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Abstract Algebra with Applications

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Part of Cambridge Mathematical Textbooks

  • Date Published: May 2019
  • availability: In stock
  • format: Hardback
  • isbn: 9781107164079

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  • 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.

    • Includes interesting computational examples where students can use their preferred software, including Mathematica, Scientific Workplace and Group Explorer
    • Connects theory with practice by featuring plenty of examples and applications
    • Emphasizes finite fields and rings and the ways in which the finite mirrors the infinite, making the subject accessible to students
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: May 2019
    • format: Hardback
    • isbn: 9781107164079
    • length: 328 pages
    • dimensions: 260 x 181 x 20 mm
    • weight: 0.87kg
    • contains: 104 b/w illus. 100 colour illus.
    • availability: In stock
  • Table of Contents

    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.

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    Abstract Algebra with Applications

    Audrey Terras

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  • Author

    Audrey Terras, University of California, San Diego
    Audrey Terras is a Professor Emeritus of Mathematics at the University of California San Diego. Awards include American Mathematical Society (AMS) Fellow, American Association for the Advancement of Science (AAAS) Fellow, and 2008 Noether lecturer of Association for Women in Mathematics (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.

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