McGill University
Department of Mathematics & Statistics
Number Theory
189346A / 377B
Detailed Syllabus
 Jan 4Jan 8: (Chapter 1). Overview of the course. Basic
properties of the integers.

Jan 11Jan 15: (Section 2.1). The GCD. The Euclidean Algorithm.
Primes, and the Fundamental Theorem of Arithmetic.
Modular arithmetic, and Fermat's Little Theorem.
 Jan 18Jan 22: (Sections 3.1, 3.2, 4.1, 4.2).
The structure of (Z/nZ)x. The Euler phifunction.
Discrete logarithms.
Application to primality testing and cryptography.
 Jan 25Jan 29: (Sections 4.3, 5.1, 5.2, 5.3).
Power residues. The law of quadratic reciprocity.
 Feb 1 Feb 5 : (Chapter 6).
Number theoretic functions and the distribution of primes.
 Feb 8  Feb 12: (Chapter 6, cont'd).
 Feb 15  Feb 19: (Chapter 6, cont'd).
 Feb 22  Feb 26: Study break. A good time to work seriously on
your project! In particular, your topic should have been chosen by then.
 March 1  March 5 :
(Chapter 7).
Sums of squares.
 March 8  March 12: (Chapter 7).
Sums of squares.
 March 15  March 19:
(Sec. 2.2 and Chapter 8).
Quadratic equations and
quadratic fields.
 March 22  March 26: (Chapter 9).
Diophantine approximation and continued fractions.
 March 29  April 2: (Chapter 9).
Diophantine approximation and continued fractions.
 April 5  April 9: Further topics (on request, time permitting).
 April 12  April 14: Further topics (on request, time permitting).