Abstract Algebra with Applications (Cambridge Mathematical Textbooks)
Cambridge University Press, 12/20/2018
EAN 9781107164079, ISBN10: 1107164079
Hardcover, 690 pages, 26 x 18.1 x 2 cm
Language: English
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.
Part I. Groups
1. Preliminaries
2. Groups
a beginning
3. Groups
there's more
4. Applications and more examples of groups
Part II. Rings
5. Rings
a beginning
6. Rings
there's more
7. Vector spaces and finite fields
8. Applications of rings
Part III. Solutions to Some Problems
9. Solution sketches for mostly odd-numbered exercises.