shortest phd thesis math

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What is the shortest Ph.D. thesis? [closed]

The question is self-explanatory, but I want to make some remarks in order to prevent the responses from going off into undesirable directions.

It seems that every few years I hear someone ask this question; it seems to hold a perennial fascination for research mathematicians, just as quests for short proofs do. The trouble is that it has strong urban-legend tendencies: someone will say, "So-and-so's thesis was only $\epsilon$ pages long!" where $\epsilon \ll 1$ . It will often be very difficult to confirm or disconfirm such claims, since Ph.D. theses are often not even published, let alone readily available online. If you Google around for a while, as I did, you will find many dubious leads and can easily waste a lot of time on wild goose chases. Frankly, I'm a bit fed up with this state of affairs. I am therefore asking this question on MO in the hope that doing so will put this old question to rest, or at least establish provable upper bounds.

I would therefore request that you set yourself a high standard before replying. Don't post a candidate unless you're sure your facts are correct, and please give some indication why you're so sure. Read the meta discussion before posting. (Note that the meta discussion illustrates that even a MathSciNet citation isn't always totally definitive.) Include information about the content and circumstances of the thesis if you know it, but resist the temptation to gossip or speculate.

I'm not making this question community wiki or big-list because it should ideally have a definite answer, though I grant that it's possible that there are some borderline cases out there (perhaps there are theses that were not written in scholarly good faith, or documents that some people would regard as equivalent to a Ph.D. thesis but that others would not, or theses in subjects that are strictly speaking distinct from mathematics but that are arguably indistinguishable from mathematics dissertations).

Finally, to anticipate a possible follow-up question, there is a list of short published papers here (search for "Nelson"). Note that the question of the shortest published paper is not as urban-legendy because the facts are easier to verify. I looked up the short papers listed there myself and found them to be quite interesting. So in addition to trying to settle an urban legend, I am hoping that this question will bring to light some interesting and lesser known mathematics.

• ho.history-overview
• 9 $\begingroup$ I think it really should be CW. It makes no sense to me that the shorter the proposed candidate, the more reputation the proposer will get. It will also lower the temptation for people to post gossipy stuff. $\endgroup$ –  Alex B. Feb 8, 2011 at 15:31
• 3 $\begingroup$ The only reasonable interpretation of the question is extremely short theses in general, because there is more than one measure of the length of a thesis. Moreover in some cases it's debatable whether a particular document really is a thesis or the full thesis. It realy should be CW. $\endgroup$ –  Greg Kuperberg Feb 8, 2011 at 15:40
• 3 $\begingroup$ How would you like to count? Do all the cover pages, table of contents, abstract, etc. count? How about references? Or do you begin with the introduction and only include the content? $\endgroup$ –  Noah Stein Feb 8, 2011 at 16:33
• 5 $\begingroup$ -1. This question is terrible. I'm sure I could reformat my thesis in a silly font size to make it have a ludicrously small number of pages. $\endgroup$ –  Peter McNamara Feb 8, 2011 at 19:50
• 8 $\begingroup$ @Peter McNamara: you probably could, but I'm pretty certain that this is not the issue being discussed here. Anyway, most universities have specific formatting standards and would not let you submit it in this form. $\endgroup$ –  Thierry Zell Feb 8, 2011 at 20:05

9 Answers 9

David Rector's thesis ("An Unstable Adams Spectral Sequence", MIT 1966) is 9 pages, according to the record at the MIT library . I haven't seen the actual thesis for many years, but I'm pretty the actual mathematical content takes about 3 pages total, and is largely identical to the published version in Topology (1966, same title, doi link: https://doi.org/10.1016/0040-9383(66)90025-5 ), which is 3 pages plus bibliography. (Dan Kan, his advisor, likes short papers.)

• 2 $\begingroup$ Probably not a coincidence. $\endgroup$ –  Tyler Lawson Feb 8, 2011 at 20:25
• 3 $\begingroup$ Accepted provisionally. Enough people seem instinctively annoyed at this question that it seems likely to be closed soon (despite the fact that I'm asking it on MO in order to prevent its proliferation elsewhere). It doesn't seem likely that a stronger candidate will emerge before then. Ideally I'd like to examine the thesis myself before accepting the answer but I don't feel like purchasing it and it may be a while before my next trip to Boston. $\endgroup$ –  Timothy Chow Feb 9, 2011 at 15:56
• 4 $\begingroup$ Aside from the library copy, there should be a slightly more accessible copy in the MIT Math reading room. (They used to keep copies of theses there, and I assume they still do.) Maybe somebody reading this could wander down the hall and take a look. :) $\endgroup$ –  Charles Rezk Feb 9, 2011 at 18:55
• 31 $\begingroup$ I'm in the reading room now. Rector's thesis comprises a title page, an abstract page, a table of contents page, 7 pages of math, a bibliography page (8 refs.), and a biographical note page. The MIT library record's "9 leaves" exclude the title/abstract/contents, which are not numbered. Except for some trivial changes in wording in the intro, the mathematical part is indeed identical to the 4-page Topology paper, vol. 5 (1966), 343-346. The thesis occupies more space since it's manually typed; not including section titles, the 4 sections are respectively 18, 23, 42, and 36 typewritten lines. $\endgroup$ –  Timothy Chow Aug 19, 2011 at 18:44
• $\begingroup$ 119 typewritten lines! $\endgroup$ –  David Roberts ♦ Oct 14, 2022 at 10:53

John Nash's thesis was 26 pages, and had two references in the bibliography.

Edmund Landau's thesis was 13 pages long.

• $\begingroup$ There is an English translation here: arxiv.org/PS_cache/arxiv/pdf/0803/0803.3787v2.pdf That document is 17 pages (including title page, etc.). $\endgroup$ –  Zach N Feb 8, 2011 at 18:06
• 2 $\begingroup$ For a link to a scanned version of Landau's thesis see here gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN317979566 The document has 18 pages, of which 2 are completely empty, indeed the catalogue of the libraries of Berlin gives 16 pages as lengths. (the French national library catalogue gives 18). Moreover, one page is a title page, one is a dedication, and one is a vita. So, depending on what one actually counts, 18, 16, or 13. According to library catalogues 16 or 18. $\endgroup$ –  user9072 Feb 8, 2011 at 18:15

I believe the shortest PhD thesis is of Burt Totaro "Milnor K-theory is the simplest part of algebraic K-theory", 12 pages.

Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989; published as: K-Theory 6 (1992), 177-189 ( Portico archived version ).

Burt Totaro's webpage at Cambridge , including a pdf of the published version .

• 1 $\begingroup$ its complete thesis. I gave two references here, Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989 and K-Theory 6 (1992), 177-189 $\endgroup$ –  J Verma Feb 8, 2011 at 17:43
• 2 $\begingroup$ I noticed, but the reference to the actual thesis does not have a page numbers (and it is somewhat surprising that the number of pages did not change from the thesis to K-theory's format) :) $\endgroup$ –  Mariano Suárez-Álvarez Feb 8, 2011 at 17:45
• 15 $\begingroup$ Totaro's 1989 thesis is titled "K-theory and algebraic cycles" and, according to ProQuest, is 20 pages. If your university library subscribes to ProQuest, you can see a PDF preview of the thesis by searching for "Totaro, Burt" in the Dissertations and Theses database. $\endgroup$ –  Zach N Feb 8, 2011 at 18:02
• 4 $\begingroup$ You can download it on mathscinet. It has 16 numbered pages, incl. 1 page of bibliography. Definitions start on page 1 though, not much of an introduction. $\endgroup$ –  fherzig Feb 9, 2011 at 2:58
• 1 $\begingroup$ I downloaded the thesis from ProQuest. It comprises a signature page, a title page, an abstract page, an epigram page, 15 pages of (TeXed) math, and a bibliography page. Short, but not as short as David Rector's thesis. $\endgroup$ –  Timothy Chow Aug 19, 2011 at 19:00

This is not really an answer because these PhD's were never actually written, but anyway: in his book A mathematicians miscellany (in the chapter on math with minimum raw material) Littlewood gave 2 examples that could have been 2-line PhDs:

(1) Cayley's projective definition of length

(2)Theorem: An integral function never 0 or 1 is a constant. Proof: $\exp(i\Omega(f(z)))$ is a bounded integral function. ($\Omega$ is inverse to the elliptic modular function.)

• 3 $\begingroup$ Richard, perhaps you overlooked that Gerry Myerson already gave this example on the meta discussion? $\endgroup$ –  Timothy Chow Feb 8, 2011 at 15:53
• 19 $\begingroup$ I don't think it is reasonable to expect people to have read all the meta discussion before posting on a regular thread. This is a sort of fluff question, so it doesn't matter much, but in general I think it should be fine to repost answers from meta, so that the main thread has the most complete record of answers to the question. $\endgroup$ –  David E Speyer Feb 8, 2011 at 16:52
• 7 $\begingroup$ While I agree with David Speyer in general, I also do not think this should have been posted as an answer to this particular question, given the questioner's emphasis on restricting the scope of the question. $\endgroup$ –  Charles Staats Feb 8, 2011 at 17:27
• 6 $\begingroup$ @David: I too would agree that in general it’s not reasonable to expect people to read meta discussions on questions before answering them. But this question specifically asks us to, and gives good reasons for it. $\endgroup$ –  Peter LeFanu Lumsdaine Feb 8, 2011 at 20:18
• $\begingroup$ (2) is a trivial corollary of Picard's little theorem. $\endgroup$ –  tst Jun 13, 2017 at 3:06

I already posted this on meta where there was some discussion of whether the page count was correct. My guess is that it is, so I will post it here too:

MR2615548 Martens, Henrik Herman Buvik A NEW PROOF OF TORELLI'S THEOREM. Thesis (Ph.D.)–New York University. 1962. 12 pp.

• 8 $\begingroup$ Compared to that, the thesis of his student Kristian Seip was a massive tome, weighing in at 30 pages. $\endgroup$ –  Harald Hanche-Olsen Feb 9, 2011 at 7:56

Kurt Gödel seems to be a good candidate for this "prize".

Let me quote from this review (see Page 74) of Kurt Gödel Collected Works.

The first three works of Godel in this volume are his dissertation of 1929 ( twenty-one pages in English ), a revised and substantially abbreviated version (eleven pages in English) published in 1930, and a brief abstract based on a presentation of Godel's results in Konigsberg on 6 September 1930. Of all of Godel's longer, published writings, his dissertation has been, until now, the most difficult to obtain, and is here translated for the first time into English, by Stefan Bauer-Mengelberg and van Heijenoort.

• 3 $\begingroup$ The original version of his thesis seems to have 33 pages; see permalink.obvsg.at/AC05181322 (the number next to "Umfangsangabe") $\endgroup$ –  user9072 Feb 8, 2011 at 16:59
• 2 $\begingroup$ I cannot say anything about the original version (my German skills are null, not almost null). But I have just checked my copy of the Collected Works (unfortunately I have not found any online library to link), and in pages 60-101 we can find Godel's dissertation (even pages match German, while odd ones match English). Thus, the description "21 pages in English" is accurate. $\endgroup$ –  boumol Feb 8, 2011 at 17:14
• 1 $\begingroup$ I did not want to imply your claim was not accurate. Only, as I understand the question, it is about the actual document the person submitted as a thesis. Thus, I supplemented this information, documenting it by the link to the entry of Goedels thesis in the joint library catalogue of Austrian (academic) libraries. It specifies title, author, year, lengths (that's the Umfangsangabe, S. abbreviates 'Seiten' i.e. pages), the type of document (thesis of University of Vienna (Wien)), and finally the specific libraries where it can be found. $\endgroup$ –  user9072 Feb 8, 2011 at 17:48

According to mathscinet, Eva Kallin's thesis was 14 pages.

• 3 $\begingroup$ This is promising, but as the question mentions and the meta thread shows, MathSciNet alone is not an authoritative reference. More documentation? $\endgroup$ –  Peter LeFanu Lumsdaine Feb 8, 2011 at 20:12

Barry Mazur's thesis on the proof of the Schoenflies conjecture (and introducing the method of infinite repetition in topology) is 5 pages long.

• 4 $\begingroup$ According to "Mathematical apocrypha redux" by Krantz, Mazur's thesis was 26 pages long. $\endgroup$ –  Michael Greinecker Feb 8, 2011 at 16:22
• 2 $\begingroup$ Mathscinet says his thesis is 30 pages. $\endgroup$ –  Jaikrishnan Feb 8, 2011 at 16:26
• 70 $\begingroup$ Well, it may not be the shortest but it surelyt appears to have the most variable number of pages! $\endgroup$ –  Mariano Suárez-Álvarez Feb 8, 2011 at 16:42
• 17 $\begingroup$ Let's please heed Timothy's call to do one's homework carefully. "Don't post a candidate unless you're sure your facts are correct, and please give some indication why you're so sure. Read the meta discussion before posting." $\endgroup$ –  Todd Trimble ♦ Feb 8, 2011 at 16:47
• $\begingroup$ Yikes. I had never looked at the thesis, but just the published version in the Bulletin of the AMS which is 5 pages long. $\endgroup$ –  Victor Miller Feb 23, 2011 at 22:12

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Doctorandum

PhD: Been There, Done That...

• The World’s Shortest PhD Dissertations

“David Lee Rector’s Ph.D. Thesis is just nine pages long plus bio and bibliography, not to mention double-spaced.” [Source & Photo Credit: Ali Almossawi ]

You have probably seen thick dissertations, too heavy to lift with one hand… but have you ever thought of how short a PhD dissertation can possibly be?

Well, John Edensor Littlewood once famously inquired “ whether a dissertation of 2 lines could deserve and get a Fellowship ” – and he seems to have meant it.

Interestingly, some of the world’s shortest PhD theses / dissertations also count among the most famous ones at the same time. Here are the Top 5 we could identify:

24 pages – John F. Nash: Non-Cooperative Games (1950)

17 pages – Albert Einstein: Eine neue Bestimmung der Moleküldimensionen (1905) / A New Determination of Molecular Dimensions (1906)

16 pages – Edmund Landau: Neuer Beweis der Gleichung (1899) / New Proof of the Equation (2007)

13 pages – Burt Totaro: Milnor K-Theory is the Simplest Part of Algebraic K-Theory (1992)

9 pages – David Lee Rector: An Unstable Adams Spectral Sequence (1966)

Please drop us a line if you know any shorter dissertations than the ones above!

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2021 Ph.D Thesis Defenses

Chengcheng yang.

Title: Properties of Shortest Length Curves inside Semi-algebraic Sets and Problems related to an Erdös Conjecture concerning Lattice Cubes Thesis Advisor: Robert Hardt

Part I: Properties of Shortest Length Curves inside Semi-algebraic Sets

This part concerns an analytical stratification question of real algebraic and semi- algebraic sets. In 1957 Whitney [ 10 ] gave a stratification of real algebraic sets, it partitions a real algebraic set into partial algebraic manifolds. In 1975 Hironaka [ 3 ] reproved that a real algebraic set is triangulable and also generalized it to sub-analytic sets, following the idea of Lojasiewicz’s [ 5 ] triangulation of semi-analytic sets in 1964. During the same year, Hardt [ 4 ] also proved the triangulation result for sub-analytic sets by inventing an- other method. Since any semi-algebraic set is also semi-analytic, thus is sub-analytic, both Hironaka and Hardt’s results showed that any semi-algebraic set is homeomorphic to the polyhedron of some simplicial complex.

Following their examples and wondering how geometry looks like locally for a semi- algebraic set, Part I of the paper tries to come up with a stratification, in particular a cell decomposition, such that it satisfies the following analytical property. Given any arbitrary semi-algebraic set X in R2, any two points in X may be joined by a continuous path γ of shortest length. We will show that there exists a semi-algebraic cell decomposition A of X such that for each A ∈ A, each component of γ ∩ A is either a singleton or a real analytic geodesic segment in A; furthermore, γ ∩ A has at most finitely many components.

Part II: Problems related to an Erd¨os conjecture concerning lattice cubes.

Part II of the paper studies a problem of Erd¨os concerning lattice cubes. Given an N × N × N lattice cube, we want to find the maximum number of vertices one can select so that no eight corners of a rectangular box are chosen simultaneously. Erd¨os conjectured that it has a sharp upper bound, which is O(N 11/4), but no example that large has been found yet. We start approaching this question for small N using the method of exhaustion, and we find that there is not necessarily a unique maximal set of vertices (counting all possible symmetries). Next, we study an equivalent two-dimensional version of this problem looking for patterns that might be useful for generalizing to the three-dimensional case. Since an n×n grid is also an n×n matrix, we rephrase and generalize the original question to: what is the minimum number α(k, n) of vertices one can put in an n × n matrix with entries 0 and 1, such that every k × k minor contains at least one entry of 1, for 1 ≤ k ≤ n? We discover some interesting formulas and asymptotic patterns that shed new light on the question. Then we examine many examples that succeed for O(n8/3) but fail for O(n11/4). Last we try to prove by contradiction that Erd¨os’ conjecture is wrong, and that O(n8/3) is the sharp upper bound for the maximum number. Here we work not only with discrete cases using combinatorics, but also with continuous cases, such as topological manifolds, using linear groups.

Contact Information

Tel (713) 348-4829

Mailing Address: Rice University Math Department -- MS 136 P.O. Box 1892 Houston, TX 77005-1892

Physical Address: Rice University Herman Brown Hall for Mathematical Sciences 6100 Main Street Houston, TX 77005

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Department of Mathematics

Doctoral theses.

About twenty to thirty doctoral students complete their doctoral thesis at the Department of Mathematics every year.

Recent doctoral examinations

Dissertations

Published after 1 January 2014. For theses published before 2014, please refer to the Research Collection .

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Mathematics PhD theses

A selection of Mathematics PhD thesis titles is listed below, some of which are available online:

2022   2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Melanie Kobras –  Low order models of storm track variability

Ed Clark –  Vectorial Variational Problems in L∞ and Applications to Data Assimilation

Katerina Christou – Modelling PDEs in Population Dynamics using Fixed and Moving Meshes  

Chiara Cecilia Maiocchi –  Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems

Samuel R Harrison – Stalactite Inspired Thin Film Flow

Elena Saggioro – Causal network approaches for the study of sub-seasonal to seasonal variability and predictability

Cathie A Wells – Reformulating aircraft routing algorithms to reduce fuel burn and thus CO 2 emissions  

Jennifer E. Israelsson –  The spatial statistical distribution for multiple rainfall intensities over Ghana

Giulia Carigi –  Ergodic properties and response theory for a stochastic two-layer model of geophysical fluid dynamics

André Macedo –  Local-global principles for norms

Tsz Yan Leung  –  Weather Predictability: Some Theoretical Considerations

Jehan Alswaihli –  Iteration of Inverse Problems and Data Assimilation Techniques for Neural Field Equations

Jemima M Tabeart –  On the treatment of correlated observation errors in data assimilation

Chris Davies –  Computer Simulation Studies of Dynamics and Self-Assembly Behaviour of Charged Polymer Systems

Birzhan Ayanbayev –  Some Problems in Vectorial Calculus of Variations in L∞

Penpark Sirimark –  Mathematical Modelling of Liquid Transport in Porous Materials at Low Levels of Saturation

Adam Barker –  Path Properties of Levy Processes

Hasen Mekki Öztürk –  Spectra of Indefinite Linear Operator Pencils

Carlo Cafaro –  Information gain that convective-scale models bring to probabilistic weather forecasts

Nicola Thorn –  The boundedness and spectral properties of multiplicative Toeplitz operators

James Jackaman  – Finite element methods as geometric structure preserving algorithms

Changqiong Wang - Applications of Monte Carlo Methods in Studying Polymer Dynamics

Jack Kirk - The molecular dynamics and rheology of polymer melts near the flat surface

Hussien Ali Hussien Abugirda - Linear and Nonlinear Non-Divergence Elliptic Systems of Partial Differential Equations

Andrew Gibbs - Numerical methods for high frequency scattering by multiple obstacles (PDF-2.63MB)

Mohammad Al Azah - Fast Evaluation of Special Functions by the Modified Trapezium Rule (PDF-913KB)

Katarzyna (Kasia) Kozlowska - Riemann-Hilbert Problems and their applications in mathematical physics (PDF-1.16MB)

Anna Watkins - A Moving Mesh Finite Element Method and its Application to Population Dynamics (PDF-2.46MB)

Niall Arthurs - An Investigation of Conservative Moving-Mesh Methods for Conservation Laws (PDF-1.1MB)

Samuel Groth - Numerical and asymptotic methods for scattering by penetrable obstacles (PDF-6.29MB)

Katherine E. Howes - Accounting for Model Error in Four-Dimensional Variational Data Assimilation (PDF-2.69MB)

Jian Zhu - Multiscale Computer Simulation Studies of Entangled Branched Polymers (PDF-1.69MB)

Tommy Liu - Stochastic Resonance for a Model with Two Pathways (PDF-11.4MB)

Matthew Paul Edgington - Mathematical modelling of bacterial chemotaxis signalling pathways (PDF-9.04MB)

Anne Reinarz - Sparse space-time boundary element methods for the heat equation (PDF-1.39MB)

Adam El-Said - Conditioning of the Weak-Constraint Variational Data Assimilation Problem for Numerical Weather Prediction (PDF-2.64MB)

Nicholas Bird - A Moving-Mesh Method for High Order Nonlinear Diffusion (PDF-1.30MB)

Charlotta Jasmine Howarth - New generation finite element methods for forward seismic modelling (PDF-5,52MB)

Aldo Rota - From the classical moment problem to the realizability problem on basic semi-algebraic sets of generalized functions (PDF-1.0MB)

Sarah Lianne Cole - Truncation Error Estimates for Mesh Refinement in Lagrangian Hydrocodes (PDF-2.84MB)

Alexander J. F. Moodey - Instability and Regularization for Data Assimilation (PDF-1.32MB)

Dale Partridge - Numerical Modelling of Glaciers: Moving Meshes and Data Assimilation (PDF-3.19MB)

Joanne A. Waller - Using Observations at Different Spatial Scales in Data Assimilation for Environmental Prediction (PDF-6.75MB)

Faez Ali AL-Maamori - Theory and Examples of Generalised Prime Systems (PDF-503KB)

Mark Parsons - Mathematical Modelling of Evolving Networks

Natalie L.H. Lowery - Classification methods for an ill-posed reconstruction with an application to fuel cell monitoring

David Gilbert - Analysis of large-scale atmospheric flows

Peter Spence - Free and Moving Boundary Problems in Ion Beam Dynamics (PDF-5MB)

Timothy S. Palmer - Modelling a single polymer entanglement (PDF-5.02MB)

Mohamad Shukor Talib - Dynamics of Entangled Polymer Chain in a Grid of Obstacles (PDF-2.49MB)

Cassandra A.J. Moran - Wave scattering by harbours and offshore structures

Ashley Twigger - Boundary element methods for high frequency scattering

David A. Smith - Spectral theory of ordinary and partial linear differential operators on finite intervals (PDF-1.05MB)

Stephen A. Haben - Conditioning and Preconditioning of the Minimisation Problem in Variational Data Assimilation (PDF-3.51MB)

Jing Cao - Molecular dynamics study of polymer melts (PDF-3.98MB)

Bonhi Bhattacharya - Mathematical Modelling of Low Density Lipoprotein Metabolism. Intracellular Cholesterol Regulation (PDF-4.06MB)

Tamsin E. Lee - Modelling time-dependent partial differential equations using a moving mesh approach based on conservation (PDF-2.17MB)

Polly J. Smith - Joint state and parameter estimation using data assimilation with application to morphodynamic modelling (PDF-3Mb)

Corinna Burkard - Three-dimensional Scattering Problems with applications to Optical Security Devices (PDF-1.85Mb)

Laura M. Stewart - Correlated observation errors in data assimilation (PDF-4.07MB)

R.D. Giddings - Mesh Movement via Optimal Transportation (PDF-29.1MbB)

G.M. Baxter - 4D-Var for high resolution, nested models with a range of scales (PDF-1.06MB)

C. Spencer - A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.

P. Jelfs - A C-property satisfying RKDG Scheme with Application to the Morphodynamic Equations (PDF-11.7MB)

L. Bennetts - Wave scattering by ice sheets of varying thickness

M. Preston - Boundary Integral Equations method for 3-D water waves

J. Percival - Displacement Assimilation for Ocean Models (PDF - 7.70MB)

D. Katz - The Application of PV-based Control Variable Transformations in Variational Data Assimilation (PDF- 1.75MB)

S. Pimentel - Estimation of the Diurnal Variability of sea surface temperatures using numerical modelling and the assimilation of satellite observations (PDF-5.9MB)

J.M. Morrell - A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian method for the numerical solution of the Euler equations (PDF-7.7MB)

L. Watkinson - Four dimensional variational data assimilation for Hamiltonian problems

M. Hunt - Unique extension of atomic functionals of JB*-Triples

D. Chilton - An alternative approach to the analysis of two-point boundary value problems for linear evolutionary PDEs and applications

T.H.A. Frame - Methods of targeting observations for the improvement of weather forecast skill

C. Hughes - On the topographical scattering and near-trapping of water waves

B.V. Wells - A moving mesh finite element method for the numerical solution of partial differential equations and systems

D.A. Bailey - A ghost fluid, finite volume continuous rezone/remap Eulerian method for time-dependent compressible Euler flows

M. Henderson - Extending the edge-colouring of graphs

K. Allen - The propagation of large scale sediment structures in closed channels

D. Cariolaro - The 1-Factorization problem and same related conjectures

A.C.P. Steptoe - Extreme functionals and Stone-Weierstrass theory of inner ideals in JB*-Triples

D.E. Brown - Preconditioners for inhomogeneous anisotropic problems with spherical geometry in ocean modelling

S.J. Fletcher - High Order Balance Conditions using Hamiltonian Dynamics for Numerical Weather Prediction

C. Johnson - Information Content of Observations in Variational Data Assimilation

M.A. Wakefield - Bounds on Quantities of Physical Interest

M. Johnson - Some problems on graphs and designs

A.C. Lemos - Numerical Methods for Singular Differential Equations Arising from Steady Flows in Channels and Ducts

R.K. Lashley - Automatic Generation of Accurate Advection Schemes on Structured Grids and their Application to Meteorological Problems

J.V. Morgan - Numerical Methods for Macroscopic Traffic Models

M.A. Wlasak - The Examination of Balanced and Unbalanced Flow using Potential Vorticity in Atmospheric Modelling

M. Martin - Data Assimilation in Ocean circulation models with systematic errors

K.W. Blake - Moving Mesh Methods for Non-Linear Parabolic Partial Differential Equations

J. Hudson - Numerical Techniques for Morphodynamic Modelling

A.S. Lawless - Development of linear models for data assimilation in numerical weather prediction .

C.J.Smith - The semi lagrangian method in atmospheric modelling

T.C. Johnson - Implicit Numerical Schemes for Transcritical Shallow Water Flow

M.J. Hoyle - Some Approximations to Water Wave Motion over Topography.

P. Samuels - An Account of Research into an Area of Analytical Fluid Mechnaics. Volume II. Some mathematical Proofs of Property u of the Weak End of Shocks.

M.J. Martin - Data Assimulation in Ocean Circulation with Systematic Errors

P. Sims - Interface Tracking using Lagrangian Eulerian Methods.

P. Macabe - The Mathematical Analysis of a Class of Singular Reaction-Diffusion Systems.

B. Sheppard - On Generalisations of the Stone-Weisstrass Theorem to Jordan Structures.

S. Leary - Least Squares Methods with Adjustable Nodes for Steady Hyperbolic PDEs.

I. Sciriha - On Some Aspects of Graph Spectra.

P.A. Burton - Convergence of flux limiter schemes for hyperbolic conservation laws with source terms.

J.F. Goodwin - Developing a practical approach to water wave scattering problems.

N.R.T. Biggs - Integral equation embedding methods in wave-diffraction methods.

L.P. Gibson - Bifurcation analysis of eigenstructure assignment control in a simple nonlinear aircraft model.

A.K. Griffith - Data assimilation for numerical weather prediction using control theory. .

J. Bryans - Denotational semantic models for real-time LOTOS.

I. MacDonald - Analysis and computation of steady open channel flow .

A. Morton - Higher order Godunov IMPES compositional modelling of oil reservoirs.

S.M. Allen - Extended edge-colourings of graphs.

M.E. Hubbard - Multidimensional upwinding and grid adaptation for conservation laws.

C.J. Chikunji - On the classification of finite rings.

S.J.G. Bell - Numerical techniques for smooth transformation and regularisation of time-varying linear descriptor systems.

D.J. Staziker - Water wave scattering by undulating bed topography .

K.J. Neylon - Non-symmetric methods in the modelling of contaminant transport in porous media. .

D.M. Littleboy - Numerical techniques for eigenstructure assignment by output feedback in aircraft applications .

M.P. Dainton - Numerical methods for the solution of systems of uncertain differential equations with application in numerical modelling of oil recovery from underground reservoirs .

M.H. Mawson - The shallow-water semi-geostrophic equations on the sphere. .

S.M. Stringer - The use of robust observers in the simulation of gas supply networks .

S.L. Wakelin - Variational principles and the finite element method for channel flows. .

E.M. Dicks - Higher order Godunov black-oil simulations for compressible flow in porous media .

C.P. Reeves - Moving finite elements and overturning solutions .

A.J. Malcolm - Data dependent triangular grid generation. .

Dissertations and Placements 2010-Present

Kimoi Kemboi Thesis: Full exceptional collections of vector bundles on linear GIT quotients Advisor: Daniel Halpern-Leistner First Position: Postdoc at the Institution for Advanced Study and Princeton

Max Lipton Thesis: Dynamical Systems in Pure Mathematics Advisor: Steven Strogatz First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology

Elise McMahon Thesis: A simplicial set approach to computing the group homology of some orthogonal subgroups of the discrete group  Advisor: Inna Zakharevich First Position: Senior Research Scientist at Two Six Technologies

Peter Uttenthal Thesis: Density of Selmer Ranks in Families of Even Galois Representations Advisor: Ravi Kumar Ramakrishna First Position: Visiting Assistant Professor at Cornell University

Liu Yun Thesis: Towers of Borel Fibrations and Generalized Quasi-Invariants Advisor: Yuri Berest First Position: Postdoc at Indiana University Bloomington

Romin Abdolahzadi Thesis: Anabelian model theory Advisor: Anil Nerode First Position: Quantitative Analyst, A.R.T. Advisors, LLC

Hannah Cairns Thesis: Abelian processes, and how they go to sleep Advisor: Lionel Levine First Position: Visiting Assistant Professor, Cornell University

Shiping Cao Thesis: Topics in scaling limits on some Sierpinski carpet type fractals Advisor: Robert Strichartz (Laurent Saloff-Coste in last semester) First Position: Postdoctoral Scholar, University of Washington

Andres Fernandes Herrero Thesis: On the boundedness of the moduli of logarithmic connections Advisor: Nicolas Templier First Position: Ritt Assistant Professor, Columbia University

Max Hallgren Thesis: Ricci Flow with a Lower Bound on Ricci Curvature Advisor: Xiaodong Cao First Position: NSF Postdoctoral Research Fellow, Rutgers University

Gautam Krishnan Thesis: Degenerate series representations for symplectic groups Advisor: Dan Barbasch First Position: Hill Assistant Professor, Rutgers University

Feng Liang Thesis: Mixing time and limit shapes of Abelian networks Advisor: Lionel Levine

David Mehrle Thesis: Commutative and Homological Algebra of Incomplete Tambara Functors Advisor: Inna Zakharevich First Position: Postdoctoral Scholar, University of Kentucky

Itamar Sales de Oliveira Thesis: A new approach to the Fourier extension problem for the paraboloid Advisor: Camil Muscalu First Position: Postdoctoral Researcher, Nantes Université

Brandon Shapiro Thesis: Shape Independent Category Theory Advisor: Inna Zakharevich First Position: Postdoctoral Fellow, Topos Institute

Ayah Almousa Thesis: Combinatorial characterizations of polarizations of powers of the graded maximal ideal Advisor: Irena Peeva First position: RTG Postdoctoral Fellow, University of Minnesota

Jose Bastidas Thesis: Species and hyperplane arrangements Advisor: Marcelo Aguiar First position: Postdoctoral Fellow, Université du Québec à Montréal

Zaoli Chen Thesis: Clustered Behaviors of Extreme Values Advisor: Gennady Samorodnitsky First Position: Postdoctoral Researcher, Department of and Statistics, University of Ottawa

Ivan Geffner Thesis: Implementing Mediators with Cheap Talk Advisor: Joe Halpern First Position: Postdoctoral Researcher, Technion – Israel Institute of Technology

Ryan McDermott Thesis: Phase Transitions and Near-Critical Phenomena in the Abelian Sandpile Model Advisor: Lionel Levine

Aleksandra Niepla Thesis:  Iterated Fractional Integrals and Applications to Fourier Integrals with Rational Symbol Advisor: Camil Muscalu First Position: Visiting Assistant Professor, College of the Holy Cross

Dylan Peifer Thesis: Reinforcement Learning in Buchberger's Algorithm Advisor: Michael Stillman First Position: Quantitative Researcher, Susquehanna International Group

Rakvi Thesis: A Classification of Genus 0 Modular Curves with Rational Points Advisor: David Zywina First Position: Hans Rademacher Instructor, University of Pennsylvania

Ana Smaranda Sandu Thesis: Knowledge of counterfactuals Advisor: Anil Nerode First Position: Instructor in Science Laboratory, Computer Science Department, Wellesley College

Maru Sarazola Thesis: Constructing K-theory spectra from algebraic structures with a class of acyclic objects Advisor: Inna Zakharevich First Position: J.J. Sylvester Assistant Professor, Johns Hopkins University

Abigail Turner Thesis: L2 Minimal Algorithms Advisor: Steven Strogatz

Yuwen Wang Thesis: Long-jump random walks on finite groups Advisor: Laurent Saloff-Coste First Position: Postdoc, University of Innsbruck, Austria

Beihui Yuan Thesis:  Applications of commutative algebra to spline theory and string theory Advisor: Michael Stillman First Position: Research Fellow, Swansea University

Elliot Cartee Thesis: Topics in Optimal Control and Game Theory Advisor: Alexander Vladimirsky First Position: L.E. Dickson Instructor, Department of , University of Chicago

Frederik de Keersmaeker Thesis: Displaceability in Symplectic Geometry Advisor: Tara Holm First Position: Consultant, Addestino Innovation Management

Lila Greco Thesis: Locally Markov Walks and Branching Processes Advisor: Lionel Levine First Position: Actuarial Assistant, Berkshire Hathaway Specialty Insurance

Benjamin Hoffman Thesis: Polytopes And Hamiltonian Geometry: Stacks, Toric Degenerations, And Partial Advisor: Reyer Sjamaar First Position: Teaching Associate, Department of , Cornell University

Daoji Huang Thesis: A Bruhat Atlas on the Wonderful Compactification of PS O(2 n )/ SO (2 n -1) and A Kazhdan-Lusztig Atlas on G/P Advisor: Allen Knutson First Position: Postdoctoral Associate, University of Minnesota

Pak-Hin Li Thesis: A Hopf Algebra from Preprojective Modules Advisor: Allen Knutson First position: Associate, Goldman Sachs

Anwesh Ray Thesis: Lifting Reducible Galois Representations Advisor: Ravi Ramakrishna First Position: Postdoctoral Fellowship, University of British Columbia

Avery St. Dizier Thesis: Combinatorics of Schubert Polynomials Advisor: Karola Meszaros First Position: Postdoctoral Fellowship, Department of , University of Illinois at Urbana-Champaign

Shihao Xiong Thesis: Forcing Axioms For Sigma-Closed Posets And Their Consequences Advisor: Justin Moore First Position: Algorithm Developer, Hudson River Trading

Swee Hong Chan Thesis: Nonhalting abelian networks Advisor: Lionel Levine First Position: Hedrick Adjunct Assistant Professor, UCLA

Joseph Gallagher Thesis: On conjectures related to character varieties of knots and Jones polynomials Advisor: Yuri Berest First Position: Data Scientist, Capital One

Jun Le Goh Thesis: Measuring the Relative Complexity of Mathematical Constructions and Theorems Advisor: Richard Shore First Position: Van Vleck Assistant Professor, University of Wisconsin-Madison

Qi Hou Thesis: Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces Advisor: Laurent Saloff-Coste First Position: Visiting Assistant Professor, Department of , Cornell University

Jingbo Liu Thesis: Heat kernel estimate of the Schrodinger operator in uniform domains Advisor: Laurent Saloff-Coste First Position: Data Scientist, Jet.com

Ian Pendleton Thesis:  The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds Advisor: Tara Holm

Amin Saied Thesis: Stable representation theory of categories and applications to families of (bi)modules over symmetric groups Advisor: Martin Kassabov First Position: Data Scientist, Microsoft

Yujia Zhai Thesis:  Study of bi-parameter flag paraproducts and bi-parameter stopping-time algorithms Advisor: Camil Muscalu First Position: Postdoctoral Associate, Université de Nantes 

Tair Akhmejanov Thesis: Growth Diagrams from Polygons in the Affine Grassmannian Advisor: Allen Knutson First position: Arthur J. Krener Assistant Professor, University of California, Davis

James Barnes Thesis:  The Theory of the Hyperarithmetic Degrees Advisor: Richard Shore First position: Visiting Lecturer, Wellesley College

Jeffrey Bergfalk Thesis:  Dimensions of ordinals: set theory, homology theory, and the first omega alephs Advisor: Justin Moore Postdoctoral Associate, UNAM - National Autonomous University of Mexico

TaoRan Chen Thesis: The Inverse Deformation Problem Advisor: Ravi Ramakrishna

Sergio Da Silva Thesis: On the Gorensteinization of Schubert varieties via boundary divisors Advisor: Allen Knutson First position: Pacific Institute for the Mathematical Sciences (PIMS) postdoctoral fellowship, University of Manitoba

Eduard Einstein Thesis:  Hierarchies for relatively hyperbolic compact special cube complexes Advisor: Jason Manning First position: Research Assistant Professor (Postdoc), University of Illinois, Chicago (UIC)

Balázs Elek Thesis:  Toric surfaces with Kazhdan-Lusztig atlases Advisor: Allen Knutson First position: Postdoctoral Fellow, University of Toronto

Kelsey Houston-Edwards Thesis:  Discrete Heat Kernel Estimates in Inner Uniform Domains Advisor: Laurent Saloff-Coste First position: Professor of Math and Science Communication, Olin College

My Huynh Thesis:  The Gromov Width of Symplectic Cuts of Symplectic Manifolds. Advisor: Tara Holm First position: Applied Mathematician, Applied Research Associates Inc., Raleigh NC.

Hossein Lamei Ramandi Thesis: On the minimality of non-σ-scattered orders Advisor: Justin Moore First position:  Postdoctoral Associate at UFT (University Toronto)

Christine McMeekin Thesis: A density of ramified primes Advisor: Ravi Ramakrishna First position: Researcher at Max Planck Institute

Aliaksandr Patotski Thesis:  Derived characters of Lie representations and Chern-Simons forms Advisor: Yuri Berest First position: Data Scientist, Microsoft

Ahmad Rafiqi Thesis:  On dilatations of surface automorphisms Advisor: John Hubbard First position: Postdoctoral Associate, Sao Palo, Brazil

Ying-Ying Tran Thesis:  Computably enumerable boolean algebras Advisor: Anil Nerode First position: Quantitative Researcher

Drew Zemke Thesis:  Surfaces in Three- and Four-Dimensional Topology Advisor: Jason Manning First position: Preceptor in , Harvard University

Heung Shan Theodore Hui Thesis: A Radical Characterization of Abelian Varieties  Advisor: David Zywina First position: Quantitative Researcher, Eastmore Group

Daniel Miller Thesis: Counterexamples related to the Sato–Tate conjecture Advisor: Ravi Ramakrishna First position: Data Scientist, Microsoft

Lihai Qian Thesis: Rigidity on Einstein manifolds and shrinking Ricci solitons in high dimensions Advisor: Xiaodong Cao First position: Quantitative Associate, Wells Fargo

Valente Ramirez Garcia Luna Thesis: Quadratic vector fields on the complex plane: rigidity and analytic invariants Advisor: Yulij Ilyashenko First position: Lebesgue Post-doc Fellow, Institut de Recherche Mathématique de Rennes

Iian Smythe Thesis: Set theory in infinite-dimensional vector spaces Advisor: Justin Moore First position: Hill Assistant Professor at Rutgers, the State University of New Jersey

Zhexiu Tu Thesis: Topological representations of matroids and the cd-index Advisor: Edward Swartz First position: Visiting Professor - Centre College, Kentucky

Wai-kit Yeung Thesis: Representation homology and knot contact homology Advisor: Yuri Berest First position: Zorn postdoctoral fellow, Indiana University

Lucien Clavier Thesis: Non-affine horocycle orbit closures on strata of translation surfaces: new examples Advisor: John Smillie First position: Consultant in Capital Markets, Financial Risk at Deloitte Luxembourg

Voula Collins Thesis: Crystal branching for non-Levi subgroups and a puzzle formula for the equivariant cohomology of the cotangent bundle on projective space Advisor: Allen Knutson FIrst position: Postdoctoral Associate, University of Connecticut

Pok Wai Fong Thesis: Smoothness Properties of symbols, Calderón Commutators and Generalizations Advisor: Camil Muscalu First position: Quantitative researcher, Two Sigma

Tom Kern Thesis: Nonstandard models of the weak second order theory of one successor Advisor: Anil Nerode First position: Visiting Assistant Professor, Cornell University

Robert Kesler Thesis: Unbounded multilinear multipliers adapted to large subspaces and estimates for degenerate simplex operators Advisor: Camil Muscalu First position: Postdoctoral Associate, Georgia Institute of Technology

Yao Liu Thesis: Riesz Distributions Assiciated to Dunkl Operators Advisor: Yuri Berest First position: Visiting Assistant Professor, Cornell University

Scott Messick Thesis: Continuous atomata, compactness, and Young measures Advisor: Anil Nerode First position: Start-up

Aaron Palmer Thesis: Incompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity Advisor: Timothy J. Healey First position: Postdoctoral fellow, University of British Columbia 

Kristen Pueschel Thesis: On Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups Advisor: Timothy Riley First position: Postdoctoral Associate, University of Arkansas

Chenxi Wu Thesis: Translation surfaces: saddle connections, triangles, and covering constructions. Advisor: John Smillie First position: Postdoctoral Associate, Max Planck Institute of

David Belanger Thesis: Sets, Models, And Proofs: Topics In The Theory Of Recursive Functions Advisor: Richard A. Shore First position: Research Fellow, National University of Singapore

Cristina Benea Thesis: Vector-Valued Extensions for Singular Bilinear Operators and Applications Advisor: Camil Muscalu First position: University of Nantes, France

Kai Fong Ernest Chong Thesis: Face Vectors and Hilbert Functions Advisor: Edward Swartz First position: Research Scientist, Agency for Science, Technology and Research, Singapore

Laura Escobar Vega Thesis: Brick Varieties and Toric Matrix Schubert Varieties Advisor: Allen Knutson First position: J. L. Doob Research Assistant Professor at UIUC

Joeun Jung Thesis: Iterated trilinear fourier integrals with arbitrary symbols Advisor: Camil Muscalu First position: Researcher, PARC (PDE and Functional Analysis Research Center) of Seoul National University

Yasemin Kara Thesis: The laplacian on hyperbolic Riemann surfaces and Maass forms Advisor: John H. Hubbard Part Time Instructor, Faculty of Engineering and Natural Sciences, Bahcesehir University

Chor Hang Lam Thesis: Homological Stability Of Diffeomorphism Groups Of 3-Manifolds Advisor: Allen Hatcher

Yash Lodha Thesis: Finiteness Properties And Piecewise Projective Homeomorphisms Advisor: Justin Moore and Timothy Riley First position: Postdoctoral fellow at Ecole Polytechnique Federale de Lausanne in Switzerland

Radoslav Zlatev Thesis: Examples of Implicitization of Hypersurfaces through Syzygies Advisor: Michael E. Stillman First position: Associate, Credit Strats, Goldman Sachs

Margarita Amchislavska Thesis: The geometry of generalized Lamplighter groups Advisor: Timothy Riley First position: Department of Defense

Hyungryul Baik Thesis: Laminations on the circle and hyperbolic geometry Advisor: John H. Hubbard First position: Postdoctoral Associate, Bonn University

Adam Bjorndahl Thesis: Language-based games Advisor: Anil Nerode and Joseph Halpern First position: Tenure Track Professor, Carnegie Mellon University Department of Philosophy

Youssef El Fassy Fihry Thesis: Graded Cherednik Algebra And Quasi-Invariant Differential Forms Advisor: Yuri Berest First position: Software Developer, Microsoft

Chikwong Fok Thesis: The Real K-theory of compact Lie groups Advisor: Reyer Sjamaar First position: Postdoctoral fellow in the National Center for Theoretical Sciences, Taiwan

Kathryn Lindsey Thesis: Families Of Dynamical Systems Associated To Translation Surfaces Advisor: John Smillie First position: Postdoctoral Associate, University of Chicago

Andrew Marshall Thesis: On configuration spaces of graphs Advisor: Allan Hatcher First position: Visiting Assistant Professor, Cornell University

Robyn Miller Thesis: Symbolic Dynamics Of Billiard Flow In Isosceles Triangles Advisor: John Smillie First position: Postdoctoral Researcher at Mind Research Network

Diana Ojeda Aristizabal Thesis: Ramsey theory and the geometry of Banach spaces Advisor: Justin Moore First position: Postdoctoral Fellow, University of Toronto

Hung Tran Thesis: Aspects of the Ricci flow Advisor: Xiaodong Cao First position: Visiting Assistant Professor, University of California at Irvine

Baris Ugurcan Thesis: LPLP-Estimates And Polyharmonic Boundary Value Problems On The Sierpinski Gasket And Gaussian Free Fields On High Dimensional Sierpinski Carpet Graphs Advisor: Robert S. Strichartz First position: Postdoctoral Fellowship, University of Western Ontario

Anna Bertiger Thesis: The Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space Advisor: Allen Knutson First position: University of Waterloo, Postdoctoral Fellow

Mariya Bessonov Thesis: Probabilistic Models for Population Dynamics Advisor: Richard Durrett First position: CUNY City Tech, Assistant Professor, Tenure Track

Igors Gorbovickis Thesis: Some Problems from Complex Dynamical Systems and Combinatorial Geometry Advisor: Yulij Ilyashenko First position: Postdoctoral Fellow, University of Toronto

Marisa Hughes Thesis: Quotients of Spheres by Linear Actions of Abelian Groups Advisor: Edward Swartz First position: Visiting Professor, Hamilton College

Kristine Jones Thesis: Generic Initial Ideals of Locally Cohen-Macaulay Space Curves Advisor: Michael E. Stillman First position: Software Developer, Microsoft

Shisen Luo Thesis: Hard Lefschetz Property of Hamiltonian GKM Manifolds Advisor: Tara Holm First position: Associate, Goldman Sachs

Peter Luthy Thesis: Bi-parameter Maximal Multilinear Operators Advisor: Camil Muscalu First position: Chauvenet Postdoctoral Lecturer at Washington University in St. Louis 

Remus Radu Thesis: Topological models for hyperbolic and semi-parabolic complex Hénon maps Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Jenna Rajchgot Thesis: Compatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane Advisor: Allen Knutson First position: Research member at the Mathematical Sciences Research Institute (fall 2012); postdoc at the University of Michigan

Raluca Tanase Thesis: Hénon maps, discrete groups and continuity of Julia sets Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Ka Yue Wong Thesis: Dixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories Advisor: Dan M. Barbasch First position: Postdoctoral fellow at Hong Kong University of Science and Technology

Tianyi Zheng Thesis: Random walks on some classes of solvable groups Advisor: Laurent Saloff-Coste First position: Postdoctoral Associate, Stanford University

Juan Alonso Thesis: Graphs of Free Groups and their Measure Equivalence Advisor: Karen Vogtmann First position: Postdoc at Uruguay University

Jason Anema Thesis: Counting Spanning Trees on Fractal Graphs Advisor: Robert S. Strichartz First position: Visiting assistant professor of mathematics at Cornell University

Saúl Blanco Rodríguez Thesis: Shortest Path Poset of Bruhat Intervals and the Completecd-Index Advisor: Louis Billera First position: Visiting assistant professor of mathematics at DePaul University

Fatima Mahmood Thesis: Jacobi Structures and Differential Forms on Contact Quotients Advisor: Reyer Sjamaar First position: Visiting assistant professor at University of Rochester

Philipp Meerkamp Thesis: Singular Hopf Bifurcation Advisor: John M. Guckenheimer First position: Financial software engineer at Bloomberg LP

Milena Pabiniak Thesis: Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology Advisor: Tara Holm First position: Postdoctoral associate at the University of Toronto

Peter Samuelson Thesis: Kauffman Bracket Skein Modules and the Quantum Torus Advisor: Yuri Berest First position: Postdoctoral associate at the University of Toronto

Mihai Bailesteanu  Thesis: The Heat Equation under the Ricci Flow Advisor: Xiaodong Cao First position: Visiting assistant professor at the University of Rochester

Owen Baker  Thesis:  The Jacobian Map on Outer Space Advisor: Karen Vogtmann First position: Postdoctoral fellow at McMaster University

Jennifer Biermann  Thesis: Free Resolutions of Monomial Ideals Advisor: Irena Peeva First position: Postdoctoral fellow at Lakehead University

Mingzhong Cai  Thesis: Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties Advisor: Richard A. Shore First position: Van Vleck visiting assistant professor at the University of Wisconsin at Madison

Ri-Xiang Chen  Thesis: Hilbert Functions and Free Resolutions Advisor: Irena Peeva First position: Instructor at Shantou University in Guangdong, China

Denise Dawson  Thesis: Complete Reducibility in Euclidean Twin Buildings Advisor: Kenneth S. Brown First position: Assistant professor of mathematics at Charleston Southern University

George Khachatryan Thesis: Derived Representation Schemes and Non-commutative Geometry Advisor: Yuri Berest First position: Reasoning Mind

Samuel Kolins  Thesis: Face Vectors of Subdivision of Balls Advisor: Edward Swartz First position: Assistant professor at Lebanon Valley College

Victor Kostyuk Thesis: Outer Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups Advisor: Karen Vogtmann First position: Knowledge engineering at Reasoning Mind

Ho Hon Leung  Thesis: K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory Advisor: Reyer Sjamaar First position: Assistant professor at the Canadian University of Dubai

Benjamin Lundell  Thesis: Selmer Groups and Ranks of Hecke Rings Advisor: Ravi Ramakrishna First position: Acting assistant professor at the University of Washington

Eyvindur Ari Palsson  Thesis: Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator Advisor: Camil Muscalu First position: Visiting assistant professor at the University of Rochester

Paul Shafer  Thesis: On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Advisor: Richard A. Shore First position: Lecturer at Appalachian State University

Michelle Snider  Thesis: Affine Patches on Positroid Varieties and Affine Pipe Dreams Advisor: Allen Knutson First position: Government consulting job in Maryland

Santi Tasena Thesis: Heat Kernel Analysis on Weighted Dirichlet Spaces Advisor: Laurent Saloff-Coste First position: Lecturer professor at Chiang Mai University, Thailand

Russ Thompson  Thesis: Random Walks and Subgroup Geometry Advisor: Laurent Saloff-Coste First position: Postdoctoral fellow at the Mathematical Sciences Research Institute

Gwyneth Whieldon Thesis: Betti Numbers of Stanley-Reisner Ideals Advisor: Michael E. Stillman First position: Assistant professor of mathematics at Hood College

Andrew Cameron Thesis: Estimates for Solutions of Elliptic Partial Differential Equations with Explicit Constants and Aspects of the Finite Element Method for Second-Order Equations Advisor: Alfred H. Schatz First position: Adjunct instructor of mathematics at Tompkins Cortland Community College

Timothy Goldberg Thesis: Hamiltonian Actions in Integral Kähler and Generalized Complex Geometry Advisor: Reyer Sjamaar First position: Visiting assistant professor of mathematics at Lenoir-Rhyne University

Gregory Muller Thesis: The Projective Geometry of Differential Operators Advisor: Yuri Berest First position: Assistant professor at Louisiana State University 

Matthew Noonan Thesis: Geometric Backlund transofrmation in homogeneous spaces Advisor: John H. Hubbard

Sergio Pulido Niño Thesis: Financial Markets with Short Sales Prohibition Advisor: Philip E. Protter First position: Postdoctoral associate in applied probability and finance at Carnegie Mellon University

How long is a PhD dissertation? [Data by field]

The final piece of the PhD journey is the PhD dissertation. It takes many years to accumulate enough original and new data to fill out a dissertation to the satisfaction of experts in your field. Interestingly, the PhD dissertation length and content vary significantly based on the field you are studying and the publishing conventions.

A PhD can be anywhere from 50 pages to over 450 pages long. This equates to between about 20,000 words to 100,000 words. Most PhD theses are between 60,000 and 80,000 words long excluding contents, citations and references.

A PhD thesis contains different sections including an introduction, methods, results and discussion, conclusions, further work, and references. Each one of these different sections will vary in length depending on the field of study and your particular topic.

Ultimately, a PhD dissertation should contain as many pages and words as it takes to communicate the results of your multi-year investigation.

It is very rewarding to see your thesis come together as you are writing day after day. When I was writing my PhD dissertation I wrote the sections separately and my heart filled with joy when I finally put them all together and compile them into a single PDF document.

Counting the pages should not be the way to determine a PhD dissertation’s value but it certainly helps when your thesis is starting to look substantial in thickness.

How many pages should a PhD dissertation be?

A PhD dissertation should contain as many pages and words as it takes to outline the current state of your field and provide adequate background information, present your results, and provide confidence in your conclusions. A PhD dissertation will also contain figures, graphs, schematics, and other large pictorial items that can easily inflate the page count.

Here is a boxplot summary of many different fields of study and the number of pages of a typical PhD dissertation in the field. It has been created by Marcus Beck from all of the dissertations at the University of Minnesota.

Typically, the mathematical sciences, economics, and biostatistics theses and dissertations tend to be shorter because they rely on mathematical formulas to provide proof of their results rather than diagrams and long explanations.

On the other end of the scale, English, communication studies, political science, history and anthropology are often the largest theses in terms of pages and word count because of the number of words it takes to provide proof and depth of their results.

At the end of the day, it is important that your thesis gets signed off by your review committee and other experts in the field. Your supervisor will be the main judge of whether or not your dissertation is capable of satisfying the requirements of a PhD in your field.

If you want to know more about how long a Masters’s thesis and PhD dissertation is you can check out my other articles:

• How Long is a Masters Thesis? [Your writing guide]
• How long is a Thesis or dissertation? [the data]

Can a PhD dissertation be too long?

A PhD thesis should contain enough evidence and discussion to report on the most significant findings of your PhD research.

A PhD dissertation should not contain everything that you have done during your PhD. It should only include the data and information required to convince your PhD examining body that wraps up and tells the full story of particular lines of investigation.

Including random results, thoughts, or superfluous explanation can result in a dissertation that is unfocused. I have heard of music PhD is being described as too verbose and physical sciences PhD dissertations as being unfocused.

Therefore, a PhD thesis can be too long if the information it contains does not form a full and cohesive story.

One of my colleagues during their PhD removed an entire chapter from the thesis after writing it as the supervisor said that it needed more experiments to be a full story. They did not want to spend the next six months gathering the data and simply removed the chapter altogether.

How short can PhD dissertation be?

The shortest PhD dissertations are typically found in mathematics.

George Bernard Danzig was an American mathematical scientist who made contributions to industrial engineering and many other mathematical-related fields. An interesting miscommunication led to 1 of the shortest PhD theses ever.

In 1939 his professor wrote two problems on the blackboard and Danzig thought they were homeless assignments. He stated that they were harder than usual but handed in solutions to the surprise of the professor.

They were, in fact, open mathematical problems in statistics.

His professor said to bind the solution to the two problems together and submit them as his thesis – the total thesis length = 14 pages.

Obviously, most PhD theses and dissertations will be so much longer than that!

My PhD dissertation was 256 pages long. It was full of schematics, diagrams, and tables to demonstrate and communicate my findings.

I would say that most people’s PhD thesis experience will be closer to mine than Prof George Bernard Danzig’s.

Why PhD dissertations are typically so long

PhD dissertations are often over 200 pages long.

One of the primary reasons they are so long is that it is a single document that summarises many years of hard work. Also, summarising the research field to date and making sure that all of your references and citations are included so you avoid plagiarism will bolster the word count of the thesis dramatically.

Here are all of the reasons PhD dissertations tend to be so long.

Many years of work

PhD theses or dissertations contain many years of research and analysis.

In many of my YouTube videos I recommend that a PhD student work towards their PhD thesis by doing at least three hours of focused work every work day.

This amount of work quickly adds up.

Of course, not every bit of work makes it into the PhD dissertation but a lot of it does. It can be difficult to work out what to include or leave out of your thesis.

As a PhD student, I perfected the art of turning one experiment into many different types of grafts and schematics to fully explore the limits of my data. The graphs can take up a lot of space in your PhD thesis and, therefore, bolster the page count significantly.

In depth literature review

One of the most substantial parts of a PhD dissertation is the literature review.

The literature review can take up a huge portion of the early part of your PhD dissertation depending on the amount of data and publications in your field.

Writing an in-depth literature review requires just as much meticulous data analysis and searching as the central part of your dissertation.

Figures and schematics

Some fields end up producing a lot of figures and schematics.

My thesis had many full-page figures of atomic force microscopy experiments with much more explanation on subsequent pages.

As they say, a picture paints a thousand words and a dissertation can really benefit from having many schematics to highlight the important aspects of your findings.

References and citations

The recommended PhD dissertation word count from an institution or university does not include citations, references, or other thesis parts such as summary of abbreviations, table of figures, et cetera.

However, these components of your dissertation can take up many pages and add to the overall thickness of your PhD dissertation.

University formatting rules

University formatting rules will also dictate how you many pages your words take up.

I often get roasted on my YouTube channel for having doublespaced lines and wide margins. Unfortunately, this layout was dictated by my university before printing.

PhD dissertations often end up going into long-term storage and therefore, need to adhere to archival and standardised formatting rules.

Deep in the depths of the University of Newcastle, there is a copy of my thesis on a shelf. The formatting and binding rules mean that my thesis looks like everyone else’s.

Universities will often have their own requirements for PhD dissertation cover colour, quality, and type of paper. Even the quality of the paper can change the thickness of the PhD dissertation significantly.

PhD by publication

It is becoming increasingly common to submit a number of peer-reviewed papers bound together with supplementary information in between instead of a PhD dissertation.

The benefits of this to the researcher and university are:

• More early career peer-reviewed journals for career advancement
• an easier review process – they have already been peer-reviewed
• an early focus on publishing means better research outcomes for the researcher, supervisor, and Department.
• No mad rush at the end to finish a thesis
• continually writing peer-reviewed papers throughout your PhD helps with timely analysis and communication of results

Even though this option has been available to PhD students for a number of years, I have only known a handful of students actually submit their PhD via publication.

Nonetheless, having this option will suit some research fields better than others and lead to a more productive PhD.

Wrapping up

This article has been through everything you need to know about the length of a PhD dissertation and the common lengths of PhD dissertations for various fields.

Ultimately, there is no predefined length of a PhD.

A PhD thesis is as long as it needs to be to convince your examiners that you have contributed significantly enough to an academic field to be awarded the title of Dr of philosophy.

Mathematical and analytical theses tend to be shorter and can be as short as 50 pages (with one of the shortest being only 14 pages long). At the other end of the spectrum, PhD students in anthropology and history tend to produce the longest dissertations.

Dr Andrew Stapleton has a Masters and PhD in Chemistry from the UK and Australia. He has many years of research experience and has worked as a Postdoctoral Fellow and Associate at a number of Universities. Although having secured funding for his own research, he left academia to help others with his YouTube channel all about the inner workings of academia and how to make it work for you.

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Read John Nash’s Super Short PhD Thesis with 26 Pages & 2 Citations: The Beauty of Inventing a Field

in Math | June 1st, 2015 1 Comment

Last week  John Nash , the Nobel Prize-win­ning math­e­mati­cian, and sub­ject of the block­buster film A Beau­ti­ful Mind , passed away at the age of 86. He died in a taxi cab acci­dent in New Jer­sey.

Days lat­er, Cliff Pick­over high­light­ed a curi­ous fac­toid: When Nash wrote his Ph.D. the­sis in 1950, “Non Coop­er­a­tive Games” at Prince­ton Uni­ver­si­ty, the dis­ser­ta­tion (you can read it online  here) was brief. It ran only 26 pages. And more par­tic­u­lar­ly, it was light on cita­tions. Nash’s diss cit­ed two texts: One was writ­ten by John von Neu­mann & Oskar Mor­gen­stern, whose book,  The­o­ry of Games and Eco­nom­ic Behav­ior   (1944), essen­tial­ly cre­at­ed game the­o­ry and rev­o­lu­tion­ized the field of eco­nom­ics; the oth­er cit­ed text, “Equi­lib­ri­um Points in n‑Person Games,”  was an arti­cle writ­ten by Nash him­self. And it laid the foun­da­tion for his dis­ser­ta­tion, anoth­er sem­i­nal work in the devel­op­ment of game the­o­ry, for which Nash won the Nobel Prize in Eco­nom­ic Sci­ences in 1994 .

The reward of invent­ing a new field, I guess, is hav­ing a slim bib­li­og­ra­phy.

Relat­ed Con­tent:

A Brilliant Madness — 2002 Film on the Nobel Prize Winning Mathematician" href="http://www.openculture.com/2012/06/john_nash_ia_brilliant_madnessi.html" rel="bookmark">John Nash: A Bril­liant Mad­ness — 2002 Film on the Nobel Prize Win­ning Math­e­mati­cian

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

The World Record for the Short­est Math Arti­cle: 2 Words

Free Online Math Cours­es

by OC | Permalink | Comments (1) |

Related posts:

Comments (1), 1 comment so far.

This was shock­ing to know about the demise of John Nash. I had a chance to view the film “a beau­ti­ful mind” with a close friend, Steve Land­fried in Wis­con­sin-Chica­go where John Nash was a sub­ject of this film. I am glad that Steve made this choice for me since I could see and feel all, that this mag­ni­fi­cient sci­en­tist had gone through.This is still my favorite film because of its sub­ject

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35 Shortest Doctoral Programs Online [Fastest Doctorate & PhD Degrees]

Have you ever dreamed of getting your PhD or doctorate without spending ages in school? We’ve got you covered!

We’ve put together a list of the 35 shortest doctoral programs available online for 2024. This is ideal for those of you looking to fast-track your education.

Online accelerated PhD programs are growing in popularity as students are searching for the shortest PhD programs with the smallest number of requirements.

Online doctoral programs vary widely in their graduation requirements which is why we put together this guide showcasing universities that require less than 60 credits hours to get your online doctorate degree.

Editorial Listing ShortCode:

The U.S. Census Bureau reports that lifetime earnings for doctorate degree holders is $900,000 more than those holding a master’s degree only. That’s almost $1 million more!!

And because a doctoral degree is the highest level of academic achievement, you will also receive the accompanying scholarly respect as you make valuable contributions to your field and society as a whole.

Accredited Schools Offering the Shortest Doctoral Program Options

Methodology

For universities to be included in our guide, we looked at a number of criteria including the total number of credit hours required , accreditation, programs offered, and quality of online programs. Each of these universities offer accredited online doctoral and graduate programs. Some universities offer both campus and online programs as noted below.

Completion time can differ for each student, but it’s exciting to note that some accredited schools are now offering doctorate degrees that require fewer than 40 credit hours for completion! This may offer more flexibility and efficiency in your educational journey.

Before you apply, make sure to take a good look at the tuition fees, graduation criteria, and the classes each university offers.

1. Boston University

• Doctor of Occupational Therapy (Online) – 33 to 37 credit hours

Boston University is accredited by the New England Commission of Higher Education.

2. Colorado Christian University

• Doctor of Nursing Practice (Online) – 30 credit hours (MSN to DNP)

Colorado Christian University is accredited by The Higher Learning Commission.

3. Concordia University Chicago

• PhD in Leadership – Gerontology (Online) – 30 credit hours
• PhD in Leadership – Health & Human Performance (Online) – 30

Concordia University Chicago is accredited by the Higher Learning Commission.

4. Duquesne University

• Doctor of Nursing Practice (Online) – 35 credit hours

Duquesne University is accredited by the Middle States Commission on Higher Education.

5. Drexel University

• Doctor of Nursing Practice (Online) – 45 credit hours

Drexel University is regionally accredited by the Middle States Commission on Higher Education.

6. East Carolina University

• Doctor of Nursing Practice (Online) – 36 credit hours

East Carolina University is accredited by the Commission on Colleges of the Southern Association of Colleges and Schools.

7. Frontier Nursing University

• Doctor of Nursing Practice (Online) – 28 credit hours

FNU is accredited by the Southern Association of Colleges and Schools Commission on Colleges.

8. Grand Canyon University

• DNP in Educational Leadership (Online) – 45 credit hours

Grand Canyon University is regionally accredited by the Higher Learning Commission.

9. Gwynedd Mercy University

• EdD in Educational Leadership (Online) – 54 credit hours

Gwynedd Mercy University is accredited by the Middle States Commission on Higher Education.

10. Hampton University

• Doctor of Nursing Practice (Online) – 33 credit hours
• PhD in Nursing (Online) – 48 (with Masters)

Hampton University is accredited by the Southern Association of Colleges and Schools Commission on Colleges.

11. Indiana State University

• Doctor of Nursing Practice (Campus) – 39 credit hours

Indiana State University has been accredited by the Higher Learning Commission (HLC) since 1915.

12. Indiana University of Pennsylvania

• PhD in Safety Sciences (Hybrid) – 54 credit hours
• PhD in Criminology (Campus) – 42

Indiana University of Pennsylvania is accredited by the Middle States Commission on Higher Education.

13. Liberty University

• Doctor of Ministry (Online) – 30 credit hours
• Doctor of Public Administration (Online) – 48
• Doctor of Education (Online) – 54
• Doctor of Strategic Leadership (Online) – 51
• Doctor of Worship Studies (Online) – 45
• Doctor of Nursing Practice (Online) – 41
• EdD in Community Care Counseling (Online) – 57
• EdD in Educational Leadership (Online) – 54
• PhD in Theology and Apologetics (Online) – 57

Liberty University is accredited by the Southern Association of Colleges and Schools Commission on Colleges.

14. Monmouth University

• EdD in Educational Leadership (Hybrid) – 54

Monmouth University is accredited by the Middle States Commission on Higher Education.

15. National University

• DNP in Executive Leadership (Online) – 46 credit hours
• Doctor of Public Administration (Online) – 54
• EdD in Instructional Design (Online) – 54
• Doctor of Criminal Justice (Online) – 54
• Doctor of Education (Online) – 48
• Doctor of Business Administration (Online) – 48

National University is accredited by the Western Association of Schools and Colleges.

16. Nova Southeastern University

• EdD in Curriculum and Teaching (Hybrid) – 57 credit hours
• EdD in Higher Education Leadership (Hybrid) – 54
• EdD in Human Services Administration (Hybrid) – 54
• EdD in Instructional Technology and Distance Education (Hybrid) – 54
• EdD in Organizational Leadership (Hybrid) – 54
• EdD in Reading Education (Hybrid) – 54
• EdD in Special Education (Hybrid) – 54
• Doctor of Nursing Practice (Online) – 38-40
• Doctor of Occupational Therapy (Hybrid) – 39

NSU is accredited by the Southern Association of Colleges and Schools Commission on Colleges.

17. Penn State World Campus

• Doctor of Nursing Practice (Online) – 38-46 credit hours(with Masters)

The Pennsylvania State University is accredited by the Middle States Commission on Higher Education.

18. Regent University

• PhD in Communication (Online w/Residency) – 56-64 credit hours
• Doctor of Strategic Communication (Online w/Residency) – 49
• Doctor of Ministry in Christian Leadership & Renewal (Online) – 36

Regent University is accredited by the Southern Association of Colleges and Schools Commission.

19. Seton Hall University

• Doctor of Nursing Practice (Online) – 73 – 79 credit hours(BSN)
• Doctor of Nursing Practice (Online) – 31 (MSN)
• EdD in K-12 Administration (Campus) – 54 – 57
• Executive EdD in K-12 Administration (Campus) – 54

Seton Hall and its online programs are accredited by the Middle States Association of Colleges and Schools.

20. University at Buffalo

• DNP in Child Health Nurse Practitioner (Online) – 36 credit hours
• DNP in Family Nurse Practitioner (Online) – 36
• DNP in Nurse Anesthesia (Online) – 36
• DNP in Psychiatric/Mental Health Nurse Practitioner (Online) – 36
• DNP in Women’s Health Practitioner (Online) – 36
• PhD in Nursing (Online) – 57

The University at Buffalo is accredited by Middle States Commission on Higher Education.

21. University of Alabama – Huntsville

• PhD in Applied Mathematics (Campus) – 54 credit hours
• PhD in Atmospheric Science (Campus) – 48
• PhD in Biotechnology Science and Engineering (Campus) – 48
• PhD in Physics (Campus) – 48

UAH is officially accredited and/or recognized by the Southern Association of Colleges and Schools Commission on Colleges.

22. University of Arkansas

• EdD in Educational Leadership (Online) – 42 credit hours

The U of A has been accredited by the Higher Learning Commission without interruption since 1924.

23. University of Bridgeport

• EdD in Educational Leadership (Hybrid) – 42 credit hours

The University of Bridgeport is fully accredited by the New England Association of Schools and Colleges.

24. University of Colorado – Denver

• PhD in Applied Mathematics (Campus) – 42 credit hours

Since 1913, the North Central Association of Colleges and Schools (NCA) has accredited all institutions in the CU system.

25. University of Florida

• Doctor of Nursing Practice (Online) – 75-78 credit hours(BSN to DNP)
• Doctor of Nursing Practice (Online) – 35 (MSN to DNP)
• EdD in Higher Education Administration (Online) – 39

The University of Florida is regionally accredited by the Southern Association of Colleges and Schools.

26. University of Michigan – Flint

• Doctor of Nursing Practice – Executive Leadership (Online) – 43 credit hours

University of Michigan-Flint is accredited by the Higher Learning Commission.

27. University of Minnesota

• Doctor of Nursing Practice (Online) – 41 credit hours
• Dozens of PhD programs are also available on campus with less than 50 credit hours required

All campuses of the University of Minnesota operate with the accreditation of the Higher Learning Commission.

28. University of Missouri

• EdD in Educational Leadership (Online) – 46 credit hours
• PhD in Nursing (Online) – 77 credit hours (BSN)
• PhD in Nursing (Online) – 56 (MSN)
• PhD in Nursing (Online) – 48 (Post Clinical)
• DNP in Nursing Leadership and Innovations in Health (Online) – 40

The University of Missouri is accredited by the Higher Learning Commission.

29. University of Montana

• PhD in Counseling – Counselor Education and Supervision (Campus) – 48 credit hours(with Master’s)

The University of Montana-Missoula is accredited by the Northwest Commission on Colleges and Universities (NWCCU).

30. University of North Carolina – Greensboro

• PhD in Economics (Campus) – 45-57 credit hours

The University of North Carolina at Greensboro is accredited by the Southern Association of Colleges and Schools Commission on Colleges.

31. University of North Dakota

• PhD in Nursing (Online) – 30 credit hours

The University of North Dakota as a whole is regionally accredited by the Higher Learning Commission of the North Central Association of Colleges and Schools.

32. University of Northern Colorado

• Doctor of Nursing Practice (Online) – 44 credit hours (with Masters)

Since 1916, the University of Northern Colorado has been accredited by the Higher Learning Commission (HLC).

33. University of Tennessee – Knoxville

University of Tennessee – Knoxville received accreditation by the Southern Association of Colleges and Schools Commission on Colleges.

34. University of Texas at Tyler

The University of Texas at Tyler is accredited by the Commission on Colleges of the Southern Association of Colleges and Schools.

35. Wilmington University

• Doctor of Business Administration (Online) – 54 credit hours
• Doctor of Nursing Practice (Online) – 33
• Doctor in Prevention Science (Online) – 39-48
• EdD in Educational Leadership (Online) – 49-51
• EdD in Higher Education (Online) – 51
• EdD in Organizational Leadership (Online) – 51

Wilmington University is accredited by the Middle States Commission on Higher Education.

Popular Online Doctoral Programs

The following doctoral programs have accelerated online courses which can help you finish your doctorate at a faster pace:

• Business Administration
• Counseling & Therapy
• Criminal Justice / Homeland Security
• Healthcare Administration

Human Services

Information systems / technology.

• Ministry / Theology

Public Administration

• Public Health
• Public Policy

By earning an accelerated doctoral program online, you will also be contributing to your field’s body of knowledge, which can be deeply rewarding and satisfying.

Accounting Doctoral Programs

If you enjoy working with numbers and financial concepts, then consider delving deep into that field with a doctorate in accounting. This degree can prepare you for a position as the chief financial officer of an organization, serve as an auditor, teach accounting at the college level, or oversee a team of accountants.

During your studies, you’ll take classes in statistical analysis, financial research methods, and accounting theories. Available concentrations may include Public Accounting and Forensic Accounting.

Another possible option if you’re looking for the shortest completion time is earning a DBA with a concentration in Accounting.

Online Doctorate in Business Administration

A doctorate in business administration is a degree program that will prepare you for leadership at various companies and skillful operation within global markets.

People with a DBA often hold leadership positions in a variety of fields, including for-profit companies, non-profit organizations, and government groups. They can also work in education, whether in an administrative role or as a professor.

In preparation for such positions, coursework may cover topics like quantitative research methods, qualitative research methods, statistics, economics, management theories, and organizational behavior.

As a more exclusive degree than an MBA, a DBA can set you apart and help you land top leadership positions. Plus, the number of courses required is often less, making it one of the shortest doctoral options.

Slightly different than the DBA degree, a PhD in Business Administration is geared more toward academia.

If you’d rather conduct original research and teach students about your specific field in business rather than take on a demanding and rigorous role as a company’s CEO, a PhD in Business might be right up your alley.

Counseling Doctoral Degree Programs

A doctoral degree in counseling or therapy can equip you to help others work through their mental health or interpersonal struggles, and it can prepare you for leadership in a counseling organization.

Professionals in this area often pursue career paths in social work, private practice, and program administration. You may also tailor your education with concentrations like Counselor Education and Supervision, Art Therapy, Marriage and Family Therapy, and Addiction Counseling.

Coursework often covers topics like group and individual counseling, trauma response, ethical behavior, and diversity. Some universities require that you already be licensed as a counselor in your state before beginning their programs.

A PhD in Counseling is designed for counselors looking to ramp up their careers by becoming college and university educators, advanced counselors who train and lead others, or primary researchers on innovative studies.

If you’re currently a counselor and training other counselors, or if managing counseling programs are career goals of yours, then a PhD in Counseling online can make those goals a reality.

Criminal Justice & Homeland Security Doctorate Degrees

When you hold a doctorate in criminal justice or homeland security, you may find work in law enforcement, government, or private practice. Your chosen career may provide opportunities to protect your community, conduct investigations, work with criminals, or collect intelligence. Often, doctoral graduates gain leadership positions, such as serving as a chief of police.

In pursuit of your doctoral degree, you may take classes in psychology, emergency and disaster situations, the justice system, and victimology.

Your program may offer concentrations like Terrorism, Criminology, Information Assurance, Security or Emergency Management.

Whether you want to teach in a classroom, serve in school administration, support teachers through an outside organization, or equip the next generation of instructors, a doctoral degree in education can help you achieve those goals.

Many graduates remain in the classroom and take on leadership roles. Others education professionals choose positions such as principals, superintendents, professors, policymakers, curriculum specialists, or educational consultants.

While earning your doctoral degree, you may take classes in curriculum, organizational leadership, student assessment, and education research. You could select an EdD concentration in an area like Special Education, Administration, Curriculum and Instruction, or Early Childhood Education.

A PhD in Education and an EdD are quite similar degrees. Both programs focus on education and prepare you for leadership roles. PhD programs, however, are more research-based.

A PhD is typically more research-based and might be a better match for someone looking for a career in research, publishing, and teaching at the university level. It focuses less on application than an Ed.D., but the same types of careers would be possible with either of these two degrees.

In terms of time to completion, the shortest program option is likely the EdD as there’s often no dissertation required.

People with strong math and money skills are good candidates for pursuing a doctoral degree in finance. Many doctoral graduates take leadership positions with investment firms, large banks, hedge funds, universities, or government agencies. Some earn CEO or other C-suite roles.

A doctorate in finance can even prepare you for an international career. As you study for your degree, your classes may cover subjects like market analysis, global markets, financial planning, theories of finance, taxation, and leadership.

Some students choose to prepare for leadership roles in this field by pursuing a DBA with a concentration in Finance.

Online Doctorate in Healthcare Administration

When you hold a doctoral degree in the field of healthcare administration, you will be well-suited for a leadership position in a healthcare or medical setting. Potential places of employment include hospitals, nursing homes, medical records companies, political think tanks, government agencies, and universities.

Students of this discipline take classes on global health, business, law and policies, finance, and organizational leadership. Many DHA programs offer concentrations like Public Health, Leadership, and Health Policy.

An alternative academic path that is available at some colleges and universities is earning a DBA with a concentration Healthcare Administration which can offer the shortest path to a doctorate when no dissertation is required.

A doctorate in human services can prepare you for a leadership position in an organization or program that provides services or assistance for various groups of people. Work settings may include schools, clinics, community outreach programs, or non-profit organizations.

Some people who pursue this degree are licensed counselors who want to serve in a leadership capacity in a mental health practice. Others desire teaching positions in human services at the university level.

Courses in a doctoral program may include grant writing, leadership, communication, financial management, and ethics. Some of the concentration options are Mental Health, Gerontology, Marriage and Family, and Leadership and Management.

A PhD in Human Services prepares graduates for leadership and as policymakers in the public and human services fields.

A PhD in Human Services is quite flexible. Students with a variety of undergraduate and master’s degrees in public service, including social services, child welfare, criminal justice, and healthcare, may find this degree interesting.

Companies and organizations rely on systems to keep their data and records safe and accessible; to be at the forefront of that field, consider a doctorate in information technology .

With this degree, you might be qualify for work as a C-suite executive, a director in a tech department, a consultant, a leader in a government agency, or a strategist. You might also be well-poised for opening your own company.

Your classes will equip you with knowledge about data collection and analysis, threat and risk management, policy-making, strategic planning, and research.

Management / Leadership Doctorate Degrees

If you want to hold one of the highest roles in an organization, then earning a doctoral degree in management may be in order. Some people who hold this degree become C-suite executives, such as chief operating officers. Others take the helm of school districts or universities, or they accept teaching or research roles in higher education.

To earn this doctorate, you will take classes on leadership, ethics, consulting, decision-making, innovation, and research. Many students pursue concentrations like Technology, Homeland Security, Non-Profit Organizations, or Healthcare.

Alternatively, some schools offer a DBA program with a Management concentration. This often adds more flexibility to the program and can make it the shortest option when compared to the PhD which usually requires a dissertation.

Ministry (D.Min.) or Theology Doctorate Programs

You can take your religious education to the next level with a doctorate in ministry or theology. After earning this degree, you may choose to put your education into practice in church, parachurch, counseling, or chaplaincy positions.

Coursework often helps students grow not only academically, but also spiritually. Topics covered may include leadership, spiritual disciplines, evangelism, social justice, and teaching methods.

Some doctoral candidates pursue a specialization; options may include Counseling, Worship, Chaplaincy, Spiritual Disciplines, and Urban Ministry.

A career as a professor is a possibility with this degree as well as a missionary leader or lead pastor at a church.

Many universities require students to hold professional ministry positions before admitting them into their programs.

Online Doctoral Nursing Programs (Doctor of Nursing Practice)

The top-educated nurses have their doctoral degrees in nursing practice. If you have this degree, you may continue offering direct patient care; for example, you may work as a specialty nurse in a healthcare clinic. You could also use your degree as a care coordinator, a manager of a nursing team, a policymaker, or a nurse educator.

For RNs (Registered Nurses) who want to teach and train other nurses in an academic setting, a PhD in Nursing is the best doctorate-level nursing degree to pursue. A PhD in Nursing also prepares graduates for a career in research as nursing scientists who can contribute to the advancement of knowledge.

Coursework may include classes on information technology, finance, organizational leadership, safety, and healthcare law. Keep in mind that a doctoral degree in nursing is a terminal degree in the field does not qualify for a position as a physician.

DNP programs have gained a lot of popularity over the years and are designed for RNs who seek advancement while remaining practicing nurses.

A DNP prepares graduates for leadership in the nursing industry by advocating for and making policy, managing and directing nursing programs at health facilities, and ensuring that their communities offer the best healthcare to citizens who need it most.

Whether you want to work in a government agency or would prefer a position with a related organization, a doctorate in public administration can help you achieve your goals.

People with this doctoral degree often serve as politicians, lobbyists, non-profit directors, grant writers, administrators, or government affairs directors. If you want to go into government or politics, you could work at the local, state, or national level.

Students in this field study human resources, public policy, budgeting, ethics, organizational leadership, and decision-making.

As a professional doctorate, the DNP may be one of the shortest paths to a doctorate when compared to the PhD which generally requires a lengthy dissertation.

Online PhD in Public Health

Many people who earn a doctoral degree in public health conduct research in the fields of epidemiology, environmental science, clinical trials, or academia.

Others choose leadership roles in public health organizations that work to better the health outcomes for populations or groups of people. For example, you could become a safety engineer, a clinic manager, or an executive of a hospital system.

Classes for this degree program often cover health equity, data analysis, biostatistics, and healthcare policy. Concentrations are available at many universities; options may include Health Education, Leadership and Laboratory Science.

Online PhD in Public Policy

If you want to have a hand in creating or modifying the policies that shape people’s lives and communities, then a doctoral program in public policy can provide the education that you need. Graduates often work for government agencies, universities, think tanks, and various institutions.

Doctoral programs often prepare students through the study of ethics, decision-making, research, leadership, and cultural diversity. Students identify problems, gather valuable data, and create effective solutions.

Doctoral candidates may focus on Urban Policy, Health Policy, Financial Management, or other areas of specialization.

Online Ph.D. in Psychology Programs

A doctoral degree in psychology can help you understand how people think and the influence that thought has on behavior. Many people pursue this degree because they want to work as licensed clinical psychologists in schools, private practices, hospitals, or organizational settings.

The doctoral curriculum often covers counseling theories, psychopathology, culture, motivation and behavior, and cognition.

Programs leading to licensure typically require students to engage in a lengthy supervised practicum.

What is the Difference Between a PhD and Doctorate?

A PhD, or Doctor of Philosophy, is just one type of doctorate degree, of which there are many.

Here’s a list of common doctorate degrees:

• Doctor of Philosophy (Ph.D.)
• Doctor of Business Administration (DBA)
• Doctor of Education (EdD)
• Doctor of Psychology (PsyD)
• Doctor of Social Work (DSW)

Although the PhD is just one type of doctorate, it does have one distinguishing feature: the dissertation requirement. Nearly every PhD program requires adding to your field’s body of knowledge by performing original research on an approved topic of interest.

So, if you’re looking for fast track doctoral programs, then professional doctorates are generally a better choice.

How Long Does It Take to Get a Doctorate?

The length of time it takes to complete your doctorate depends on the university and type of doctoral program.

On average, it takes 3-5 years.

Here are a few things that significantly impact completion time:

• Does the doctorate require a dissertation?
• How many classes can you take at one time?
• Are you transferring any credits into the program?
• How many weeks are classes?
• Is there a residency requirement?
• Is there a professional internship requirement?

As you can see, the best answer we can give you is: it depends.

To give you a ballpark, if you are working toward a professional doctorate (DBA, EdD, PsyD, etc.) and there is no dissertation requirement, you should be able to complete your program in about 2-3 years. Some people may be able to complete the degree in less time, of course. This is simply an average.

For students pursuing Ph.D. programs, the dissertation requirement significantly impacts your completion time. Generally speaking, it takes most doctoral students 3 years to 5 years for degree completion.

What’s the Quickest Way to Earn a Doctorate Degree?

The shortest path to a doctorate varies depending on your background, the program selected, and the university’s requirements.

The time it takes to complete a doctoral program online varies widely by the university. For some universities, 3 year PhD programs are the norm. One common question we hear asked is if there are any 1 year online doctoral programs. For most students, the answer is somewhere in the middle if you already hold a master’s degree.

The official timeline given on most university websites is about 3 – 5 years to complete your degree, but that’s just a general guideline.

If you are looking for the shortest PhD programs, you’ll want to select a program that does not require a dissertation. Dissertations are notorious for taking 2+ years to complete beyond the actual course requirements.

The following doctoral programs often do not always require a dissertation: EdD, PsyD, DBA, DPA, and similar professional degrees. Most PhD programs require a dissertation (which means it’ll take you longer to complete).

Another way to speed up your degree is by enrolling at a university that offers accelerated doctoral courses (8 weeks long). Since the courses take half the time to complete, you can finish your doctoral studies in the shortest possible timeframe.

And finally, you’ll want to pick a program that requires fewer credit hours. For example, one university may require 64 credit hours for an EdD while another may only require 42 credits. When looking for the shortest doctorate programs, you’ll want to examine the credit hour requirements closely. Plus, this is a great way to find the cheapest online PhD, EdD, DBA, and other doctoral programs. Generally, you’ll pay less tuition if you don’t need as many credit hours for program completion.

Are There Any One Year Online Doctoral Programs?

While some schools offer the possibility of finishing a professional doctorate in 12 months to 18 months, most accredited universities generally promote their doctorate programs as taking 3 years or more to complete. Here’s a breakdown of what to expect:

Standard PhD Duration

The usual time frame for completing a PhD is about 3 to 5 years. Occasionally, you might come across a 2-year PhD program, but these are quite rare.

No-Dissertation Degrees

Choosing a program without a dissertation requirement can speed up the process. Typically, no-dissertation doctorates are found in professional fields, such as:

• Other career-focused doctorates

Strategies for Accelerated Completion

• Select an online program with fewer credit hours required.
• Enroll in accelerated courses, often structured as 8-week classes.
• Consider no-dissertation programs
• Look for programs that don’t require a GRE for admission.

Capstone Project as an Alternative

Instead of a traditional dissertation, consider programs offering a capstone project. Capstone projects require research but generally take less time to complete than dissertations.

So, while 1-year online doctorate programs are not commonly available, especially from accredited institutions, the strategies outlined above can help in finding and completing a doctorate program in a significantly shorter time frame than the standard duration.

Do All PhD Programs Require Students to Complete a Dissertation?

An accelerated PhD program usually requires a dissertation, but professional doctorates such as a Doctor of Business Administration or Doctor of Education generally do not require a dissertation. Instead, you complete a capstone project.

We’ve assembled a list of doctorate degrees that don’t require a dissertation here.

What is the Fastest PhD Program Available?

The fastest PhDs available will be those that require 30 credit hours or less to complete. As noted in the guide, we selected a number of fast PhD programs which meet this requirement. Once you’ve selected a PhD that requires fewer credit hours than the norm, try to narrow your list further by selecting a university with accelerated PhD classes which generally only take 8 weeks to complete.

If you don’t absolutely have to have a PhD, you will likely find it easier to locate a professional doctorate program that meets all of these criteria with the added benefit of no dissertation requirement. For example, it will likely take you longer to complete a PhD in Business Administration with 36 credit hours and a dissertation than it will to complete a Doctor of Business Administration of the same length without the dissertation requirement.

If speed is the most important factor for you, than a professional or applied doctorate such as an online Doctor of Business Administration, Doctor of Psychology, or Doctorate of Education will likely be the fastest online doctorate you can find.

Looking For the Fastest Doctorate Programs?

Whether you’re trying to get your doctorate in one year or you’re just looking for the fastest doctorate degrees available from accredited universities, the first step is decide how much you’re willing to compromise in the name of speed.

Yes, there are accredited online doctoral programs that can be completed in less time than traditional campus-based programs. The key is finding the shortest doctoral program that’s offering the exact program you’re seeking.

In your search for efficiency, focusing on programs with short completion times and fewer course requirements can be a strategic choice.

This guide is a good place to start:

• We only included accredited universities with the shortest doctoral and Ph.D. requirements (measured by the smallest number of classes required)
• Accelerated doctorate courses are available online
• A growing number of online doctoral degree programs don’t require a dissertation (especially professional doctorate degree programs)

Choosing a fast-track online Ph.D. or doctorate program with minimal required courses, accelerated online classes, and no dissertation requirements could be a smart move towards achieving your academic goals more efficiently.

Senior Thesis

This page is for Undergraduate Senior Theses.  For Ph.D. Theses, see here .

So that Math Department senior theses can more easily benefit other undergraduate, we would like to exhibit more senior theses online (while all theses are available through Harvard University Archives , it would be more convenient to have them online). It is absolutely voluntary, but if you decide to give us your permission, please send an electronic version of your thesis to cindy@math. The format can be in order of preference: DVI, PS, PDF. In the case of submitting a DVI format, make sure to include all EPS figures. You can also submit Latex or MS word source files.

If you are looking for information and advice from students and faculty about writing a senior thesis, look at this document . It was compiled from comments of students and faculty in preparation for, and during, an information session. Let Wes Cain ([email protected]) know if you have any questions not addressed in the document.

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• Summer 2024

MATH 800 A: Doctoral Dissertation

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Doctoral Candidate Presents Dissertation Findings at National Conference

Karmen Yu’s research addresses the question: How do undergraduate Calculus I students experience and navigate their learning of calculus in the parallel spaces of coursework and inquiry-oriented complementary instruction?

Posted in: Research Presentations

Doctoral candidate Karmen Yu recently presented findings from her dissertation study at the annual Research in Undergraduate Mathematics Education conference in Omaha, NE. Karmen’s talk, entitled Case Studies of Undergraduate Students’ Agentive Participation in the Parallel Spaces of Calculus I Coursework and Peer-Led, Inquiry-Oriented, Complementary Instruction.  She shared findings from one case study that included characterizations of the different forms of agentive participation afforded to students in each of the two spaces, as well as their complementary nature relative to learning calculus with understanding. It was a fantastic presentation. Karmen’s advisor, Dr. Steven Greenstein, was a contributor to the presentation and was there to support her. Great work, Karmen!