Current
Update: |
12/11/08 |
The solutions to Problem Set 11
are now available. I will have office hours as usual on Thursday, Dec. 11. During finals week, Sawyer will have an office hour on Tues, Dec. 16 from 1-2, and I will hold a session on Wed., Dec. 17 from 2 - 3:30. You may pick up your graded PSets during office hours (or we can arrange another time if needed). You may now download review problems for the Final Exam. |
Course Information |
Scheduled
Time |
Room |
Lectures | TR 1:00 |
2-102 |
Office Hours (Karl Mahlburg) | R 3:00 - 4:00 | 2-173 |
Office Hours (Sawyer Tabony) |
M 2:00 - 3:00 |
2-094 |
Textbooks (recommended) | I.
Niven, H. Zuckerman, H. Montgomery, An Introduction to
the Theory of Numbers G. H. Hardy, E. Wright, An Introduction to the Theory of Numbers |
Instructor: |
Karl |
Mahlburg |
Phone: | (617) 253-2685 | |
e-mail: | mahlburg (at) math (dot) mit (dot) edu. | |
Office: | 2-173 (First floor of Math building, south wing) | |
Teaching
Assistant: |
Sawyer |
Tabony |
Phone: | (617) 452-1199 | |
e-mail: | sawyer (at) math (dot) mit (dot) edu. | |
Office: | 2-094 (Basement) |
Date
|
Topics |
Reading |
Sep. 4 (R) |
Intro;
Pythagorean Numbers I |
Niven 5.3,
1.2 |
Sep. 9 (T) | Pythagorean
Numbers II; Division algorithm; gcd's & Euclidean algorithm |
Niven 1.2,
1.3 |
Sep. 11 (R) |
More gcd's;
lcm's; linear equations; primes |
Niven 1.3 |
Sep. 16 (T) |
Fundamental
theorem of arithmetic; factorization; congruences |
Niven 1.3,
2.1, 2.2 |
Sep. 18 (R) |
Solving
linear congruence equations; residue systems; Fermat's little
theorem |
Niven 2.1,
2.2 |
Sep. 23 (T) |
Chinese
remainder theorem; Euler's totient function |
Niven 2.3 |
Sep. 25 (R) |
Arithmetic
functions |
Niven 4.2 |
Sep. 30 (T) |
Mobius inversion; Computational techniques; primality testing | Niven 4.3,
2.4 |
Oct. 2 (R) |
Primality
testing |
Niven 2.4 |
Oct. 7 (T) |
RSA
cryptography; Multiplicative structure modulo primes |
Niven 2.5,
2.8 |
Oct. 9 (R) |
Midterm Exam I |
|
Oct. 14 (T) |
Primitive
roots modulo primes and composites; binomial coefficients |
Niven 2.8,
1.4 |
Oct. 16 (R) |
Binomial
coefficients; primitive roots modulo odd prime powers |
Niven 1.4,
2.8 |
Oct. 21 (T) |
Primitive
roots modulo powers of 2; solving polynomial congruences modulo prime
powers |
Niven 2.8,
2.6 |
Oct. 23 (R) |
Quadratic
equations modulo primes; quadratic residues and Legendre symbol |
Niven 3.1 |
Oct. 28 (T) |
Quadratic
reciprocity |
Niven 3.2 |
Oct. 30 (R) |
Jacobi
symbol; generalized quadratic reciprocity |
Niven 3.3 |
Nov. 4 (T) |
Pell's
equation; rational continued
fractions |
Niven 7.1,
7.2 |
Nov. 6 (R) |
Periodic
continued fractions; Pell's equation |
Niven 7.3,
7.7, 7.8 |
Nov. 11 (T) |
No class -
Veteran's Day |
|
Nov. 13 (R) |
Midterm Exam II |
|
Nov. 18 (T) |
Rational
approximations of irrationals |
Niven 7.4,
7.5 |
Nov. 20 (R) |
Periodic
continued fractions and quadratic irrationals; Pell's equation |
Niven 7.6,
7.7, 7.8 |
Nov. 25 (T) |
Farey fractions; rational approximations revisited | Niven 6.1, 6.2 |
Nov. 27 (R) |
No class -
Thanksgiving |
|
Dec. 2 (T) |
Rational
approximations; partitions; algebraic numbers |
Niven 6.2,
10.1, 10.2, 10.3, 9.2 |
Dec. 4 (R) |
Algebraic
integers; unique factorization; Riemann hypothesis |
Niven 9.2 -
9.8 |
Dec. 9 (T) |
Ramsey
Theory; Van der Waerden's theorem |
Final
Exam |
Thursday, Dec. 18
1:30PM - 4:30PM
|
Room 56-154 |