Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys 2nd Edition by David Joyner (PDF)

Description

This updated and revised edition of David Joyner’s entertaining “hands-on” tour of group theory and abstract algebra brings life, levity, and practicality to the topics through mathematical toys.Joyner uses permutation puzzles such as the Rubik’s Cube and its variants, the 15 puzzle, the Rainbow Masterball, Merlin’s Machine, the Pyraminx, and the Skewb to explain the basics of introductory algebra and group theory. Subjects covered include the Cayley graphs, symmetries, isomorphisms, wreath products, free groups, and finite fields of group theory, as well as algebraic matrices, combinatorics, and permutations.Featuring strategies for solving the puzzles and computations illustrated using the SAGE open-source computer algebra system, the second edition of Adventures in Group Theory is perfect for mathematics enthusiasts and for use as a supplementary textbook.

User’s Reviews

Editorial Reviews: Review Adventures in Group Theory is a tour through the algebra of several ‘permutation puzzles’ . . . If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book.–MAA OnlineJoyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik’s Cube. Enthusiastic students will learn a lot of mathematics from this book.–American ScientistJoyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts.–ChoiceThe book begins with some lecture notes of discrete mathematics and group theory. These theoretical notions are very nicely applied to some practical problems, e.g.: Rubik’s cube, Rubik-like puzzle groups, crossing the rubicon, God’s algorithm and graphs. The work ends with a rich bibliography and index.–Zentralblatt Math Review Adventures in Group Theory is a tour through the algebra of several ‘permutation puzzles’ . . . If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book.―MAA OnlineJoyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts.―ChoiceJoyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik’s Cube. Enthusiastic students will learn a lot of mathematics from this book.―American ScientistThe book begins with some lecture notes of discrete mathematics and group theory. These theoretical notions are very nicely applied to some practical problems, e.g.: Rubik’s cube, Rubik-like puzzle groups, crossing the rubicon, God’s algorithm and graphs. The work ends with a rich bibliography and index.―Zentralblatt Math Review “Adventures in Group Theory is a tour through the algebra of several ‘permutation puzzles’… If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book.””Joyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts.””Joyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik’s Cube. Enthusiastic students will learn a lot of mathematics from this book.””The book begins with some lecture notes of discrete mathematics and group theory. These theoretical notions are very nicely applied to some practical problems, e.g.: Rubik’s cube, Rubik-like puzzle groups, crossing the rubicon, God’s algorithm and graphs. The work ends with a rich bibliography and index.” About the Author David Joyner is a professor in the Mathematics Department at the U.S. Naval Academy. He is the author of Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys, also published by Johns Hopkins. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A great book… a bit advanced though… not as much Rubiks Cube as I had hoped! Foolishly ~ my bad!

⭐This book is good, mathematical point of view , connections between rubic cube and other similar puzzles with the group theory, the seller is fine , I can recommend it.

⭐Very interesting book!

⭐Good for learning Group Theory terminology, extremely confusing at best to know how to apply it, especially to solving the Rubik’s Cube, which the author is both fascinated by and teases with a promise to understand the solution to many puzzles, especially to the 3 x 3 Rubik’s cube, but it very poorly delivers. The book gives no practical way of a non-mathematician to understand how any of this leads anywhere for any of the games mentioned, it simply seems that it shows how to describe math games in terms of group theory, without any ramifications as to what this is good for!

⭐I can’t figure out who the intended audience is for this book. It’s not a textbook; the subject is not developed in a systematic manner, nor are there useful problems sets. The reader exercises, referred to as ‘Ponderables’ in the book, can be extremely challenging and off-topic, beginning with the chess problems in the first chapter. It’s also too technical to be a popularization, although it seems to be targeted as such. I was looking for friendly introduction to group theory, and the core concepts are there. However, a focus on the Rubik’s cube and other similar games as primary examples of groups introduces a lot of complexity.The book is written in an entertaining fashion with many historical references, quotes, puns and quips. I often found them to be a distraction.The SAGE programming code provides quite a few examples but it is often not decipherable to a reader unfamiliar with this relatively obscure language based on Python; a little explanation would have gone a long way. Frequently terminology and notation are used before they are defined. Apparently this second edition cleaned up some errors, but there are still a number of typos and statements which are simply wrong. Theorems are stated imprecisely, and the proofs in the book are often hand-waving exercises rather than actual proofs. Important results are presented without justification or the proof left to the reader.I don’t intend to imply there is no value here. Parts of the book provide a relatively accessible introduction to group theory, but the reading experience can be very frustrating.

⭐My 17 year old LOVES this book. He is mad on maths and has really enjoyed reading a challenging maths book. Thank you for an excellent service.

⭐Very good.

⭐Si le côte mathématique du puzzle vous intéresse, c’est ce livre qu’il faut acheter. le N°1 de la théorie des twists. Il faut absolument en avoir un.

⭐

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