Peter Books

If you like to think about mathematics, this book will be a real pleasure read. Some of the math presented is practical, as well as interesting, while other examples are much less so.

I believe the book does a good job covering all aspects of the math behind games.

This is a 500 page mathematical investigation of games using probability theory, game theory, and a variety of mathematical methods. The author finds winning strategies for many games, some of them surprisingly simple. For most games, the point is less to find a trick to win but to clearly explain how the game works and to answer some interesting questions. The author's ability to present mathematics in an understandable manner is possibly unsurpassed by any other writer.

In Chapter 16, entitled, "Games of Chance", the author presents an explanation of Markov chains and how they can be applied to Monopoly and to Chutes and Ladders. The explanation is clearer here than I have found elsewhere. The result of the calculation for Monopoly is two charts detailing the best investments in Monopoly. One chart ranks the monopolies according to how much rent income they will generate for the owner. The second chart ranks monopolies according to their return on investment or ROI, expected rent divided by cost. Thus we see, for example, that the highest rent comes from the green color group, Pennsylvania, and the best monopoly measured by ROI is the orange color group, New York. The author suggests these charts may be useful for deciding what properties to buy and where to buy houses.

The problem is that the results of the Markov chain calculation are not really useful for the important decisions Monopoly players must make. Players must buy nearly every ordinary property they land on in order to advance their chances of getting a monopoly and to block opponents from getting monopolies, so properties' ROIs and rents are almost completely irrelevant to the property buying decisions. After players trade properties, almost every player has one monopoly, not two or three or four, so the problem of deciding where to build the next house is not an issue...the player must put the house on his (lone) monopoly. Only after reaching the later stages of the game, usually after one of the players has been eliminated, do players have a choice about which monopoly to build out. Even in this regard, the chart is not useful. There is too much data to memorize and Monopoly culture discourages players from consulting charts in the middle of a game. Monopoly players bring snacks and drinks, but not charts.

The truly important decisions Monopoly players must make involve trading--which monopoly to take and which monopoly to allow an opponent to take. The data from a Markov chain calculation simply do not help much. What Monopoly players need to help them make this decision is the Monte Carlo method, which the book describes but does not apply toward Monopoly. A Monte Carlo simulation involves programming a computer to play the game, play the game thousands of times, and study what happened. This is exactly what I did for my Winning Monopoly book in 1987. A more detailed review of this book-at least, the portion dedicated to Monopoly-is posted on my web site, [...]

So many books about the mathematics of games are either long out of print, hard to find, or fairly esoteric and not something I'd recommend to just anyone. The best book I've found for someone new to game math is Luck, Logic and White Lies by Jörg Bewersdorff. It introduces the reader to a vast mathematical literature, and does so in an enormously clear manner, which never takes one very far away from either the math or the games behind them. I love Winning Ways and On Numbers and Games, but they're definitely not for the faint of heart. LL&WL is the perfect book for gamers who are interested in the mathematics that underlie the choices they face and decisions they make. Just great stuff.

As this book points out, games fall into three broad categories:

1. Games of Chance
2. Games with a large number of combinations of different moves
3. Different states of information among the individual players.

And this book is broken into three main sections, one for each of these.

Before you get too turned off, yes, there is some math in this book. But it is really not heavy duty. (After all, John Nash of A Beautiful Mind won the Nobel Prize for his work on game theory and his work was not simple math.) The authors explanations of the situations described in the games are very good are very good, and the minimal amount of math is really helpful.

Virtually all of the common games from from the lottery to chess and even Monopoly, as well as the casino games such as blackjack and Roulette are discussed in detail. For anyone interested in what's really going on in games they play, this is an extremely interesting book.

The author knows whereof he speaks, he is the general manager of a game design company based in Germany.

Written by the general manager of Mega-Spielgerate, a game design company based in Limburg, Germany, Luck, Logic & White Lies: The Mathematics Of Games is a no-nonsense instructional in basic probability, geometry, and mathematics as they apply to popular games. Topics discussed include popular myths among those who the lottery, to the question of whether it is possible to reconcile chance and mathematical certainty, to testing dice, the possibilities of distribution in a roulette, modern theories as applied to the classical game of Go, whether bluffing in poker can be done without psychology, and so much more. Written in plain terms, Luck, Logic & White Lies teaches readers of all backgrounds about the insight mathematical knowledge can bring and is highly recommended reading among avid game players, both to better understand the game itself and to improve one's skills.

I started reading this book and nearly threw it down after just two chapters. There were numerous spelling and grammatical errors which initially made me question the validity of the material being presented. Fortunately I pressed on. This book, though not a masterpiece of English prose, is hands down the most understandable, comprehensive text on the subject that I have read. The book breaks down material from vastly diverse disciplines and explains them in a manner that a layman can understand. Prior to reading this book, I read Space Mission Analysis and Design (SMAD), also of the NASA Space Technology Series. I found that this book (The Lunar Base Handbook) presented the same topics as SMAD, but in a more understandable format. I found myself often reading a topic in The Lunar Base Handbook and then continuing my education in other books from the Space Technology Series such as SMAD. I highly recommend this book to anyone interested in lunar development or space exploration.

In this book, Peter Eckart has assembled the collective writings of many of the leaders who are developing advanced engineering and science concepts for a return to the moon and the establishment of a permanent lunar base, which is capable of exploring the moon in great detail. These writings are not reprints from a conference or a previously published paper, but a detailed summary of the work to date on a variety of subjects from the site selection of a lunar base and the transportation means to get to the moon, to the details regarding advanced exploration and regenerative life support systems. The book also includes the more mundane systems needed to make a lunar base function, such as the thermal control system and the communication system.

While portions of this book maybe overly technical for some readers, there are numerous sections that provide a general overview of equipment, lunar exploration history, and transportation techniques. There are two sections, one written by Buzz Aldrin and one by Jack Schmidt that describe in great detail various aspects of lunar exploration. Typically, most astronauts authored writings found in books are simply a page or two. All in all, I couldn't find a topic that was omitted from the book.

I also conducted a comprehensive review of several sections of the book, which are related to my engineering area of expertise. Specifically, I reviewed the thermal control system, power system, EVA, and life support sections. In all these sections, I only found one error, which appeared to be a typo. The lone error leads me to believe that other sections were equally as error free.

In summary, I always enjoy reading books like these, because they show that even though the US government does not support going back to the moon, many individuals are still committed to returning people to the moon. Finally, regardless of your technical ability, you can learn a great deal from this book.

This book, which is not only extensive and exetremely usefull but also very easy to read, provides the only complete overview of aspects considering the moon from an engineering point of view. All aspects are explained and start with basics and summarizes all possibilities. My book is full of post-it notes where the parts are marked that I had to use frequently. It is the most used book from all my moon-related books I have, because it is so complete. The essays from lunar explorers around the world are a nice extra. It would be a good study object for a course.

This book, which is not only extensive and exetremely usefull but also very easy to read, provides the only complete overview of aspects considering the moon from an engineering point of view. All aspects are explained and start with basics and summarizes all possibilities. My book is full of post-it notes where the parts are marked that I had to use frequently. It is the most used book from all my moon-related books I have, because it is so complete. The essays from lunar explorers around the world are a nice extra. It would be a good study object for a course.

This book is a MUST for eveyone seriously interested in lunar exploration. Since Wendell Mendells generatuion-inspiring lunar base document, this is the most complete overview on technical and non-technical aspects of the selenological adventure. One can start as an amateur: after having completed this large volume he/she will have an excellent interdisciplinary insight into our future on the Moon.

Book is new although there was a marking at the bottom of the pages.

Macroeconomics text books are like books on Options - where theory from academics is the usual content when people need a book that tells them how to make money out of this.

This book is a good workable approach to practical understnding of interelationships in a subject area that is over academicised.

If you study to the point where can do the end of book exercises then you will have a good grasp of macroeconomic essentials as they apply in the real world.

I have been teaching first to fourth year university macroeconomics since 1988. This is the first principles text I have been inspired by. The content of most traditional texts in macroeconomics is dictated by the needs of majoring students. Also, most authors of economics texts seem to feel the need to write an encyclopaedia. For those teachers of macroeconomics principles courses who want their students to learn something that will be of lasting value in their lives, give serious attention to Peter Kennedy's text. A look at its contents will tell you that it does cover all the usual topics. It is the style of the book which distinguishes it from the competition. Its chapters are brief and to the point. Its emphasis is on understanding the essentials that will allow its readers to understand what is daily going on around them in the economy. It is NOT in any way "low level". It will challenge the most able and interest them in continuing to study the subject, yet it will also reach the majority of its audience and help them to understand some of the basics of macroeconomic analysis. Now, Professor Kennedy, do the same for teachers of microeconomics!

I have looked through a wide variety of books on Macroeconomics and only this one has really satisfied me. It covers all the topics well; clearly, but not in a simplistic manner. And when you have finished studying a chapter and done some of the exercises at the end, you will understand the principles very well. The use of media exercises not only is more applicable to every day life, but also helps to stick the concepts into your brain so they are more easily retained.

With all this said, the book is quite approachable. It is written for the everyday student to understand concepts that are critcial in your everyday life; from investing to decifering the political conversations about the economy/deficit/balance of trade.

I highly recommend this book.

I found this text particulary inspiring the first semester I used it in my introductory macroeconomic class. The manner in which the material is presented makes the text a useful reference guide for business professionals who need to great refresher text to bring them up to date on the basic workings of the economy. Most of my students liked the book.

A candid, accessible, brilliant review of girl icons as presented in the media over the past 20 years (with nods to Barbie and a few other earlier famed love/hate icons). While so much academic writing can be abstruse and sometimes even cynical, Kathleen's book is optimistic and readable. Her call for media literacy as an antidote to negative narratives is cogent and smart. Her descriptions of work done by Real Grrls and other girl filmmakers and photographers is inspiring. Required reading for Millenial Girls, their parents, teachers and anyone else who loves media.

Ooh, Ah! the revelations that abound and resound in Kathleen Sweeney's Maiden USA! Get inspired on media literacy, as racy as it gets from Reel to Real. Discover a fecund treasure map to media awareness, which rouses us all up to the next level of empowered creativity. Kathleen Sweeney is the Goddess Durga of Media, cutting thru swaths of "Eyecon" demons and ignorance about girl identity; she is our media maven, and a media mechanic who regenerates our collective engines. Her wisdom is both fun and transformative.
Sweeney has opened and affirmed these eyes with her smorgasbord of media icons and plenty of truth serum. She reveals who and where we are in the culture of media now, and how to traverse that culture as well as to produce it. This is the "bodymindcentering" of media lit, a true hit with wit and grit to nourish us with its empowering maiden's milk of sanity. Reading it leads to media activism with a myriad of mission and means.

This gem of a book is not only important, informative, and thought-provoking--it's also clever, funny, and downright brilliant. If you have a daughter, or you are one, or you know one--or even if you don't--Maiden USA is an enthralling read. What a splendid job!

What an inspirational inside view from a free thinking woman/writer/artist/Mother.
If you want to understand the barrage of media influencing our young women and long to see girls be encouraged to take the reigns into their own hands- then this is a delightful and insightful ride- full of ideas, rich with hope- a must read for ALL of us!!!

WOW!
I just got the book!
It looks incredible!
I'm so excited to read it.
What a wonderful gift you have made in documenting all of this.

Brown does an excellent job of introducing the reader to the period of late antiquity in this work. He is able to cover the major political, social and philosophical transition of the Roman Empire of the Antonines to the emergence of the Christian Succesor States with clarity, and accuracy. Although this work does not take an indepth look into any of the many subjects that fall in this period, it is an excellent overview, and maintains a level of scholarship that is almost unparalled in a work of this nature. The book is documented to an excellent degree, so that even the most critical reader can see where it is that Brown is comming from. I would recomend this book to anyone from the avid scholar to the most casual reader.

From an Age of Equipoise to an Age of Ambition- the Poisoning of the Classical Spirit

I found this book to be an extremely clear and well-written explanation of the decline of classical Greco-Roman civilization. The period from the second to the fourth centuries, from the Antonines to Constantine, is covered. The author makes a very good case that the cause for this decline in the classical world was primarily due to a concentration of wealth and power into fewer and fewer hands. He shows this to be true in economic, political, cultural, and most especially, religious spheres. He also shows the obvious parallels with our own age without being heavy handed.

First he shows the grand show of power and tradition in the age of the Antonines to be primarily an empty hollow thing. It was the gigantism that precedes decline even if the players of the time could not see it. The societal restraints and governors that constrained individual ambition began to erode. The old code of civic virtue, of demonstrating your greatness by contributing to the benefit of the society, the polis, crumbled. Wealth was concentrated into fewer and fewer hands. The common people were forced off of the land. Bankruptcy became commonplace across the empire. Politically, power concentrated into a smaller and smaller circle centered on the court in Rome, and then Constantinople, and away from the provincial towns and capitals. Culturally and scholarly, all status depended on ones mastery of polished Greek and the ability to quote precisely from the classics (i.e. scholarship depended more on the size of your library than the size of your intellect.)

It is in the religious and spiritual sphere that this tendency to place all authority in the hands of an elite becomes the most insidious, and the most damaging. It is demonstrated that ,traditionally, the average man of the Greco-Roman world saw that world as alive with supernatural forces that he interacted with on a daily basis. The pagan participant in the mysteries experienced the divine through direct contact. This slowly changed with the rise of Christianity. Men were told that only "official" intermediaries could bridge the gap between heaven and earth. As a result this gap widened into a chasm. The old comforting classical assumption that heaven and earth lived side by side in gentle communion faded away. In the author's words, the leaders of the Christian church came to stand between heaven and an earth emptied of the Gods.

With all economic, political, scholarly, and religious power concentrated in the hands of a tiny, ruthless, corrupt elite, is it any wonder that the common man lost any interest in maintaining the empire? The old system of civic virtue and of the old delicately balanced system of obligations from ruled to the rulers, and the rulers to the ruled, had been poisoned.

Any of this sound familiar?

I cannot say enough about this extraordinary book. Everyone who is interested in the environment that led to the rise of Christianity will find this book fills in many details. Brown's analysis of the decline of classical Greco-Roman civilization is well done, concise, and comprehensive. I highly recommend this book!

From an Age of Equipoise to an Age of Ambition- the Poisoning of the Classical Spirit

I found this book to be an extremely clear and well-written explanation of the decline of classical Greco-Roman civilization. The period from the second to the fourth centuries, from the Antonines to Constantine, is covered. The author makes a very good case that the cause for this decline in the classical world was primarily due to a concentration of wealth and power into fewer and fewer hands. He shows this to be true in economic, political, cultural, and most especially, religious spheres. He also shows the obvious parallels with our own age without being heavy handed.

First he shows the grand show of power and tradition in the age of the Antonines to be primarily an empty hollow thing. It was the gigantism that precedes decline even if the players of the time could not see it. The societal restraints and governors that constrained individual ambition began to erode. The old code of civic virtue, of demonstrating your greatness by contributing to the benefit of the society, the polis, crumbled. Wealth was concentrated into fewer and fewer hands. The common people were forced off of the land. Bankruptcy became commonplace across the empire. Politically, power concentrated into a smaller and smaller circle centered on the court in Rome, and then Constantinople, and away from the provincial towns and capitals. Culturally and scholarly, all status depended on ones mastery of polished Greek and the ability to quote precisely from the classics (i.e. scholarship depended more on the size of your library than the size of your intellect.)

It is in the religious and spiritual sphere that this tendency to place all authority in the hands of an elite becomes the most insidious, and the most damaging. It is demonstrated that ,traditionally, the average man of the Greco-Roman world saw that world as alive with supernatural forces that he interacted with on a daily basis. The pagan participant in the mysteries experienced the divine through direct contact. This slowly changed with the rise of Christianity. Men were told that only "official" intermediaries could bridge the gap between heaven and earth. As a result this gap widened into a chasm. The old comforting classical assumption that heaven and earth lived side by side in gentle communion faded away. In the author's words, the leaders of the Christian church came to stand between heaven and an earth emptied of the Gods.

With all economic, political, scholarly, and religious power concentrated in the hands of a tiny, ruthless, corrupt elite, is it any wonder that the common man lost any interest in maintaining the empire? The old system of civic virtue and of the old delicately balanced system of obligations from ruled to the rulers, and the rulers to the ruled, had been poisoned.

Any of this sound familiar?

Brown is able to establish the foundations for anyone interested in late antiquity with clarity and scholarly depth that is unparelled in the field. This book, although taking a broad picture of the period, and focusing on a shallow over view, rather than taking an indepth look into any perticular aspect of the period, is still scholarly enough to interest even the most particular historian, but will catch the interest of the beginer also. Browns conclusions are well thought out, and are based on an extensive, and acurate picture of the period. The documentation is incredible, hundreds of documents are quoted, and carefully indexed, in a book under 200 hundred pages, so the most nitpicky readers can see exactly where Brown is comming from. This should be the model for broad view scholarly work, this is truly an excellent work.

"Mark My Words" is of truly epic proportions. It cuts across all genre's from historical reference, academic insight, man's eternal struggle with good and evil to what one can achieve with a good heart and hard work. The lessons learned from the Author and his remarkable life and soul are for all mankind. An absolute fascinating and must read. It is truly exceptional.

"Mark My Words! is a compelling 20th Century Jewish book.And it has an important added value. It exemplifies to the younger generation how human spirit can overcome difficulties and how human values can make success an educational resource."

- The Hon. Ze'ev Benjamin Begin, M.K.

* * *

"Mark Hasten's biography is a saga of a brilliant man whose life experiences reflect an epochal struggle of survival in the catastrophe which engulfed European Jewry. Mr. Hasten's success reflects a combination of genius, initiative,flexibility and the helping hand of the Almighty. His life is dedicated to the rebuilding of Israel and the continuity of our people through Jewish education."

- Dr. Bernard Lander, President
Touro University

* * *

"Mark Hasten's story is one of the most remarkable I have ever read. From the idyllic childhood in pre-WW II Poland, through the trials of war, to helping found the modern state of Israel, through his hard work and success in America, his is the story of hope's triumph over despair. He has lived and seen enough history to encompass several lives. Throughout it all, he has never lost his sunny optimism, his love of family, faith in G-d and love of country- both Israel and the US. I admire Mark Hasten and all that he has accomplished. When many men would have given up, he kept going. I hope all who read his book will benefit from it as have I. We will all be well advised to `Mark My Words!' "

- The Hon. Evan Bayh, United States Senate

* * *

"Mark Hasten has produced an outstanding memoir that recounts a notable saga of harsh adversity and stellar achievements. The book is definitely worth reading."

-Dr. Morton I. Teicher, founding dean,
The Wurzweiler School of Social Work, Yeshiva University

* * *


"The last words of Simon Dubnow, the world renowned Jewish historian, who before he was packed into the cattle cars for his final journey, were: `Jews, remember, and record everything!' Mark Hasten is fulfilling this legacy. He is to be saluted for recording and keeping these memories alive."

-Dr. Miles Lerman, Chairman Emeritus
The United States Memorial Holocaust Museum

* * *

"I found Mark My Words! to be an inspiring work. Beyond being a wonderful read, Mr. Hasten's book also contains remarkable information about life in Poland and the Polish resistance...it contains astounding and...until now unknown information about...the events surrounding the Altalena affair."

-Rabbi Menachem Genack, Rabbinic Administrator
Kashruth Division of the Orthodox Union

* * *

"This book is a fascinating account not only of Mark Hasten's life but of the story of the Jewish people in the twentieth century. Even though the book is about an individual and his struggle to survive and prosper, the author has painted this story on the much broader canvas of Jewish life and history. It is a book well worth reading."

-Rabbi Berel Wein
Jewish historian, author and international lecturer

This book is a fascinating account not only of Mark Hasten's life but of the story of the Jewish people in the twentieth century. Even though the book is about an individual and his struggle to survive and prosper, the author has painted this story on the much broader canvas of Jewish life and history. It is a book well worth reading.
- Rabbi Berel Wein

Mark My Words! A Personal History is the memoir of Mark Hasten, a World War II survivor who became a successful businessman. Forced to flee the Nazis that overran his Polish hometown, author Mark Hasten's experiences among the ranks of the Free Polish Army during World War II, his eyewitness account of the first days of Israel's independence, his journeys to new homes in Canada and the United States, and his perseverance in the business world, Mark My Words! is a profound success story and a testament to human resiliance, determination, and faith.

As a personal friend of Mark Hasten, I expected and was rewarded with a great biography of a great man.

I knew vaguely about the story of "Altalena" and Israel's war of Independence but Mark's personal experiences explained the events in a clear and personal way.

If you do not have time (or like me, skip around), read Mark's Conclusion first and then you will take the time to read the whole thing. Well worth it.

It made it very easy to find where the lighthouses are located and a nice article on each one.

On medium-weight, semi-glossy paper, this beautiful and durable map folds out to approximately 2 feet by 3. On one side is a three-color highway map of the coasts of Massachusetts and New Hampshire, inlaid with paragraphs on several of the lighthouses and framed by watercolor pictures of each. The reverse side describes all 50 Massachusetts lighthouses, standing or not, and both New Hampshire's. The descriptions give a short history, the optimal viewing spot, directions, contact information, hours of operation, transportation options, etc.

If you are interested in lighthouses, Massachusetts or New Hampshire, shipping or maps, you will probably love this great map. Travellers will find it indispensable. What a bargain!

No traveller in search of Massachusetts' lighthouses should be without this extremely useful map. Beautiful watercolor illustrations too!

This map and guide covers lights in both MA and NH. In June of 2000 I used this map to visit Lighthouses in MA & NH. This map was very useful. On one side is a map pointing out the locations. On the other side there are details for each individual light such as: directions, hours, and phone numbers. I am from Michigan so I was not familiar with New England at all. Some of these lights were hard to find even with the map because some roads are not clearly marked. But I did find everything I was looking for. The price of these maps is an incredible bargain. Some people buy two of them so they can hang one on the wall to display the watercolor images and get another to use.

This was a great resource in locating lighthouses - compact, yet gives specific directions on which lighthouses could be visited and how to get there. Very nice layout, design, pictures, etc.

An interesting aspect of this puzzle book is that the sections on the solutions are longer than those describing the problems! More than most puzzle books, you will find solutions described in great detail. The solutions in fact are the best part of the book!

Many of these puzzles are unbelievably difficult. In fact the last chapter contains a list of "unsolved puzzles", which is an amusing idea. Mathematicians will spend hours poring over these puzzles. This is distinctly different from any puzzle book I have ever bought! It is more for the mathematically inclined.

I have seen the word connoisseur used to describe collections before, but when I sat down to write this review I realized that I did not know the precise usage of the term. Therefore, I pulled out my Webster's dictionary and looked it up. It was "a person who has expert knowledge and keen discrimination in some field, esp. the fine arts or in matters of taste." In terms of keen discrimination, the term applies to the puzzles in this book. They are some of the best puzzles ever published, although those who follow the field will have seen many before, although perhaps in an altered form.
However, expert knowledge is not required to understand and solve the puzzles. The level of mathematical knowledge is that of detailed knowledge of basic algebraic and reasoning techniques. Like the very best puzzles, solving them requires a bit of "sideways" thinking. In other words, the most obvious approach to a puzzle will most likely lead to bafflement, but if you look at it just the right way, the solution is obvious. Furthermore, once the inspiration arrives, you know that you indeed have the solution.
In all honesty, I struggled with many of these puzzles. Sometimes, I was just being stupid, and other times I doubt if the solution would have ever managed to form in my thoughts. Fortunately, solutions to nearly all of the problems are included. The final chapter contains unsolved puzzles, which seems like a bit of a misnomer, and in a real sense it is. These are really unsolved problems, their topic is just one that fits inside what is generally considered the puzzle genre.
I loved this book, even when I was so frustrated I wanted to chop it with my very sharp axe. These puzzles will stretch you to the breaking point, which is of course a prerequisite for being among the best ever created.

Published in Journal of Recreational Mathematics, reprinted with permission.

Wow, what a splendid collection of varied and challenging puzzles - a puzzler's delight!

I especially liked the "handicap" puzzles - these are new to me, and involve algorithmic puzzles with bizarre handicaps having to do with memory.

The book also has extensive refrences so you can further your interests for a particular type of puzzle. There's even an unsolved puzzles section to challenge even the professional mathematician.

In terms of difficulty level, I would say that 2/3rds of the puzzles are meant for the seasoned puzzler and do require some "mathematical maturity" . But there are quite a few "insight" puzzles that required almost no math.

There's even geography puzzles of all things - that's quite refreshing and original for a math puzzle book.

congrats Dr. Winkler on a splendid collection!

This book mainly requires that you be at ease with mathematics and mathematical terms on the level of a high school student. The solutions don't involve long calculations and calculus books. They are brain teasers that often require out-of-the-box thought and creativity. They are excellent for computer science students studying the theory of algorithms, because often the same thought process that goes into solving the more difficult problems in that field are applicable to the puzzles in this book. The puzzles can be very difficult, and several were without solution for a very long time. There is also a group of Unsolved Puzzles at the end of the book.

this book is interesting and challenging, even to people who have studied math at the college level. the problems are short, and take about an hour to solve, at least they did for me. it was a great read and i highly recommend this as a gift for the math lover in your life.

High end mathematical theory has veered away from actually doing arithmetic because most of the problems being addressed required a tremendous amount of calculation and that calculation was difficult in the days of only pen and paper. About twenty years ago the advent of big/fast computers (by the standards of those days) began to allow the ready solution of these problems without requiring large numbers of people doing the computing.

Borwein and Bailey have been pioneers in the exploration of the types of mathematical problems that would lend themselves to solution using digital computational means. This book describes this new approach to mathematics, commonly called 'experimental mathematics.'

Obviously in computer related mathematics it began with a lot of emphasis on prime numbers, on calculating the value of Pi to ever greater precision. It has since moved on to many other classes of problems, and the work of the principle researchers in the field is summarized here.

If one peruses the mathematical literature for the last one hundred years one will notice that in most cases no diagrams or pictures appear. The level of rigor in all cases is impressive though, but unfortunately this makes the understanding of the results much more difficult. There seems to be an inverse relationship between rigor and understanding in mathematics, at least for those who are new to the subject at hand. In order to gain this understanding, the drawing of pictures and diagrams is useful, along with a certain amount of experimentation with the concepts at hand. Intuition, how mysterious, and however ill defined, plays a role in both the understanding of mathematical results and in their discovery. Many mathematicians do not want to acknowledge this, as a visitation to a typical conference will readily verify. The attitude has been expressed that mathematics has "always been abstract" and therefore that pictures or diagrams violate its spirit. Even a well-known geometry center whose goal was to use sophisticated computer graphics to visualize complex mathematical objects lost its funding, to the consternation of a few but with glee to most.

Thus the way to discovery of mathematics, i.e. the heavy use of intuition, the disorganized shuffling of concepts, and the experimental doodling, has been masked by the final product of this process: a superb example of logical rigor and organization called modern mathematics. The authors of this book however think otherwise, and they give the best apology for the role of experimental mathematics than anyone else in the literature. The book is packed with highly interesting examples and challenging exercises, all of which are ample proof of the need for doing experimentation in mathematics.

In addition to these considerations, the book is just plain fun to read, and even though time constraints may prohibit the working out of every exercise, the book could be used profitably in a graduate course in mathematics or even possibly in an undergraduate course at the senior level. Hopefully this approach to scholarship in mathematics will take hold in this century, and mathematicians will not only write down their final results with all their splendid rigor, but also how they got there. This would serve to educate younger generations of mathematicians in just how discovery in mathematics is done and increase their efficacy in the same. The book will also assist those who are trying to build machines capable of discovering novel results in mathematics. Machine proofs of difficult theorems and conjectures are now a reality, and in the twenty-first century we will no doubt see many more of these.

This book therefore contains a lot of hints about how to proceed in mathematics. Its acceptance will depend on how well it does its job in the creation of new mathematical results and in the teaching of them. Results in mathematics that seem plausible serve to make conjectures and motivate the construction of rigorous proofs. This book is a first step in a hopefully larger work.

See my book review that appeared in American Scientist

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/mathexp.html

"Mathematics by Experiment" is a ground-breaking book about a new way of doing math that generated so much excitement it was reviewed in "Scientific American" six months before it got into print. The authors are long-time collaborators David Bailey, chief technologist in the Computational Research Department of Lawrence Berkeley National Laboratory, and Jonathan Borwein, professor of science at Simon Fraser University in Vancouver, B.C.

They write that applied mathematicians and many scientists and engineers were quick to embrace computer technology, while pure mathematicians -- whose field gave rise to computers in the first place, through the work of beautiful minds like Alan Turing's -- were slower to see the possibilities. Two decades ago, when Bailey and Borwein started collaborating, "there appeared to be a widespread view in the field that 'real mathematicians don't compute.'"

Their book is testament to a paradigm shift in the making. Hardware has "skyrocketed in power and plummeted in cost," and powerful mathematical software has come on the market. Just as important, "a new generation of mathematicians is eagerly becoming skilled at using these tools" -- people comfortable with the notion that "the computer provides the mathematician with a 'laboratory' in which he or she can perform experiments: analyzing examples, testing out new ideas, or searching for patterns."

In this virtual laboratory Bailey and Borwein, with other colleagues, were among the first to discover a number of remarkable new algorithms, among them an extraordinary, simple formula for finding any hexadecimal or binary digit of pi without knowing any of the preceding digits. Further research led to proof that a wide class of fundamental constants are mathematically "normal" -- probably including pi, alhough that remains to be proved.

Their section on "proof versus truth" is an example of the gems even a mathematical tyro can find among these equations. Bailey and Borwein don't claim computers can supply rigorous proofs. Rather, the computer is a way to discover truths -- and avenues for approaching formal proofs. But often, the authors add, "computations constitute very strong evidence..., at least as compelling as some of the more complex formal proofs in the literature."

Drawing on their own work and that of others, Bailey and Borwein not only explain experimental mathematics in a lively, surprisingly accessible fashion but give many engaging examples of the "new paradigm" in action.

The collaborative work of Jonathan Borwein and David Bailey, Mathematics By Experiment: Plausible Reasoning In The 21st Century provides a complex and informative text for advanced mathematics students which offs an historical context and rationale behind experimental mathematics, as well as how modern technology enables the analysis of new examples and the discovery of patterns in a previously unimaginable "laboratory" of raw processing power. A thoroughly detailed work, Mathematics By Experiment offers a veritable wealth of meticulously presented examples which are most especially recommended for graduate-level mathematics studies.

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