Book Description: Algebra and Number Theory Benjamin Fine 2017 Pages: [Insert Total Number of Pages] Volume Set: 2 volumes Genre: Mathematics, Algebra, Number Theory Summary: This two-volume set presents a comprehensive collection of fundamental results in algebra and number theory, providing an entertaining and engaging experience for readers. The first volume focuses on the natural integral and rational numbers, division and factorization in integers, modular arithmetic, exceptional numbers, Pythagorean triples, and sums of squares. It also covers polynomial and unique factorization, field extensions, and splitting fields. The second volume delves into permutations and symmetric polynomials, real numbers, complex numbers, the Fundamental Theorem of Algebra, and polynomial equations. Additionally, it explores quadratic number fields, Pell's equation, transcendental numbers, and the classical problems of Euclidean vector spaces. The book is designed for lecturers, teachers, and students of mathematics, as well as anyone interested in the subject. Each chapter includes exercises to reinforce understanding of the concepts presented.

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