linear regression-based statistical models, to measure the potential of loss on an investment profile. They also run stress tests to gauge the effectiveness of their models. 

Necessary Skills : strong skills in communication and detail orientation, quantitative and financial modeling skills, programming abilities using tools like VBA, Python, R, and SAS, as well as knowledge of various statistical and volatility models.

Traders analyze market data, such as price and volume, and use mathematical and statistical models to identify and execute trading decisions that may involve hundreds of thousands of shares and securities.

A trader develops a strategy and applies the model to historical market data so that it can be back-tested and optimized. If the strategy yields profit, it is then applied onto real-time markets to implement an automated trading process. Quantitative trading techniques also include high-frequency trading, algorithmic trading and statistical arbitrage.

Necessary Skills : a strong background in programming skills in Python, C++, SQL, R, and/ or Java. Ability to navigate price indexes, such as SPX and VIX. It also requires the knowledge of statistical analysis, numerical linear algebra, and machine learning processes. In addition, traders must possess the ability to thrive under pressure, maintain focus despite long hours, withstand an often competitive/intense environment, and respond well to failure.

Data Science and Analytics

As financial institutions further integrate the practice of collecting and analyzing data to gauge profit, loss, and client satisfaction, data science continues to be the fastest growing area of quantitative finance.

Professionals in this area work on data mining, gathering data sets, and deriving insights from these data sets. Data Scientists work in many data driven companies, such as investment banks, asset management firms, and technology companies. Their roles typically focus on risk management and predictive analytics.  Data Scientists are increasingly using machine learning, clustering algorithms, and artificial intelligence to identify unusual data patterns.

Necessary Skills : command of programming languages used in statistical modeling, such as Python and R, ability to work with large sets of financial data, and strong quantitative analysis skills. Time Series Analysis is also key to analyzing financial data. Machine learning and AI re also areas of growing importance in this field. 

Other Career Paths

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PhD in Mathematics – Concentration in Actuarial Science and Risk Analytics

This PhD concentration is intended for students with strong quantitative skills who want to acquire advanced analytical tools for academic careers and research and development careers  in insurance, consulting, investment, pension, healthcare, banking and financial services .

The University of Illinois is an ideal place for education and research in actuarial, financial and risk management, due to its well-established system of interdisciplinary collaborations among various units. Highlights of the University’s achievements in these areas can be found  here . Based in the renowned Department of Mathematics, this program offers a unique blend of a world-class rigorous mathematical education with practical research and professional training in actuarial science, quantitative finance and risk analytics. Read more at our  poster for graduate studies in actuarial science and risk management .

PhD candidates cover most of the material for professional exams, and build on that foundation to receive in-depth education on modern techniques and challenges in the financial, actuarial and risk management professions through coursework, seminars, internships and research. Due to the interdisciplinary nature of actuarial and financial research, PhD candidates are encouraged to broaden their knowledge by taking courses in statistics, finance, insurance, risk management, data analytics, etc.

The Department of Mathematics offers a unique multi-year internship program where PhD candidates are encouraged and supported to receive internship experience in summer breaks during their PhD studies. More information can be found  here . There are also internship opportunities on campus at the  University of Illinois Research Park . 

Our program offers opportunities for PhD candidates to work in a wide range of research areas, including stochastic analysis in actuarial and financial modeling, quantitative risk management of equity-linked insurance, pension and social security, industry solvency assessment, collective risk theory, Monte Carlo simulations, and more. The  Illinois Risk Lab  also provides a channel for practical research to address emerging problems from industrial partners and professional organizations.

Financial support is offered for up to six years to every student admitted to our PhD program, in the form of teaching assistantships, research assistantships and corporate-sponsored fellowships. We also provide full reimbursement of exam fees for those who choose to take professional exams. To help students develop communication and networking skills, we also provide financial support for PhD candidate to travel to research summer schools and conferences in related areas.

Admissions Requirements

Students with a Bachelor’s degree in any quantitative field can apply directly to the PhD program. Applicants are expected to demonstrate competence in real analysis, linear algebra, and probability and statistics, either through undergraduate coursework or by means of Graduate Record Examination (GRE) mathematics subject test.

Complete information regarding graduation requirements can be found in the  Guide for Graduate Students in Mathematics . The following list only serves as a summary for prospective students.

PhD candidates in this concentration are required to complete the core courses: MATH 540 (Real Analysis) MATH 561 (Theory of Probability I) MATH 563 (Risk Modeling and Analysis) STAT 510 (Mathematical Statistics I) One additional course from a list of approved core courses for all PhD students.

PhD candidates in this concentration must also demonstrate competence in three additional supporting courses: MATH 564 (Applied Stochastic Processes) STAT 425 (Applied Regression and Design) FIN 591 (Theory of Finance)

and in two of the following actuarial graduate courses: MATH 565 (Actuarial Models for Life Contingencies) MATH 567 (Actuarial Models for Financial Economics) MATH 568 (Actuarial Loss Models)

Although not required, many PhD candidates in the Actuarial Science and Risk Analytics Concentration take elective courses in functional analysis, partial differential equations, linear and nonlinear programming, multivariate analysis, statistical computing, macro and micro economics, portfolio management, predictive modeling, machine learning.

How to Apply

The application process for this concentration is the same as the regular Mathematics PhD program. Detailed instruction as well as general requirements can be found  here . Candidates should clearly identify the Actuarial Science and Risk Analytics Concentration on the application form, and in their personal statement.

Frequently Asked Questions

If I want to become a practicing actuary, should I consider PhD education in Actuarial Science?

The actuarial profession in North America highly values professional credentials obtained through passing professional exams with credentialing bodies such as the Society of Actuaries and Casualty Actuarial Society. A PhD education in Actuarial Science is not a necessary component for a career path as an actuary. Students who are interested in career paths in traditional actuarial roles should pursue our MS program in Actuarial Science. The PhD concentration prepares students for academic careers and research and development offices/departments in the insurance and financial service industries. For example, a graduate may find a tenure-system position in a university, work as a quantitative reinsurance analyst, a catastrophe modeling analyst, a quantitative strategy researcher in a proprietary trading firm, and so on.

What qualifications are you looking for in admissions?

A typical PhD applicant should have a bachelor’s degree or its equivalent in a quantitative field, including but not limited to pure mathematics, applied mathematics, statistics, engineering, quantitative finance, physics, etc. Students should take the GRE General test.

How much do GRE scores get weighted into the application of a prospective student? What other factors weigh the most in an application?

We consider the whole application to find students with sufficient preparation and motivation to succeed in our program. Applicants typically perform strongly on the GRE General exam (80th percentile and above on the quantitative portion, and we like to see good scores on the other sections too). Scores on the GRE Mathematics subject exam (if taken) vary quite widely. Coursework relevant to actuarial science and risk analytics is valuable. 

The transcripts from your bachelor’s and master’s institutions are important. We pay close attention to courses and grades. If you come in with an actuarial or financial mathematics background, we do consider your track record of passing professional exams. However, students in this concentration also come from other quantitative fields.

What funding is available to students ?

All admitted students are offered a full tuition waiver, and a teaching assistantship (the stipend is $20,000 for the academic year; most students get some summer funding too). The funding offer runs for 5 or 6 years, depending on your level of preparation. Fellowship and RA support is available to some continuing students who perform strongly in the program.

How do the requirements for those pursuing the Actuarial Science emphasis differ from those pursuing other fields of study?

Notably, students in the Actuarial Science and Risk Analytics Concentration are not required to take Math 500 Abstract Algebra. Instead, they take Stat 510 Mathematical Statistics I. The full requirements for students in the Concentration are listed  here .

What should be my focus to prepare for this program beyond admissions?

Take as much undergraduate real analysis as possible (called “advanced calculus” at some universities), and tackle the hardest problems you can get your hands on. Learn metric space topology, with normed vector spaces being an important example. Get familiar with spherical coordinates, the divergence theorem (Gauss theorem), and  Green’s first and second identities .

Real analysis lays the foundation for probability, stochastic processes, and differential equations, at the graduate level. If you are strong in real analysis, then you can learn and pass the material in the first year comprehensive courses in a PhD program like ours.

Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Learn more about Harvard’s Math community and our statement on diversity and inclusion.

The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers diversity resources and student affinity groups for graduate students.

The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.

open. The application deadline is December 15, 2021. -->

The pure math PhD admissions application is open. The application submission deadline is December 15, 2024.

For information on admissions and financial support , please visit the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.

Note for Harvard College Undergraduates

Since it is better for a student’s mathematical development to learn mathematics at different institutions so as to be exposed to a broader range of mathematical perspectives, ordinarily applications for the mathematics PhD program from Harvard College undergraduates are not considered. If exceptional circumstances warrant an application from a Harvard undergraduate, an advisor or mentor of that student should seek approval from the Director of Graduate Studies before the student submits an application.

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Mathematical Finance

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.

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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.

19 November 2024, 11.00 – 12.00

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19 November 2024, 15.00 – 16.00

26 November 2024, 11.00 – 12.00

26 November 2024, 15.00 – 16.00

03 December 2024, 11.00 – 12.00

Postdoctoral Fellowship in Mathematical Finance

The Center of Mathematical Sciences and Applications at Harvard University welcomes applications for a two-year Postdoctoral position at the intersection of mathematics and economics, with a particular preference for finance. The area of research interests is understood broadly (for example, they may include but are not limited to asset pricing and corporate finance, macro-finance and monetary economics, operations research and financial engineering , economic theory and  game theory, industrial organization and market design, econometrics and machine learning). That said, there is some preference for candidates working with modern empirical methods in addition to theory.

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Mathematical Sciences

Mellon college of science, ph.d. programs, doctor of philosophy in mathematical sciences.

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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MPhil/PhD Mathematics

Introduction.

You’ll have the chance to produce work that makes an original contribution to the field of mathematics and its applications. You have a wide range of topics to choose from, including combinatorics, control theory, discrete mathematics, financial mathematics, game theory, graph theory, mathematical optimisation, machine learning, mechanism design, operations research, probabilistic analysis, theory of computation and algorithms, and the applications of mathematics.

In the most recent Research Excellence Framework, all aspects of our research were ranked as world-leading or internationally excellent. So, you’ll be learning alongside the best in the field.

You’ll attend personal development workshops to support your studies and help prepare for your future career. You’ll benefit from our close links with related departments at LSE, such as Statistics, Finance, Economics and Management. We play a central role in the mathematics community of London.

When you graduate, you’ll be well-equipped for a career in academia or industry, including in financial services, data science, consulting, and technology.

Each year, research students receive funding to help with their research activities, such as attending conferences, and buying books or technology. Additional research funds are also available on application.

Entry requirements

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

Please select your country from the dropdown list below 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.

English language requirements

The English language requirement for this programme is Research . Read more about our English language requirements .

Competition for places at LSE is strong. So, even if you meet the minimum entry requirements, this does not guarantee you an offer of a place.

However, please don’t feel deterred from applying – we want to hear from all suitably qualified students. Think carefully about how you can put together the strongest possible application to help you stand out from other students.

Programme content

In addition to progressing with your research, you're 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'll 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 master's courses, where appropriate.

Transferable skills courses – Compulsory (not examined)

Mathematics: Seminar on Combinatorics, Games and Optimisation

Research student seminar, programme regulations at lse.

For the latest list of courses, please go to the relevant School Calendar page .

A few important points you’ll need to know:

We may need to change, suspend or withdraw a course or programme of study, or change the fees due to unforeseen circumstances. We’ll always notify you as early as possible and recommend alternatives where we can.

The School is not liable for changes to published information or for changing, suspending or withdrawing a course or programme of study due to events outside our control (including a lack of demand, industrial action, fire, flooding or other damage to premises).

Places are limited on some courses and/or subject to specific entry requirements so we cannot therefore guarantee you a place.

Changes to programmes and courses may be made after you’ve accepted your offer of a place – normally due to global developments in the discipline or student feedback. We may also make changes to course content, teaching formats or assessment methods but these are always made to improve the learning experience.

For full details about the availability or content of courses and programmes, please take a look at the School’s  Calendar , or contact the relevant academic department.

Some major changes to programmes/courses are posted on our  updated graduate course and programme information page .

Why study with us

Read our alumni stories and discover more about our department.

Meet the department

The Department of Mathematics aims to be a leading centre for the study of mathematics in the social sciences.

The department has a vibrant intellectual community, with fantastic students, internationally respected academics and high-achieving alumni. Our department has grown rapidly in recent years, with exciting developments in research and new teaching programmes and courses.

This research encompasses four main overlapping areas:

• discrete mathematics and algorithms
• mathematical game theory
• financial and related mathematics
• operational research.

All aspects of our research were ranked world-leading or internationally excellent in the most recent Research Excellence Framework (2021), submitted jointly with the Department of Statistics.

We embrace the School’s ethos of research-led teaching. Currently, we offer four undergraduate and three postgraduate programmes, as well as doctoral research opportunities on our MPhil/PhD in Mathematics. These programmes are all in high demand – attracting talented students from diverse backgrounds.

Our programmes are highly interdisciplinary and we have close ties with other departments at LSE, including Statistics, Economics, Finance, Management and the Data Science Institute.

Whatever your study route, you’ll benefit from a welcoming, inclusive and friendly learning environment where students and staff are supported to achieve their best.

Learn more about our programmes , recent research and regular events and seminars .

Department of Mathematics

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1st in london for the 13th year running, 6th in the world.

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Your application, when to apply, making an application.

We welcome applications for research programmes that complement the academic interests of our staff at LSE. For this reason, we recommend that you take a look at our staff research interests before applying.

We carefully consider each application and take into account all the information included on your form, including your:

• academic achievement (including existing and pending qualifications)
• statement of academic purpose
• outline research proposal
• sample of written work.

You may need to provide evidence of your English language proficiency. See our English language requirements .

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

• 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 long)

• 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 long)

Many applicants will have little or no prior experience of research and therefore we don't 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've 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 long)

Submit something that showcases your mathematical writing and that is single-authored by you. For example, this could 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. If you've contributed substantially to any co-authored paper/report that you'd like to be considered as part of your application, you can include this in addition to your single-authored sample of written work.

See further information on supporting documents .

You'll need to nominate two referees. Academic referees are preferred, ie, 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 haven't 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.

Application consideration

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.

Part-time PhD study

Please note that LSE allows part-time PhD study only under limited circumstances . If you wish to study part-time, you should mention this (and the reasons for it) in your statement of academic purpose, and discuss it at interview if you're shortlisted.

We'll 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'd need to see evidence that you:

• would be available to participate in activities that are essential to becoming an independent researcher (eg, attend seminars, go to conferences, follow taught courses in their first year(s), and so on)
• can find mutual times to work with your proposed supervisor
• can spend sufficient time on their PhD research.

Frequently askend questions

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'm 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 doesn't 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.

The application deadline for this programme is 22 May 2025 .

However, if you’d like to be considered for any funding opportunities, you must submit your application (and all supporting documents) by the funding deadline.

See the fees and funding section below for more details.

Fees and funding

The table of fees shows the latest tuition fees for all programmes.

You're charged a fee for your programme. Your tuition 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 doesn't cover living costs or travel or fieldwork.

Home student fee (2025/26)

The fee is likely to rise over the full duration of the programme. The School charges home research students in line with fee levels recommended by the Research Councils.

Learn more about fee status classification .

Overseas student fee (2025/26)

The fee is likely to rise over the full duration of the programme in line with the assumed percentage increase in pay costs (ie, four per cent each year).

At LSE, your tuition fees, and eligibility for any financial support, will depend on whether you’re classified as a home or overseas student (known as your fee status). We assess your fee status based on guidelines provided by the Department for Education.

Further information about fee status classification .

Scholarships, bursaries and loans

Scholarships, studentships and other funding

We recognise that the  cost of living in London  may be higher than in your home town/city or country and we provide generous scholarships to help both home and overseas students.

For this programme, students can apply for  LSE PhD Studentships , and  Economic and Social Research Council (ESRC) funding . To be considered, you’ll need to submit your application (and any supporting documents) before the funding deadline.

Funding deadlines

Funding deadline for the LSE PhD Studentships and ESRC funding: 15 January 2025 .

In addition to our needs-based awards, we offer scholarships for students from specific regions of the world and awards for certain subjects .

PhD Prize for Outstanding Academic Performance

Students on this programme are also 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

Additional funding opportunities may be available through other organisations or governments. We strongly recommend you investigate these options as well.

Further information

Learn more about fees and funding , including external funding opportunities.

Learning and assessment

How you learn, how you're assessed, supervision.

Supervisors are selected during the application process, where we take into account the information and preferences you mention in your application. You'll 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 Department of Mathematics. Where appropriate, a second or joint supervisor may be appointed from another department or institution.

Teaching 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.

Additional funding to support conference attendance, book purchases and so on

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.

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'll also benefit from the IT and other facilities available at the School.

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'll 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'll 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.

Graduate destinations

Career support.

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

Further information on graduate destinations for this programme

Top 5 sectors our students work in:

From CV workshops through to careers fairs, LSE offers lots of information and support to help you make that all-important step from education into work.

Many of the UK’s top employers give careers presentations at the School during the year and there are numerous workshops covering topics such as job hunting, managing interviews, writing a cover letter and using LinkedIn.

See LSE Careers for further details.

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