GALOIS THEORY - University of Bristol.
In fact, I use a lot of background knowledge of field theory -- some of it that I know full well is not taught in most standard courses, some of it that I only thought about myself rather recently -- and judging from students' questions and solutions to problems, good old finite Galois theory is a relatively known subject, compared to say infinite Galois theory (e.g. the Krull topology) and.
The upside to Hawking's book (whose title is part of a quote by Kronecker, by the way) is that you get much more than just Galois's three papers. There are original works of Euclid, Archimedes, Descartes, Riemann, Cantor, Dedekind, and quite a few more (ironically, no Kronecker from what I can see!).
These notes are based on “T opics in Galois Theory,” a course giv en b y J-P. Serre at Harv ard Universit y in the F all semester of 1988 and written do wn b y H. Darmon.
Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century.
The ideas behind Galois Theory were developed through the work of Newton, La- grange, Galois, Kronecker, Artin and Grothendieck. Before Galois it was known the following, that we write here using.
GALOIS THEORY: LECTURE 8 LEO GOLDMAKHER 1. EISENSTEIN’S CRITERION, ROUND TWO We ended last lecture by discussing the irreducibility of polynomials and several tests that could be used to determine irreducibility, including Eisenstein’s criterion. The formulation of the criterion from last lecture can be replaced by the following equivalent.
Langlands Program. The main websource is of course the one containing lots of Langlands own writings.; On the web page of A. Raghuram you will find his thesis on representation theory of GL(2,D) over p-adic division algebras D, notes for Ram Murty's Lectures on Artin L-functions and for D. Prasad's Automorphic forms on GL(n) (both dvi).