Description:

1. Algebraic and transcendental numbers
2. Algebraic number fields, field isomorphisms
3. Rational approximations, continued fractions
4. Diophantic equations, Pell's equation
5. Rings of integers in algebraic number fields and divisibility
6. Number representation in non-integer bases, finite and periodic expansions

Recommended literature:

Obligatory:
[1] Takahasshi Ono, An Introduction to Algebraic Number Theory, Springer-Verlag New York Inc.; 2013

Optional:
[2] E. B. Burger, R. Tubbs, Making transcendence transparent, Springer-Verlag 2004.
[3] M. Křížek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag 2001.

Keywords:

Algebraic number, number field, algebraic integer, continued fraction, diphantine equation, beta-expansions

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar