Elementary Number Theory II
Added August 15, 2017. Revised notes (mainly through formatting: now A5 paper, 12 point type, 121 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:
(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.
- Exercise set I:
- Exercise set II:
- Exercise set III:
- Exercise set IV:
- Exercise set V:
Examinations
All solutions are now available. (Final-exam solutions corrected and expanded, June 12, 2008.)- Monday, March 24, 17.40. The exam: Solutions:
- Monday, May 26, 17.40, in M–103. The exam: Solutions:
- Final exam: Monday, June 2, at 16.30, in M–08. Problems and solutions together:
Grading
The best two in-term exams count 30% each; the final, 40%.
Results (here are: last two digits of ID number; letter grade)