|
Subject |
Lecture slides |
Lecture notes |
| Lecture 1 |
Divisiblity and modular arithmetic |
(PDF) |
(PDF)
(PS) |
| Lecture 2 |
Primes and GCD |
(PDF) |
(PDF)
(PS) |
| Lecture 3 |
End of GCD / Review |
|
|
| Lecture 4 |
Polynomials |
(PDF) |
(PDF)
(PS) |
| Lecture 5 |
More Polynomials |
(PDF) |
(PDF)
(PS) |
| Lecture 6 |
Extended Euclid |
|
(PDF)
(PS) |
| Lecture 7 |
Chinese Remainder |
|
| Lecture 8 |
Fermat's Little Theorem |
(PDF) |
(PDF)
(PS) |
| Lecture 9 |
Square Roots Modulo Primes |
(PDF) |
(PDF)
(PS) |
| Lecture 10 |
Roots Modulo Composites, Repeated Squaring |
|
(PDF)
(PS) |
| Lectures 11-12 |
Cryptography and RSA |
|
Section 4.7 of textbook |
| Lecture 13 |
Midterm |
|
|
| Lecture 14 |
Midterm solutions / review |
|
(PDF)
(PS) |
| Lecture 15 |
Introduction to groups |
|
(PDF)
(PS) |
| Lecture 16 |
Subgroups and isomorphisms |
|
| Lecture 17-19 |
Examples of groups. Counting. |
|
|
| Lecture 20-21 |
Normal subgroups and quotient groups |
|
(PDF)
(PS) |
| Lecture 22-23 |
Finite fields |
|
(PDF)
(PS) |
| Lecture 24-25 |
Error-correcting codes |
|
(PDF)
(PS) |
| Lecture 26-27 |
Correcting Errors in Reed-Solomon Codes |
|
(PDF)
(PS) |