McGill University

Department of Mathematics & Statistics

Number Theory

189-346A / 377B

Detailed Syllabus

1. Jan 4-Jan 8: (Chapter 1). Overview of the course. Basic properties of the integers.
   
   
2. Jan 11-Jan 15: (Section 2.1). The GCD. The Euclidean Algorithm. Primes, and the Fundamental Theorem of Arithmetic. Modular arithmetic, and Fermat's Little Theorem.
   
   
3. Jan 18-Jan 22: (Sections 3.1, 3.2, 4.1, 4.2). The structure of (Z/nZ)x. The Euler phi-function. Discrete logarithms. Application to primality testing and cryptography.
   
   
4. Jan 25-Jan 29: (Sections 4.3, 5.1, 5.2, 5.3). Power residues. The law of quadratic reciprocity.
   
   
5. Feb 1- Feb 5 : (Chapter 6). Number theoretic functions and the distribution of primes.
   
   
6. Feb 8 - Feb 12: (Chapter 6, cont'd).
   
   
7. Feb 15 - Feb 19: (Chapter 6, cont'd).
   
   
8. 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.
   
   
9. March 1 - March 5 : (Chapter 7). Sums of squares.
   
   
10. March 8 - March 12: (Chapter 7). Sums of squares.
    
    
11. March 15 - March 19: (Sec. 2.2 and Chapter 8). Quadratic equations and quadratic fields.
    
    
12. March 22 - March 26: (Chapter 9). Diophantine approximation and continued fractions.
    
    
13. March 29 - April 2: (Chapter 9). Diophantine approximation and continued fractions.
    
    
14. April 5 - April 9: Further topics (on request, time permitting).
    
    
15. April 12 - April 14: Further topics (on request, time permitting).