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 12, 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 
2102 
Office Hours (Karl Mahlburg)  R 3:00  4:00  2173 
Office Hours (Sawyer Tabony) 
M 2:00  3:00 
2094 
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) 2532685  
email:  mahlburg (at) math (dot) mit (dot) edu.  
Office:  2173 (First floor of Math building, south wing)  
Teaching
Assistant: 
Sawyer 
Tabony 
Phone:  (617) 4521199  
email:  sawyer (at) math (dot) mit (dot) edu.  
Office:  2094 (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 56154 