
Content by Charles Ashbacher
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Reviews Written by Charles Ashbacher (Marion, Iowa United States)





5.0 out of 5 stars
Refreshing and entertaining book of popular mathematics, Dec 18 2014
This book on popular mathematics has some of the old (fractals), but most of it is relatively new. Chartier also includes formulas when needed; it is a rare occasion when integrals and inverse trig functions appear in popular mathematics books. While this may intimidate some readers, it is refreshing to people that expect the mathematics to be accurate and complete. A mathematical topic is examined in detail in eleven of the chapters. I found the most entertaining one to be “Ranking a Google of Bits”, where the topic is the algorithm Google uses to rank the search results. While the specifics of the algorithm are a closely guarded trade secret, enough is publicly known so that it can be explained in a book. It was amusing to read the sidebar about the “Google bomb.” In 2003 a person exploited the rank algorithm so that the highest ranked response to the query “miserable failure” was the official White House biography of then President George W. Bush. Later, other wellknown and controversial personalities were included in the highest rankings. While the mathematical explanation is more complex than many can understand, all will appreciate the section on how to properly fire off an “Angry Bird” as the advice in the conclusion is easy to understand. The chapter on various mathematical ways to fill out a March Madness NCAA basketball tournament bracket is also one that will amuse all that succumb to that particular malady. It is a very entertaining book with many areas of popular mathematics examined that have rarely been covered before. This makes it very refreshing as there has been a stale sameness to so many that have appeared in recent years.
Published in Journal of Recreational Mathematics, reprinted with permission







5.0 out of 5 stars
It will make you appreciate the utility of compact mathematical notation, Dec 18 2014
I have a standard opening speech that I give in all of the math classes that I teach and one component of that monologue is the role of notation. I point out that one of the things that make mathematics difficult to understand is the fact that the symbols are compact representations of operations. I also point out that this compact representation is preferable over having every problem expressed as a “story problem”, the problem form that is most widely feared by students. What I found most enlightening about this book is the clear conclusion that the mathematical education of the masses would not be possible if the compact and efficient notation was not being used. Trying to decipher the rhetorical forms of the problems was really hard, even after reading the explanations. Furthermore, some of the examples where a long paragraph of text is translated to a simple equality are one of the most dramatic alterations you can find in mathematics. Even if you allow for the greater understanding of the rhetorical form based on extensive practice, it is hard to see how large numbers of students could solve them. Finally, it is also hard to see how mathematics could advance as fast as it has using only rhetorical forms or nonstandard notation. This book is written in a popular style, there are a few equations, but nothing that a reader with a background in basic algebra can’t handle. It also has the interesting characteristic that the sections that the nonprofessional and professional mathematicians will have difficulty understanding coincide. In some ways modern mathematical notation has a short history and we should all be grateful for what it has done for the world. This book will make you appreciate that.
Published in Journal of Recreational Mathematics, reprinted with permission







5.0 out of 5 stars
Should be read by every prospective math major as well as the people providing the instruction, Dec 18 2014
As the breadth of the coverage of the various careers available in mathematics expands, this book series continues to get better and better. New profiles have been added to those in the previous editions and there are updates of those that appeared earlier. The scope of the jobs available in mathematics will impress and surprise even veteran mathematicians. In addition to the information gleaned from the interviewees, there is a series of supplemental material in appendices. The titles are:
*) Seven Steps to Finding a Job *) Interviewing Tips from the Pros *) So You Want to Work in Industry *) Teamwork – The Special Challenge of Industry
Like the predecessors, there should be multiple copies of this book in every college mathematics library as well as in the lounge. Those that advise math student should also read it once and then scan it regularly when specific information is needed.
Published in Journal of Recreational Mathematics, reprinted with permission







5.0 out of 5 stars
A look into how mathematics is formed and reformed, Dec 18 2014
Principia Mathematica (PM) was a threevolume work covering the foundations of mathematics. Written by Bertrand Russell and Alfred North Whitehead, their goal was to describe a set of axioms and rules of inference so that all mathematical truths could be derived. The three volumes were published in 1910, 1912 and 1913 and one of the primary inspirations was Russell’s defining a set that was internally contradictory. Like all other works of mathematics, there were errors and improvements that could be made as well as new advances in mathematics that could be examined. As is generally the case, and what happened with PM is that a second edition was developed and published in 1925 and 1927. The purpose of this book is to shed light on the changes that were made, the work of others that necessitated a response and the thought processes that Russell went through as he made the changes to create the second edition. Russell’s papers have been examined in detail so that the reader can learn the thought processes that Russell went through as he wrote the new material and made modifications to the content of the first edition. It is a look at Russell’s goals, motivations and the history of logic during the interlude between the two editions. Published mathematics tends to be extremely crisp and complete, while valuable, the path there is generally lost. Advances in mathematics build on what came before and it is often helpful to learn the sequence of thoughts that led to the polished result. In this case we see the evolution of the ideas and how they logically fall into sequence before they emerged in the finished form. Working mathematicians can see that the path to achievement is a meandering one, while the goal is clear, getting there involves a lot of weaving, bobbing, failure and recovery. Even for someone as talented as Bertrand Russell.
Published in Journal of Recreational Mathematics, reprinted with permission







5.0 out of 5 stars
A scientific peek behind the curtain of plausibility, Dec 18 2014
This is one of the books that all fans of science fiction in all forms should read. While for some it may be too much of a peek behind the curtain hiding the implausibility, for most it will be an educational look at what is considered the possible courses of science and technology. One needs look no further than the communicators used in the original Star Trek series and today’s cell phones to see that science fiction can be predictive of the future. Adler does a superb job in putting forward wellknown examples from fantasy and science fiction and then describing the various levels of possibility. Adler covers topics from the magic of the Harry Potter series to human activity in space, how you get there and how you move from location to location once you are off the Earth’s surface to the possibilities of communicating with extraterrestrial species. In all cases, whatever you plan to do, it all comes down to how much extractible energy you have at your disposal, which is the overall and often repeated theme of the book. Equations and images are used when necessary, albeit somewhat sparingly and the most complex mathematics used is logarithms and the hyperbolic trig functions. The writing is excellent; Adler is one of the best expository writers of science currently active. By its’ very description, science fiction is a combination of science wrapped within a fictional construct. In reading this book you will learn how much the science in many stories is reasonable and what is considered extremely unlikely, the scientific term for impossible.
Published in Journal of Recreational Mathematics, reprinted with permission







5.0 out of 5 stars
Challenging, yet a welcome diversion from the standard curriculum, Dec 18 2014
This book contains a set of 128 number cross puzzles; they look like crossword puzzles with intersecting down and across sections. You are given a set of numbers that are to be placed in the puzzle along with four that will not be used. In general, the sizes of the numbers start at four digits with several of each size. The puzzles are essentially pattern matching, the key is to find the start point where there is only one choice for a number in that section that has the proper digit(s) in the position(s) of intersection so that another number can be uniquely determined. The early puzzles start with 14 sections to fill while the later ones have 18. The content matches the title, for they are challenging, yet if you find the correct start point in most cases the remainder of the puzzle falls into place rather easily. Solutions to all of the puzzles are included. While the value of these puzzles as intellectual exercises for the mathematically interested is clear, it is also easy to see where the problems could be used in upper K12 classes. They are an exercise in logical thinking rather than abstract mathematical ability. For some students such problems would be a welcome break from their other mathematical exercises.







4.0 out of 5 stars
Right messages, repeated a few times too many, Dec 17 2014
Although labels are powerful and often have a great deal of influence on our lives, in most cases that will happen only if you allow them to be in control. That is the dominant message of this book and it is of course correct, albeit repeated too often. Many examples are given of labels that were placed on someone and were negative in connotation and practice. That should be expected, it is natural for humans to place people in categories, organizing the world in this way allows for a rapid evaluation of the situation and can help a person cope with new experiences. It is also common for humans to label others negatively, for many believe that is the only way they can feel competent, capable and even superior. Therefore, the first step in overcoming negative labels is to recognize that it is the nature of humans to use them as tools. Once that is acknowledged, the next step is to identify and overcome them when they are negative, independent of whether you are the labeled or labeler. Beron describes the steps in this process and they are logical, understandable and generally within reach. Major success in life is often due to a willingness to go beyond labels, do the hitherto undone and to aspire to be better. Throwing off negative labels, either selfinflicted or imposed by others, can be the first step to greatness and a happy and healthy life. Beron shows you the way, although the steps along that way are repeated a few too many times. Some of the examples could have been left out and the point will still have effectively been made.







5.0 out of 5 stars
A fun book to end a two semester calculus sequence, Dec 17 2014
This book is a perfect book to use in the last two weeks of a twosemester calculus sequence where it is time to demonstrate some realworld applications of calculus and rekindle the interest of the students. It opens with a calculus class being interrupted by the appearance of a zombie with an overriding urge to consume human flesh and create even more zombies. The narrator is a professor of mathematics at Roberts College, a small liberal arts college in Westbridge, Massachusetts and it is his class that is interrupted. As the zombie menace spreads, the professor uses calculus in order to extract and understand critical information such as how fast the disease will spread, the path to run if you want to avoid a single zombie, the average life span of a zombie and how rapidly a zombie will cool to the point where they will be inert. A great deal of differential and integral calculus is reviewed in the course of what is essentially a novel about understanding and surviving a zombie apocalypse. This book is an existence proof that mathematics can be presented in a fun and engaging manner.







3.0 out of 5 stars
Even a positive story about a black trailblazer contains racial denigration, Dec 16 2014
With one glaring exception, this is a good biography of the man that did more than almost anyone else to remove the barriers of segregation. A solid argument can be made that only Martin Luther King Jr. did more to advance the cause of black civil rights than Jackie Robinson. For decades, there had been an unwritten rule that black men would not be allowed to play in the major leagues. Their teams could play against barnstorming teams of major leaguers but they could not play in a league game. For many players, it was a case of maintaining their jobs as major league players for as long as possible. Stars such as Ted Williams and Bob Feller were open in their comments about the high level of talent exhibited by many colored league players and that they would be superstars if allowed to play in the majors. Jackie Robinson demonstrated that almost immediately when he was finally given the chance. This book is a biography of Jackie Robinson from his birth until his retirement from baseball. In general it is a good biography; it is written at the level of the adolescent reader and is a solid chronicle of his life. There is mention of the transforming effect he had on baseball and the country, but less than there should have been. He was a true trailblazer for social justice and equality. The one glaring problem with the book appears at several points; I will illustrate it by quoting page 232. The reference is to James “Junior” Gilliam. “A Tennesseeborn colored boy, Gilliam reached Vero Beach in the spring of 1953 by way of two impressive years at Jackie’s alma mater, Montreal.” Nothing more needs to be said.







5.0 out of 5 stars
A verbal biography of an incredible woman that is largely unknown, Dec 16 2014
Altina Schinasi was an artist whose work almost everyone has seen yet almost no one knows about. She was the designer of the Harlequin “cat’seye” glasses that were the definition of facial glamour in the 1930’s and were worn by socialites and movie stars. Her life began as a wealthy heiress of tobacco tycoon Morris Schinasi, the man that invented the cigarette rolling machine. Unconventional in her personal and professional life, Altina became known as Tina and this film is a series of interviews of her, her successful children and the men, women and artists in her life. Tina possessed that relentless unsettled nature that seems necessary for success in art and so many other fields. In the interviews she is very matteroffact in her renditions of the events that had a dramatic impact on her life and career. She was filled with energy at very levels, from the dramatic and talented artist to the sexual arena. Her living husbands describe her as kind and considerate, yet with a drive to succeed that kept her moving, pushing against social and political convention. During the worst of the McCarthy era, she sheltered a man that had been subpoenaed by Congress. Everyone that understands what was happening at that time knows how much courage that took. Tina also signed many affidavits in support of Jews fleeing the Hitler regime, seeking asylum in the United States. So it is no exaggeration to say that she also saved lives. A sculptor, painter, designer and film maker, Tina was in many ways a role model for the dynamic, versatile female artist. She stood her ground for what she thought was right while creating dramatic pieces of art. This is her story and it is told by Tina and those that knew her best, she had a dramatic effect on the world of art and the world in general.
This film was made available for free for review purposes.


