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

The early history of the United Nations, as Gaglione (political science, late of East Stroudsburg U., Pennsylvania) tells it, spans the later years of World War II, the milieu of confusion and hope immediately after, and the beginning of the Cold War when relations between the east and west completely broke down. He argues that the end of great power cooperation prevented the UN from taking an active role in promoting international cooperation, and made it into an arena for some of the most dangerous confrontations between the Soviet Union and the west. c. Book News Inc.

Anthony Gaglione

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