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).

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):