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  • Symmetry: An Introduction to Group Theory and Its Applications (Dover Books on Physics)

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Symmetry: An Introduction to Group Theory and Its Applications (Dover Books on Physics) Unabridged Edition

by Roy McWeeny (Author)
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The crucial significance of symmetry to the development of group theory and in the fields of physics and chemistry cannot be overstated, and this well-organized volume provides an excellent introduction to the topic.
The text develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion, leading students to a point from which they can proceed easily to more elaborate applications. The finite groups describing the symmetry of regular polyhedral and of repeating patterns are emphasized, and geometric illustrations of all main processes appear here — including more than 100 fully worked examples.
Designed to be read at a variety of levels and to allow students to focus on any of the main fields of application, this volume is geared toward advanced undergraduate and graduate physics and chemistry students with the requisite mathematical background.

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  1. ISBN-10
    0486421821
  2. ISBN-13
    978-0486421827
  3. Edition
    Unabridged
  4. Publisher
    Dover Publications
  5. Publication date
    June 12, 2002
  6. Language
    English
  7. Dimensions
    5.56 x 0.58 x 8.5 inches
  8. Print length
    256 pages
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Customer reviews

4.5 out of 5 stars
50 global ratings

Top reviews from the United States

  • Jason Dowd
    5.0 out of 5 stars Highly Recommended for Chemistry and Physics Students
    Reviewed in the United States on July 25, 2011
    Format: PaperbackVerified Purchase
    The author states in the preface that this book was written to serve readers at a variety of levels. In fact this rather short book is almost three books in one.

    The first two chapters provide an introduction to groups, vector spaces, and lattices. The material here is elementary, but the author is to be commended both for clear explanations as well as excellent notation. My only complaint is that the notation is useful to read, but not really to write as it relies on different typefaces.

    The next two chapters dig into translation groups, point groups, and space groups in three dimensions. Chapter 5 focuses on the theory of irreducible representations, and in many ways forms the core of the book. The material in these chapters is definitely more challenging than the material in the first two chapters.

    The final three chapters are devoted to applications. Chapter 6 covers applications to algebraic forms particularly as applied to vibrational modes as encountered in spectroscopy. Chapter 7 focuses on applications to functions and operators. Finally, chapter 8 is devoted to tensors and tensor operators. These three chapters are the most advanced in the book, and each is successively more advanced than the preceding one. These chapters will serve more advanced readers.

    Early on the author introduces the group which comes to be known as C_3v. This groups is used as an example throughout the book and comes fully to life in chapter 6 where it is used to analyze the vibrational modes of the ammonia molecule. I really appreciated the continuity of and the elaboration on this one example as a unifying thread in the text.

    The entire book contains copious tables and figures which are extremely helpful. In particular, chapters 3 and 4 contain detailed tables of the groups considered as well as their representations. The book has no exercises, but does offer a nice collection of suggestions for further reading at the end of each chapter. Finally, this book has remarkably few errors which is actually somewhat surprising just given the level of detail in some sections such as the group tables mentioned above.

    Sure to be useful in particular to students of quantum chemistry and spectroscopy, this book is excellent and repays multiple readings, but I'd recommend the prospective reader bring a background in linear algebra and some quantum chemistry.
    54 people found this helpful
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  • SchmidtD
    5.0 out of 5 stars Best intro to group theory I've seen
    Reviewed in the United States on March 24, 2010
    Format: PaperbackVerified Purchase
    This is one of the finest examples of didactic mathematics I have ever seen. Good teaching is rare in mathematics...sorry, I wish it weren't so, but mathematicians often suffer from profound cluelessness about what is obvious and what is a stumbling block to understanding. Not so McWeeney, who understands the didactic principle of a continuing example that is developed and built upon along with the theory (here a simple rotation group of the triangular lamina, i.e. turning and flipping a triangle cutout). And no super-challenging problem sets and unfinished proofs that just make the math mortal feel stupid and want to give up.

    This presentation could take any avid high school Algebra II student well into group theory and matrix representations.

    That said, one would be better off with a background of basic matrix theory such as identity matrix, inverse matrix, etc., and some comfort with row/column language and the dual subscripts of matrices. But even that would not be necessary for anyone who comprehends sigma notation of sums and the basic principles of subscripting/indexing.

    The first chapter is harder by far than the second. Readers should just remember that fraction groups are like riding a bike; once seen for what they are it will all come into place.

    If you need a companion to this you might consider Byron and Fuller's Dover classic text, which develops vectors even more rigorously and from a more numeric perspective.
    92 people found this helpful
    Helpful
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  • Kirtland E Hobler
    4.0 out of 5 stars A valuable way of thinking about the periodic table
    Reviewed in the United States on August 18, 2019
    Format: eTextbookVerified Purchase
    I wanted to learn about symmetry for use in understanding the quantum understanding of the periodic table. The orbital groups, labeled with the letters S, P, D, and F seem to involve symmetry. They are often said to be solutions to the Schrodinger equation. However this book gives a mathematical description of symmetry groups and a geometric way of thinking about including and excluding various possibilities as solutions. The pragmatics seem very powerful.

    This book is designed for mathematicians. Since I am not and I am only interested in learning and teaching about the periodic table, I skipped over the mathematical notation’s and was able to extract principles of group theory and symmetry as it pertains to the periodic table. Therefore I found the book very valuable.
    2 people found this helpful
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  • James Stroud
    5.0 out of 5 stars Thorough Enough for Professionals
    Reviewed in the United States on May 16, 2013
    Format: PaperbackVerified Purchase
    I read the first four chapters of this book to get up to speed on group theory and symmetry because I needed the knowledge to write a peer reviewed paper in crystallography (original research). Other than reading a short introduction on-line, my knowledge of group theory before reading this book could be boiled down to one sentence: "There is something called 'group theory'." I literally didn't even realize that the "group" in "symmetry group" related to group theory.

    The point is, this book had everything I needed to turn my vague ideas about symmetry in protein secondary structure into a cohesive group theoretic treatment and formal proof. After re-formulating my paper using the concepts presented in this book, I was able to send my paper into one of the top crystallography journals with all referees enthusiastically recommending publication. Google "The Zipper Groups of the Amyloid State of Proteins" (it's an open access article).

    What's more, this book had much more about symmetry than I needed. I stopped reading before the chapters on chemistry (5-8) because of time. I hope one day to go back and read those chapters because I am sure that this book will benefit my understanding of chemistry as much as it has my understanding of symmetry.
    13 people found this helpful
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Top reviews from other countries

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  • Luicol
    5.0 out of 5 stars Muy buen texto
    Reviewed in Spain on June 9, 2014
    Format: PaperbackVerified Purchase
    Los textos sobre la materia acostumbran a ser una especie de libros de leyes donde te vienen a enumerar las propiedades, ecuaciones, etc, demostrándotelas desde un punto de vista puramente formal, sin conexión alguna con la realidad. Este libro es un prodigio de dicáctica, sin perder la profundidad necesaria, y está lleno de ideas, de ideas normales escritas con palabras normales en inglés. Si alguna persona está buscando un libro que le explique bien que es la Teoría de Grupos pienso que éste es el texto. Para su lectura es necesaria una base mínima en álgebra y en las cuestiones básicas de las matemáticas.
    Report
  • James M Long
    5.0 out of 5 stars Five Stars
    Reviewed in Canada on February 2, 2016
    Format: PaperbackVerified Purchase
    very pleased with every thing
    Report
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