390 Pages
23 B/W Illustrations
by
Chapman & Hall
390 Pages
23 B/W Illustrations
by
Chapman & Hall
390 Pages
23 B/W Illustrations
by
Chapman & Hall
Also available as eBook on:
Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics.
To begin this journey of discovery, some experience with... Read more
Preface
Symbols
1.Review of Sets, Functions, and Proofs
2.Introduction: A Number Game
3.Groups
4.Subgroups
5.Symmetry
6.Free Groups
7.Group Homomorphisms
8.Lagrange’s Theorem
9.Special Types of Homomorphisms
10.Making Groups
11.Rings
12.Results on Commutative Rings
13.Vector Spaces
14.Polynomial Rings
15.Field Theory
16.Galois Theory
17.Direct Sums and Direct Products
18.The Structure of Finite Abelian Groups
19.Group Actions
20.Learning from Z
21.The Problems of the Ancients
22.Solvability of Polynomial Equations by Radicals
23.Projects
Bibliography
Index
Symbols
1.Review of Sets, Functions, and Proofs
2.Introduction: A Number Game
3.Groups
4.Subgroups
5.Symmetry
6.Free Groups
7.Group Homomorphisms
8.Lagrange’s Theorem
9.Special Types of Homomorphisms
10.Making Groups
11.Rings
12.Results on Commutative Rings
13.Vector Spaces
14.Polynomial Rings
15.Field Theory
16.Galois Theory
17.Direct Sums and Direct Products
18.The Structure of Finite Abelian Groups
19.Group Actions
20.Learning from Z
21.The Problems of the Ancients
22.Solvability of Polynomial Equations by Radicals
23.Projects
Bibliography
Index
Biography
Steve Rosenberg is a professor in the Mathematics and Computer Science Department at the University of Wisconsin-Superior. He received his Ph.D. from the Ohio State University. As an educator, Dr. Rosenberg has both developed and taught a wide array of courses in mathematics and computer science. As a researcher, he has published results in the areas of algebraic number theory, cryptographic protocols, and combinatorial designs, among others. As a software developer, his clients included Coca-Cola Enterprises and the pension agency of Cook County Illinois. He has extensive experience in computer science and software engineering.
