Algebra and number theory: a selection of highlights/ Benjamin Fine & et al

Includes bibliography and index

The Natural integral and rational number 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 pai -- Compass and straightedge constructions and the classical problems -- Euclidean vector spaces

In the two-volume set ‘A Selection of Highlights’ we present basics of mathematics in an exciting and pedagogically sound way. This volume examines fundamental results in Algebra and Number Theory along with their proofs and their history. In the second edition, we include additional material on perfect and triangular numbers. We also added new sections on elementary Group Theory, p-adic numbers, and Galois Theory.

A true collection of mathematical gems in Algebra and Number Theory, including the integers, the reals, and the complex numbers, along with beautiful results from Galois Theory and associated geometric applications.
Valuable for lecturers, teachers and students of mathematics as well as for all who are mathematically interested.