- 1. Basics: divisibility, unique factorization, congruences, primes, . . .
- 2. Usual Suspects: infinitude of primes, theorems of Fermat-Euler, two squares, quadratic reciprocity, . . .
- 3. Simple applications to cryptography, codes, primality tests, . . .
- 4. Rational Function Fields
- 5. Quadratic forms

- 07.02.06 homework 1; solutions.
- 14.02.06 homework 2; solutions.
- 23.02.06 homework 3 You can hand in problem 1 (RSA) later. Here's a windows executable of pari. If you type in ?, you'll get a list of chapters; ?4 lists e.g. the number theoretical functions, and ?gcd tells you what gcd does. You can find a more detailed manual at the pari homepage in Bordeaux.
- 14.03.06 homework 4; solutions.
- 11.04.06 homework 5; solutions.
- 27.04.06 homework 6; solutions.

- Rose: A course in number theory
- Hardy and Wright: An introduction to the theory of numbers
- Ireland and Rosen: A classical introduction to modern number theory

- 02.02.06 Monoids, unique factorization (sorry for hurrying through the last proof; I'll do it again next time).
- 07.02.06 residue classes
- 09.02.06 greatest common divisors, Euclidean algorithm
- 14.02.06 Euclidean algorithm, Pythagorean triples
- 16.02.06 Fermat's Theorem on the diophantine equation
x
^{4}+ y^{4}= z^{4}. - 21.02.06 Fermat's Little Theorem; Z/pZ is a field.
- 23.02.06 RSA
- 28.02.06 Residue class rings; Pollard's p-1 method. here you can find the record factors found with this method.
- 02.03.06 NO CLASS: moved to 04.03.06
- Sat. 04.03.06, 10:30-12:30 Midterm 1 in BZ08 (Computer Center Building). We will cover the material up to 21.02.06. Average: 67/100. Here are a few similar problems for those who need more practice.
- 07.03.06 Discussion of Midterm 1. Theorem of Euler-Fermat
- 09.03.06 Chinese Remainder Theorem
- 14.03.06 Chinese Remainder Theorem (applications); order of elements; Mersenne and Fermat numbers
- 16.03.06 primitive roots
- 21.03.06 primitive roots; quadratic reciprocity
- 23.03.06 NO CLASS: moved to 04.03
- 04.04.06 quadratic residues; Legendre symbol.
- 06.04.06 the quadratic reciprocity law
- 11.04.06 Quadratic reciprocity; Jacobi symbol.
- 13.04.06 discussion of homework; binary quadratic forms
- 18.04.06 homework; review; quadratic forms
- 20.04.06 Midterm 2, SBZ03, 5:40 - 7:40 pm (no class at 9:40). We will cover phi function, Euler-Fermat, RSA, Chinese Remainder Theorem, order of residue classes, primitive roots, quadratic reciprocity. Average: 71/100.
- 25.04.06 Reduction.
- 27.04.06 Class numbers
- 02.05.06 Class numbers
- 04.05.06 Quadratic number fields
- 09.05.06 Unique Factorization and class number 1
- 11.05.06 Composition
- 16.05.06 Composition; review
- 17.05.06 Final 12.15, SAZ04.
- Here is the complete set of notes.
- Here are a few problems for the last two chapters. Here are the problems for a make up midterm 2, along with partial solutions.
- Final problems solutions. Average 73.5/100
- We 18.05, 10:30 - 12:00 I'll be in my office.
- Next week: Oberwolfach. Mathematicians at work.
- Mo 29.05, 13:30 make up