Fine Benjamin, Gaglione Anthony, Moldenhauer Anja, Rosenberger Gerhard, Spellman Dennis. Algebra and Number Theory: A Selection of Highlights

De Gruyter, 2017. — 344 p. — ISBN: 9783110515848 3110515849.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.
first volume: Algebra and Number Theory: A Selection of Highlights.
second volume: Geometry and Discrete Mathematics: A Selection of Highlights.
This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history.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{u2019}s equation
Transcendental numbers and the numbers e and s
Compass and straightedge constructions and the classical problems
Euclidean vector spaces