Math 118, Advanced
Number Theory, Winter 2000
- Classes: T, Th, 12:00-1:45, AS 372.
- Instructor: Robert Boltje; office: AS 365C; Tel.:
459-5001; Email:
boltje@math.ucsc.edu; office hours: Thursday,
2:00-3:00 or by appointment.
- Problem sessions: Th 4:00-5:30, AS 358.
- Homework: Completed homework to be handed in every
Thursday at the beginning of problem session.
- Passing requirements: Homework, midterm exam, final exam
with equal weight.
- Textbook: [IR] Kenneth Ireland, Michael Rosen: A
classical introduction to modern number theory, 2nd edition,
Springer 1998.
[R] Kenneth H. Rosen: Elementary number theory and its
applications. Third edition. Addison Wesley 1993.
- Midterm: Thursday, February 10, 4:00-7:00, AS 358.
Problems as PDF-file or
PS-file.
- Final: Friday, March 17, 8:00-11:00am, in AS 372
Problems as PDF-file or
PS-file.
- Exercises: Problems as PDF-file or PS-file.
Syllabus:
- Prime numbers (cf. [IR, 2.1, 2.3, 2.4], Week 1)
- Unique factorization (cf. [IR, 1.1, 1.2, 1.3, 1.4], Week 1-2)
- Euclidean domains (cf. [IR, 1.2, 1.3, 1.4], Week 2-3)
- Prime elements in Z[i] and the equation
n=x2+y2 (no suitable reference in
[IR], Week 3)
- The Group U(Z/nZ) (cf. [IR, 3.4,
4.1], Week 4-5)
- Quadratic residues and quadratic reciprocity (cf. [IR,
5.1-5.3], Week 5-6)
- Some diophantine equations (cf. [IR, parts of 17], Week 7-8)
- Continued fractions (cf. [R, 10.2, 10.3, 10.4], Week 9-10)