As the class progresses, I will add links to websites, such as Wikipedia, which contain additional information on topics mentioned in class. Visiting these sites is purely optional, but you might find a lot of interesting and fun information.
Biographies of mathematicians
It's fun to learn math, but it's also fun to learn about the people who discovered and invented the ideas we're learning about. Here are some links to webpages with brief biographies of mathematicians we've met during our class. There are two reasonably good resources on the Internet for short biographies of mathematicians: Wikipedia and the MacTutor history of mathematics archive.
- Pythagoras (~575BC - ~490BC), Wikipedia biography, MacTutor biography.
- Euclid (~300 BC - ??), Wikipedia biography, MacTutor biography.
- Marin Mersenne (1588 - 1648), Wikipedia biography, MacTutor biography.
- Pierre de Fermat (~1601 - 1665), Wikipedia biography, MacTutor biography.
- Leonhard Euler (1707 - 1783), Wikipedia biography, MacTutor biography.
- Carl Friedrich Gauss (1777 -1855), Wikipedia biography, MacTutor biography.
- Adrien-Marie Legendre (1752 - 1833), Wikipedia biography, MacTutor biography.
More information on mathematical topics
This section will contain links to Wikipedia articles about various topics we touched on in class. There may be a few instances where there will be links to other resources as well.
- Primality testing: trial division, Lucas-Lehmer, Fermat pseudoprimes, strong pseudoprimes, Miller-Rabin, AKS. At the bottom of some of these articles there are links to many other articles about algorithms in number theory.
- Integer factorization: trial division.
- Mersenne primes: Wikipedia article, GIMPS project.
- Constructing regular polygons: Wikipedia article, case of the 17-gon.
- Counting primes: Prime number counting function, prime number theorem, Riemann hypothesis.
- The Chinese Remainder Theorem: The Chinese Remainder Theorem.
- Hensel's Lemma: Hensel's Lemma.
- Fermat's Little Theorem: Fermat's Little Theorem, Fermat-Euler theorem.
- Primitive roots: Primitive roots, multiplicative order, Lagrange's Theorem, unit groups.
- Quadratic residues: quadratic residues, Legendre symbol, Jacobi symbol, quadratic reciprocity.
Other interesting links
Here's a miscellaneous link section. Enjoy!