Abstract Algebra with Applications

This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.

Audrey Terras (Author)

9781107164079, Cambridge University Press

Hardback, published 20 December 2018

328 pages, 104 b/w illus. 100 colour illus.
26 x 18.1 x 2 cm, 0.87 kg

'Perhaps no other subject of undergraduate mathematics is as challenging to learn (and to teach) as abstract algebra. The high level of abstraction, the sophistication of the logic and the vocabulary, and the deep understanding of mathematical structures required all pose difficulties for the student. Professor Terras has addressed these issues by writing a textbook which, while uncompromising in its rigor and breadth, is also entertaining and full of insights, useful visualizations and historical asides. Many of the applications of modern algebra are explained in a thoughtful way that will help motivate students to study abstract concepts. Recommended as a textbook for the first semester of abstract algebra.' Jenia Tevelev, University of Massachusetts, Amherst

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.

Subject Areas: Maths for engineers [TBJ], Mathematical modelling [PBWH], Algebra [PBF]