**Title of the course:** Continued fractions

**Instructor:** Prof. David Pierce

**Institution:** MSGSÜ

**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