Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

Cornelia Busch: Catalogue data in Spring Semester 2017

Name Dr. Cornelia Busch
Address
Lehre Mathematik
ETH Zürich, HG E 64
Rämistrasse 101
8092 Zürich
SWITZERLAND
E-mailcornelia.busch@math.ethz.ch
DepartmentMathematics
RelationshipLecturer

NumberTitleECTSHoursLecturers
401-3112-17LIntroduction to Number Theory4 credits2VC. Busch
AbstractThis course gives an introduction to number theory. The focus will be on algebraic number theory.
Objective
ContentThe following subjects will be covered:
- Euclidean algorithm, greatest common divisor, ...
- Congruences, Chinese Remainder Theorem
- Quadratic residues, Legendre symbol, law of quadratic reciprocity
- Quadratic number fields, integers and primes
- Units of quadratic number fields, Pell's equation, Dirichlet unit theorem
- Continued fractions and quadratic irrationalities, Theorem of Euler Lagrange, relation to units.
Literature- A. Fröhlich, M.J. Taylor, Algebraic number theory, Cambridge studies in advanced mathematics 27, Cambridge University Press, 1991
- S. Lang, Algebraic Number Theory, Second Edition, Graduate Texts in Mathematics, 110, Springer, 1994
- J. Neukirch, Algebraic number theory, Grundlehren der mathematischen Wissenschaften 322, Springer 1999
- R. Remmert, P. Ullrich, Elementare Zahlentheorie, Grundstudium Mathematik, Basel Birkhäuser, 2008
- P. Samuel, Algebraic Theory of Numbers, Kershaw Publishing Company LTD, 1972 (Original edition in French at Hermann)
- J.-P. Serre, A Course in Arithmetic, Graduate Texts in Mathematics 7, Springer 1973 (Original edition in French at Presses Universitaires de France)
Prerequisites / NoticeBasic knowledge of Algebra as taught in a course Algebra I + II.