Arxiv: A collection of preprints maintained by Cornell University. This is a standard place for mathematicians to place their preprints and papers.
IHES: The library for the IHES. Grothendieck’s works can be found here.
AMS Journals: A collection of journals overseen by the American Mathematical Society.
Opportunities in Mathematics
Travel Grants: The American Mathematical Society page with list of AMS meetings with opportunities for funding to visit or speak at these conferences.
Programs for Graduate Students: American Mathematical Society (AMS) career and professional development opportunities for graduate students.
Math Programs: A website dedicated to compiling research and job opportunities, especially for graduate and undergraduate students, in Mathematics and other STEM fields.
Math Jobs: A website compiling professorships, postdoc positions, and other related mathematical positions.
WolframAlpha: A wonderful and free computation an searchable knowledge database. The system takes verbal commands such as ‘integrate x^3 sin(2x)’, ‘plot x^2-y^2+z^2=6’, ‘barometric pressure May 5, 2014 Ithaca, NY’, ‘number of Spanish speakers in the US’, ‘map of Germany’, ‘sum of alternating harmonic series’, etc.
LMFDB: An online database of Number Fields, L-functions, and modular forms. This site is compatible with MAGMA, Sage, Pari, GAP, and Mathematica.
WolframMathWorld: An extensive resource of mathematics definitions and examples.
Math History: An online encyclopedia of mathematicians, mathematics history, and other mathematical objects.
Mathematical Symbols: A nearly comprehensive list of symbols used in mathematical writing.
Random: A website dedicated to demonstrating the need/usefulness of random numbers.
Math Genealogy: A compilation of students/advisors dating back hundreds of years. The genealogy of the Mathematics Department at Syracuse University can can be found at this link.
Mathematics Help
MathOverflow: A site for professional and other research mathematicians to ask research level questions. For general, non-research level questions, use MathStackExchange instead.
MathStackExchange: A site for mathematics students everywhere to ask/answer questions and obtain mathematics advice.
Questionable Publishers: A list of questionable publishers that graduate students should avoid submitting any papers to.
Math Gen: A site that automatically generates (fake) ‘publishable’ mathematics papers.
MR Lookup: A reference tool for BibTeX referencing.
Mathematical Comics and Blogs
Tao’s Blog: The blog of famous mathematician and expositor Terence Tao.
XKCD: A thrice-weekly comedy comic strip with topics relevant to STEM fields.
XKCD What-If: Run by the XKCD comic creator, this site dedicates itself to answering, as accurately as possible, strange questions poised by its readers.
American Mathematical Society Blog: A list of blogs sponsored by the American Mathematical Society, including a blog by mathematics graduate students about life as a mathematics graduate student.
Inside Higher Ed: A page with news and blogs relating to higher education.
PhD Comics: A comedic comic strip relating to the graduate school experience.
Teaching College-Level Science & Engineering: This OCW MIT course contains wonderful lectures given by Dr. Sanjoy Mahajan on how to teach effectively and engagingly in STEM fields. The video lectures can be found on the website as well as at this link. You can find another iteration of this course at this link.
Undergraduate Research Opportunities
NFS Listing: The National Science Foundation’s list of summer undergraduate Math research programs.
AMS Listing: The American Mathematical Society’s list of summer undergraduate Math research programs.
Math Programs : A useful site for Math REU programs where one can apply to many programs with one application form.
