A website dedicated to mathematics would not be complete without a list of links. I felt the urge to provide only what I think to be the most valuable of them, thereby renouncing exhaustiveness; however, I also referred to other pages of abundant links for the curious reader. Finally, I affixed a star to the most interesting links in order to attract attention primarily on the most outstanding resources.


Problem solving:

• http://www.problemcorner.org/
(*) : 20,000 problems, most of them being very hard, and given without solutions. This is a wonderful collection, but be warned, this could be particularly inefficient for academic training.
• http://www.math.ca/Competitions/MOCP/
: a training program for math olympiads, featuring a few problems to solve every month.
• www.math.purdue.edu/pow/
: a problem of the week with average difficulty.
• http://www.fen.bilkent.edu.tr/~cvmath/Problem/problem.htm
: a problem of the month, whose level usually is that of an easy math olympiad.
• http://www.cut-the-knot.org/index.shtml
: various mathematical problems and anecdotes for everyone.

Online Math encyclopediae:

• http://mathworld.wolfram.com/
(*): very useful, even though there are inaccuracies scattered in many places. Always double-check the information you get there.
• http://planetmath.org/
(*): very useful as well, but keep in mind that everybody can contribute to this online encyclopedia.
• http://www.research.att.com/~njas/sequences/
(*): an inventory of all remarkable strings of integers. A precious work for researchers.

Ebooks and courses:

• http://www.jmilne.org/math/
(*): various courses in higher algebra: Galois theory, algebraic geometry, etc ... The style of the writer is wonderfully clear, its mastery of the subjects is complete and his books give a lot of insight. No extraneous technical propositions are given, allowing the reader to abstract the essence of the notions. Each of his works is a pearl.
• http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/
(*): simply the best ebook on graph theory available for free online.
• http://www.math.harvard.edu/people/SternbergShlomo.html
(*): his book named "Advanced Calculus" contains basically everything you need to know in college analysis. Only reproach: the style is a little dry at times, but considering the scope of this book, it is easily forgivable.
• http://www.ima.umn.edu/~arnold/502.s97/
: a basic course in complex analysis. It is short, clear, and provides enough background for a good start.

Collections of links:

• http://mathres.kevius.com/problem.htmln
(*)
• http://departments.oxy.edu/math/links/links.htm
• http://archives.math.utk.edu/
(*): huge database of links searchable by topics.
• http://us.geocities.com/alex_stef/mylist.html
(*): impressive list of links pointing to free math ebooks collections in various fields of mathematics.

Software:

• http://www.miktex.org/
(*): a very good Latex distribution.
• http://www.winedt.com/
(*): a good text editor compatible with Miktex.
• http://www.maplesoft.com/
(*): a very powerful commercial software (very expensive also).
• http://www.wolfram.com/
(*): another powerful commercial software, which is the only real rival of Maple.

History of mathematics:

• http://www-history.mcs.st-and.ac.uk/history/
(*): very rich: contains biographies of mathematicians, quotations, and much more. Highly recommended.
• http://www.numdam.org/?lang=en
(*): ancient math texts numerized and browsable for free.

Preliminary exams:

Preliminary exams (also called qualifying exams, prelims or qualifs) are those taken before full acceptation into a PhD program. The links below point to archives of problems from those exams.

• http://www.math.ufl.edu/other/quals.html
• http://www.math.ucsb.edu/~jon.mccammond/courses/fall03/260/quals.html
• http://www.math.purdue.edu/~bell/Quals/

Various:

• http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
: an online browsable version of the Elements (Euclid).
• http://primes.utm.edu/
: a page devoted to large prime numbers.
• http://www.claymath.org/millennium/
: featuring open problems whose solutions are worth $1,000,000 apiece.
• http://forumgeom.fau.edu/
(*): free journal on euclidean geometry.
• http://www.ics.uci.edu/%7Eeppstein/junkyard/
(*): everything related to geometry.

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