Abstract Algebra with Applications

Inbunden, Engelska, 2018

Del i serien Cambridge Mathematical Textbooks

723 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2018-12-20
Mått:181 x 260 x 20 mm
Vikt:870 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Mathematical Textbooks
Antal sidor:328
Förlag:Cambridge University Press
ISBN:9781107164079

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

Audrey Terras is a Professor Emeritus of Mathematics at University of California San Diego. Awards include AMS Fellow, AAAS Fellow, and 2008 Noether lecturer of AWM. She has published four books and many research papers. Research interests include number theory, harmonic analysis on symmetric spaces and finite groups, algebraic graph theory, zeta functions of graphs, and Selberg's trace formula. When lecturing, she believes in giving examples, applications, and colorful pictures.

Recensioner i media

'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

Innehållsförteckning

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.