**The Analytics Book Club**

I cannot remember when I became a compulsive book reader. As a kid, I used to read mostly comic books. Then I missed the whole phase of teenage fiction books like The Hardy Boys, etc. I did read a few Agatha Christie novels in school and later in college but that was about it. I got hooked onto books after the completion of my formal education. I guess for me the real education started after school.

I, along with my wife, am a proud owner of more than a thousand books. I am starting this new series on YOU CANalytics to share with you a few of my favorite books. I am going to call it The Analytics Book Club. I will try to keep the books for this series related to logic and analytics. In this first part of the series let me share some of my favorite popular mathematics books. I have organized these books in the following four categories.

(i) Evolution and History of Mathematics

(ii) Mathematical and Logical Puzzles

(iii) Some Cool Topics in Mathematics (Next Article)

(iv) Great Pupils of Mathematics (Next Article)

In each of these four categories, I have selected three books each. That will make it 12 popular mathematics books from my bookshelves. In this part, I will cover the first two categories i.e. the first six books. Hope, you will enjoy reading these books as I did.

**(i) Evolution of Mathematical & History**

1) Fermat’s Last Theorem (a.k.a. Fermat’s Enigma)– By Simon Singh

I have reorganized the categories of this article to bring this book on the top of the list. If you ever have to read just one book on mathematics, I recommend you read this. We have all learned Pythagoras theorem in primary school. The simple property about right triangles makes the square of the hypotenuse (z) equal to the sum of the squares of the remaining two sides (x and y). Mathematically represented as

x=3, y=4 and z=5 is one of the complete whole number solutions to infinite such solutions. Pierre de Fermat, a French amateur mathematician, unleashed a demon in the mid-17th century by proposing a twist to Pythagoras’ theorem. He stated that there is no solution with all x, y and z as whole numbers for the following equation

This is another way of saying that there is no whole number solution to the above equation beyond Pythagoras’ theorem. To rub salt in the wounds of generations of mathematicians to come, he also wrote that he had a solution to this but found the margin of his notebook too small to write it down. With this statement, he started one of the most brilliant quests in mathematics that lasted for more than 350 years. When we say n>2 this includes infinity. Karl Gauss, one of the greatest mathematicians, described this problem as worthless chasing – many would call it a case of sour grapes. Finally, Andrew Wiles proved the theorem right in 1995. Simon Singh captures the history of number theory while narrating this incredible story. You will get a feeling of what infinity means while reading this book. A definite must read!

Both kids and adults will like The Math Book equally. This book will make a perfect coffee table book for people who have the liking for mathematics. The main contents of the book are presented in 500 pages covering 250 milestones in the history of mathematics. The book is arranged in chronological order. Each milestone is covered on a couple of pages, with a full-page picture and a short write-up by Mr. Pickover. The first milestone, set in 150 million BC, describes the sophisticated computer inside the Saharan desert ant, *Cataglyphis fortis*, to locate its path on an ever changing landscape of the desert. The last milestone is as recent as the year 2007, describing Mathematical Universe Hypothesis (MUH) proposed by cosmologist Max Tegmark. MUH describes that everything in the universe is purely mathematical.

This book is not so much a history but a collection of mathematical ideas we learn over the course of education in mathematics. The ideas we learn as early as in the preschool i.e. concept of counting on Sesame Street and as late as during a Master’s degree in mathematics i.e. group theory. Steven Strogratz has done a good job of giving a non-mathematical account of these concepts that most people can follow. For instance, in one of the chapters titled Love Me, Love Me Not, the concept of differential calculus is explained using the fickleness of love. This is a bit farfetched and loose relationship, however, it still does the trick of explaining the concepts of calculus to an unaware audience. Additionally, this book can make a seasoned mathematician look at mathematics from a different point of view. As you could imagine the focus of the book is on width rather than depth, hence for the more curious audience, there are some references at the end of the book. However, one may have to rely on Google to access the depth of the topics described in the book.

**(ii) Mathematical & Logical Puzzles Books**

4) Professor Stewart’s Cabinet of Mathematical Curiosities– By Ian Stewart

Ian Stewart is a professor of mathematics at the University of Warwick and a renowned popular science author. This book is presented as a compilation from a series of notebooks Professor Stewart has maintained since he was 14 years old. He records curious mathematical facts and puzzles in these notebooks. The book contains several short write-ups on interesting mathematical concepts like Chaos Theory, Pi, Euler’s constant (e), Riemann Hypothesis etc. Additionally, the book is full of lots of mathematical puzzles.

For instance, a puzzle on page 22 is about extracting a cherry from a cocktail glass made of matchsticks (shown adjacent). The condition is to do it while moving just 2 matchsticks and maintaining the structure of cocktail glass. This solution for this puzzle is a good example of lateral thinking. Recently in 2012, Ian Stewart has released a sequel to the book called Professor Stewart’s Hoard of Mathematical Treasures. After reading the “Cabinet” you might want to move to the “Hoard”.

This book contains slightly more than 400 pages with each page, on average, containing 7-8 logical puzzles and interesting mathematics facts. A little more than hundred pages at the end are the solutions to these puzzles. The book is divided into seven chapters with topics covering cool numbers, probability, algebra, geometry and big numbers. The first page of the book starts with the question; do humans invent mathematics or discover mathematics? To answer this question recall, earlier in this article, I have listed another book (The Math Book) by the same author Clifford A. Pickover. In that book, the last milestone i.e. Mathematical Universe Hypothesis state that numbers and mathematics are embedded in the universe and we are discovering them through our knowledge. Like Professor Stewart’s Cabinet of Mathematical Curiosities, this is a nice book to have on your bedside table to pick up and solve a few puzzles before a good night sleep.

6) 50 Challenging Problems in Probability with Solutions– By Frederick Mosteller

This is a really short book with 50 challenging problems in probability contained in just 88 pages. The problems are presented in the first 14 pages followed by solutions to these problems on the remaining pages. The level of difficulty for the problems goes up as you move further in the book. The solutions are presented in a fairly intuitive and friendly manner. Though I must tell you that the solutions used some advanced concepts in mathematics which could be daunting for some.

To give you a feel for the problems, one of the problems on the first page goes like – “ To encourage Elmer’s promising tennis career, his father offers him a prize if he wins (at least) two tennis sets in a row in a three-set series to be played with his father and the club champion alternately: father-champion-father or champion-father-champion, according to Elmer’s choice. The champion is a better player than Elmer’s father. Which series should Elmer choose?”

The solution to this problem is quite non-intuitive as is the case with several problems in probability. Elmer would improve his chances if he chooses to play more sets with the champion. I will leave it up to you to figure out how this is possible.

**Sign-off Note**

See you soon with the next six popular mathematics and logic books from the following categories

(iii) Some Cool Topics in Mathematics

(iv) Great Pupils of Mathematics

This is a really interesting selection of mathematics book, I am wondering if you could suggest some good books on information theory?

Thanks Mark, there is a book by James Gleick called ‘The Information’: not thoroughly an engrossing read but it has some really interesting chapters particularly on entropy and randomness. There is another book which you may find interesting by John R. Pierce names ‘An Introduction to Information Theory: Symbols, Signals and Noise’, this one is a bit more technical but still an enjoyable introductory text.

These are only six books, where are the remaining six!

Thanks

They are in the 2nd part of this article, please follow the link to the next set of books. Enjoy!

A very interesting book on Mathematics is

THE UNFATHOMABLE WORLD OF AMAZING NUMBERS.

The information in the book is put together in such a way that it starts penetrating the reader’s mind. It appears that a mystery is being solved layer by layer.

It contains information which I had never known before.

For instance, it contains information on e, which is used in Mathematics.

It explains the concept of intercalary years or leap years.

Hi Roopam, this fater-champion-father or champion-father-champion kept me awake this night, but I solved it.

You have to win at least once from the person you play twice and you MUST win from the person you play once. The chances of these 2 separate ‘items’ must be multiplied to get the overall chance of success. You can also win twice from the person you play twice. So the chance for the person you play twice is 1-p(l)^2 (1 minus the chance of loosing twice in a row, which leaves all the chance for winning once or twice). Multiply this by p(w) from the person you play once. Lets assume that your chances of winning from dad are 0.8 and your chances to win from the champion is 0.3. Then fcf chance of success is 0.288, the cfc chance of success is 0.408. Indeed, very counter intuitive!

Cool mystery ;-), I’m going to get that book!

Best regards,

Hans