David Pierce | Matematik | M.S.G.S.Ü.

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# Quadratic Fields

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

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 + …) …)

See also last summer’s course, Continued Fractions.

# The Prime Number Theorem

Nesin Mathematics Village, February 4–10, 2019.

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).

See also last summer’s course, Prime Numbers.

Son değişiklik: Thursday, 13 September 2018, 16:50:23 EEST