Contents of this page:

# Quadratic Fields

Nesin Mathematics Village, January 28–February 3, 2019.

See also last summer’s course, Continued Fractions.

- Başlık:
- Quadratic Fields
- Eğitmen:
- Prof. David Pierce
- Kurum:
- MSGSÜ
- Tarih:
- 28 Ocak–3 Şubat 2019
- Önkoşul:
- yok
- İçerik:
- A quadratic equation in two variables may have
infinitely many integral solutions, but we shall develop a technique for
finding all of them. This starts with the Euclidean Algorithm, which we
can use to write any real number as a continued fraction
*a*+ 1 / (*b*+ 1 / (*c*+ …) …)

# The Prime Number Theorem

Nesin Mathematics Village, February 4–10, 2019.

Course notes (44 pages, size A5, 12 point type, dated February 14, 2019):

See also last summer’s course, Prime Numbers.

- Başlık:
- The Prime Number Theorem
- Eğitmen:
- Prof. David Pierce
- Kurum:
- MSGSÜ
- Tarih:
- 4–10 Şubat 2019
- Önkoşul:
- Calculus
- İçerik:
- We shall work through a proof that the limit at infinity
of π(
*x*) log*x*/*x*is 1, where π(*x*) is the number of primes that are no greater than*x*. The needed number theory is minimal; the needed complex analysis is not minimal; but we shall assume only real calculus (L’Hôpital’s Rule and improper integrals).

# Hyperbolic Geometry

Nesin Mathematics Village, July 15–21, 2019. Given jointly with Ayşe Berkman.

Course notes (56 pages, size A5, 12 point type, dated August 5, 2019):