Название: Abstract Algebra with Applications
Автор: Audrey Terras
Издательство: Cambridge University Press
Серия: Cambridge Mathematical Textbooks
Год: 2019
Страниц: 327
Язык: английский
Формат: pdf (true)
Размер: 26.3 MB

Abstract Algebra with Applications provides a friendly and concise introduction to algebra, with an emphasis on its uses in the modern world. The first part of this book covers groups, after some preliminaries on sets, functions, relations, and induction, and features applications such as public-key cryptography, Sudoku, the finite Fourier transform, and symmetry in chemistry and physics. The second part of this book covers rings and fields, and features applications such as random number generators, error correcting codes, the Google page rank algorithm, communication networks, and elliptic curve cryptography. The book's masterful use of colorful figures and images helps illustrate the applications and concepts in the text. Real-world examples and exercises will help students contextualize the information. Intended for a year-long undergraduate course in algebra for mathematics, engineering, and computer science majors, the only prerequisites are calculus and a bit of courage when asked to do a short proof.

The book is intended for a year-long undergraduate course in algebra. The intended audience is the less theoretically inclined undergraduates majoring in mathematics, the physical and social sciences, or engineering – including those in applied mathematics or those intending to get a teaching credential. The prerequisites are minimal: comfort with the real numbers, the complex numbers, matrices, vector spaces at the level of calculus courses – and a bit of courage when asked to do a short proof. In this age of computers, algebra may have replaced calculus (analysis) as the most important part of mathematics.