Algebra and Number Theory. A Selection of Highlights

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

• An exciting collection of fundamental results in algebra and number theory
• Aimed at lecturers, teachers, and students of mathematics, and at all mathematically interested
• Contains many exercises related to the content of each chapter