Professor:
Dr. Janet Vassilev
Office: SMLC 324
Office
Hours: MWF 23 pm and by appointment.
Telephone: (505)
2772214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Date

Section

Topic

Homework

1/19


Introduction, Induction^{} 

1/21

1.1.1

Prime Numbers

HW 1

1/24

1.1.2

Division Algorithm


1/26

1.1.2

Euclidean
Algorithm


1/28

1.1.31.2.3

Fundamental
Theorem of Arithmetic, cardinality of primes, prime sieve and Mersenne primes

HW2

1/31

1.2.41.2.5

Primes of the
form ax+b and the Prime Number Theorem


2/2


Classes canceled due to closure^{} 

2/4


Classes canceled due to closure_{} 

2/7

2.1

Congruence
modulo n,


2/9

2.1

Congruence
modulo n and solving equations modulo n


2/11

2.1, 2.3

Euler’s Theorem
and

HW3

2/14

2.2

Chinese
Remainder Theorem


2/16

2.2

Chinese Remainder
Theorem


2/18

2.5

Order and
Primitive roots

HW4 due Monday 2/28

2/21

2.5

Primitive roots


2/23


Review


2/25


Midterm 1


2/28

2.5,3.2

Primitive roots
and Diffie Hellman


3/2

3.2

Diffie Hellman and RSA


3/4

3.3

RSA and ciphers

HW5 p 4647
2.17, 2.25, 2.27a, 2.28, 2.30, 2.33
P 67 3.4 and
3.5

3/7

3.4

Attacking RSA


3/9

3.4

Attacking RSA


3/11

4.1

Quadratic
reciprocity

HW6

3/21

4.2

Euler’s
Criterion


3/23

4.3

Gauss’ Lemma


3/25

4.3

Gauss’ Lemma

HW7

3/28

4.4

Gauss Sums


3/30

4.4

Gauss Sums


4/1

4.5

Square roots

HW8

4/4

5.1

Continued
Fractions


4/6


Review


4/8


Midterm 2


4/11

5.2

Continued Fractions


4/13

5.3

Convergence of
infinite continued fractions


4/15

5.5

Quadratic
irrationals

HW9

4/18

5.7

Sums of Two
Squares


4/20

5.7

Sum of Two
Squares


4/22

6.16.2

Elliptic curves

HW10

4/25

6.2

Elliptic curves


4/27

6.3

Integer
factorizations using elliptic curves


4/29

6.3

Integer
factorizations using elliptic curves

HW11

5/2


Review


5/4


Review


5/6


Review


5/11


Final exam

