4 comments about Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys.

1. I just got this book yesterday and I have not read it fully, but I had to write a quick review to say how excited I am about this book. The Rubik's Cube craze hit when I was young. I loved solving the cube and have loved puzzles ever since. I did start trying to describe a solution mathematically when I was at college, but got side tracked and bogged down in some of the math. So this book was a great find for me. I am going to enjoy reading this book and following the mathematical proof. Even though there does seem to be a lot of equations and for the casual reader this might put them off, but from my first browse of the book the math isn't too complex and should be something that anyone who has taken some introductory math courses at the college level should be able to follow.

   If you love puzzles and especially the Rubik's cube and math doesn't frighten you then I highly recommend this book.




2. I am old enough to remember the original appearance of the Rubik's cube puzzle. I examined it a few times while in a store, but never put any effort into it. Later, I looked at some of the literature that explained how "easy" it was to solve the puzzle. The solution involves the use of some advanced topics in group theory, so it is a puzzle with a mathematical twist. However, that is not the only application of group theory, there are many ways in which it can be used. Joyner shows us many of them, and provides the foundation before he tackles the problems.
   This is an excellent book that can be used to either refresh your understanding of group theory or teach it to advanced undergraduates. The objects being manipulated are easy to understand, sometimes easy to build or acquire and the explanations are easy to follow. They are also different from those found in the standard group theory text. Puzzles are an area that fascinates many people, so it is often an advantage to present mathematical instruction in the form of a puzzle rather than in the standard sequence of background notation, theorem and then proof.
   Finally, the author is to be commended for donating all of the profits from the book to the Earth Island Institute. It is a non-profit organization dedicated to environmental projects throughout the world. Therefore, not only can a purchase of this book do your mathematical skills some good, it can also improve the quality of life for everyone on the planet.

   Published in the recreational mathematics newsletter, reprinted with permission.




3. I have never seen so many typos, omissions, and errors in a published book. Many of the examples are poorly introduced, theorems are mentioned that don't exist in the book, etc. Other than Rubik's cube, most of the other puzzles are presented in a completely incomprehensible manner. It's very annoying, in a book that's otherwise just what I want. It does give a good quick and dirty intro to the group theory needed, however.



4. I was thinking of buying this book, but when I read that it is riddled with typos, I declined. Perhaps publishers will get the message that not doing proper editing results in lost sales.

2 comments about Will Shortz Presents Easy to Hard Sudoku Volume 2.

1. This puzzle book was for my husband and he has thoroughly enjoyed working them. He opened the book and started the puzzles the day they arrived, great book.



2. Will Shortz does a great job on his Sudoku books. Volume 2, however, is smaller sizewise and harder to work with than Volume 1. That is my only problem with it.

No comments about The Contest Problem: Book VIII (MAA Problem Book Series).

4 comments about Amusements in Mathematics.

1. This excellent collection of teasers has inferential problems in arithmetic and algebra, and includes geometry, mazes, magic squares and a lot of chess-board tours. The answers are often gems in themselves -- things mentioned in passing and left to the reader to establish -- e.g. "... of the twelve ways that eight queens can be placed on a chessboard without attacking one another..." At twelve years old I spent many an hour finding those twelve ways. There is a small problem with the age of the book, first published in 1917. You could buy an airplane for 400 pounds ($1,680) then, and the money puzzles in the first chapter assume familiarity with British pounds, shillings and pence (and ha'pennies and farthings). The Dover edition of 1958 included a preface on British coins and stamps, and another on the game of cricket, but this edition was in 8vo rather than the original quarto, making some of the diagrams very small. I received my copy in 1936, at age eleven, and have cherished it ever since. I still find challenges in it in spite of my Masters degree in Mathematical Physics!



2. Dudeney was one of the two fathers of puzzles today. Amusements in Mathematics has many of Dudeney's best puzzles. An excellent book.



3. 
   With 430 puzzles, problems, paradoxes, and brain teasers, this book is a mammoth puzzle collection, compared with most math teasers and puzzles book available. But what is important is not the quantity, but the quality and charm of the problems presented. Each problem is presented with a full length solutions that makes the book absolutely an instructive experience for the reader. In some cases the author even discussed on how others had attacked and failed the problems.
   
   Additionally the book is fully illustrated with clever diagrams and sketches, which make the reading even more pleasant for everyone. You, your freinds and family will spend many hours trying the vast array of puzzles prented in this book.



4. I found this book simply sensational, once it has hundreds of interesting puzzles on math and logic. One learns a lot by reading it.

3 comments about Mathematical Footprints: Discovering Mathematics Everywhere.

1. What role has math played since prehistoric times? This considers math's many uses in medicine and art, its role in the development of computers and information systems, and its systematic importance to daily living. From the math involved in weather forecasting to math in art, this is packed with important details presented in a lively manner.



2. Thumbed through this book in the store... Loved the idea, and the selection of topics - architecture, natural phenomena, etc. - really wanted to buy it. Ran across some typos... some missing information... and ultimately just plain bogus "mathematics": sin^2 + cos^2 =1. Well, sin and cos of what? As written, it's nonsense... there's nonsense all around us too, but I wouldn't want to read a book about it. Wondered why the publisher did not employ an editor... put it back on the shelf.



3. Dear Amazon Staff.

   A recent review for this book was obviously written by someone who is unfamiliar with geometry and trigonometry. The pythagorian theoren states that the relationship between the two sides and the hypotenuse of a right triangle is A^2 = B^2 + C^2 since sin and cosine are defined to be the two sides of a right triangle whose hypotenuse is 1, the theorem which you reviewer claims to be false is in fact true. It is always the case that 1 = sin^2 w + cos^2 w regardless of the value of w. I am writing to you because the majority of people rating your more recent customer review of this book are rating his review as being useful. This is really unfortunate.

   I am considering using this book for a course. I will write a
   review for it if we use it.

   Barbara Nostrand, Ph.D. (Mathematics - Northeastern University)
   Assistant Professor of Computer Science
   SUNY College at Potsdam
   Potsdam, New York 13676

No comments about More Math Games & Activities from Around the World.

1 comments about The Simple Book of Not-So-Simple Puzzles.

1. These puzzles are highly original, and quite different from what you find in most puzzle books. I was impressed with the large variety of challenges presented. Why do word puzzles all day when you can cross train your brain with spatial, math, visual, and logical problems? This book has them all. The illustrations that accompany each puzzle are also very nice. Get your thinking caps on, though-these highly enjoyable puzzles are "Not-So-Simple"!

2 comments about The Arithmetic of Life and Death.

1. While books on arithmetic certainly aren't for everyone, I found this one to be interesting, and at times fascinating. My favorite chapter, and one that I plan to use at my daughter's school is on how 8th graders can get a job that pays $45/hour. "What kind of job is that," I'm sure you ask... The answer, of course, is "Stay in School". Since high school graduates on average make significantly more than dropouts, you can assign that difference an hourly rate for the hours that remain till graduation day. Sometimes interesting, sometimes fascinating, sometimes a bit of a stretch, but for an engineer, math fan, statistician, etc., definitely worth the buy.



2. This excellent book answers several questions that I have always wondered about - but never knew how to approach them. It also provideds support for issues I feel strongly about but did not understand why. It clarifies why some counter intuitive actions may be so effective. Finally it provides support to those of us working with young adults on how and why to take the proper long term actions. He hints at why rapidly finishing high school and college will provide much more income over the long run.

   Math is really only a small building block in this book. No advanced math is required, just addition and averaging. The math is a tool - a simple effective one at that- and nothing more. The main focus is providing solutions to issues one feels strongly about but does not have a clue on how to attack them.

   This book has also reminded me of a few ways I better improve myself. I stick to the speed limit and no longer tailgate!!!!!

   I just wish Mr. Shaffner would write another book!!!!!

5 comments about Conned Again, Watson! Cautionary Tales of Logic, Math, and Probability.

1. Some time ago, Lamarr Widmer, the editor of the problem column of "Journal of Recreational Mathematics" submitted a review of this book to me, in my capacity as book reviews editor of JRM. As soon as I read the first two paragraphs of the review, I knew that I had to read the book. Sherlock Holmes is without question the greatest character to appear in fiction, the style of the stories still inspire many spin-offs. In the science fiction television series, "Star Trek: The Next Generation", the Holmes style of problem solving is used in many episodes. This book presents several stories where Holmes solves problems with a mathematical theme. Each of them is a delight to read and I did a good deal of head scratching as I tried to anticipate the solution to the puzzle.
   My favorite story in the collection is "The Case of the Martian Invasion", which, set at the turn of the twentieth century, covers the possibility of heavier-than-air flying machines, "Martian" images on the Moon, crop circles and secret messages being embedded in biblical verse. The proponent of a Martian invasion believes that heavier-than-air machines are possible, putting forward the fundamental principle of using complex machines. That is of course redundancy, where multiple engines are placed on the aircraft in such a way that it can fly with any subset above a certain size. The explanation of the "secret messages" is easy, nothing more than a simple exercise in the probability of the frequency of the appearance of letters and looking hard enough.
   The other stories were nearly as interesting and cover many areas of life, the probability of various events being the most common scenario. Game theory and decision theory is also used to solve the cases brought before the greatest detective of all time. Although they are set in the time of Holmes, the events described in the puzzles can still be applied to life in the twenty-first century.
   I found this to be one of the best demonstrations of logical deduction based on sound mathematical principles that I have ever seen. Although he is constantly praised for his skill in logical deduction, Holmes also possesses another talent, that of a master teacher.

   Published in the recreational mathematics newsletter, reprinted with permission.




2. I have read seven chapters of this book so far and I ask all readers of this book to beware! Even though the author Bruce Collins attempts to explain some math, probability and logic in pedagogical stories using Sherlock Holmes and Dr. Watson, readers of this release of the book (2001) should be careful of errors. For example as explained on pages 72 & 73 have both Holmes and Watson made a mistake by saying or agreeing that there are six ways to get to the middle point of the diagram called "A Walk Along the Pier"? There may be six routes to get to that point labelled "6" but Holmes mentions flipping a coin 6 times (e.g. Head, Head, Head, Tail, Tail, Tail). For an equal number of heads and tails with six flips of a coin, wouldn't Watson get to the point labelled "20" (for 20 routes) on the diagram because there are 20 possible configurations of getting 3 heads and 3 tails (e.g. Head, Head, Head, Tail, Tail, Tail; Head, Head, Tail, Head, Tail, Tail;...Tail, Tail, Tail, Head, Head, Head etc)? Another example is in the story "The Case of the Martian Invasion" where Holmes is explaining a failure mode of a powered airplane by a "bird strike" (as in a flock of birds which could cause one or more engines to fail). Remember these stories take place around 1900 and the Wright Brothers have not yet had a sucessful powered airplane flight. Would Holmes be seriously considering multiple engine failure modes due to a "bird strike"?! Also, readers get introduced to a Reverend Dodgson as Lewis Carroll (writer of "Alice's Adventures in Wonderland") in one of the earlier stories but in this story of the Martian invasion, readers get introduced to an Alexander Smith, designer of the Titanic! According to what I've looked up using Google, Alexander Carlisle and Thomas Andrews were designers of the Titanic. The captian of the ship, however, was Captain Smith (not Captain Alexander Smith)! So, do not assume you'll be getting necessarily an accurate history lesson. And what kind of thing is it for Holmes to say "...Love is all very well, Watson, but there comes a point where Darwin's laws must be left to take their course"! Do you think the author is trying to tease us? So too, another example occurs in the story called "Three Cases of Unfair Preferment" where a set of weirdly constructed dice are described; one die is colored red; another is colored black and another is colored white. It turns out that these dice are biased based on how they are made. Now, isn't "Watson" mistaken by saying "The red dice..." - should he say "The red die..." instead (p148)? Holmes goes on to describe how that in this case the red die has a higher probablity of winning over black; the black has a higher probability of winning over than white (per Holmes "5/9 of the time" as mentioned on p158) and how "white is better than red." He then compares these dice to the paper, rock ("stone") and scissors game. But is it fair, logically speaking, to compare the paper-rock-scissors game to these dice? Where are the set probabilities of a piece of paper winning over a rock (for example)? It's not a fair comparison because in the case of these dice, even though "black wins over white," white can still win over black albeit with a smaller probability. But can you imagine, for example, a piece of a paper winning over a scissor (some of the time)? It doesn't go both ways. So, is Holmes wrong? Thus after reading this, let me ask you if you would think that Sherlock Holmes and Dr. Watson are making these kind of errors? Perhaps the reader himself should ask, who is really doing the conning?



3. I am frankly shocked by the negative reviews, although it could be that the reviewers are math-lovers who just find the stories too basic or something. For me, a relative novice to math thinking, the book is a delight. Bruce manages to capture much of the tone of the original Holmes books and works interesting math illustrations (some, to be fair, a little contrivedly) into the stories. Minus the math, the stories still have enough whimsy, flair, and character development to warrant reading them. Perhaps my expectations were so low for anything to do with a subject I avoid that "Conned Again" is getting all but a free pass from me, but I really enjoy this work and will look for more of Bruce's writing.



4. The author does a marvelous job of presenting Sherlock Holmes stories through the thought of Dr. Watson, very much in the style of Sir Arthur Conan Doyle. However instead of simple detective mysteries each story has a probabilistic theme.
   
   After reading the first couple of chapters I thought this is great for me but I am a statistician. Could a novice understand the complex explanations and story that enhances ones memory about the principles as the author suggests? I think so. The later chapters convince me.
   
   There the author goes over the waiting time paradox, capture-recapture methods and other related problems in the chapter on the poor observer. The famous Monte Hall problem and the birthday problem are also covered and well explained through the eyes of Watson based on the work of Sherlock Holmes and his brother.



5. Twelve short Sherlock Holmes stories challanging logic, probability, statistic, game theory, more or less relevant to daily life. The authors approach of telling the story seen through Holmes and Watson is brilliant (incl. the dialogue between the two). Some stories are a bit simple and boring while others were quite amazing. Example Chapter 7 illustrates the error of assuming that a well-defined ordering retlation must also define a unique hierarchy. In higher mathematics it is quite possible to have x greater than y, y greater than z, and yet z greater than x! Last but not least, the afterword is extremely useful where the author sheds more light on each chapter.

No comments about Nets, Puzzles and Postmen: An Exploration of Mathematical Connections.