Topics in Algebra
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.