Mathematics

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.

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.
American Mathematics Society: The homepage for the American Mathematical Society (AMS).

Conference Videos: An open collection of videos of talks from various workshops and conferences.
MIT OCW: MIT OpenCourseware offers lecture videos and other courseware for free.
MSRI: A collection of lectures maintained by the MSRI.
Clay Math: A collection of videos maintained by the Clay Mathematics Foundation.

Mathematica: Mathematica is a powerful computational mathematical software. You can find the general website here, the demonstrations page here, and the blog page here.
MAGMA: A large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatorics.
Sage: A free-source mathematics software system, similar to Mathematica.
GAP: A computational device for discrete algebra.
WolframAlpha: A useful site for making computations and pulling up data.
Symbolab: Another symbolic calculator.
Geogebra: A great piece of free software for all sorts of Geometry. (You can find how to use it here .)
Calculator Programs: A site full of useful programs for the TI-83, TI-84, and TI-89.
Rice ODE Software: A useful website for visualizing vector fields.

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.
Online Integer Sequences: An online searchable database of integer sequences.
Number Field Database: A database of Number Fields.
Elliptic Curve Data: A database for Elliptic Curves.
Inverse Symbolic Calculator: A free online inverse symbolic calculator.

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.

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.
Conrad’s Expository Papers: Keith Conrad’s collection of fine expository papers.
Milne’s Books: Milne’s website containing his many books, all freely accessible.
Math Counterexamples: A website dedicated to demonstrating various counterexamples in Mathematics.
Algebraic Identities: A collection of algebraic identities.
Proof is Trivial: A fun website for ‘solving’ difficult proofs.
Mathematical Jargon: A wiki list of common mathematical jargon.

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.

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.
LEGO Grad Student: Life as a graduate student, all told through LEGOs.
Wolfam Blog: A blog of Mathematics and Computer Science topics using Mathematica.
Advice for Amateur Mathematicians: Professor Henry Cohn’s advice for new mathematicians.
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.

Putnam Exams: A collection of Putnam Exams.
Mathematical Olympiad: A collection of Mathematical Olympiad problems.
Project Euler: A series of challenging problems in Mathematics and Computer Science. The challenges slowly increase in difficulty.
Open Problems Wiki: A list of unsolved problems in various mathematical fields.
Open Questions: A list of various major open problems in Mathematics.

Paul Nylander Artwork: Paul Nylander’s website containing his mathematical artwork.

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.

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.