LYCOS RETRIEVER 
Galois Theory
built 671 days ago
One of the great triumphs of Galois Theory was the proof that for every n > 4, there exist polynomials of degree n which are not solvable by radicals—the Abel-Ruffini theorem. This is due to the fact that for n > 4 the symmetric group Sn contains a simple, non-cyclic, normal subgroup.
Source:
This volume is based on talks given at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories held at The Fields Institute for Research in Mathematical Sciences (Toronto, ON, Canada). The meeting brought together researchers working in these interrelated areas. This collection of survey and research papers gives an up-to-date account of the many current connections among Galois theories, Hopf algebras, and semiabelian categories. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higher-dimensional structures. Articles are suitable for graduate students and researchers, specifically those interested in Galois theory and Hopf algebras and their categorical unification.
Source:
Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book ... delves into more novel topics, including Abel’s theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami. Anyone fascinated by abstract algebra will find careful discussions of such topics as:
Source:
Combining a concrete perspective with an exploration-based approach, this analysis develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and only requires knowledge of a first course in abstract algebra. It introduces tools for hands-on experimentation with finite extensions of the rational numbers for readers with Maple or Mathematica. Please visit the author's website at: http://www.davidson.edu/academic/math/swallow/john.htm
Source:
Classical Galois theory studied extension fields of a given field. Techniques of descent provided ways of glueing local information together to obtain global information. Algebraic homotopy concerns the use of both algebraic models for homotopy types and homotopy theory applied to algebraic objects. It is closely related to homotopical algebra.
Source:
This proposal seeks ACS funding to complete the technology portion of an ongoing project: the creation of a course in undergraduate Galois theory which brings abstraction and computation together in the service of learning an important mathematical discipline. Such a course has a natural place in the mathematics curricula of many institutions, including 13 members of the ACS. Specifically, ACS funding during the summer of 2002 would support the design of packages in two computer algebra systems, Mathematica and Maple, to permit students to calculate complicated examples with ease. In addition, this project would involve ACS mathematics faculty in the review and evaluation of these materials. Taken in context of the larger project, the ACS grant would allow the proposer to finish the course development project, and the text would reach a publisher during the following year.
Source:
MORE ABOUT
Galois Theory