This page (created by Kiran Kedlaya) is meant to provide links of use to undergraduate and graduate students, and to professional mathematicians. I maintain a separate links page for the American Mathematics Competitions, focused on precollege students and their parents and teachers. Perhaps even more useful in this regard is the set of lists maintained by Art of Problem Solving, which also includes some book recommendations (click on "Resources").
This page used to live within my personal web site, but I decided to try setting it up as a wiki. Unfortunately, I had to limit edit access to credentialed users; if you want to make changes, email me with a proposed account name and I'll send you back a password.
For undergraduate students
- The undergraduate math clubs of MIT, Duke, Princeton and Harvard.
- An archive of problems and solutions from the Putnam competition. If you have no idea what that is, see the official Putnam home page. (If your school administers the Putnam, there should be a particular person in charge of it; ask around.)
- Speaking of competitions, the International Mathematics Competition for University Students loosely emulates the IMO at the university level, but on a much smaller budget. It seems to be mostly attended by Eastern Europeans.
- The Morgan Prize for undergraduate research.
- The National Science Foundation funds a number of REU (Research Experience for Undergraduate) summer programs, in math and the sciences; the Harvard undergraduate math club keeps a database of reviews of math REUs attended by Harvard students. For example...
- The summer math research program in combinatorics and graph theory at the University of Minnesota, Duluth, directed by Joe Gallian.
- Study abroad opportunities in mathematics:
- ALGANT (ALgebra, Geometry, And Number Theory) is a Masters-level program between four European universities (Bordeaux, Leiden, Padova, Paris-Sud), but is not restricted to Europeans.
- The original Eastern European study abroad program: Budapest Semesters in Mathematics. (I attended this program, so can comment from personal experience on it.)
- The Cambridge University Certificate of Advanced Study in Mathematics ("Part 3") is an intense one-year program at the Masters level (i.e., typically appropriate for students just after finishing an undergraduate program).
- Mathematics Advanced Study Semesters is held at Penn State but follows an Eastern European model.
- Math in Moscow is sponsored by the Independent University of Moscow (and last I checked, also by the American Mathematical Society).
For graduate students
See also "Funding sources" below.
- Steven Miller's information for first-year graduate students is targeted at Princeton students, but may be helpful for others, particularly those considering Princeton for graduate school in mathematics.
- Ditto for the Berkeley Math Graduate Students Association web site.
- Qualifying exam questions:
For recent PhDs
See also "Funding sources" below.
- Mathjobs is a new site for processing online job applications.
- PhDs.org has many more links.
- Young Mathematicians' Network is, well, what it says.
These are mostly aimed at graduate students and older, since there are much better resources elsewhere aimed at undergraduates and younger. See also the AMS funding page. And beware that applications/nominations for a program starting in fall of a given year may be as due as early as June of the previous year!
Guide to terminology: "graduate" fellowships typically begin at the start of graduate students or a year later. "Postdoctoral" fellowships typically begin at receipt of the PhD. "Junior" fellowships are sometimes awarded to fresh PhDs in exceptional cases, but are targeted at those who have already completed a postdoc (and are now "junior faculty", i.e., tenure-track).
Not listed separately are postdocs funded by NSF grants to individual schools (e.g., through the RTG program). Such positions are usually limited by NSF rules to US citizens and permanent residents. Also not listed separately are postdocs at research institutes; see below.
- American Institute of Mathematics (postdoctoral fellowship)
- American Mathematical Society Centennial Fellowship (junior fellowship)
- Centre National de la Recherche Scientifique (French analogue of NSF)
- Clay Mathematics Institute (postdoctoral fellowship and several other programs)
- Department of Defense/NDSEG (graduate fellowship)
- Guggenheim Foundation (fellowship for "advanced professionals", whatever that means)
- Harvard Society of Fellows (junior fellowship at Harvard)
- Hertz Foundation (graduate fellowship)
- Hodge Fellowship (en français) (postdoctoral fellowship at IHES)
- IBM PhD Fellowship (graduate fellowship for 2nd year or older students)
- Macarthur Foundation (the "genius grants"; sometimes awarded like a junior fellowship, but with a closed nomination process)
- Microsoft Research (graduate fellowship for 2nd and 3rd year students, postdoctoral internship)
- Miller Institute (postdoctoral fellowship, visiting professorship at Berkeley)
- National Physical Science Consortium (graduate fellowship, with an emphasis on underrepresented minorities)
- National Science Foundation funding opportunities include:
- National Security Agency Mathematical Sciences Program (grants, particularly for junior researchers)
- Natural Sciences and Engineering Research Council (Canadian analogue of NSF)
- Number Theory Foundation (grants to support conferences and other projects)
- Packard Foundation (junior fellowship)
- Radcliffe Institute for Advanced Study (junior/senior; not exclusively for women, but it probably helps)
- Sloan Foundation (postdoctoral/junior fellowship; no citizenship requirement)
These are sorted by full name (omitting first names in eponyms, except the "Max" in "Max Planck" by convention), but many of these are commonly known by acronyms, so these are included as well. See also the unified home page for all of the NSF-funded institutes.
In a couple of cases, these are not really single physical locations, but abstract entities (with money) that include several locations. These are characterized as "distributed".
Institutes that typically host and fund postdocs (often in accordance with a semester-long or year-long themed program) include: CRM (Montréal), Fields, IAS, IHES, IMA, MPI, MSRI, Newton, RIMS. Institutes that run primarily as conference centers (with few long-term visitors or faculty) include: AIM, BIRS, CIRM, Oberwolfach.
- Abdus Salam International Centre for Theoretical Physics (Trieste, Italy)
- Algebra, Geometry, and Number Theory (ALGANT) (Erasmus Mundus Master program; distributed, several European locations)
- American Institute of Mathematics (AIM) (Palo Alto, CA)
- Banff International Research Station (BIRS) (Banff, AB)
- Center for Communications Research (CCR): Princeton, NJ, La Jolla, CA (associated with NSA)
- Centre de Recerca Matemàtica (Barcelona, Spain)
- Centre de Recherches Mathématiques (CRM) (Montreal, QC)
- Centre International de Mathématiques Pure et Appliqueés (CIMPA) (based in Nice, France, but holds events in developing countries)
- Centre International de Rencontres Mathématiques (CIRM; more commonly "Luminy") (Luminy (near Marseille), France)
- Chennai Mathematical Institute (CMI) (Chennai, India)
- Clay Mathematics Institute (CMI) (Cambridge, MA)
- DIMACS Center for Discrete Mathematics and Theoretical Computer Science (New Brunswick, NJ)
- Fields Institute for Research in Mathematical Sciences (Toronto, ON)
- Harish-Chandra Research Institute (Allahabad, India)
- Heilbronn Institute for Mathematical Research (Bristol, England; affiliated with GCHQ, the British analogue of NSA)
- Institut des Hautes Études Scientifiques (IHES) (Paris, France)
- Institute for Advanced Study (IAS) (Princeton, NJ)
- Institute for Mathematics and its Applications (IMA) (Minneapolis, MN)
- Institute for Pure and Applied Mathematics (IPAM) (Los Angeles, CA)
- Institute of Mathematical Sciences (IMSc) (Chennai, India)
- Institut Mittag-Leffler (Djursholm, Sweden)
- Instituto Nacional de Matemática Pura e Aplicada (IMPA) (Rio de Janeiro, Brazil)
- International Centre for Mathematical Sciences (ICMS) (Edinburgh, Scotland)
- Isaac Newton Institute for Mathematical Sciences (Cambridge, England)
- Japanese American Mathematics Institute (JAMI) (Baltimore, MD)
- Lorentz Center (Leiden, Netherlands)
- Mathematical Sciences Research Institute (MSRI) (Berkeley, CA)
- Mathematisches Forschungsinstitut Oberwolfach (MFO; more commonly "Oberwolfach") (Black Forest, Germany)
- Max-Planck-Institut für Mathematik (MPI) (Bonn, Germany)
- Microsoft Research (Seattle, WA, Cambridge, MA, Mountain View, CA, Cambridge, UK, Bangalore, India, Beijing, China; see theory, cryptography groups)
- Pacific Institute for the Mathematical Sciences (PIMS) (Vancouver, BC and Banff, AB)
- Rényi Institute of Mathematics (Budapest, Hungary)
- Research Institute for Mathematical Sciences (RIMS) (Kyoto, Japan)
- SFB 478 "Geometrische Strukturen in der Mathematik" (Münster, Germany)
- Claude Shannon Institute for Discrete Mathematics, Coding and Cryptography (Dublin, Ireland)
- Southwestern Center in Arithmetic Algebraic Geometry (distributed; based in Tucson, AZ)
- Tata Institute for Fundamental Research (TIFR) (Mumbai (Bombay) and Bangalore, India)
I'm sure there are more of these out there!
- commalg.org (commutative algebra)
- Galois Theory Web Page
- K-theory Preprint Server
- Quantum computing: directory of home pages, Quantum Pontiff blog, conference list
- Number Theory Web
- Valuation Theory Home Page
- The AMS maintains a web directory of mathematics journals.
- The UC Davis front end to the arXiv preprint server.
- Neil Sloane's Encyclopedia of Integer Sequences needs no introduction.
- The MacTutor History of Mathematics is a comprehensive history of mathematics, including biographies and histories of particular topics.
- Eric Weisstein's MathWorld is a surprisingly detailed glossary of mathematics terms.
Professional societies and organizations
Many countries have their own national societies; I have not listed all of these, again because of the North American-centric nature of this site.
- American Mathematical Society (AMS)
- Association of Women in Mathematics (AWM); see also the Noetherian Ring at Berkeley (the latter has links to more such sites).
- Canadian Mathematical Society (CMS)
- International Mathematical Union (IMU), the umbrella organization for the quadrennial International Congress of Mathematicians. See also ICM 2006 (Madrid, Spain).
- Mathematical Association of America (MAA)
- Society for Industrial and Applied Mathematics (SIAM)
- Jordan Ellenberg writes a regular column for Slate called Do the Math.
- The Clay Mathematics Institute's million dollar problems.
- Ravi Vakil maintains a long list of conferences in algebraic geometry.
- Ed Pegg, Jr.'s site mathpuzzle.com has a lot of interesting stuff and more links than any one human being has a right to have.
- My math competition archive and problem directory now reside on the American Mathematics Competitions site.
- Carl Miller's math problem of the week archives.
- NUMDAM has posted copies of the IHES Publications Mathematiques through 2000.
- The TeXer is a handy web page (provided by Art of Problem Solving) for converting TeX code into images for use on the web.