Author : Mark A. Armstrong
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 11,96 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 1475740344
This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.
Author : David W. Farmer
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 29,84 MB
Release : 1996
Category : Mathematics
ISBN : 0821804502
Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.
Author : R. McWeeny
Publisher : Elsevier
Page : 263 pages
File Size : 23,4 MB
Release : 2013-09-03
Category : Mathematics
ISBN : 1483226247
Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.
Author :
Publisher : Academic Press
Page : 445 pages
File Size : 49,60 MB
Release : 1973-03-02
Category : Mathematics
ISBN : 0080873650
Symmetry Groups and Their Applications
Author : Bijan Davvaz
Publisher : Springer Nature
Page : 285 pages
File Size : 19,20 MB
Release : 2021-11-17
Category : Mathematics
ISBN : 9811661081
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow’s theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Author : M Ladd
Publisher : Elsevier
Page : 424 pages
File Size : 32,8 MB
Release : 1998-09-01
Category : Mathematics
ISBN : 0857099779
A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries. Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetry Covers both point-group and space-group symmetries Includes tutorial solutions
Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 19,60 MB
Release : 2021-06-08
Category : Education
ISBN : 1470464330
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Author : Robert L. Carter
Publisher : John Wiley & Sons
Page : 326 pages
File Size : 37,54 MB
Release : 1997-12-16
Category : Science
ISBN : 0471149551
A Thorough But Understandable Introduction To Molecular Symmetry And Group Theory As Applied To Chemical Problems! In a friendly, easy-to-understand style, this new book invites the reader to discover by example the power of symmetry arguments for understanding theoretical problems in chemistry. The author shows the evolution of ideas and demonstrates the centrality of symmetry and group theory to a complete understanding of the theory of structure and bonding. Plus, the book offers explicit demonstrations of the most effective techniques for applying group theory to chemical problems, including the tabular method of reducing representations and the use of group-subgroup relationships for dealing with infinite-order groups. Also Available From Wiley: * Concepts and Models of Inorganic Chemistry, 3/E, by Bodie E. Douglas, Darl H. McDaniel, and John J. Alexander 0-471-62978-2 * Basic Inorganic Chemistry, 3/E, by F. Albert Cotton, Paul Gaus, and Geoffrey Wilkinson 0-471-50532-3
Author : Alex Berke
Publisher : MIT Press
Page : 165 pages
File Size : 33,54 MB
Release : 2020-02-18
Category : Mathematics
ISBN : 026253892X
A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.
Author : Diane L. Herrmann
Publisher : CRC Press
Page : 446 pages
File Size : 38,9 MB
Release : 2012-10-18
Category : Mathematics
ISBN : 1466554649
Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
