Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Saturday, September 16, 2017

Games Indians Play - V. Raghunathan


Why we are the way we are 
In a rare attempt to understand the Indianness of Indians—among the most intelligent people in the world; but also; to a dispassionate eye; perhaps the most baffling—V. Raghunathan uses the props of game theory and behavioural economics to provide an insight into the difficult conundrum of why we are the way we are. 
He puts under the scanner our attitudes towards rationality and irrationality; selflessness and selfishness; competition and cooperation; and collaboration and deception. 
Drawing examples from the way we behave in day-to-day situations; Games Indians Play tries to show how in the long run each one of us—whether businessmen; politicians; bureaucrats; or just plain us—stand to profit more if we were to assume a little self-regulation; give fairness a chance and strive to cooperate and collaborate a little more even if self-interest were to be our main driving force.
[Book Description Source: www.amazon.in ]

India is blessed with many intelligent minds.
Most Indians are more adept at maths and logic than people around the globe.
However, as a nation, we are still falling behind.
Our collective naiveté might be to blame, but how is it that we boast equal parts intelligence and naiveté?
In this book, the writer explains that Indians mistake talk for action. He tries to help readers understand why this happens and how we can change this.
He uses game theory to explain the behaviour of Indians and tries to combine these explanations with concepts of behavioural economics.
The author also presents his twelve points on the fallacies of Indians, explaining that our low trustworthiness, private smartness and public dumbness, fatalist outlook, over-intelligence, lack of public hygiene, self-regulation or a sense of fairness, reluctance to penalize wrong conduct, mistaking talk for action, deep-rooted corruption, inability to follow systems, a sense of self-worth and a propensity to look for loopholes in laws.
He helps readers understand how to break this vicious cycle and how to bring a change in the image Indians have around the world.
This is a definite read for all Indians who are trying to understand what is keeping them one step behind in the rise to success 

[Book Summary Source: Flipkart.com]


Ratings
Goodreads Rating - 3.45 out of 5 ( 507 Ratings , 78 Reviews  - As on September 16 2017)
My Rating  3 out of 5
My Comments:
Interesting analysis through Game Theory of the typical behaviors observed in the Indian society with a nice touch of humor and food for thought.


Buying Options 
  
Buy from Amazon.com  Buy from Amazon.in Buy the Kindle Version

Saturday, March 18, 2017

Fermat's Last Theorem by Simon Singh


This is the story of the puzzle that had confounded mathematicians since the 17th century. 
‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’
It was with these words, written in the 1630s, that Pierre de Fermat intrigued and infuriated the mathematics community. 
For over 350 years, proving Fermat’s Last Theorem was the most notorious unsolved mathematical problem, a puzzle whose basics most children could grasp but whose solution eluded the greatest minds in the world. 
Many people had tried and failed, including an 18th-century philanderer who was killed in a duel. 
An 18th-century Frenchwoman made a major breakthrough in solving the riddle, but she had to attend maths lectures at the Ecole Polytechnique disguised as a man. 

In 1963, a schoolboy Andrew Wiles browsing in his local library stumbled across Fermat's Last Theorem. Aged just ten, he dreamed he would crack it.
In 1993, after years of secret toil, Andrew Wiles  announced to an astounded audience that he had cracked Fermat’s Last Theorem. 
The solution of the Theorem was one of the most important mathematical developments of the 20th century. 
In ‘Fermat’s Last Theorem’ Simon Singh has crafted a remarkable tale of intellectual endeavour spanning three centuries, and a moving testament to the obsession, sacrifice and extraordinary determination of Andrew Wiles: one man against all the odds.


[Book Description Source: www.amazon.com  and www.amazon.in] 


Ratings
Goodreads Rating - 4.21 out of 5 (17,874 Ratings; 739 Reviews - As on February 18 2017)
My Rating 4 out of 5
My Comments:  Gripping narration about an esoteric mathematical subject. Not a single dull moment throughout the book.


Buying Options 
Buy from Amazon.com  Buy from Amazon.in Buy the Kindle Version

Sunday, June 12, 2016

The Man Who Knew Infinity - Robert Kanigel


A Life of the Genius Ramanujan 
In 1913, a young unschooled Indian clerk wrote a letter to G H Hardy, begging the preeminent English mathematician's opinion on several ideas he had about numbers. 
Realizing the letter was the work of a genius, Hardy arranged for Srinivasa Ramanujan to come to England. 
Thus began one of the most improbable and productive collaborations ever chronicled. 
With a passion for rich and evocative detail, Robert Kanigel takes us from the temples and slums of Madras to the courts and chapels of Cambridge University, where the devout Hindu Ramanujan, 'the Prince of Intuition,' tested his brilliant theories alongside the sophisticated and eccentric Hardy, 'the Apostle of Proof.' 
In time, Ramanujan's creative intensity took its toll: he died at the age of thirty-two and left behind a magical and inspired legacy that is still being plumbed for its secrets today.
[Book Description Source: www.amazon.com ] 

Ratings
Goodreads Rating - 4.15 out of 5 (3,410 Ratings; 204 Reviews)
My Rating 4 out of 5
My Comments: A very well researched biography that brings out the personality of both Ramanujan and Hardy very vividly. Readers not exposed to college level mathematics may find some parts tedious.

Buying Options 
Buy from Amazon.com  Buy from Amazon.in  Buy Kindle Version
(Anybody can read Kindle books—even without a Kindle device—with the FREE Kindle app for smartphones and tablets.)

Saturday, December 28, 2013

Medical Statistics from Scratch by David Bowers

Statistics plays a key role in medical research and investigations.

The field of Medical Statistics focuses statistical procedures well-suited to the analysis of healthcare related data.
David Bowers, the author of this book introduces the readers to medical statistics without resorting to complex mathematics. 
He  focuses more on the understanding of the key concepts behind the statistical procedures. The book provides useful advice on which procedure to  choose for data analysis and under what circumstances.
The author also explains how to interpret outputs from statistical programs like Minitab.
The topics covered in this book include - Data description, designing a statistical study, making statistical inferences about the population based on samples, confidence interval estimation, test of hypothesis, measuring associations and agreement between two variables, regression models, survival analysis, meta-analysis.
The theory discussed in the book is well-supported by lots of examples and exercises based on  the data  drawn from the latest medical research literature. 
On several occasions the discussions in the book in a particular chapter make references to the tables and graphs introduced in  earlier chapters. This is somewhat annoying since one has to search for them and keep juggling between pages. It would have been better if such tables and graphs  were repeated where they are discussed or been collated in form of an appendix. This is the only drawback of this well-written , interesting and reader-friendly book.

Highly recommend it as an introductory text on medical statistics. ! 


   


Wednesday, November 27, 2013

Here's Looking at Euclid by Alex Bellos

"Math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place", says the Alex Bellos, the author of this book.
And he takes the reader on a very fascinating journey through this wonderful world of maths.
He narrates exciting stories about - the Euclidean geometry; the mathematics behind origami the art of paper folding; a tribe in the wilds of the Amazon who can count only up to five; how ants can actually count how many steps they have taken; the mathematical insights of Buddha; Sudoku and other mathematical games; the random numbers ; the number pi and many more.

The book is packed with very interesting information and  anecdotes written in a very humorous and engaging style.
This is probably the best book I have read in this genre.
Don't miss it if you like maths ! 
And even if you don't like maths, at least browse through some sections of this book. It may change the way you look at maths.

 Read an Excerpt from the book. 

 

Also published under the title : Alex's Adventures in Numberland
Buy Alex's Adventures in Numberland from Flipkart


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Saturday, April 13, 2013

Mathematics of Life: Unlocking the Secrets of Existence

Author:       Ian Stewart
Published:  2011
Publisher:  Profile Books Ltd.
Hardcover: 368 pages


 I remember my high school days in late seventies, when the students who wanted to join the science stream but were not confident about their mathematical abilities would choose PCB (Physics, Chemistry, Biology) instead of PCM (Physics, Chemistry, Mathematics)  as their subjects. 
Seems like this escape from mathematics is no longer an option in twenty-first century !

Many of the important questions opened up by modern discoveries in biology cannot be answered without significantly drawing upon the knowledge of mathematics.
Therefore in the present times biologists and mathematicians are collaborating on finding solutions to such questions especially those related to nature and origins of life itself.
The former pose the biological questions or describe a set of experiments, while the later develop a mathematical models to simulate them.

Welcome to the field of Mathematical Biology ! This book is a layman's primer on this subject.

It explores several connections between mathematics and biology, viz; -  the Human Genome Project; the structure and function of the complex molecules that coordinate the complex process of life; the shape of viruses; the organization of cells; the form and behavior of entire organisms and their interaction in the global ecosystem; evolutionary games that led to huge diversity of life in earth; the workings of the nervous system and the brain; nature of life; possibility of alien life forms.
The theory behind these connections encompass a wide range of mathematical concepts - probability, dynamics, chaos theory, symmetry, networks, mechanics, elasticity, knot theory.


While I don't claim to have understood each and every topic discussed in this book, I found it a really interesting read and would recommend it to anyone who is a keen reader of  popular science genre.
 Pythagoras the renowned mathematician of ancient Greece once said,"All things are numbers" Ian Stewart, the author of this book and a mathematician of the modern era  has shown that this statement is true to a great extent in life forms.

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Wednesday, October 17, 2012

Newton and his Falling Apple

Author:         Kjartan Poskitt
Illustrator:     Philip Reeve 
Published    2011
Publisher:    Scholastic
Paperback:  192  pages

Any school student would have definitely come across - Newton's Laws of Motion, Newton's Law of Gravity, Newton's Law of Cooling, Newton Rings and so on.
But how many of us know the man - Newton - behind these laws that have given sleepless nights to so many students  while they prepared for the exams. How they  wish that Newton was never born !
This  little book meant primarily meant for students (that includes me too an eternal student , though I am over ....well never mind!) is a delightful humorous, illustrated biography of Newton. I came to know many facts about Newton which I was not aware of.
Want to know more about this book ? Well get hold of a copy  and read it. Too good to be missed !
4 out of 5 !


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Thursday, September 20, 2012

Understand Calculus

Author:          P. Abbott & Hugh Neill
Published    1992 
Publisher:     Hodder Education
Paperback:  400 pages
Over the last decade and a half I have not got enough opportunities to exercise my grey cells that are responsible for solving mathematical problems. I was concerned that I may eventually loose the skill which I had painstakingly acquired through almost  20 years of maths education. Hence I picked up this book on introductory calculus when I saw it in a library and read through it like a novel. Well that's not exactly how you go through a mathematics book . You need to actually do the exercises given in the book. But then the purpose was served. I was able to refresh many differentiation and integration concepts and techniques which I had struggled with during my college days.
Though I felt the treatment of integral calculus could have been better, I would recommend this book to anyone interested in learning or brushing up the fundamentals of calculus.

Links:
Table of  Contents
  • Functions
  • Variations in functions; limits
  • Gradient
  • Rate of change
  • Differentiation
  • Some rules for differentiation
  • Maxima, minima and points of inflexion
  • Differentiating the trigonometric functions
  • Exponential and logarithmic functions
  • Hyperbolic functions
  • Integration; standard integrals
  • Methods of integration
  • Integration of algebraic fractions
  • Area and definite integrals
  • The integral as a sum; areas
  • Approximate integration
  • Volumes of revolution
  • Lengths of curves
  • Taylor's and Maclaurin's series
  • Differential equations
  • Applications of differential equations

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Friday, March 2, 2012

A Slice of Pi - All the Maths You Forgot to Remember from School

Author:         Liz Strachan  
Published:   2009
Publisher:    Constable & Robinson  Ltd.
Hardcover:  176  pages
 


I am always on the lookout for tips and guidance on how to make a subject interesting while teaching it.
This compact book written by Liz Strachan, a school teacher whose experience spans 36 long years, is about how to make mathematics enjoyable to the students.
This book is a compilation of about 66 short 5-minute reads consisting of - anecdotes about famous mathematicians, her experiences from her classroom,  facts and stories behind some mathematical principles,  trivia, puzzles, tricks and short-cut calculations.

The author is able to demonstrate that mathematics can be fun and is not just a mysterious subject meant for those with high IQs.
No wonder she  was one of the four writers shortlisted  for Educational Writers Award 2010.
A right book to be presented to those who hate or  are scared of mathematics !


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Thursday, September 29, 2011

Understand Statistics

 Author:         Alan Graham 
 Published:     2010
 Publisher:     Hodder Education

I am always on the lookout for good ideas to enhance my training and consulting   approaches. Therefore I read from time to time, from a purely pedagogical perspective, introductory level books on the subjects which I am quite well versed with. The intention is to study the manner in which authors introduce the nuances of  a subject to the novices. Statistics is one such subject.
While facilitating the implementation of high CMMI maturity level practices in companies I previously worked for, I felt that the  project managers and senior level management need to have at least a basic knowledge of statistics to properly understand and use the metrics which such organizations churn out. I wish I had read this book then and recommended it to them. I must admit that even I learnt  a few new things in this book.

The book starts with a very warm and personal introduction by the author, where he sets the expectations from this book very clearly. He says " ...the focus is on understanding the key concepts and principles of the subject" and it "...does not provide a comprehensive guide to statistical techniques".

Chapter 1 introduces the subject of statistics. It describes the reasons why learning statistics is a worthwhile exercise; provides examples of everyday situations where knowledge of statistics will be helpful; what kind of statistical questions can be asked and how they are investigated.
Chapter 2 serves as an introduction or a refresher to some basic mathematical concepts which are necessary for understanding statistics.
Chapter 3 & 4, describes different types of graphs - bar chart, pie chart, histograms, scattergraphs etc. - and provides guidelines for choosing the most appropriate type of graph to represent the data.
Chapter 5 deals with the concept of central value ( i.e. mean, median, mode) and the spread (i.e. variance and standard deviation) around the central value.
Chapter 6 entitled Lies and Statistics is perhaps the most useful chapter in this book from a layperson's perspective. In real life we often come across deceptive representation of facts by means of misleading graphs, confusing percentages and inappropriate averages. This chapter tells us how to see through these deceptions and avoid making regrettable decisions based on them.
Chapter 7 introduces us to the sampling techniques viz; random and systematic and also deals with variations in samples and errors associated with sampling.
Chapter 8 tells us how to collect data samples and to check and ensure data accuracy.
Chapter 9 teaches the basics of using a spreadsheet to do data analysis.
Chapter 10 is about interpreting the data in the tables and reorganize the data to make convey the key information  more clearly.
Chapter 11 and 12 deal with concepts of Regression and Correlation respectively.
Chapter 13 and 14 is about Probability. After introducing the concept of probability, probability models like uniform, normal and binomial distributions are discussed.
Chapter 15, the last chapter tells us how to conduct test of significance in terms of z test and binomial test.
 
This book is one of the best introduction to the principles of statistics I have  ever read. Simple and easy to understand language; packed with practical examples and exercises and interesting stories revolving around statistics.

So if you want to learn statistics, start with this book !

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Wednesday, June 15, 2011

25 Big Ideas - the Science that's Changing our World

Author:         Robert Matthews
Published:   2007
Publisher:    Oneworld Publications
Paperback: 200 Pages


The 25 Big Ideas described in this book are based on the discoveries which make a point that the universe in which we live in is magical, bizarre, strange and defies common sense. These ideas have challenged many eminent scientists and mathematicians. These ideas prove that in reality science is not as objective as it is made out to be but it has its own uncertainties and subjectivity since it is a human endeavor. There is still a long way to go before we understand completely our universe.

The book consists of 25 chapters (one for each idea) categorized under the following heads as follows:
  • Ourselves - and Others: Consciousness, Small World Theory, Game Theory
  • Doing the Impossible: Artificial Intelligence, Information Theory, GM Crops
  • Life: Out of Africa, Nature versus Nurture, The Selfish Gene
  • The Earth: Catastrophism, Plate Tectonics
  • Mathematics that Counts: Bayes's Theorem, Chaos, Cellular Automata, Extreme Value Theory
  • In Sickness and in Health: Evidence-based Medicine, Epidemiology
  • The Physics of Reality: Special Relativity, Quantum Entanglement, The Standard Model, The Theory of Everything
  • The Universe- and Our Place In It: The Big Bang, Dark Energy, Parallel Universe, The Anthropic Principle

Each chapter is brief (6-8 pages) and self-contained. It begins with a very succinct summary which introduces the idea in a nutshell and explains it relevance in our day to day life. This serves as an appetizer for the the reader to proceed with the chapter. The chapter then takes us through the story of how the idea evolved, its current state of understanding. It also explains the associated technical terms  and provides suggestions for further reading.

A very well-written book which attempts to explain the abstruse ideas in a very interesting manner . But it requires the reader to have at least a high-school level knowledge of science and mathematics to fully appreciate and enjoy it.

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Wednesday, March 16, 2011

Introducing Statistics - A Graphic Guide

Authors:        Eileen Magnello & 
                      Borin Van Loon
Published:    2009
Publisher:    Icon Books Ltd.
Paperback: 176 pages
Readers in India



The history of statistics and its basic concepts have been explained completely through comic-book like illustrations and blurbs. 
The concepts explained are -  distributions, sampling, summarizing data, variation, correlation, regression, chi-squared, hypothesis testing, the analysis of variance etc.


I bought this book after a quick browse through its pages, since I felt that it would be an useful aid for my training and consulting assignments .  I could surely use some of the material for my training classes on  Statistical Analysis of  Software Metrics(With due attribution of course ! Don't want to be branded as a plagiarist (-: ! ).  


But on the whole I felt that the explanations of concepts could have been better. So it may not hold the interest of an absolute layperson. However it is  a fairly good supplement to an introductory text book on statistics as the well drawn illustrations and cartoons, several of them quite humorous,  will reinforce the concepts learnt in the classroom.


You may have sneak peek of the first 30 odd pages of this book at http://www.introducingbooks.com/book/sneak_peek/statistics

An Interesting Fact mentioned in this book:  
Florence Nightingale, known to everyone as the "Lady with the Lamp" who made nursing a respectable profession, was a passionate statistician. During Crimean War in 1850s  she discovered that due to unhygienic sanitary conditions in  military hospitals an annual mortality rate of 60 % from diseases like typhus, typhoid and cholera was greater than the Great Plague in London. She used the technique of Polar Area Graph to illustrate such data  which dramatized the extent of needless deaths during the war and was successful in persuading the medical profession that deaths were preventable if sanitation reforms were implemented in hospitals.
Have a look at the Polar Area Graph used by her at  http://en.wikipedia.org/wiki/File:Nightingale-mortality.jpg