MASS - Summer REU 2005 (Course Outline)

June 26 - August 11

TIME: MWF 10:10 am - 12:05 pm

INSTRUCTOR: YURI ZARHIN

MAIN TOPICS include:

Divisibility of integers. Prime numbers and their distribution; Chebyshev's theorem.
Polynomials, their roots and derivatives. B'ezout theorem, Lagrange interpolation formula. Binomial coefficients, Bernoulli numbers and Bernoulli polynomials.
Algebraic and transcendental numbers, the field of all algebraic numbers. The transcendence of e and π.
Resultants, algebraic curves, Study's lemma, a rational parameterization of plane quadrics.