Articles which may be of interest, which further explore some of the topics we cover in class, may be found in the course dropbox.
The current world record for the largest known prime number was set on August 23, 2008, as part of the Great Internet Mersenne Prime Search (GIMPS). It has 12,978,189 digits. Amazingly, two weeks later, a second Mersenne prime, having 11,185,272 was found. The first will almost surely be confirmed as the winner of the Electronic Frontier Foundation's $100,000 prize as the first 10,000,000 digit prime ever found.
In 2002, the first algorithm was found that determines if a number is prime, and which is known to run in polynomial time - in this case, the length of time required is on the order of the number of digits of the number being tested, to about the fourth (4th) power.
The Online Encyclopedia of Integer Sequences will allow you to type in the first few terms of a sequence you suspect has a pattern, and will match it against any known integer sequence in its database. Several published results have a search of this database as an important initial component!
Numbers of the form 2(2n)+1 which are prime are called Fermat primes; they appear to be very rare. More generally, numbers of the form a(2n)+1 are called (surprise) generalized Fermat primes. There are some lists of generalized Fermat primes for (relatively) small values of a and n.
This page will compute the continued fraction expansion of any quadratic irrational of reasonable size (e.g, the integer in the square root should be less than 10,000,000,000).
This page lists all of the prine numbers up to 10 million.
A site called SOS Math
offers pages of material on topics ranging from polynomial long
division, the quadratic formula, and trigonometric identities, to Taylor polynomials,
the Cauchy-Riemann equations, and Matrix algebra.
Another site covering similar material, including solved homework problems for you to practice on, is kept in Belgium.
Dan Sloughter has a web page containing Java programs for visualizing various mathematical concepts. My favorite is one which will draw the Taylor polynomial approximations for y=sin(x) .
A site called Karl's Calculus Tutor currently covers most of what would qualify as first-semester calculus, and some of the second semester, as well.
Forget a geometry formula? Check this page at Ask Dr. Math.