David Pierce | Matematik | M.S.G.S.Ü.

# Elementary Number Theory II

Added January 5, 2018. Revised notes (A5 paper, 12 point type, 153 pages):

Math 366, spring, 2007/8 (section 1, the unique section)

## Schedule

• Tuesdays, 13:40–15:30, in M-105;
• Fridays, 13:40–14.30, in M-07 (changed from 12:40–13:30, in M-105).

## Text

The official text for the course is the lectures. My own notes are available:

• through April 15:
• through May 20:
(The earlier notes changed little in the preparation of the later version: the main change was the addition of new equation numbers for later reference.)

Works consulted in preparing the lectures include:

• William W. Adams and Larry Joel Goldstein, Introduction to Number Theory (Prentice-Hall, 1976): on reserve in the library
• David M. Burton, Elementary Number Theory (6th ed., McGraw-Hill, 2007): for the Pell equation, especially
• Graham Everest and Tom Ward, An Introduction to Number Theory (Springer, 2005): high-level, but recent, and available to us electronically through the METU catalogue
• Carl Friedrich Gauss, Disquisitiones Arithmeticae (Springer, 1986; original Latin publication, 1801): the origin of much of what we do
• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (fifth ed., Oxford, 1979; first edition, 1938)
• D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination (Chelsea, 1952; original German publication, 1932): for the number-theoretic proof that π/4 = 1 - 1/3 + 1/5 - 1/7 + …
• Edmund Landau, Elementary Number Theory (Chelsea, 1958; original German publication, 1927)
• Serge Lang, Elliptic Functions (2nd ed., Springer, 1987): on lattices and orders in quadratic fields

## Homework

I can talk about any of the following exercises in class, if you ask me the day before.

1. Exercise set I:
2. Exercise set II:
3. Exercise set III:
4. Exercise set IV:
5. Exercise set V:

## Examinations

All solutions are now available. (Final-exam solutions corrected and expanded, June 12, 2008.)
1. Monday, March 24, 17.40. The exam: Solutions:
2. Monday, May 26, 17.40, in M–103. The exam: Solutions:
3. Final exam: Monday, June 2, at 16.30, in M–08. Problems and solutions together: