406-2004-AAL Algebra II
Semester | Autumn Semester 2019 |
Lecturers | R. Pandharipande |
Periodicity | every semester recurring course |
Language of instruction | English |
Comment | Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. |
Abstract | Galois theory and related topics. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |
Objective | Introduction to fundamentals of field extensions, Galois theory, and related topics. |
Content | The main topic is Galois Theory. Starting point is the problem of solvability of algebraic equations by radicals. Galois theory solves this problem by making a connection between field extensions and group theory. Galois theory will enable us to prove the theorem of Abel-Ruffini, that there are polynomials of degree 5 that are not solvable by radicals, as well as Galois' theorem characterizing those polynomials which are solvable by radicals. |
Literature | Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society Galois Theory is the topic treated in Chapter A5. |
Prerequisites / Notice | Algebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4. |