cambridge applied math phd

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PhD in Applied Mathematics and Theoretical Physics

University of cambridge, different course options.

• Key information

Course Summary

Tuition fees, entry requirements, similar courses at different universities, key information data source : idp connect, qualification type.

PhD/DPhil - Doctor of Philosophy

Subject areas

Applied Mathematics Theoretical Physics Applied Physics

Course type

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

Assessment for the PhD is by submission of a thesis and oral examination only. There is no standard format for the thesis in mathematics (ie no prescribed word limit). Candidates should discuss the format appropriate to their topic with their supervisor.

The Mathematics Degree Committee oversees the examinations process and is responsible for approving the research title of the thesis, appointing examiners and scrutinising the reports of those examiners before making a decision on the outcome.

UK fees Course fees for UK students

For this course (per year)

International fees Course fees for EU and international students

Applicants for this course should have achieved a UK First class Honours Degree. The usual minimum entry requirement is a first-class honours degree, awarded after a four-year course in physics, mathematics or engineering, or a three-year degree together with a one-year postgraduate course on advanced mathematics and theoretical physics. Part III (MMath/MASt) of the Mathematical Tripos provides such a course. Note, however, that entry is competitive and a higher level of preparation may be required for research in some subject areas.

MSc Applied Mathematical Sciences

Heriot-watt university, phd applied mathematics, university of essex, applied mathematics phd, university of birmingham, applied mathematics mres, mphil applied mathematics.

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Universities attended by math PhD students at Harvard and UC Berkeley

On another thread I left a comment with some data I'd compiled about grad students in math at Harvard. I went through the list of grad students there and compiled the undergraduate universities for those that I could find. I'll copy the results over here, for ease (but see this comment for some updates to this from a Harvard PhD student):

I just went through the list of Harvard grad students. Of the 43 I could find information about (which is a large majority but not everyone), 25 did their undergrad in the USA and 18 did so internationally. The breakdown is as follows:

|University | Number| |:---------|--------:| |MIT |9| |Stanford |4| |Princeton |3| |Caltech |2| |Columbia |2| |University of Chicago |2| |Notre Dame |1| |University of Illinois Urbana-Champaign |1| |University of Washington |1|

And for international universities:

|University | Number| |:---------|--------:| |Cambridge [UK] |5| |University of Toronto [Canada] |3| |Chennai Mathematical Institute [India] |1| |ETH Zurich [Switzerland] |1| |Jacobs University [Germany] |1| |McGill [Canada] |1| |National Taiwan University [Taiwan] |1| |Sharif University of Technology [Iran] |1| |Taida Institute for Mathematical Sciences [Taiwan] |1| |Tsinghua University [China] |1| |University of Moscow [Russia] |1| |University of Pisa [Italy] |1|

Some further notes:

There are only three people from what I'd consider domestic, non-elite undergrads. I know one of them was a huge prodigy.

Many of the Americans did very well on the Putnam (Harvard's Putnam Fellowship probably doesn't hurt here), while many of the international students were IMO medalists. Of the Cambridge students, at least one was Senior Wrangler (single best student of the year, out of a couple hundred) and at least one more was like top 2-3.

The people I couldn't find data on seemed disproportionately to have Chinese names, so China is almost certainly better-represented than my data makes it seem.

Anyway, I spent the past couple hours compiling the same data for UC Berkeley, and since I thought this might be quite interesting to people, here it is.

There are somewhere around ~190 or so Berkeley grad students (this is just an estimate). I found undergraduate university for 144 of them, around 75%. Of those 144, 106 went to US universities (74%) while the other 38 went to international universities (26%). Here's the breakdown:

And the internationals:

Some notes on this:

Berkeley has people with a wide range of backgrounds. There was somebody who'd taken about 30 years in industry and was only just going back for his PhD. There were people who hadn't majored in math for undergrad. And, of course, there's a far wider ranger of universities than there is at Harvard.

A few people at some of the lower-ranked domestic universities had done masters degrees at higher-ranked places. A nontrivial number of people had also done Part III at Cambridge.

High scorers on the Putnam were still to be found, but not nearly as abundantly as at Harvard. As with Harvard, however, many of the international students had IMO experience. Given also the relative number of domestic vs international students at Berkeley, I suspect the bar for internationals is rather higher than for domestic students.

One final note: Columbia publishes data about their incoming classes here , so it would be relatively easy to compile the same data for Columbia. I would take maybe the last five years worth of incoming classes, which is probably approximately the makeup of their grad students. I'll leave that for someone else to do.

If anyone has the stamina to do this for another university, I think MIT and Stanford could be quite interesting. Princeton would be interesting in the sense that I strongly suspect that a majority of their grad students are from either MIT or Harvard.

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Applied Mathematics

Cambridge is a leading global publisher in applied mathematics, with an extensive programme of high-quality journals that reaches into every corner of the subject.

Our catalogue of 18 journals in applied mathematics reflects not only the breadth of mathematics but also its depth, with titles read by undergraduate students, for graduate students, for researchers and for users of mathematics. 

Below are examples of some of the popular books within the discipline, including complimentary access to free sample chapters. You can search for applied mathematics books  here .

Learn more about  mathematics on Cambridge Core by visiting the subject page .

Journals and free articles  

Resources for authors

Books and sample chapters  

Applied mathematics journals from Cambridge

Cambridge publishes 18 journals in the discipline of applied mathematics. Here is a selection of some of the high-quality peer reviewed titles. To find out more information including the scope, the editorial board, and how you can submit your article, click on the journal cover.

Advances in Applied Probability

European Journal of Applied Mathematics

The ANZIAM Journal

Acta Numerica

Journal of Applied Probability

Journal of Fluid Mechanics

The Mathematical Gazette

Probability in the Engineering and Informational Sciences

Each of the following papers is available with complimentary access, representing the wide array of mathematics journals available from Cambridge.

Finite-volume schemes for shallow-water equations

• Alexander Kurganov
• Acta Numerica , Volume 27

Applied probability as theoretical science: 50 years in the applied probability community

• Peter Jagers
• Advances in Applied Probability , Volume 50 , Issue A

OPTIMAL INVESTMENT AND CONSUMPTION WITH STOCHASTIC FACTOR AND DELAY

• L. LI , H. MI
• The ANZIAM Journal , Volume 61 , Issue 1

A new class of costs for optimal transport planning

• J.-J. ALIBERT , G. BOUCHITTÉ , T. CHAMPION
• European Journal of Applied Mathematics , Volume 30 , Issue 6

Mixing hot and cold with sound

• Nitesh Nama
• Journal of Fluid Mechanics , Volume 866

Reliability assessment of system under a generalized run shock model

• Min Gong , Min Xie , Yaning Yang
• Journal of Applied Probability , Volume 55 , Issue 4

Calculation of π with a needle

• Athina Lorentziadi
• The Mathematical Gazette , Volume 103 , Issue 556

A generalisation of von Staudt’s theorem on cross-ratios

• YATIR HALEVI , ITAY KAPLAN
• Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 3

A case study in programming coinductive proofs: Howe’s method

• ALBERTO MOMIGLIANO , BRIGITTE PIENTKA , DAVID THIBODEAU
• Mathematical Structures in Computer Science , Volume 29 , Issue 8

ELLIPSOIDS ARE THE ONLY LOCAL MAXIMIZERS OF THE VOLUME PRODUCT

• Mathieu Meyer , Shlomo Reisner
• Mathematika , Volume 65 , Issue 3

A PARTICULAR BIDIMENSIONAL TIME-DEPENDENT RENEWAL RISK MODEL WITH CONSTANT INTEREST RATES

• Ke-Ang Fu , Chang Ni , Hao Chen
• Probability in the Engineering and Informational Sciences , Volume 34 , Issue 2

Duality between p -groups with three characteristic subgroups and semisimple anti-commutative algebras

• S. P. Glasby , Frederico A. M. Ribeiro , Csaba Schneider
• Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , Volume 150 , Issue 4

Relevant books

The Fluid Dynamics of Cell Motility

Think Before You Compute

• E. J. Hinch

Data-Driven Science and Engineering

• 2nd edition
• Steven L. Brunton , J. Nathan Kutz

Data-Driven Fluid Mechanics

• Edited by Miguel A. Mendez , Andrea Ianiro , Bernd R. Noack , Steven L. Brunton

Network Models for Data Science

• Alan Julian Izenman

Transport Barriers and Coherent Structures in Flow Data

• George Haller

Click on the links below to read chapter samples for free

1 - topological spaces.

• from Part I - Topological Preliminaries
• Jean-Daniel Boissonnat , Frédéric Chazal , Mariette Yvinec
• Book: Geometric and Topological Inference

1 - Analytical Methods

• from Part One - Theory
• Yuri A. Kuznetsov , Universiteit Utrecht, The Netherlands , Hil G. E. Meijer , University of Twente, Enschede, The Netherlands
• Book: Numerical Bifurcation Analysis of Maps

1 - Singular Value Decomposition (SVD)

• from Part I - Dimensionality Reduction and Transforms
• Steven L. Brunton , University of Washington , J. Nathan Kutz , University of Washington
• Book: Data-Driven Science and Engineering

Chapter 1 - Approximation of Univariate Functions

• V. Temlyakov , University of South Carolina
• Book: Multivariate Approximation

1 - Introduction and Problem Formulation

• W. O. Criminale , University of Washington , T. L. Jackson , University of Florida , R. D. Joslin
• Book: Theory and Computation in Hydrodynamic Stability

1 - Introduction to Analysis of Low-Speed Impact

• W. J. Stronge , University of Cambridge
• Book: Impact Mechanics

1 - Kinematics, Balance Equations, and Principles of Stokes Flow

• Michael D. Graham , University of Wisconsin, Madison
• Book: Microhydrodynamics, Brownian Motion, and Complex Fluids

Professor Raymond Goldstein, Batchelor Prize lecture 2016

An interview with JFM Batchelor Prize winner Prof. Raymond E. Goldstein

• Email & phone list
• PhD projects

Professor Anders C. Hansen

Anders C. Hansen leads the Applied Functional and Harmonic Analysis group within the Faculty of Mathematics at the University of Cambridge and Department of Applied Mathematics and Theoretical Physics (DAMTP) . He is a Professor of mathematics  at the University of Cambridge, Professor of Mathematics at the University of Oslo , a Royal Society University Research Fellow and also a Fellow of Peterhouse . For further information, see Wikipedia .

Email: [email protected] Tel: +44 1223 760403 Office: F2.01

Research Interests

Functional Analysis, Artificial Intelligence, Foundations of Computational Mathematics, Solvability Complexity Index hierarchy, Generalised Hardness of Approximation,  Optimisation, Inverse Problems, Medical Imaging,   Operator/Spectral Theory,  Numerical Analysis, Computational Harmonic Analysis, PDEs, Compressed Sensing,   Mathematical Signal Processing, Sampling Theory, Geometric Integration, Operator Algebras

Selected Talks and Events

• Plenary speaker at  International Conference on Mathematical Theory of Deep Learning  (August 5-9, 2024).
• Plenary speaker at  10th International Conference on Mathematical Methods for Curves and Surfaces  (June 26-28, 2024).
• Plenary speaker at  Nordic Perspectives on Artificial Intelligence  (Oct. 12-13, 2023).
• Organizing the workshop Computational mathematics in computer assisted proofs  (Sept 12-16, 2022) together with Charles Fefferman and Svetlana Jitomirskaya.
• Plenary speaker at  Thirty years of Acta Numerica  (26 June - 02 July 2022).
• Speaking at King's College London Mathematics Colloquium  (12 May, 2022).
• Organizing the workshop Interpretability, safety, and security in AI  (Dec 13-15, 2021) together with Rich Baraniuk , Miguel Rodrigues and Adrian Weller.
• Speaking (online) at the University of Chicago Mathematics Colloquium  (April 7, 2021).
• Speaking (online) at the Cambridge Science Festival  (March 29, 2021).
• Speaking at the University of Minnesota, Applied and Computational Math Colloquium  (Feb. 3 2020)
• Plenary speaker at the   National Academy of Sciences, Arthur M. Sackler Colloquim: The Science of Deep Learning, Washington D.C. (March 2019) .
• Plenary speaker at SPARS (2017).
• Plenary speaker at Structured Regularization for High-Dimensional Data Analysis, Institut Henri Poincaré (2017).
• Plenary speaker at Strobl16: Time-Frequency Analysis and Related Topics (2016) .
• Plenary speaker at UCL-Duke Workshop on Sensing and Analysis of High-Dimensional Data (2014) .

Prizes and Awards

1. PROSE Award Finalist 2022 - Computing & Information Science .

2. Whitehead Prize 2019 .

3.  2018 IMA Prize in Mathematics and Applications .

4.  Leverhulme Prize in Mathematics and Statistics 2017 .

5.  Royal Society University Research Fellow 2012 .

1.  SIAM News  reports (front page) on our work in the recent May edition:  Proving existence is not enough: Mathematical paradoxes unravel the limits of neural networks in AI .

2.  IEEE Spectrum Magazine  reports on our paper   "The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem."  

3. Proc. Natl. Acad. Sci. published our paper   "The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem."   Here is the announcement from Cambridge University News.   Further press coverage here.  

for our book   Compressive Imaging: Structure, Sampling, Learning   (with B. Adcock) on   Cambridge University Press .

5.  SIAM News  reports (front page) on our work from the paper   "The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks"   in the recent October edition:  Deep Learning: What Could Go Wrong? .

6.  SIAM News  reports on our work on deep learning in scientific computing in the recent March edition:  Deep Learning in Scientific Computing: Understanding the Instability Mystery .

7. Proc. Natl. Acad. Sci. published our paper   On instabilities of deep learning in image reconstruction and the potential costs of AI Here is some of the press coverage: Cambridge University News,   Physics World,   EurekAlert,   The Register,   Health Care Business,   Radiology Business,   Science Daily,   Psychology Today,   Government Computing,   Diagnostic Imaging,   News Medical,   Press Release Point,   Tech Xplore,   Aunt Minnie,   My Science,   Digit,   The Talking Machines,   MC.AI,   Rama on Healthcare,   News8PLus,   Genethique,   Healthcare in Europe,   AuntminnieEurope,   Newsbreak,   AI Development Hub,   FirstWord MedTech,   AI Daily.  

8. Our paper  How to compute spectra with error control   is on the cover of the last June edition of Physical Review Letters .

9. The Sackler Colloquium at the US National Academy of Sciences: "The Science of deep learning" . Watch the presentation "On instabilities in deep learning - Does AI come at a cost?"  

10.  SIAM News  has our work on the  Restricted Isometry Property in Levels  in compressed sensing on the front page of the October edition:  From Global to Local: Getting More from Compressed Sensing .

“[...] The image resolution has been greatly improved [...]. Current results practically demonstrated that it is possible to break the coherence barrier by increasing the spatial resolution in MR acquisitions. This likewise implies that the full potential of the compressed sensing is unleashed only if asymptotic sparsity and asymptotic incoherence is achieved.”

Their work  Novel Sampling Strategies for Sparse MR Image Reconstruction  was published in May 2014 in the Proceedings of the International Society for Magnetic Resonance in Medicine.

Students and Post-Docs

Post-docs: 1. Jonathan Ben-Artzi ( 2011-2014, PhD: Brown University), 2. Bogdan Roman ( 2013-2016, 2016-2019, PhD: University of Cambridge), 3. Priscilla Canizares (2015-2016, PhD: Autonomous University of Barcelona), 4. Milana Gataric (2015-2016, PhD: University of Cambridge), 5. Francesco Renna (2016-2018, PhD: University of Padova), 6. Alexander Bastounis (2019-2021, PhD: University of Cambridge), 7. Vegard Antun (2020-, PhD: University of Oslo), 8. Alexei Stepanenko (2022-2023, PhD: Cardiff University).

NST Part IA Mathematical Methods I - Course A .

Part II Numerical Analysis .

Part III course on Compressed Sensing .

Proceedings of the Royal Society Series A (2014-2020)

Networks & Heterogeneous Media (2021- )

SIAM Journal on Imaging Sciences (2022- )

BIT Numerical Mathematics (2023- )

Books  

• B. Adcock, A. C. Hansen,  Compressive Imaging: Structure, Sampling, Learning ,  Cambridge University Press (2021)

Selected Papers  

• A. C. Hansen, On the Solvability Complexity Index, the n-Pseudospectrum and Approximations of Spectra of Operators , J. Amer. Math. Soc. 24, no. 1, 81-124
• J. Ben-Artzi, M. Colbrook, A. C. Hansen, O. Nevanlinna, M. Seidel, Computing spectra - On the Solvability Complexity Index hierarchy and towers of algorithms .
• A. Bastounis, A. C. Hansen, V. Vlacic,   The extended Smale's 9th problem. 
• V. Antun, F. Renna, C. Poon, B. Adcock, A. C. Hansen,  On instabilities of deep learning in image reconstruction and the potential costs of AI ,  Proc. Natl. Acad. Sci. 2020, no. 5, 201907377
• M, Colbrook, V. Antun, A. C. Hansen,  The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem. 
• B. Adcock, A. C. Hansen, C. Poon, B. Roman,  Breaking the coherence barrier: A new theory for compressed sensing , Forum of Mathematics, Sigma  5(4):1-84
• M. Colbrook, A. C. Hansen,  The foundations of spectral computations via the Solvability Complexity Index hierarchy  
• B. Adcock, A. C. Hansen, Generalized Sampling and Infinite Dimensional Compressed Sensing , Found. Comp. Math.  16, no. 5, 1263-1323
• M. Colbrook,  B. Roman, A. C. Hansen,  How to compute spectra with error control ,  Phys. Rev. Lett. 122, 250201 (front cover)

SIAM News  

• V. Antun, M, Colbrook, A. C. Hansen,  Proving existence is not enough: Mathematical paradoxes unravel the limits of neural networks in AI. 
• A. Bastounis, A. C. Hansen, D. Higham, I. Tyukin, V. Vlacic,   Deep Learning: What Could Go Wrong? 
• V. Antun, N. Gottschling, A. C. Hansen, B. Adcock, Deep Learning in Scientific Computing: Understanding the Instability Mystery . SIAM News, 54, no. 2 March 2021
• A. Bastounis, B. Adcock, A. C. Hansen, From Global to Local: Getting More from Compressed Sensing , SIAM News, 50, no. 8 October 2017 (front cover)

Papers in Chronological Order  

• A. Bastounis, F. Cucker, A. C. Hansen,   When can you trust feature selection? -- I: A condition-based analysis of LASSO and generalised hardness of approximation. 
• A. Bastounis, F. Cucker, A. C. Hansen,   When can you trust feature selection? -- II: On the effects of random data on condition in statistics and optimisation. 
• N. Gottschling, P. Campodonico, V. Antun, A. C. Hansen, On the existence of optimal multi-valued decoders and their accuracy bounds for undersampled inverse problems  .
• J. S. Wind, V. Antun, A. C. Hansen,   Implicit regularization in AI meets generalized hardness of approximation in optimization -- Sharp results for diagonal linear networks. 
• A. Bastounis, A. C. Hansen, V. Vlacic,   The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning. 
• S. Becker, A. C. Hansen,  Computing solutions of Schrodinger equations on unbounded domains - On the brink of numerical algorithms. 
• A. Bastounis, A. C. Hansen, V. Vlacic,   The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks. 
• N. Gottschling, V. Antun, B. Adcock, A. C. Hansen,  The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems. 
• Z. Liu, A. C. Hansen,   Do stable neural networks exist for classification problems? -- A new view on stability in AI. 
• L. Gazdag, A. C. Hansen,   Generalised hardness of approximation and the SCI hierarchy - On determining the boundaries of training algorithms in AI. 
• L. Thesing, A. C. Hansen,   Which neural networks can be computed by an algorithm? -- Generalised hardness of approximation meets Deep Learning. 
• V. Antun, M, Colbrook, A. C. Hansen,  The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem. 
• T. Loss, M, Colbrook, A. C. Hansen,  Stratified Sampling Based Compressed Sensing for Structured Signals. 
• M. Colbrook, A. C. Hansen,  The foundations of spectral computations via the Solvability Complexity Index hierarchy. 
•  L. Thesing, V. Antun, A. C. Hansen,  What do AI algorithms actually learn - On false structures in deep learning. 
•  L. Thesing, A. C. Hansen,  Non-uniform recovery guarantees for binary measurements and infinite-dimensional compressed sensing. 
• B. Adcock, V. Antun,  A. C. Hansen,  Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
• J. Schoormans, G. J. Strijkers, A. C. Hansen, A. J. Nederveen, B. F. Coolen,  Compressed Sensing MRI with Variable Density Averaging (CS-VDA) Outperforms Full Sampling at Low SNR .
• M. Colbrook,  B. Roman, A. C. Hansen,  How to compute spectra with error control ,  Phys. Rev. Lett. 122, 250201
• A. C. Hansen, B. Roman,  Structure and Optimisation in Computational Harmonic Analysis: On Key Aspects in Sparse Regularisation ,  Springer Optimization and Its Applications  vol. 168: 125-172 (2021)  
• M. Colbrook, A. C. Hansen,  On the Infinite-dimensional QR Algorithm ,   Numerische Mathematik   143:17�83 (2019)
• R. Calderbank, A. C. Hansen, L. Thesing, B. Roman  On reconstructions from measurements with binary functions,    Applied and Numerical Harmonic Analysis. Birkhauser  97-128 (2019)  
• L. Thesing, A. C. Hansen,  Linear reconstructions and the analysis of the stable sampling rate ,   Sampl. Theory Signal Image Process.   17:103-126 (2018)  
• A. C. Hansen, L. Thesing,  On the Stable Sampling rate for binary measurements and wavelet reconstruction ,   Appl. Comput. Harmon. Anal.  48(2): 630-654 (2020)  
• A. Bastounis, B. Adcock, A. C. Hansen, From Global to Local: Getting More from Compressed Sensing , SIAM News, 50, no. 8 October 2017
• A. C. Hansen, L. Thesing, Sampling from binary measurements - On Reconstructions from Walsh coefficients, IEEE 2017 Int. Conf. on Samp. Theory and Appl.  256-260 (2017)
• A. Bastounis, A. C. Hansen, On the absence of uniform recovery in many real-world applications of compressed sensing and the RIP & nullspace property in levels. SIAM Jour. Imag. Scienc. 10(1):335-371
• A. C. Hansen, O. Nevanlinna,  Complexity Issues in Computing Spectra, Pseudospectra and Resolvents ,  Banach Centre Pub.  112:171-194
• B. Adcock, M. Gataric, A. C. Hansen,  Density theorems for nonuniform sampling of bandlimited functions using derivatives or bunched  measurements, J. Fourier Anal. Appl. 23(6):1311-1347
• B. Adcock, A. C. Hansen, B. Roman, A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements , IEEE Signal Process. Lett.   23(5):732 - 736 
• A. Jones , A. Tamtogl, I. Calvo-Almazan, A. C. Hansen, Continuous compressed sensing of inelastic and quasielastic Helium Atom Scattering spectra , Nature, Sci. Rep. 6, Art. num.: 27776
• A. Jones , A. Tamtogl, I. Calvo-Almazan, A. C. Hansen, Continuous compressed sensing of inelastic and quasielastic Helium Atom Scattering spectra (supplementary material), Nature, Sci. Rep.  6, Art. num.: 27776
• J. Ben-Artzi, A. C. Hansen, O. Nevanlinna, M. Seidel, New barriers in complexity theory: On the Solvability Complexity Index and towers of algorithms , C. R. Acad. Sci. Paris Sér. I Math. 353, no. 10, 931-936
• J. Ben-Artzi, A. C. Hansen, O. Nevanlinna, M. Seidel,  The Solvability Complexity Index - Computer science and logic meet scientific computing .
• B. Adcock, M. Gataric, A. C. Hansen, Recovering piecewise smooth functions from nonuniform Fourier measuremets , Springer Lect. Notes in Comp. Sci. and Eng. 2015
• A. Bastounis, A. C. Hansen,  On random and deterministic compressed sensing and the Restricted Isometry Property in Levels, IEEE 2015 Int. Conf. on Samp. Theory and Appl.
• B. Adcock, A. C. Hansen, M. Gataric, Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples , Appl. Comput. Harmon. Anal.  42(3):508-535
• B. Adcock, M. Gataric, A. C. Hansen, Stable nonuniform sampling with weighted Fourier frames and recovery in arbitrary spaces, IEEE 2015 Int. Conf. on Samp. Theory and Appl.
• B. Adcock, A. C. Hansen, A. Jones, On asymptotic incoherence and its implications for compressed sensing for inverse problems , IEEE Trans. Inf. Theory, 62, no. 2, 1020-1032
• B. Roman, B. Adcock, A. C. Hansen, On asymptotic structure in compressed sensing.
• B. Adcock, G. Kutyniok, A. C. Hansen, J. Ma, Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements , SIAM J. Math. Anal. 47(2), 1196–1233
• B. Adcock, A. C. Hansen, B. Roman The quest for optimal sampling: computationally efficient, structure-exploiting measurements for compressed sensing , Springer , 2015
• B. Roman, A. Bastounis, B. Adcock, A. C. Hansen, On fundamentals of models and sampling in compressed sensing.
• A. Jones, B. Adcock, A. C. Hansen Analyzing the structure of multidimensional compressed sensing problems through coherence .
• B. Adcock, M. Gataric, A. C. Hansen, On stable reconstructions from univariate nonuniform Fourier measurements , SIAM Jour. Imag. Scienc. 7(3):1690-1723
• B. Adcock, A. C. Hansen, B. Roman, G. Teschke, Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum , Adv. in Imag. and Electr. Phys. vol 182, 187-279, Elsevier, 2014
• B. Adcock, A. C. Hansen, A. Shadrin, A stability barrier for reconstructions from Fourier samples , SIAM Jour. on Num. Anal.  52, no. 1, 125-139
• B. Adcock, A. C. Hansen, C. Poon, B. Roman, Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing , Proc. of the 10th Int. Conf. on Samp. Theory and Appl., 2013
• B. Adcock, A. C. Hansen, C. Poon, Optimal wavelet reconstructions from Fourier samples via generalized sampling , Proc. of the 10th Int. Conf. on Samp. Theory and Appl., 2013
• B. Adcock, A. C. Hansen, C. Poon, Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem, SIAM J. Math. Anal.  45, no. 5, 3132-3167
• B. Adcock, A. C. Hansen, C. Poon, On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate , Appl. Comput. Harmon. Anal.  36, no. 3, 387-415
• B. Adcock, A. C. Hansen, Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients , Math. Comp. 84, 237-270
• B. Adcock, A. C. Hansen, E. Herrholz, G. Teschke, Generalized Sampling: Extensions to Frames and Inverse and Ill-Posed Problems , Inverse Prob. 29, no 1, 015008
• B. Adcock, A. C. Hansen, Reduced Consistency Sampling in Hilbert Spaces , Proc. of the 9th Int. Conf. on Samp. Theory and Appl., 2011
• B. Adcock, A. C. Hansen, Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon , Appl. Comput. Harmon. Anal. 32, no. 3, 357-388
• B. Adcock, A. C. Hansen, A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases , J. Fourier Anal. Appl. 18, no. 4, 685-716
• A. C. Hansen, A theoretical framework for backward error analysis on manifolds , J. Geom. Mech. 3, no. 1, 81 - 111
• A. C. Hansen, J. Strain, On the order of deferred correction , Appl. Numer. Math. 61, no. 8, 961-973
• A. C. Hansen, Infinite dimensional numerical linear algebra; theory and applications , Proc. R. Soc. Lond. Ser. A. 466, no. 2124, 3539-3559
• A. C. Hansen, On the approximation of spectra of linear operators on Hilbert spaces , J. Funct. Anal. 254, no. 8, 2092--2126
• A. C. Hansen, J. Strain, Convergence theory for spectral deferred correction , Preprint, UC Berkeley

Previous Events

• Speaking (online) at University of Oxford Data Science Seminar  (Feb. 21, 2022).
• Speaking (online) at IST  (Jan. 20, 2022).
• Speaking (online) at the University of Leicester  (Oct. 14, 2021).
• Speaking at EPFL  (Sept. 21, 2021).
• Speaking (online) at the One World IMAGing and INvErse problems (IMAGINE) seminar  (Feb 17, 2021).
• Speaking (online) at the Gran Sasso Science Institute Mathematics Colloquium  (Jan 28, 2021).
• Speaking (online) at XAI: Explaining what goes on inside DNN/AI  (Oct 20, 2020).
• Speaking (online) at the Max Planck Institute of Molecular Cell Biology and Genetics  (Sept 24, 2020).
• Speaking (online) at the Mathematics of Machine Learning, LMS-Bath Symposium  (Aug 6, 2020). Watch the talk.
• Speaking (online) at the One World Seminar Series on the Mathematics of Machine Learning  (July 5, 2020). Watch the talk.
• Invited speaker at  Computational Harmonic Analysis and Data Science, Banff International Research Station (Nov 2019) .
• Speaking at EPFL, Imaging in the Age of Machine Learning (Oct 25, 2019)
• Speaking at the University of Pittsburgh, Algebra-combinatorics-geometry seminar (Sept 26, 2019)
• Invited speaker at Workshop on Harmonic analysis and Machine Learning (Sept 2019) .
• Invited speaker at  Algorithms and Complexity for Continuous Problems, Dagstuhl (Aug 2019) .
• Plenary speaker at  National Academy of Sciences, Arthur M. Sackler Colloquim: The Science of Deep Learning, Washington D.C. (March 2019) .
• Speaking at Imperial College/University College London, Numerical Analysis Semina r (Feb. 20 2019)
• Invited speaker at Variational methods and optimization in imaging, Institut Henri  Poincaré   (Feb. 2019) .
• Speaking at Imperial College, Pure Analysis Seminar (Jan. 10 2019).
• Invited speaker at  Analysis and Computation in High Dimensions, Hausdorff Institute (Oct. 2018) .
• Invited speaker at  Measuring the Complexity of Computational Content: From Combinatorial Problems to Analysis, Dagstuhl (Sept. 2018) .
• Invited speaker at the  Algebraic and geometric aspects of numerical methods for differential equations, Mittag-Leffler Institute  (July 5 2018)
• Invited speaker at  Isaac Newton Institute  (May 24 2018)
• Speaking at the University of Oslo (May 14-16 2018, slides ).
• Speaking at the University of Manchester (May 4 2018).
• Invited speaker at   Banff Research Station  (April 25 2018).
• Invited speaker at the  Institut Henri Poincaré  (Feb 12 2018).
• Organizing the program Approximation, sampling and compression in data science , Isaac Newton Institute (Jan-June 2019).
• Organizing the workshop Mathematics of data: Structured representations for sensing, approximation and learning , Alan Turing Institute (May 27-May 31, 2019) .
• Speaking at LMU Munich (Jan 31, 2018).
• Organizing the workshop Inverse Problems Network Meeting 2 , Isaac Newton Institute (Nov 23-Nov 24, 2017) .
• Speaking at the University of Warwick (Nov 15, 2017).
• Invited speaker at Generative models, parameter learning and sparsity , Isaac Newton Institute (2017) .
• Plenary speaker at the Fourteenth International Conference on Computability and Complexity in Analysis (2017).
• Keynote speaker at FoCM: Approximation Theory Workshop (2017) .
• Invited speaker at FoCM:  Information-Based Complexity Workshop (2017) .
• Invited speaker at Multiscale and High-Dimensional Problems, Oberwolfach (2017) .
• Plenary speaker at The 14th International workshop on Quantum Chromodynamics (QCD) in extreme conditions (2016) .
• Plenary speaker at Computational and Analytic Problems in Spectral Theory (2016) .
• Invited speaker at Low Complexity Models in Signal Processing, Hausdorff Institute (2016) .
• Plenary speaker at The Bath/RAL Numerical Analysis Day (2015) .
• Plenary speaker at Pseudospectra of operators: spectral singularities, semiclassics, pencils and random matrices (2014) .
• Invited speaker at FoCM: Real Number Complexity Workshop (2014) .
• Plenary speaker at iTWIST'14 (2014) .
• Plenary speaker at French-German Conference on Mathematical Image Analysis, Institut Henri Poincaré (2014) .
• Invited speaker at The 5th International Conference on Computational Harmonic Analysis (2014) .
• Invited speaker at Compressed sensing and its Applications (2013) .
• Plenary speaker at Sparse Representation of Functions: Analytic and Computational Aspects (2012) .
• Plenary speaker at Sparsity, Localization and Dictionary Learning (2012) .

A. C. Hansen, On the approximation of spectra of linear Hilbert space operators , PhD Thesis.

Student Awards

• Smith-Knight/Rayleigh-Knight Prize 2007, On the approximation of spectra and pseudospectra of linear operators on Hilbert spaces
• John Butcher Award 2007 (joint with T. Schmelzer (Oxford)), A theoretical framework for backward error analysis on manifolds .
• © Applied Functional and Harmonic Analysis, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA. Page last saved: 11th November 2019. Contact Us

Overview of the PhD Program

For specific information on the Applied Mathematics PhD program, see the navigation links to the right. 

What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the  Graduate Policies  pages. 

General Ph.D. Requirements

• 10 semester-long graduate courses, including at least 8 disciplinary.   At least 5 of the 10 should be graduate-level SEAS "technical" courses (or FAS graduate-level technical courses taught by SEAS faculty), not including seminar/reading/project courses.  Undergraduate-level courses cannot be used.  For details on course requirements, see the school's overall PhD course requirements  and the individual program pages linked therein.
• Program Plan (i.e., the set of courses to be used towards the degree) approval by the  Committee on Higher Degrees  (CHD).
• Minimum full-time academic residency of two years .
• Serve as a Teaching Fellow (TF) in one semester of the second year.
• Oral Qualifying Examination Preparation in the major field is evaluated in an oral examination by a qualifying committee. The examination has the dual purpose of verifying the adequacy of the student's preparation for undertaking research in a chosen field and of assessing the student's ability to synthesize knowledge already acquired. For details on arranging your Qualifying Exam, see the exam policies and the individual program pages linked therein.
• Committee Meetings : PhD students' research committees meet according to the guidelines in each area's "Committee Meetings" listing.  For details see the "G3+ Committee Meetings" section of the Policies of the CHD  and the individual program pages linked therein.
• Final Oral Examination (Defense) This public examination devoted to the field of the dissertation is conducted by the student's research committee. It includes, but is not restricted to, a defense of the dissertation itself.  For details of arranging your final oral exam see the  Ph.D. Timeline  page.
• Dissertation Upon successful completion of the qualifying examination, a committee chaired by the research supervisor is constituted to oversee the dissertation research. The dissertation must, in the judgment of the research committee, meet the standards of significant and original research.

Optional additions to the Ph.D. program

Harvard PhD students may choose to pursue these additional aspects:

• a Secondary Field (which is similar to a "minor" subject area).  SEAS offers PhD Secondary Field programs in  Data Science and in  Computational Science and Engineering .   GSAS  lists  secondary fields offered by other programs.
• a Master of Science (S.M.) degree conferred  en route to the Ph.D in one of several of SEAS's subject areas.  For details see here .
• a Teaching Certificate awarded by the Derek Bok Center for Teaching and Learning .

SEAS PhD students may apply to participate in the  Health Sciences and Technology graduate program  with Harvard Medical School and MIT.  Please check with the HST program for details on eligibility (e.g., only students in their G1 year may apply) and the application process.

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MPhil in Mathematics

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Primary tabs

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• Requirements
• How To Apply

Course closed:

Mathematics is no longer accepting new applications.

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

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

Programme Structure

The MPhil is a 12-month full-time programme and involves minimal formal teaching: students are integrated into the research culture of the Department of Pure Mathematics & Mathematical Statistics (DPMMS), or the Department of Applied Mathematics and Theoretical Physics (DAMTP), as appropriate. They may attend the Departments’ programmes of research seminars and other postgraduate courses, but most research training is overseen by their research supervisor, and, where appropriate, within a research group. 

Opportunities to develop research and transferable skills also exist through attendance at training sessions organised at Department, School or University level as part of the wider postgraduate programme, and informally through mentoring by fellow students and members of staff.

Partnership with St John's College

The Martingale Foundation, Faculty of Mathematics and St John's College ( https://www.joh.cam.ac.uk/ )  have partnered to ensure that students admitted via the Martingale Scholars Programme will typically be admitted as members of St John's College and become part of a Martingale Scholars Cohort.  If you would like more information on this partnership, please contact the Faculty directly. 

Learning Outcomes

By the end of the programme, students will have:

• acquired a comprehensive understanding of techniques, and a thorough knowledge of the literature, applicable to their own research;
• demonstrated originality in the application of knowledge, together with a practical understanding of how research and enquiry are used to create and interpret knowledge in their field;
• shown abilities in the critical evaluation of current research and research techniques and methodologies;
• demonstrated some self-direction and originality in tackling and solving problems, and acted autonomously in the planning and implementation of research.

MPhil students wishing to apply for a PhD at Cambridge must apply via the Postgraduate Admissions Office for continuation by the relevant deadline.

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

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

Departments

This course is advertised in the following departments:

• Faculty of Mathematics
• Department of Applied Mathematics and Theoretical Physics
• Department of Pure Mathematics and Mathematical Statistics

Key Information

12 months full-time, 2 years part-time, study mode : research, master of philosophy, department of applied mathematics and theoretical physics this course is advertised in multiple departments. please see the overview tab for more details., course - related enquiries, application - related enquiries, course on department website, dates and deadlines:, michaelmas 2024 (closed).

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

Funding Deadlines

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

Similar Courses

• Applied Mathematics and Theoretical Physics PhD
• Pure Mathematics and Mathematical Statistics PhD
• Mathematics (Mathematical Statistics) MASt
• Mathematics (Pure Mathematics) MASt
• Mathematics (Applied Mathematics) MASt

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School of Engineering welcomes new faculty

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The School of Engineering welcomes 15 new faculty members across six of its academic departments. This new cohort of faculty members, who have either recently started their roles at MIT or will start within the next year, conduct research across a diverse range of disciplines.

Many of these new faculty specialize in research that intersects with multiple fields. In addition to positions in the School of Engineering, a number of these faculty have positions at other units across MIT. Faculty with appointments in the Department of Electrical Engineering and Computer Science (EECS) report into both the School of Engineering and the MIT Stephen A. Schwarzman College of Computing. This year, new faculty also have joint appointments between the School of Engineering and the School of Humanities, Arts, and Social Sciences and the School of Science.

“I am delighted to welcome this cohort of talented new faculty to the School of Engineering,” says Anantha Chandrakasan, chief innovation and strategy officer, dean of engineering, and Vannevar Bush Professor of Electrical Engineering and Computer Science. “I am particularly struck by the interdisciplinary approach many of these new faculty take in their research. They are working in areas that are poised to have tremendous impact. I look forward to seeing them grow as researchers and educators.”

The new engineering faculty include:

Stephen Bates joined the Department of Electrical Engineering and Computer Science as an assistant professor in September 2023. He is also a member of the Laboratory for Information and Decision Systems (LIDS). Bates uses data and AI for reliable decision-making in the presence of uncertainty. In particular, he develops tools for statistical inference with AI models, data impacted by strategic behavior, and settings with distribution shift. Bates also works on applications in life sciences and sustainability. He previously worked as a postdoc in the Statistics and EECS departments at the University of California at Berkeley (UC Berkeley). Bates received a BS in statistics and mathematics at Harvard University and a PhD from Stanford University.

Abigail Bodner joined the Department of EECS and Department of Earth, Atmospheric and Planetary Sciences as an assistant professor in January. She is also a member of the LIDS. Bodner’s research interests span climate, physical oceanography, geophysical fluid dynamics, and turbulence. Previously, she worked as a Simons Junior Fellow at the Courant Institute of Mathematical Sciences at New York University. Bodner received her BS in geophysics and mathematics and MS in geophysics from Tel Aviv University, and her SM in applied mathematics and PhD from Brown University.

Andreea Bobu ’17 will join the Department of Aeronautics and Astronautics as an assistant professor in July. Her research sits at the intersection of robotics, mathematical human modeling, and deep learning. Previously, she was a research scientist at the Boston Dynamics AI Institute, focusing on how robots and humans can efficiently arrive at shared representations of their tasks for more seamless and reliable interactions. Bobu earned a BS in computer science and engineering from MIT and a PhD in electrical engineering and computer science from UC Berkeley.

Suraj Cheema will join the Department of Materials Science and Engineering, with a joint appointment in the Department of EECS, as an assistant professor in July. His research explores atomic-scale engineering of electronic materials to tackle challenges related to energy consumption, storage, and generation, aiming for more sustainable microelectronics. This spans computing and energy technologies via integrated ferroelectric devices. He previously worked as a postdoc at UC Berkeley. Cheema earned a BS in applied physics and applied mathematics from Columbia University and a PhD in materials science and engineering from UC Berkeley.

Samantha Coday joins the Department of EECS as an assistant professor in July. She will also be a member of the MIT Research Laboratory of Electronics. Her research interests include ultra-dense power converters enabling renewable energy integration, hybrid electric aircraft and future space exploration. To enable high-performance converters for these critical applications her research focuses on the optimization, design, and control of hybrid switched-capacitor converters. Coday earned a BS in electrical engineering and mathematics from Southern Methodist University and an MS and a PhD in electrical engineering and computer science from UC Berkeley.

Mitchell Gordon will join the Department of EECS as an assistant professor in July. He will also be a member of the MIT Computer Science and Artificial Intelligence Laboratory. In his research, Gordon designs interactive systems and evaluation approaches that bridge principles of human-computer interaction with the realities of machine learning. He currently works as a postdoc at the University of Washington. Gordon received a BS from the University of Rochester, and MS and PhD from Stanford University, all in computer science.

Kaiming He joined the Department of EECS as an associate professor in February. He will also be a member of the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL). His research interests cover a wide range of topics in computer vision and deep learning. He is currently focused on building computer models that can learn representations and develop intelligence from and for the complex world. Long term, he hopes to augment human intelligence with improved artificial intelligence. Before joining MIT, He was a research scientist at Facebook AI. He earned a BS from Tsinghua University and a PhD from the Chinese University of Hong Kong.

Anna Huang SM ’08 will join the departments of EECS and Music and Theater Arts as assistant professor in September. She will help develop graduate programming focused on music technology. Previously, she spent eight years with Magenta at Google Brain and DeepMind, spearheading efforts in generative modeling, reinforcement learning, and human-computer interaction to support human-AI partnerships in music-making. She is the creator of Music Transformer and Coconet (which powered the Bach Google Doodle). She was a judge and organizer for the AI Song Contest. Anna holds a Canada CIFAR AI Chair at Mila, a BM in music composition, and BS in computer science from the University of Southern California, an MS from the MIT Media Lab, and a PhD from Harvard University.

Yael Kalai PhD ’06 will join the Department of EECS as a professor in September. She is also a member of CSAIL. Her research interests include cryptography, the theory of computation, and security and privacy. Kalai currently focuses on both the theoretical and real-world applications of cryptography, including work on succinct and easily verifiable non-interactive proofs. She received her bachelor’s degree from the Hebrew University of Jerusalem, a master’s degree at the Weizmann Institute of Science, and a PhD from MIT.

Sendhil Mullainathan will join the departments of EECS and Economics as a professor in July. His research uses machine learning to understand complex problems in human behavior, social policy, and medicine. Previously, Mullainathan spent five years at MIT before joining the faculty at Harvard in 2004, and then the University of Chicago in 2018. He received his BA in computer science, mathematics, and economics from Cornell University and his PhD from Harvard University.

Alex Rives  will join the Department of EECS as an assistant professor in September, with a core membership in the Broad Institute of MIT and Harvard. In his research, Rives is focused on AI for scientific understanding, discovery, and design for biology. Rives worked with Meta as a New York University graduate student, where he founded and led the Evolutionary Scale Modeling team that developed large language models for proteins. Rives received his BS in philosophy and biology from Yale University and is completing his PhD in computer science at NYU.

Sungho Shin will join the Department of Chemical Engineering as an assistant professor in July. His research interests include control theory, optimization algorithms, high-performance computing, and their applications to decision-making in complex systems, such as energy infrastructures. Shin is a postdoc at the Mathematics and Computer Science Division at Argonne National Laboratory. He received a BS in mathematics and chemical engineering from Seoul National University and a PhD in chemical engineering from the University of Wisconsin-Madison.

Jessica Stark joined the Department of Biological Engineering as an assistant professor in January. In her research, Stark is developing technologies to realize the largely untapped potential of cell-surface sugars, called glycans, for immunological discovery and immunotherapy. Previously, Stark was an American Cancer Society postdoc at Stanford University. She earned a BS in chemical and biomolecular engineering from Cornell University and a PhD in chemical and biological engineering at Northwestern University.

Thomas John “T.J.” Wallin joined the Department of Materials Science and Engineering as an assistant professor in January. As a researcher, Wallin’s interests lay in advanced manufacturing of functional soft matter, with an emphasis on soft wearable technologies and their applications in human-computer interfaces. Previously, he was a research scientist at Meta’s Reality Labs Research working in their haptic interaction team. Wallin earned a BS in physics and chemistry from the College of William and Mary, and an MS and PhD in materials science and engineering from Cornell University.

Gioele Zardini joined the Department of Civil and Environmental Engineering as an assistant professor in September. He will also join LIDS and the Institute for Data, Systems, and Society. Driven by societal challenges, Zardini’s research interests include the co-design of sociotechnical systems, compositionality in engineering, applied category theory, decision and control, optimization, and game theory, with society-critical applications to intelligent transportation systems, autonomy, and complex networks and infrastructures. He received his BS, MS, and PhD in mechanical engineering with a focus on robotics, systems, and control from ETH Zurich, and spent time at MIT, Stanford University, and Motional.

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This cutting-edge training centre in the Mathematics of Information will produce a new generation of leaders in the theory and practice of modern data science, with an emphasis on the mathematical underpinnings of this new scientific field. The programme builds on the activities of CCIMI as well as those of CCA , with significant new components. As the relevant skill sets are multi-faceted in nature, ranging from computational, algorithmic to analytical and statistical expertise, they are best acquired in an interdisciplinary, cohort-based education system that exposes all students simultaneously to the many interlaced aspects of mathematics in data science, with the possibility of industrial collaboration. Subject areas of key importance are identified: large scale optimisation and variational methods, high-dimensional and non-parametric statistics, functional data analysis, Bayesian inference, mathematical inverse problems, partial differential equations, quantum information theory and computing, operations research and statistical learning theory, probability & random matrix theory, ergodic- & computational complexity theory. The centre will provide the opportunity to write a PhD thesis in any of these subject areas in pure or applied mathematics.

• Current CCIMI projects
• Details of our current students

For further information please contact [email protected]

Applications for October 2025 Entry

Applications to the CMI PhD have been suspended for the academic year 2025- 2026.

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