Week Topics Homework (due Thursday)
7/6 1. Early Number Theory
Pythagorean Triples,
Fermat Last Theorem,
Division Algorithm, 

Euclidean algorithm
Unique factorization
2.Induction
1.Induction and applications
 Fill this form.

Here are the slides of the first week.

Goodie bag: Terence Tao Talk: "Structure and Randomness in the Prime Numbers”
7/13 2.Induction (cont.)
2. Binomial Theorem
(Excluding the section about Differential Equations)
3. Renaissance
Cubics, quartics
Complex numbers
Algebraic operations
Here are the slides of this week.

1.1:  1.2, 1.4,  1.6(i) to (iv)., 1.8, 1.10, 1.11,  1.14, 1.15, 1.19 (one of the answers in the book is wrong), 1.21, 1.22, 1.26.
1.2: 1.31,1.33
1.3: 1.38, 1.40, 1.43, 1.47, 1.48.
1.4 1.51, 1.55, 1.57, 1.58, 1.60, 1.61,1.62, 1.64 (in iv) replace "y=a.x+b" by " a.x+b.y=c, with a,b,c integers), 1.65, 1.66, 1.67 (ii and v)

2.1: 2.1, 2.4, 2.5, 2.12, 2.13, 2.16 , 2.17 . Optional: 2.14.

Goodie bag: Induction and dominoes.

7/20		 Chapter 3 (cont)
Roots and powers
4. Modular Arithmetic
1.Congruence

Private Key Cryptography (Caeaser, Affine, Vignere amd matrix ciphers) (You can find a discussion of Caesar, affine and matrix cipheres in section 7.1 of
Abstract Algebra: Theory and Applications . 
 
Here are week 3 slides.

2.2: 2.21, 2.23, 2.24, 2.25, 
       2.33, 2.34, 2.39, 2.40, 2.41
3.1: 3.1 (i, ii,iii, vii, viii, ix, x. For each equation find all the solutions in R and all the solutions in C, i.e., two set of solutions for each equation), 3.2, 3.3,3.4(i) and (v), 3.5, 3.10,  3.13 , 3.14(i and ii), 3.15, 3.17(i)
3.2 3.23, 3.24, 3.28,  3.29, 3.30, 3.32,  3.36, 3.37, 3.38, 3.39.



Goodie bag: Encryption and HUGE numbers.
7/27
4. Modular Arithmetic
2.Public Key codes

(More cryptography material in Chapters 7 and 8 of Abstract Algebra: Theory and Applications.

Ciphers: Caesar, Affine.

The list of review problems is here

3.3: 3.46, 3.47, 3.49(i), 3.51(i),  3.52, 3.53(iv), 3.54, 3.55, 3.56.
4.1: 4.1, 4.3, 4.4, 4.6, 4.9, 4.10, 4.11, 4.13, 4.14

MIDTERM (on Thursday July 30th. Chapter 1, 2, 3 and Section 4.1 up to but not including linear congruences)

Goodie bag: The enigma machine

In this site you will find an interesting account of RSA.
8/2


Ciphers: Caesar, Affine, Hill, Vigenere, Pohlig- Hellman, RSA.
Here you will find an account of most of the ciphers we will discuss.
Here is a detailed example of the Vigenere cipher.
In this website, you will find a description of Pohlig-Hellman and RSA. Here there is another explanation Pohlig-Hellman.
The problems this week are from three different sources:

4.1: 4.16, 4.18, 4.23

From Chapter 7 of Abstract Algebra: Theory and Applications.: problems 1 ,2,4,5,6.  (Problems 7.3, and 7.5 are optional).

Problems 1 to 4 from this set.

Summary of the discussion about Caesar and affine ciphers (among others)  is here.

Midterm 1 solution is here.

The histogram for midterm 1 is here, with approximate letter grades.
8/9 Review

FINAL (on Thursday )
 Optional: 4.2: 4.25, 4.26, 4.27.
 To submit: Problems 8 to 14 of  this set.

Here is an updated version of the slides about Cryptography.

Here is a list the review problems for the final. This list does not include any cryptography problems, nor the topics covered in the first midterm. Use the review for the midterm (or the midterm itself) for review those.
Use the list of homework problems for review of cryptography (take into account that no calculators will be allowed during the exam, but of course computations will not require them).



Final on the last day of class


Grades are posted. You can find your final grade in Blackboard and the course grade in Solar.

Here is a histogram of the final scores and here a histogram of the weighted averagea.







Table Design by Scott Sutherland