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Postgraduate mathematics courses at UCL - University College London

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Geometry and Number Theory

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Data Science MSc

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Energy Systems and Data Analytics (ESDA) MSc

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Financial Mathematics MSc

Mathematical modelling msc, medical statistics and data science msc, statistics msc.

Thomas Evans Profile page

• Lecturer in Quantitative Methods Centre for Advanced Spatial Analysis
• [email protected]

Thomas P. Oléron-Evans is a mathematician, who gained his PhD at UCL in 2015, under the supervision of Professors Steven Bishop and Frank Smith. The topics of his doctoral research were the mathematical foundations of agent-based modelling and the application of game theory to general models of search and patrol. He has worked on the EPSRC funded research project ENFOLD-ing and the EU funded projects 3cixty and HARMONY, and he has published research on the control of dengue-carrying mosquitoes with the sterile insect technique (SIT), modelling international trade through linking national input-output tables, and the optimisation of land use around Heathrow Airport using multi-objective linear programming. His career before joining UCL encompassed teaching experience in the UK, France, Kenya and Ghana, in various forms.

UNIVERSITY COLLEGE LONDON APPOINTMENTS

• Lecturer in Quantitative Methods University College London, Centre for Advanced Spatial Analysis

ACADEMIC POSITIONS

• Doctoral Researcher UCL, Mathematics, UK 1 Oct 2011 - 1 Oct 2014
• Postgraduate Teaching Assistant UCL, UK 1 Jan 2013 - 1 Jun 2014
• Research Assistant UCL, CASA, UK 1 Oct 2014 - 16 Mar 2015
• Research Associate UCL, CASA, UK 16 Mar 2015 - 1 Sep 2015
• Teaching Fellow UCL, CASA, UK 1 Sep 2015 - 14 Jan 2019
• Lecturer in Quantitative Methods UCL, CASA, London, United Kingdom 15 Jan 2019 - present

NON-ACADEMIC POSITIONS

• Teacher (11-16) Bow School, Mathematics 1 Sep 2009 - 31 Aug 2011
• MSci Mathematics with a Year in Europe Imperial College London, UK 1 Oct 2003 - 1 Aug 2007
• PGCE Postgraduate Certificate of Education Canterbury Christ Church University, UK 1 Jul 2009 - 1 Aug 2010
• PhD Mathematics UCL, UK 1 Oct 2011 - 27 May 2015
• French Can read, write, speak, understand and peer review

FIELDS OF RESEARCH

• Applied mathematics
• Optimisation
• Autonomous agents and multiagent systems
• Dynamical systems in applications
• Modelling and simulation
• Stochastic analysis and modelling
• Time series and spatial modelling

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Course type

Qualification, university name, phd mathematics in london.

19 degrees at 10 universities in London.

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Select the start date, qualification, and how you want to study

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• PhD Mathematics
• PhD Applied Mathematics
• PhD General Mathematics
• PhD Mathematics for Specific Applications
• PhD Operational Research (OR)
• PhD Pure Mathematics
• PhD Statistics
• PhD Statistics, Probability and Operational Research

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Statistical Science MPhil/PhD

Ucl (university college london).

The demand for numerate graduates exceeds the supply in most areas. Many new and existing opportunities – in industry, medicine, Read more...

• 3 years Full time degree: £6,035 per year (UK)
• 5 years Part time degree: £2,930 per year (UK)

Mathematics PhD

Royal holloway, university of london.

About us Academic staff in the Department of Mathematics carry out pioneering research which is making an impressive impact on the world Read more...

• 4 years Full time degree: £4,786 per year (UK)

Mathematical Sciences Integrated PhD

Brunel university london.

Research profile Our research-active academics are involved in cutting-edge research covering a range of topics including applied Read more...

• 4 years Full time degree

Queen Mary University of London

The School of Mathematical Sciences at QMUL is home to a thriving community of postgraduate research students currently numbering Read more...

• 3 years Full time degree: £4,786 per year (UK)
• 6 years Part time degree: £2,393 per year (UK)

University of West London

This PhD in Mathematics course allows you to use theoretical, applied, and computational research methods to solve a wide range of Read more...

• 4 years Full time degree: £3,995 per year (UK)
• 6 years Part time degree: £2,000 per year (UK)

PhD/MPhil Mathematics

City, university of london.

You will conduct world class research for Mathematics at City in topics such as representation theory, mathematical physics or applied Read more...

• 2 years Full time degree: £4,770 per year (UK)
• 3 years Part time degree: £2,390 per year (UK)

Mathematics MPhil/PhD

We offer research supervision across a broad range of pure and applied mathematics. General areas of expertise in pure mathematics include Read more...

• 3 years Full time degree
• 6 years Part time degree

You should ensure that you have a realistic plan to secure sufficient funding to complete the research and writing-up process within the Read more...

Smart Power Networks PhD

Research profile Our research focuses on the development of algorithms to improve distribution efficiency, and strategies to allow mass Read more...

• 3 years Full time degree: £4,712 per year (UK)

Mathematics and Statistics PhD

Birkbeck, university of london.

An PhD is an advanced postgraduate research degree that requires original research and the submission of a substantial dissertation of Read more...

• 4 years Full time degree: £4,712 per year (UK)
• 7 years Part time degree: £2,500 per year (UK)

Imperial College London

A research degree is a very individual experience, more so than an undergraduate degree. While the overarching structure will be identical Read more...

• 5 years Part time degree: £2,393 per year (UK)

Pure Mathematics Research MPhil/PhD

King's college london, university of london.

We have a wide range of research opportunities in the three groups that make up the Pure section of the Department of Mathematics, namely Read more...

• 3 years Full time degree: £6,936 per year (UK)
• 6 years Part time degree: £3,468 per year (UK)

MPhil/PhD Statistics

London school of economics and political science, university of london.

This programme offers the chance to undertake a substantial piece of work that is worthy of publication and which makes an original Read more...

• 3 years Full time degree: £4,829 per year (UK)

Statistics Research MPhil/PhD

Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The Statistics Read more...

MPhil/PhD Mathematics

Biostatistics and health informatics research md(res)/mphil/phd.

Our PhD programme is designed to train and guide students for a research-intensive career in the academia or industry. Our aim is to Read more...

• 3 years Full time degree: £7,950 per year (UK)
• 6 years Part time degree: £3,975 per year (UK)

MPhil/PhD Data, Networks and Society

Media and communications research is developing rapidly, both theoretically and methodologically, in keeping with the vast expansion in the Read more...

Applied Mathematics Research MPhil/PhD

Description Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The Read more...

Course type:

• Full time PhD
• Part time PhD

Qualification:

Related subjects:.

Research interests

I'm interested in the interactions between geometry, algebra and theoretical physics. More specifically, I work on derived categories of coherent sheaves and their various generalizations. A longer summary of my research, written for the general public, is here .

Publications and preprints (arXiv)

(xix) The McKay correspondence in type D 4 via VGIT   (with Tarig Abdelgadir )

(xviii) Equivariant Fukaya categories at singular values   (with Yankı Lekili )

(xvii) Serre functors of residual categories via hybrid models   (with Federico Barbacovi ) Bull. London Math. Soc. 55 (2023), no. 5, 2505-2514.

(xvi) Line fields on punctured surfaces and twisted derived categories

(xv) Discriminants and semi-orthogonal decompositions   (with Alex Kite ) Comm. Math. Phys. 390 (2022), 907-931

(xiv) A non-commutative Bertini theorem   (with Jørgen Rennemo and Michel Van den Bergh ) J. Noncommutative Geometry 13 (2019), no. 2, 609-616.

(xiii) Hori-mological projective duality   (with Jørgen Rennemo) Duke Math. J. 168 (2019), no. 11, 2127-2205. Some supporting calculations are in this addendum .

(xii) All autoequivalences are spherical twists Int. Math. Res. Not. 2018 (2018), no. 10, 3137-3154.

(xi) A new 5-fold flop and derived equivalence Bull. London Math. Soc 48 (2016), no. 3, 533-538.

(x) Quintic threefolds and Fano elevenfolds   (with Richard Thomas ) J. Reine Angew. Math. (Crelle). (2018), 743, 245-259.

(ix) K-theoretic and categorical properties of toric Deligne-Mumford stacks    (with Tom Coates , Hiroshi Iritani and Yunfeng Jiang ) Pure Appl. Math. Q. 11 (2015) no. 2, 239-266.

(viii) The Pfaffian-Grassmannian equivalence revisited   (with Nick Addington and Will Donovan ) Alg. Geom. 2 (2015), no. 3, 332-364. Here's a video of a lecture I gave at the Newton Institute on this topic.

(vii) Mixed braid group actions from deformations of surface singularities   (with Will Donovan) Comm. Math. Phys. 335 (2015), no. 1, 497-543.

(vi) D-brane probes, branched double covers, and non-commutative resolutions   (with Nick Addington and Eric Sharpe ) Adv. Theor. Math. Phys. 18 (2014), no. 6, 1369-1436.

(v) Window shifts, flop equivalences and Grassmannian twists   (with Will Donovan) Compositio Math. 150 (2014), no. 6, 942-978.

(iv) The closed state space of affine Landau-Ginzburg B-models J. Noncommutative Geometry. 7 (2013), no. 3, 857-883.

(iii) Equivalences between GIT quotients of Landau-Ginzburg B-models Comm. Math. Phys. 304 (2011), no. 2, 411-432.

(ii) Gauge theory in higher dimensions, II   (with Simon Donaldson ) Surveys in Differential Geometry 16 (2011), 1-14.

(i) The A-infinity deformation theory of a point and the derived categories of local Calabi-Yaus J. Algebra 320 (2008), no. 8, 3232-3268. This is essentially my PhD thesis , my advisor was Richard Thomas. The thesis version has an extra appendix on A-infinity algebras with some pretty pictures.

Lecture Notes

Manifolds These are the complete lecture notes for a 4th-year undergraduate/MSc level course on differential geometry, which I taught at Imperial College for three years. They cover the foundations of manifolds, tangent vectors, and differential forms, up to Stokes' Theorem. Here are the exercises .

Group Representation Theory Complete notes for a 3rd-year undergraduate course on representation theory, which I also taught for three years at Imperial. They cover the basics of representations of finite groups over the complex numbers (Maschke's Theorem, Schur's Lemma, character tables) and finish with the classification of semi-simple algebras. Here are the exercises .

Graduate students

Aporva Varshney

Michela Barbieri

Edwin Hollands

Federico Barbacovi (graduated 2023) Thesis: Flop-flop autoequivalences and compositions of spherical twists .

Bradley Doyle (graduated 2021) Thesis: Homological Projective Duality for the Plücker embedding of the Grassmannian .

Alex Kite (graduated 2019) Thesis: Fundamental group actions on derived categories , parts of which became paper (xv) above and also arXiv:1711.08940 .

If you're interested in doing a PhD with me you should apply to the LSGNT . Applications are normally open in November/December each year.

Miscellaneous

The universal closed state space of an open TFT These are some short notes on a particular result in 2-dimensional topological field theory.

The 7 Colour Theorem I gave a talk at the KCL Maths School and one of the students made these beautiful notes.

The Incredible Predictive Power of String Theory A pop-maths article I wrote for the De Morgan newsletter.

LSGNT Topics in Geometry

The Geometry of Gauged Linear Sigma Models A workshop I co-organised in June 2022 at the University of Birmingham.

Study at Cambridge

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Research Programmes

• Prospective Students
• Postgraduate Study

The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes.

Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.

Research Areas and Potential Supervisors

Determining whether your interests and ambitions align with our research and expertise is a vital part of the application and admissions process. When we receive your formal application, we will consider the information you provide on your research interests carefully, alongside other factors such as your academic suitability and potential, how you compare to other applicants in the field, and whether we have a suitable academic supervisor with the capacity to take on new students.

We are committed to widening participation in mathematical research at Cambridge. We welcome and encourage applications from people from groups underrepresented in postgraduate study.

Before making an application to study with us we recommend you:

• Investigate our areas of research and consider how they fit with your interests and ambitions.

A list of broad research areas is provided below, together with links to further information. Your interests may span more than one area. On your application form you will be asked to indicate at least one broad area of interest. This is to help us direct your application to the most suitable group of people to review it.

• Identify 2 or 3 appropriate supervisor(s) with whom you might work.

The information linked below will take you to lists of supervisors working in each broad research area, with an indication of their availability. You are encouraged to make informal contact with potential supervisors prior to making an application. Initial contact should be made by email. In your email we recommend you provide a concise explanation of your areas of interest, how your research interests align with the supervisor(s) research, and that you highlight any relevant work you have done in this area. We recommend that you attach an up-to-date CV. The purpose of this contact is to enquire on supervisor capacity and willingness to supervise, and to see if there is a good fit between your interests and theirs.

If you haven’t had a response to an informal enquiry, you are still welcome to apply and list the individual concerned on your application form, although you may also wish to consider other options.

• Give some thought to your intended research and why you want to study with us.

On your application form you will be asked to submit a short research summary, details of your research experience and your reasons for applying to undertake a PhD/MPhil with us. Whilst you are not expected to submit a detailed research proposal at any stage of the process, we do want to know that you have considered the areas of research that you wish to pursue.

Research areas

Click on a research area to find out more about available supervisors and their research:

Please note that a  large majority of the successful applicants for PhD studentships with  the High Energy Physics, and General Relativity & Cosmology (GR) groups   will have taken Part III of the Mathematical Tripos.

Funding Opportunities

Each Department works hard to secure funding for as many offer holders as possible, either from within its own funds, in collaboration with funding partners, or via the University Postgraduate Funding Competition. However, funding is not guaranteed via these routes, and you should investigate funding opportunities early in the process to be sure that you can meet advertised deadlines.

All application deadlines are 23:59pm (midnight) UK time on the stated date. So that your application can be given full consideration please apply by the following deadlines:

Note for PhD applicants:

We will accept applications for an October start up until the general University deadline in May, but your chances of obtaining funding are significantly reduced. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Only in exceptional circumstances will we consider admission to a later start date in the academic year (i.e., January or April). If you intend to apply for a later start date please contact us at [email protected] so we can advise you on the feasibility of your plan.

Note for MPhil applicants:

We will accept applications until the general University deadline in February, but you will not be considered for funding. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Most interviews are expected to take place in the second half of January.

The purpose of the interview is to try to ascertain the extent of the applicant's relevant knowledge and experience, and to gauge whether their interests and abilities align with the research of the potential supervisor and/or research group. It will most likely consist of a discussion of your background and motivations for applying to the course, as well as some questions on relevant topics.

Not all applicants will be selected for interview.

If you are selected for interview, you will be contacted by email at the address you provided on your application. The email should confirm:

• the location of the interview (it may be in-person or on-line dependent upon interviewer availability, your distance from Cambridge, as well as individual preferences),
• the interview format and whether you should prepare anything specific in advance,
• the approximate duration of the interview,
• who you will be meeting.

Prior to interview you may declare a disability, serious health problem or caring responsibility which may require reasonable adjustments for the interview to be made.

Due to interviewer availability and the tight admissions timetable, we can usually only rearrange the time and date of your interview under exceptional circumstances.

Decision timeline

Both DAMTP and DPMMS make most of their PhD/MPhil admissions decisions for October entry in January and early February, and you should not expect to receive a decision on your application before mid-February (even if you apply much earlier). We expect to have made decisions on all applications by mid-July. The Department makes every effort to take decisions on applications at the earliest opportunity. In some cases, however, it may take some time for a decision to be made. Applications may need to be viewed by several potential supervisors before a final decision can be reached.

To consider your application formally we must receive a complete application form, together with all supporting documents, by the deadline.

Communication of outcomes

You will be notified of the formal outcome of your application via the Applicant Portal.

Following an interview, you can normally expect to receive notification of the outcome within a week or two.

If you are successful, the University’s Postgraduate Admissions Office will issue a formal offer of admission which will outline all your conditions. As processing times can vary, we may also contact you informally to notify you of our decision.

We do not provide formal feedback to applicants who are unsuccessful at either the application or interview stage.

Take a look at our frequently asked questions for PhD applicants.

Forthcoming Seminars

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• Isaac Newton Institute Seminars

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graduate admissions

Frequently Asked Questions

More information for international students

Dear Prospective Applicant,

Thank you for your interest in graduate studies in the Department of Mathematics at UCLA. Applications are accepted for Fall quarter matriculation only. The application deadline is December 15. Application review process begins in late December; to ensure full consideration, applications should be complete, with all supporting material submitted, by that time.  Please note that admissions to the M.A. and M.A.T. programs have been suspended indefinitely, so if you’re interested in doing graduate work in our department you must apply for admission to the Ph.D. program.

You must submit the UCLA Graduate Admissions Application (see  http://www.gdnet.ucla.edu/gasaa/admissions/applicat.htm ). You also must submit the Application Fee for the UCLA Graduate Admissions Application. Instructions for this payment are given online. As part of the Graduate Division Application, you will be required to submit:

• Transcripts (scans and originals)
• Statement of Purpose
• Letters of Recommendation (see online UCLA application)
• List of Mathematics Courses taken
• Applicants whose native language is not English must take the TOEFL/IELTS exam and submit their TOEFL/IELTS score.

Each applicant must select an area (pure or applied) and a field of interest as part of the application. The two areas have slightly different course requirements, but both allow for flexibility to take many combinations of courses and qualifying exams throughout the department. Students can ask to switch areas or fields after starting the program if their interests change.

Transcripts (and TOEFL/IELTS scores, if required) should be mailed to:

Graduate Advisor UCLA Mathematics Department 520 Portola Plaza Los Angeles, CA 90095-1555

Admissions Requirements

The minimum Department requirements for applicants, in addition to the minimum University requirements, are:

*Applicants for the PhD program  must have a 3.5 GPA in upper division math courses.

Prospective students do not need to have an undergraduate mathematics major, but must complete at least 12-quarter, or 8-semester courses in substantial upper division mathematics.  Comparable Upper Division Courses at UCLA:

• Algebra 110AB : Ring of integers, integral domains, fields, polynomial domains, unique factorization. Groups, structure of finite groups.
• Linear Algebra 115AH : Abstract vector spaces, linear transformations, and matrices; determinants; inner product spaces; eigenvector theory.
• Analysis 131ABH : Rigorous introduction to foundations of real analysis; real numbers, point set topology in Euclidean space, functions, continuity. Derivatives, Riemann integral, sequences and series of functions, power series, Fourier series.
• Differential Geometry 120A : Curves in 3-space, Frenet formulas, surfaces in 3-space, normal curvature. Gaussian curvature. Congruence of curves and surfaces. Intrinsic geometry of surfaces, isometrics, geodesics, Gauss/Bonnet theorem.
• Ordinary Differential Equations 135AB : Systems of differential equations; linear systems with constant coefficients, analytic coefficients, periodic coefficients, and linear systems with regular singular points; existence and uniqueness results; linear boundary and eigenvalue problems; two-dimensional autonomous systems, phase/plane analysis, stability and asymptotic behavior of solutions.
• Applied Numerical Methods 151AB : Introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation issues. Solution of non-linear equations, numerical differentiation, integration, and interpolation. Numerical solution of differential equations.
• Three letters of recommendation with preferably all, but always at least 2, from mathematicians who are familiar with the student’s work.

The GRE Math Subject test . 

A General Recommendation:

The UCLA Mathematics Department encourages students to change their educational institution between their Bachelor and PhD degrees to broaden their horizons. In particular, no admissions advantage is given to UCLA undergraduates.

international students

Dear Prospective Applicant,

Thank you for your interest in graduate studies in the Department of Mathematics at UCLA. Applications are accepted for the Fall quarter only. The application deadline is December 15. The application review process begins late December; please ensure that all supporting documents, including reference letters and test scores, are received by that time. Please read all the information very carefully. In addition to the requirements below, return to Graduate Admissions for complete details.

Please note: THE UCLA Graduate Admissions Application fee is MANDATORY!! If the application fee is not paid, the UCLA Admissions Office cannot process the application.

Please note: DO NOT send publications.

Financial Support: International students are supported through a mix of fellowships, research assistantships, and teaching assistantships. Support is normally guaranteed for four years. A 5th year of support is usually provided if the student is in good standing and advanced to candidacy. Guaranteed support normally provides income that is enough for living expenses (exact amounts vary from year to year), and in addition provides full registration fees, health insurance, and non-resident tuition. All applicants are automatically considered for this financial support; no separate application is required. Students who have access to other means of support, for example scholarships from their own governments or international organizations, should apply for those separately.

Students whose first language is not English must pass UCLA’s “Test of Oral Proficiency” (TOP) before they can become teaching assistants at UCLA. Offers of support for international students are conditioned on passing this exam within the first year.

Required Tests

• GRE: Math Subject Test
• TOEFL/IELTS: Your TOEFL score on the paper and pencil test must be at least 560 (600 is recommended) or at least 87 on the internet-based test. Your IELTS Academic overall band score should be at least 7.0. 7.0 is the  minimum  required.
• TOP (Test of Oral Proficiency):  Minimum score of 6.4 is a provisional pass permitting the student to TA.

frequently asked questions

Thank you for your interest in graduate studies in the Department of Mathematics at UCLA. Applications are accepted for the fall quarter only. The application deadline is December 15. The application review process begins late December; please ensure that all supporting documents, including reference letters and test scores, are received by that time. Please return to Graduate Admissions for more detailed information or email  [email protected]  for very specific questions.

The on-line University application must be submitted by December 15. We will accept scores, letters and other materials after the December 15th deadline, but your application package will be considered incomplete and will not be reviewed if we do not have all materials by the end of the second week in January.

Not really.  Three letters are sufficient for the review committee to get a sense of your abilities and strengths. 

Either way is acceptable as long as they are officially sealed when we receive them.

International applicants that have received a Bachelor’s degree or higher from a university located in the United States, or from another country in which English is both the spoken language and the medium of instruction are exempted from the TOEFL.  Please include this information in your application package.

It is University policy that you score at least a 560 on the pencil and paper test, 220 on the electronic test, or 87 on the iBT.

Students who wish to apply for admission to our graduate program for the 2024-2025 academic year are to submit a GRE Math subject test score report as part of their application package. However, students are NOT required to submit the GRE General test score.

Please note that admissions to the M.A. and M.A.T. programs have been suspended until further notice. 

Be aware that when we talk about a successful applicant, numbers are only one part of the total package. That being said; the minimum GPA is 3.5 for a PhD and 3.2 for a Master’s, and although there is no minimum GRE, you must keep in mind that admission is very competitive and the higher your score, the better.  On the average, those we offer admission to have GRE subject scores in or above the 80th percentile. Our GPA range is from about 3.6 to 4.0, though again there can be exceptions. Keep in mind that we look at the entire package and although we have a minimum, the average is higher. Also, there is no score at any level, which insures admission.

The Statement is your opportunity to explain your reasons for pursuing graduate study in mathematics, and to let us get a sense of who you are.  You may mention any relevant facts about your education or experience with mathematics that are not apparent in the other materials you submit.  You might want to note what kind of mathematics you find interesting and wish to pursue in graduate school, and what you plan to do after obtaining a Ph.D. It may include information about your background, interests, or career goals, and how UCLA might help you meet those career and educational goals.  There is no specific length, but one or two pages are typical.

Your application will be accepted if we receive your scores by the end of the first week in January.

Admission decisions are based on an applicant’s entire package.  Weaknesses in one area may be offset by strengths in another. The committee weighs many factors in addition to GPAs.  These may include the breadth of your undergraduate courses, your letters of recommendation, statement of purpose and GRE subject score.

You may apply for admission to our program before your actual degree date as long as you have your Bachelor degree by the fall enrollment date.

The UCLA code is 4837 and the Mathematics department code is 0703.

One of the most important things you can do is to get to know your professors. You want to have letters of recommendation that tell us knowledgeably and personally about your qualifications and abilities. Your letters of recommendation should attest to the fact that you have the potential and mathematical background to be a research mathematician. It is already expected that all applicants to UCLA have a solid preparation in undergraduate math, with strong grades and GRE scores, that allows them at a minimum to pass our Basic Qualifying Exam in their first year. What we would also like to see in addition is that you have potential for advanced mathematical research. This can be demonstrated through courses that are heavy in proof oriented math, honors and graduate courses, a senior research project, a senior thesis, or a summer REU program.

You will receive an official letter by the first week of March.

Imperial College London Imperial College London

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Doctoral programme

Doctoral programme information

Prospective PhD students

Find out more about doctoral study in the Department of Mathematics including entry requirements, funding, how to apply and our areas of research.

Current PhD students

Information for current doctoral students in the Department of Mathematics. Prospective students are also welcome to view these pages.

King's College London

Applied mathematics research: disordered systems/financial mathematics/probability mphil/phd, key information.

We have a wide range of research opportunities in the Department of Mathematics. We recommend that you explore and identify research topics and academic staff in your area of interest.

You can explore potential supervisors on our research group pages . Click here for all the details on how to make an application.

If you apply for this programme you will be doing research in one of our research groups which are listed below. You can click to explore more information about them:

Disordered Systems

Financial mathematics, probability.

If you are interested in Theoretical Physics, please visit this page: Applied Mathematics Research: Theoretical Physics - King's College London (kcl.ac.uk)

Head of Department: Professor Steven Gilmour

Course intake

PhD: 8-20 full-time, 2-5 part-time per year MPhil: 5-10 full-time, 1-5 part-time per year

Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The research groups organise regular seminars, where top-ranking scientists from around the world present new results, which our research students can witness first hand. The students also organise their own informal seminars and discussion groups. The lively environment and the exceptionally friendly atmosphere at our department contribute to the high success rate of our students. You can apply for supervision in all fields of interest of our staff members. The department provides funding for PhD students to attend suitable schools and conferences during their studies.

More than 80% of the PhD students at the department are fully funded through a number of funding schemes; the most common is departmental funding which covers tuition as well as a living stipend. In recent years, on average, 10 students per year have been admitted to a PhD programme with funding from the department.

• How to apply
• Fees or Funding

For funding opportunities please explore these pages:

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

UK Tuition 2023/24

Full time tuition fees: £6,540 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £3,270 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £6,540 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £3,270 per year (MPhil/PhD, Mathematics Research)

International Tuition Fees 2023/24

Full time tuition fees: £24,360 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £12,180 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £24,360 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £12,180 per year (MPhil/PhD, Mathematics Research)

UK Tuition 2024/25

Full time tuition fees: £6,936 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £3,468 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £6,936 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £3,468 per year (MPhil/PhD, Mathematics Research)

International Tuition Fees 2024/25

Full time tuition fees: £26,070 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £13,035 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £26,070 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £13,035 per year (MPhil/PhD, Mathematics Research)

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

Full time tuition fees:

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

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

Part time tuition fees:

£12,180 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

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

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

£13,035 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

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

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

• Study environment

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

Postgraduate training

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

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

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

• Entry requirements
• Research groups

The Disordered Systems group at King's is at the forefront of research in statistical mechanics of disordered and complex systems.

King’s College has a large and thriving Financial Mathematics group, with an international reputation for research excellence. 

The Probability group in the Department of Mathematics at King's College London.

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Softening the sharp edges in mathematics.

For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start — to approach the subject with playfulness and curiosity, not anxiety or dread.

“Most people have only ever experienced what I call narrow mathematics — a set of procedures they need to follow, at speed,” Boaler says. “Mathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.”

“Mathematics should be flexible, conceptual, a place where we play with ideas and make connections," says Professor Jo Boaler. (Photo: Robert Houser Photography)

Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced “How to Learn Math,” the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users. 

In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls “ishing” a math problem can help students make better sense of the answer. 

What do you mean by “math-ish” thinking?

It’s a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport – these are generally answered with what I call “ish” numbers, and that’s very different from the way we use and learn numbers in school.

In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. They’re given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 — but the most common answer 13-year-olds gave was 19. The second most common was 21. 

I’m not surprised, because when students learn fractions, they often don’t learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.

But don’t you also risk sending the message that mathematical precision isn’t important? 

I’m not saying precision isn’t important. What I’m suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, they’ll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.

Some people ask me, “Isn’t ‘ishing’ just estimating?” It is, but when we ask students to estimate, they often groan, thinking it’s yet another mathematical method. But when we ask them to “ish” a number, they're more willing to offer their thinking.

Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mind-set. I think we all need a little more ish in our lives. 

You also argue that mathematics should be taught in more visual ways. What do you mean by that? 

For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things — all of that contributes to our understanding of how it works. 

There’s an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubik’s Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking. 

Some years back we were interviewing students a year after they’d done that activity in our summer camp and asked what had stayed with them. One student said, ‘I’m in geometry class now, and I still remember that  sugar cube, what it looked like and felt like.’ His class had been asked to estimate the volume of their shoes, and he said he’d imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.

When we learn about cubes, most of us don’t get to see and manipulate them. When we learn about square roots, we don’t take squares and look at their diagonals. We just manipulate numbers.

I wonder if people consider the physical representations more appropriate for younger kids.

That’s the thing — elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school it’s all symbolic. There’s a myth that there’s a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.

Click to enlarge: A depiction of various ways to calculate 38 x 5, numerically and visually. (Image: Courtesy of Jo Boaler)

There’s an example in the book where you’ve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldn’t it be easier to teach students one standard method?

That narrow, rigid version of mathematics where there’s only one right approach is what most students experience, and it’s a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, they’re not developing number sense. They don’t learn how to use numbers flexibly in different situations. It also makes students who think differently believe there’s something wrong with them. 

When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, it’s powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.

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PhD position in mathematics or mathematical statistics, with focus on geometric deep learning

Job Information

Offer description.

The Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematics or mathematical statistics, focusing on geometric deep learning. The position covers four years of third-cycle studies, including participation in research and third-cycle courses. The last day to apply is August 26th 2024.

Project description and tasks  Machine learning (‘artificial intelligence’) is having an immense impact on both society at large and research especially, and this impact is expected to increase. This boom is driven by so-called deep neural networks, a class of machine learning models proven incredibly powerful, versatile, and capable of solving many machine learning tasks. Mathematicians have taken huge steps towards theoretically understanding their empirical success, but many open questions remain.

A subfield within neural network theory is geometric deep learning. It concerns symmetries in the data or the learning task and constructing neural networks that react properly to them (equivariant networks). Examples of such symmetries are symmetries towards rotations of point clouds, translations of images or permutations of nodes in graphs. Combining the geometric/algebraic theory of (group) symmetries with the more analytical/statistical theory of machine learning allows for mathematically multifaceted research.

The project aims at deepening the mathematical theory of geometric deep learning. Exciting research questions include the development of new ways of constructing equivariant networks, describing the resulting models mathematically, and directly analyzing how symmetries affect the training of neural networks.

The project is affiliated with the AI/Math track within Wallenberg AI, Autonomous Systems and Software Program (WASP), and the PhD student will take part in the WASP graduate school.

Qualifications  The doctoral student will be admitted to study one of the two third-cycle programmes: Mathematics or Mathematical Statistics. To fulfil the general entry requirements, the applicant must have qualifications equivalent to a completed degree at second-cycle level or completed course requirements of at least 240 ECTS credits, including at least 60 ECTS credits at second-cycle level. 

To fulfil the specific entry requirements to be admitted for studies in either mathematics or mathematical statistics, the applicant is required to have completed at least 60 ECTS credits within mathematics or mathematical statistics, of which at least 15 ECTS credits shall have been acquired at second-cycle level. Applicants who have acquired largely equivalent skills in some other system, either within Sweden or abroad, are also eligible. 

Good programming skills (preferably Matlab or Python) and good written and spoken English knowledge are required. Documented knowledge and experience in machine learning, image analysis, probability theory, differential geometry, algebra, optimization, representation theory and functional analysis are merits. Note that you are not expected to have specialist knowledge in all of the above-listed fields. You will acquire knowledge as a part of your doctoral studies and be able to collaborate with others to complement your specific skill set.

You are expected to take an active role in this project and institutional work. You have a scientific mindset and are determined to continuously develop your skills and contribute to mathematical machine learning research. 

The assessment of applicants is based on their qualifications and ability to benefit from the doctoral study they will receive. 

About the employment  The employment is a full-time paid position, for a fixed term of four years full-time or up to five years when teaching part-time. The position is intended to result in a doctoral degree.  The position is intended to result in a doctoral degree. The main task of doctoral students is to pursue their third-cycle studies, including active participation in research and third-cycle courses and activities and courses at the WASP graduate school. The duties may include teaching or other departmental work, although duties of this kind may not comprise more than 20 per cent of a full-time post. Salary is set according to the salary ladder for PhD positions at Umeå University. Employment commences in the winter of 2024/2025 or by agreement. 

You will become a part of the young and growing research group Mathematical Foundations of Artificial Intelligence at the Department of Mathematics and Mathematical Statistics. Most junior and senior researchers in this group are connected to WASP and research topics similar to those with which this project is concerned. This provides opportunities for exciting collaborations, both internally and externally. For more information, see https://www.umu.se/en/department-of-mathematics-and-mathematical-statis…

The WASP graduate school is dedicated to providing the skills needed to analyze, develop, and contribute to the interdisciplinary area of artificial intelligence, autonomous systems and software. The graduate school actively supports forming a strong multi-disciplinary and international professional network between PhD students, researchers, and industry through an ambitious program that includes research visits, partner universities, and visiting lecturers. Read more: https://wasp-sweden.org/graduate-school/&nbsp ;

Application  Application should be made in our electronic recruitment system before August 26th 2024. Log in and apply using the button at the bottom of the page. The application must include the following documents written in English or Swedish: 

• a personal letter with a brief description of your qualifications and research interests. Motivate why you are applying for the position and how your qualifications and merits are relevant.
• a curriculum vitae.
• authenticated copies of degree certificates, diplomas or equivalent, including documentation of completed academic courses, received grades, and possibly other certificates.
• copies of relevant work such as a Master’s thesis or articles you have authored or co-authored. If the master’s thesis has not been completed before the application deadline, a summary of the master’s thesis project and current progress shall be included. The summary can be at most five pages, including figures and references.
• contact information for at least two reference persons.
• if available, GMAT, GRE, TOEFL or IELTS scores may be submitted.

Umeå University wants an equal environment where open dialogue between people with different perspectives lays the foundation for learning, creativity and development. The people working at the Department of Mathematics and Mathematical Statistics have diverse backgrounds and experiences, which we value. Work-life balance is essential for us: Employees are supported in caring for their mental and physical health, and we accommodate students taking parental leave during their studies – this is not uncommon. In this spirit, we encourage everyone to apply. 

Pursuant to Chapter 12 Section 2 of the Swedish Higher Education Ordinance (SFS 1993:100), the decision regarding the position cannot be appealed.

More information Further information is provided by Professor Jun Yu ( [email protected] ) or Assistant Professor Axel Flinth ( [email protected] ).

More information about the Department of Mathematics and Mathematical Statistics: https://www.umu.se/en/department-of-mathematics-and-mathematical-statis… ;

Wallenberg AI, Autonomous Systems and Software Program (WASP) is Sweden’s largest individual research program ever, a major national initiative for strategically motivated basic research, education, and faculty recruitment. The program addresses research on artificial intelligence and autonomous systems acting in collaboration with humans, adapting to their environment through sensors, information and knowledge, and forming intelligent systems-of-systems. The vision of WASP is excellent research and competence in artificial intelligence, autonomous systems and software for the benefit of Swedish society and industry. Read more: https://wasp-sweden.org/&nbsp ;

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2023 Spring EDUC 131AC 001 SEM 001

Institute of Brand and Innovation Law

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UCL LLM graduate, Dheemanth Vangimalla, wins an international research essay prize

22 May 2024

UCL Laws LLM graduate, Dheemanth Vangimalla, wins the top award in the 4iP Council Research Awards 2023 for a paper based on his LLM research dissertation. Dheemanth will be speaking about his research topic at a webinar organised by 4iP Council, on 30th May.

We are delighted to announce that Dheemanth Vangimalla, a recent UCL Laws graduate of the LLM in Intellectual Property Law has received the top award in the prestigious 4iP Council Research Awards for 2023 for his paper entitled ‘Plausibility and the flotilla: have the English courts drifted from the commodore’s approach to the evidential requirement for patent validity, and if so, is this divergence justified?’

The 4iP Council Research Award is an international research competition for European University students studying at Masters and PhD levels. It seeks to promote new ideas on topics pertinent to the interplay between intellectual property rights and innovation. Submissions, based on a student’s Masters or PhD research, are assessed by 4iP Council’s Research Award Jury made up of intellectual property experts from academia, government and industry. The papers are evaluated based on criteria including:

• Original thinking that broadens the debate on the chosen topic;
• High quality written expression; and
• Relevance to current IP problems and debate

and up to three prizes are awarded (winner and two runners-up).

In his winning paper, Dheemanth considered the origins of ‘plausibility’ and explored the evidential requirement that the term represents. His research revealed that there is divergence between the EPO and English courts in the evidential standard applied by the two decision-making bodies when assessing patent validity. He argues that the English courts adopting a higher standard lacks cogent justification as the standard neither reflects a balance between the competing objectives of the patent system nor limits a plausibility assessment to its targeted mischief. 

This paper was based on Dheemanth’s dissertation for his LLM in Intellectual Property Law, which was also recently awarded the IBIL Prize for Top Performance in an IP-related Research Essay on the LLM . During his LLM, Dheemanth was supervised by our IBIL scholarship PhD researcher, Joshua Bradley .

As part of the prize, the winning essay has been published on 4iP Council’s website , and Dheemanth will be speaking at a webinar about plausibility - orgainised by 4iP - along with IBIL's Professor Jacob, on 30 May. More details of the event can be found here . 

Having completed his LLM in the summer of 2023, Dheemanth has been working as a Research Assistant at the UCL Institute of Brand and Innovation Law  (IBIL), while also completing his bar exams. He will join Three New Square Chambers in the autumn as a pupil barrister.

• Read Dheemanth’s paper here .
• Find out more about the 4iP Council Research Awards
• Register to attend:  Plausibility: from herbicides to insecticides and beyond .