Month 
Date 
Topic 
Sections 



August 
27 
Introduction: course overview / Divisibility 
1 

29 
The division algorithm / The gcd / the Euclidean algorithm 
2.52.7 

31 
The extended Euclidean algorithm / Other bases 
2.72.8

September 
5 
Other bases / The extended Euclidean algorithm / Fermat & Mersenne Primes

2.72.9


7 
Fermat & Mersenne Primes / Review / Theorem 3.1

3.13.2 

10 
Theorem 3.1

3.13.2 

12 
The exact change problem / postage stamp problem

3.2 

14 
Fundamental Theorem of Arithmetic

4.14.2


17 
Rational Root Theorem (with proof) / Pythagorean triples (no proof)

5.15.4 

21 
Riemann zeta function

5.7 


24 
Divergence of the sum of reciprocals of primes

5.7.1


26 
Congruences  definitions and basic properties

6.1


28 
Quizterm 1


October 
1 
Modular exponentiation / divisibility tests / Linear congruences

6.26.4 

3 
Linear congruences

6.4


5 
The Chinese remainder theorem

6.5 

8 
Simple ciphers

7.27.4 

10 
Stream and block ciphers

7.57.6


12 
Review

Ch. 26 

15 
Quizterm 2



17 
Modular polynomials information sharing / Fermat's little theorem

7.7, 8.1 

19 
Euler's theorem

8.2


22 
Euler's theorem / Euler's phi function
 8.2


24 
Euler's phi function / RSA

8.4, 9.1


26 
RSA / digital signatures

9.19.2


29 
Order / application to Fermat numbers / Primitive
roots

11.111.2 

31 
Primitive roots / Decimal criterion for
rationality 
11.211.3 
November 
2 
Quizterm 3




5 
The discrete log problem / DiffieHelman /
ElGamal 
11.5, 12.1, 12.4 


7 
Squares mod p 
13.1 


9 
Squares mod p / Statement of Quadratic Reciprocity /
Primality
testing and Carmichael numbers 
13.1, 14.2 


12 
Statement of Minkowski's theorem / volume
computations 
15.1 


14 
Fermat's theorem on sums of squares 
15.2 


16 
Conclusion of the proof of Minkowski's theorem

15.1 


19 
Quizterm 4 


26 
Elliptic curves mod p 



28 
Elliptic curve addition law 



30 
Elliptic curve addition law, discrete log problem, DiffieHelman, ElGamal 


December 
3 
Quizterm 5 


5 
Associativity of the group law 



7 
Review  part 1 



10 
Review  part 2 



17 
Final exam 
