Title of the course: Continued fractions
Instructor: Prof. David Pierce
Dates: 13-19 August 2018
Prerequisites: None. We shall study some topics that may be studied in a second-semester number-theory course; however, no specific results are required from a first-semester course.
Level: Graduate, advanced undergraduate
Abstract: We accept from childhood that multiplication of whole numbers is commutative; but Euclid gives a rigorous proof based on what we now call the Euclidean algorithm. This algorithm can be used to write any real number as a continued fraction. The continued fraction repeats when the real number is the solution of a quadratic equation. This case yields the solutions of a so-called Pell equation, x^2 - dy^2 = 1, an example of a Diophantine equation.
Textbook or/and course webpage: http://mat.msgsu.edu.tr/~dpierce/Courses/Sirince/ (in preparation)
Language: TR; EN