Number Theory (Summer 2003)
Information on Math 356:B6 taught by Sasa Radomirovic is kept here.
Final Exam Information
The final exam will be on Thursday, July 3rd, 6-9pm in the usual classroom.
You are allowed to use 1 letter sized, single sided page of handwritten
notes (no Xerox copies, no printouts). The notes will be collected with the exam at the end. It is your resonsibility to bring these notes along with you. No calculator will be allowed.
Now that it's all over, here's the final with solutions
Schedule & Office Hours
The course runs from May 28 until July 3, 2003.
Classes meet in Beck 121 (on Livingston Campus) Mondays, Wednesdays and Thursdays 6:15-8:45pm.
Office hours are held Mondays before class in the classroom.
Syllabus
The text book is Elementary Number Theory and its applications by Kenneth H. Rosen. The sections below refer to the sections in the text book.
| Day |
Topics planned |
Topics covered |
Suggested Problems |
Homework (due next class)
|
| Wed 5/28 |
Chapter 1 |
1.1-1.3 |
Problem Set 1 |
Section 1.2: #6
|
| Thu 5/29 |
3.1-3.2 |
1.4, 3.1 |
Problem Set 2 |
Section 3.1: #10
|
| Mon 6/02 |
3.3,3.4 |
3.2, 3.3 |
Problem Set 3 |
Section 3.4: #8
|
| Wed 6/04 |
3.6, Quiz I |
Quiz, 3.4 |
Problem Set 4 |
Section 3.6: #16
|
| Thu 6/05 |
4.1,4.2 |
3.4, 3.6 |
Problem Set 5 |
Section 4.1: #4
|
| Mon 6/09 |
4.3,4.4 |
4.1, 4.2 |
Problem Set 6 |
Section 4.3: #12
|
| Wed 6/11 |
4.6, Review |
4.3, Review |
Problem Set 7 |
|
| Thu 6/12 |
|
4.4 |
|
2.3: #6 OR 4.1: #34
|
| Mon 6/16 |
Chapter 6 - Wilson, Fermat, Euler |
Chapter 6 |
Problem Set 8 |
Section 6.3: #10
|
| Wed 6/18 |
Chapter 7 - Multiplicative Functions |
7.1, 7.2, 7.4 |
Problem Set 9 |
Section 7.2: #10
|
| Thu 6/19 |
Cryptography Introduction |
Lecture Notes |
Problem Set 10 |
Homework
|
| Mon 6/23 |
Chapter 9 - Primitive Roots |
9.1, discussed prob. sets 8, 9, 10 |
Problem Set 11 |
Section 9.2: #10
|
| Wed 6/25 |
Chapter 9, Quiz II |
9.2, 9.3 |
Problem Set 12 |
Section 11.1: #6
|
| Thu 6/26 |
Chapter 11 - Quadratic Residues |
11.1, 11.2, 11.3 |
Problem Set 13 |
Section 11.4: #2
|
| Mon 6/30 |
Chapter 12 - Continued Fractions |
12.1, 12.2, 12.3 |
|
|
| Wed 7/02 |
Review |
Review |
|
|
| Thu 7/03 |
Final |
Final is cumulative |
|
|
Course structure and Grades
Every day 1 Homework Problem will be assigned, due next class.
There will be 2 Quizzes, each 30 minutes long, with problems chosen from the problem sets. There will be 1 Midterm, 80 minutes long, with problems very similar to those in the problem sets. The Final will be 3 hours long, again with problems very similar to the problem sets.
The final grade will consist of the following parts:
10% Homework
20% Quizzes
30% Midterm Exam
40% Final Exam
No grades will be dropped. Instead, extra credit problems (see problem sets)
can be solved. Extra credit will be applied towards Homeworks and Quizzes (in that order).
Links, Feedback and further information
You can give me some feedback about the lecture using the random
number you have received on the first day of class by going to
this page.
Working demos and solutions to programming exercises are posted on this page.
History of Mathematics and biographies of mathematicians (MacTutor)
Random Links More or less Number Theoretic links. New links are being added as I stumble over them.
Links ordered by sections:
- 1.3: The Fibonacci Numbers
- 3.1: Prime Numbers
- The Prime Page contains probably everything you ever wanted to know about primes and much more.
- The Prime Page also features source code for the Sieve of Erathostenes in many programming languages.
- 3.3: The Extended Euclidean Algorithm (and a few more) in the C programming language
- 3.6: Linear Diophantine Equations
- 4.1: Square and Multiply Algorithm in the C programming language
- 4.2: Modular Inverses in the C programming language
- 4.6: More on Factorization Algorithms:
- Links to short overviews of many Factorization Algorithms are given in Eric Weisstein's World of Mathematics.
- The Question "What are the best factoring methods in use today?" is answered in the RSA Labs FAQ.
- Find out about the RSA Factoring Challenge at the RSA Data Security site.
- 6.1: Primality Testing:
- Last summer's big buzz about primality testing explained by D. Bernstein (draft) and the actual paper by Agrawal, Kayal, and Saxena.
- 7.3: Perfect Numbers and Mersenne Primes
- Chapter 8:
- The first paper on public key cryptosystems:
W. Diffie and M. Hellman. "New Directions in Cryptography." IEEE Transactions on Information Theory, IT-22(6), November 1976
- The first paper that turned Diffie and Hellmans idea into a an
actual cryptosystem was the famous RSA paper: R. L. Rivest, A. Shamir,
and L. M. Adleman. "A Method for
Obtaining Digital Signatures and Public-Key Cryptosystems."
Communications of the ACM,
Vol. 21, No. 2, February 1978.
- Shamir's paper on secret sharing: A. Shamir, "How to Share a Secret." Communications of the ACM, Vol. 22, No. 11, November 1979
- Answers to frequently asked questions about cryptography
are available here
(Cryptography FAQ Index) and
at the RSA Labs.
- If you want to learn cryptography then a good start would be to read Shafi Goldwasser and Mihir Bellare's Lecture Notes on Cryptography, written for a summer course taught at MIT, and now available online (290 pages).
- 9.1: Order of an Integer and Primitive Roots
- 11.2: Quadratic Reciprocity
- 12.2: Continued Fractions
- You can learn about the connection between continued fractions and the Euclidean Algorithm, the Fibonacci numbers, jigsaw puzzles and more on this page.
If you know of another interesting link, you can let me know on this page
Go to main page.
Saa Radomirović