Actions of Groups: A Second Course in Algebra

by John McCleary

Overview

Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in the solutions of polynomial equations. Because groups may act as permutations of a set, as linear transformations on a vector space, or as automorphisms of a field, the deeper structure of a group may emerge from these viewpoints, two different groups can be distinguished, or a polynomial equation can be shown to be solvable by radicals. By developing the properties of these group actions, readers encounter essential algebra topics like the Sylow theorems and their applications, Galois theory, and representation theory. Warmup chapters that review and build on the first course and active learning modules help students transition to a deeper understanding of ideas.

Product Details

ISBN-13:	9781009158114
Publisher:	Cambridge University Press
Publication date:	01/05/2023
Pages:	226
Product dimensions:	5.94(w) x 9.02(h) x 0.71(d)

About the Author

John McCleary is Professor of Mathematics on the Elizabeth Stillman Williams Chair at Vassar College. He received his Ph.D. in mathematics from Temple University, where he completed a thesis on algebraic topology under the direction of James Stasheff. The author of several books, including A User's Guide to Spectral Sequences and Geometry from a Differentiable Viewpoint, McCleary has published extensively on topology, the history of mathematics, and other topics. His current research focuses on algebraic topology – specifically, where algebra reveals what topology may conceal.

Table of Contents

Preface; 1. Warmup: more group theory; 2. Groups acting on sets; 3. Warmup: some linear algebra; 4. Representation theory; 5. Warmup: fields and polynomials; 6. Galois theory; 7. Epilogue; References; Index.