Benjamin Fine

Gerhard Rosenberger

Anthony Gaglione

Anja Moldenhauer

Dennis Spellman

This two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner. The present volume examines many of the most important basic results in algebra and number theory, along with their proofs, and also their history. Contents The natural, integral and rational numbers Division and factorization in the integers Modular arithmetic Exceptional numbers Pythagorean triples and sums of squares Polynomials and unique factorization Field extensions and splitting fields Permutations and symmetric polynomials Real numbers The complex numbers, the Fundamental Theorem of Algebra and polynomial equations Quadratic number fields and Pell’s equation Transcendental numbers and the numbers e and π Compass and straightedge constructions and the classical problems Euclidean vector spaces

A Selection of Highlights

Algebra and Number Theory

This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.

Dennis Spellman

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