The Joy of Numbers

on April 30, 2006 with 0 comments » |

This blog post was started on reading the books, Imagining Numbers by Barry Mazur and The Joy of Pi by David Blatner. I hope to add to it by including books, interesting snippets, and sometimes my own comments as I read and research the joy of numbers and mathematics in this thread.


Etymology of Algebra: Via Italian, Spanish or mediaeval Latin, from Arabic 'al-jabr' or the ‘reunion, resetting of broken parts’, used in the title of al-Khwarizmi’s influential work, ‘ilm al-jabr wa’l-muqābala, or 'the science of restoration and equating like with like’.

Pre-Modern Algebra (pdf)

Bertrand Russell's Definition of a Number


Some books shortlisted to read
Number by Tobias Dantzig
The Constants of Nature : From Alpha to Omega--the Numbers That Encode the Deepest Secrets of the Universe by John Barrow

A related book is Just Six Numbers: The Deep Forces That Shape the Universe by Martin J. Rees, which discusses the recurring six numbers that come up in explaining the universe around us – which are:

  • nu (a ratio of the strength of electrical forces that hold atoms together compared to the force of gravity which is 10 to the 37th power)
  • epsilon (how firmly the atomic nuclei bind together which is 0.004)
  • omega (amount of material in the universe)
  • lambda (force of cosmic "antigravity" discovered in 1998, which is a very small number)
  • Q (ratio of two fundamental energies, which is 1/100,000)
  • delta (number of spatial dimensions in our universe)

Other related books of interest on numbers:

1. A History of Pi by Petr Beckmann

2. Pi: A Biography of the World's Most Mysterious Number by Alfred Posamentier & Ingmar Lehmann

3. Squaring the Circle by Tom Stoppard

4. The Golden Ratio : The Story of PHI, the World's Most Astonishing Number by Mario Livio

5. Zero: The Biography of a Dangerous Idea by Charles Seife

6. To Infinity and Beyond by Eli Maor

7. The Infinite Book by John D. Barrow

8. An Imaginary Tale Hardcover by Paul J. Nahin

9. Fortune's Formula by William Poundstone

10. e by Eli Maor

11. The Heart of Mathematics : An invitation to effective thinking by Edward Burger

12. Coincidences, Chaos, and All That Math Jazz by Edward B. Burger & Michael Starbird

13. Beyond Coincidence : Amazing Stories of Coincidence and the Mystery and Mathematics Behind Them by Martin Plimmer

14. Trigonometric Delights by Eli Maor

15. Gamma : Exploring Euler's Constant by Julian Havil

16. Prime Obsession : Berhhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire

17. The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh (On the subject, for a mathematical treatise, read: Riemann's Zeta Function by Harold M. Edwards)

18. The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry by Mario Livio

19. Fermat's Enigma : The Epic Quest to Solve the World's Greatest Mathematical Problem by Simon Singh

20. The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time by Keith J. Devlin

21. The Equation That Couldn't Be Solved by Mario Livio

22. The Mathematical Universe : An Alphabetical Journey Through the Great Proofs, Problems, and Personalities by William Dunham

23. God Created the Integers: The Mathematical Breakthroughs That Changed History by Stephen W. Hawking

24. The Triumph of Numbers: How Counting Shaped Modern Life by I. B. Cohen

25. Wonders of Numbers: Adventures in Math, Mind, and Meaning by Clifford A. Pickover

26. Meta Math! : The Quest for Omega by Gregory Chaitin, renowned for finding another proof of Kurt Godel's incompleteness theorem and another for Alan Turing's "halting problem" in computation and discoverer of the Omega number, which is an exquisitely complex representation of unknowability in mathematics.

Also see my compilation of links on Mathematics.

Famous Indian Mathematicians.. - not talking about ancient Indian math stalwarts from centuries ago like Brahamagupta, Bhaskara or Aryabhatta nor THE famous Indian math wizard of the last couple centuries - Srinivasa Ramanujan ..

But want to bring to your attention two mathematicians making the headlines/news in the last 5-6 years..

1. Chandrakant Khare - Read my blog post about 'Chandrakant Khare and Fermat's Last Theorem' for further details..

2. Also another mathematician making the news recently.. - Divakar Viswanath of Univ. of Michigan-Ann Arbor (PhD at Cornell). In 1999, he wrote a paper about "Divakar's constant" which is the 'limit of the ratio of consecutive random fibonacci numbers'. Lot of discussion around this since with some people calling this new constant almost as important as the "golden ratio" (I need to find a reference/citation for this bold statement - for someone calling the constant as important as the much vaunted golden ratio - it was quoted to me by a friend).

I had seen Simon Singh on Book-TV some years back talk about this book, Fermat's Enigma regarding the quest to solve Fermat’s Last Theorem (FMT) but though its been at the back of my mind, I never read up more about it till yesterday when I found a great website, Larry Freeman‘s blog on the subject.

The blog is a great site for amateur readers like me to read about ‘the story behind FMT and Wiles' proof in a way accessible to the mathematical amateur.’ You can also read about the intrigue and excitement that caught even the fancy of the media when
Andrew Wiles, with the help of Richard Taylor, proposed that he had a solution to FMT in 1995. (If you insist on reading it, here are the papers, all 129 pages of it – most mathematicians also do not follow it – so, do not say you were not forewarned!)

In 2006, another mathematician, Chandrashekhar Khare (previously at TIFR and now Associate Prof at University of Utah), has provided a very significant result (here is the paper) that builds on the work done by Wiles.

The Slashtdot entry on this says:"An Indian mathematician, Chandrashekhar Khare, is poised to make a significant breakthrough in the field of number theory with his solution of part of a major outstanding problem in algebraic number theory. He is currently an associate professor in Mathematics Department of University of Utah. "

Actually, Khare does not provide another proof of the FMT but proved what is known to experts as the ‘level-one Serre conjecture’. This conjecture was posed in 1972 by the Fields medallist Jean-Pierre Serre, and belongs to the field of Arithmetic Algebraic Geometry.


Chandrashekhar Khare, a mathematician from the University of Utah, has announced that he has Serre's conjecture is in a sense a parent of Fermat's last theorem: mathematicians have known for some time that if the first is true then so is the second. In fact, it is a certain part of the conjecture which implies Fermat's last theorem, and this part was proved by Khare and his collaborator J.P. Wintenberger, and independently by the mathematician Dieulefait.

Fermat's last theorem as well as the conjecture by Serre, are ingredients of a wider program to unify various areas of mathematics, known as Langlands philosophy, (conceived by the mathematician Robert Langland in the 1960's and consists of a set of conjectures concerning the intimate relationship between number theory, geometry and algebra). The idea behind such unifying theories is that it should be possible to directly translate every concept in a given area of maths into all the other areas of maths……and the relationship between the objects should be the same in both areas.

See more on other recent work on Serre’s conjectures

Recommended Books from Larry Freeman‘s blog: Fermat Last Theorem

Recommended Reading from Larry Freeman‘s blog: Fermat Last Theorem

Other references gleaned from other resources on the web – in addition to those already hyperlinked in the text above:

Read about Serre's work in the Plus article En-Abeled.

Sidenote: I debated titling this only as 'Fermat's Last Theorem' but I think FMT has got lots of media coverage over the years (including a PBS dedicated episode on Nova called The Proof, which dealt with the investigation of the theorem and its solution by Wiles) while Khare, being an Indian and having worked mainly in India until recently has not (outside of mathematicians involved in number, as an Indian, I put him right up there on the title along with Fermat ;)

Godel - 100th birthday today

on April 28, 2006 with 0 comments » |

Centenary today - Kurt Gödel, arguably the leading mathematician/philosophers/logician of the 20th century was born April 28, 1906, in Brünn (now Brno), Moravia, Austria-Hungary (now the Czech Republic).

From my Mathematics thread:
Kurt Gödel (1906-1978) was a mathematician and philosopher of mathematics, most famous for his incompleteness theorems (read an explanation of the theorems here) and is considered to be one of the three greatest logicians of all time along with Aristotle and Gottlob Frege. Godel's theorems have been used to extrapolate a great many "truths" about the world. Torkel Franzen sets the record straight in his new book Godel's Theorem: An Incomplete Guide to Its Use and Abuse. (Read the introduction, pdf).

Godel also shared a unique friendship with Einstein at Princeton (see my blogpost on Astronomy - Time, Relativity, Black Holes, and the Universe). He spent his last years suffering from paranoic delusions, which essentially led him to starve himself to death. Also read
Palle Yourgrau's books: The Disappearance of Time : Kurt Gödel and the Idealistic Tradition in Philosophy, A World Without Time: The Forgotten Legacy Of Godel And Einstein and Godel Meets Einstein

A recent book by Rebecca Goldstein , Incompleteness - The Proof and Paradox of Kurt Godel last year 'reinterprets the evidence and restores to Gödel's famous idea the meaning he claimed he intended: that there is a mathematical truth--an objective certainty--underlying everything and existing independently of human thought.' Godel was in the news 25 years ago also because of a book - the 1979 Pulitzer-Prize winning book Godel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter. An earlier book in 1958 - Godel's Proof by James Newman and Ernest Nagel - presented the main results of Gödel's incompleteness theorem and the mathematical work and philosophies leading up to its discovery in a more accessible manner. This book inspired Hofstadter to take up the study of mathematical logic, write the book Gödel, Escher, Bach, and prepare a second edition of Gödel's Proof, published in 2002.

Also see:
Collected Works : Volume I: Publications 1929-1936
Collected Works : Volume II: Publications 1938-1974
Collected Works : Volume III: Unpublished essays and lectures
Collected Works : Volume V: Correspondence, H-Z (Godel, Kurt//Collected Works)
Reflections on Kurt Gödel by Hao Wang
Logical Dilemmas: The Life and Work of Kurt Godel by John W. Dawson Jr

Can't believe this is for real..!!!! 'Pataka Cool'...'Hasmukh'...sound like good summer drinks or something!.

After kids and the young Indian male, it is now the turn of urban Indian women to be 'studied' and segmented

The findings give five distinct segments with more details about the demographic, lifestyle, psychographics and brand skew of these segments. Lowe India has labelled these as Mrs. 'Hasmukh' Popular (27 per cent), Mrs. 'Meri Awaaz Suno' Attention Seeker (31 per cent), Mrs. 'Gharelu' Homepride (18 per cent), Mrs. 'Pataka' Cool (12 per cent) and Mrs. 'Hey Bhagwan' Moaner (12 per cent).

Apparently, there was a survey late last year that rated India as the second-sexiest nation (beating Brazil by 0.2%).

Well... like one of the comments at this post says.. Our capacity to delude ourselves is unlimited.

In today’s world of fragmented families, war-torn countries, and individual discontent, I would argue that perhaps the need for a faith-based society can only be understated. This is a particularly big step for a cynical agnostic like me. However, I restate my position about the need for faith in our lives while taking the complementary position that religion and spirituality need not be about dogma. Faith, as an internalized emotion that provides an individual with the tool set for dealing with the challenges in life, can be empowering, rewarding, and a source of inspiration to some. However, faith, manifested as an external set of rules and regulations imposed on a populace becomes a matter of great friction and fosters the kind of hatred that can only lead to timeless wars and unending grief. The solution becomes the problem and what is left behind is a set of dogmas ingrained into the minds of the 'faithful'. Religion too often becomes captive to the divisive forces of fundamentalism. Instead, it should foster the kind of tolerance that is innate in the basic tenets of most religions. Prejudice and intolerance foster a narrow-minded focus that shy away from these religious tenets and beget a divisive mentality – doing more to separate people rather than to unite them.

Like Deepak Chopra, whose fan I am not,
writes eloquently in a post on Arriana Huffington's blog:

Heresy is a pointless label in a free society. Spiritual freedom should be seen for what it is, a natural evolution, a step toward becoming more human. This step can occur without God. There's a famous saying in Buddhism: If you ever meet the Buddha on the path, kill him. What this means is that a literal person who stands for Buddha cannot actually be Buddha. Buddha is wakefulness, the state of a fully developed soul. It is not a statue, a person, or a set of dogmatic beliefs… Mainstream religion has been left with resounding moral teachings but little power elsewhere.

Chopra goes on to write about the inner revolution that is needed in religion. And it is not Imams or Bishops and Cardinals or Priests or even lawmakers who will bring about this revolution. While the church, the temple, and the mosque may remain the central disseminators of religious teachings, the implementation of these religious tenets in our day-to-day life cannot be dictated or guided based on the words of these religious leaders and politicians. Too often mankind has been led on misguided crusades (no pun intended) in the name of religion – the fervor of this vicious agenda matched only by the brutal rapaciousness of its bloody aftermath.

Deepak Chopra's series of posts on the subject are also cross-posted at the IntentBlog.
March 17, 2006 -
Does God Have a Future? (Part 3)
March 13, 2006 -
Does God Have a Future (Part 2)
March 10, 2006 -
Does God Have a Future?

For another interesting perspective on the subject read What I Believe by E. M. Forster from his book of essays, Two Cheers for Democracy. Without realizing it, I guess some of my own outlook in life reflect what is well known in philosophical circles as 'Secular Humanism'.

From the wiki article on the subject:

Secular humanism is a humanist philosophy that upholds reason, ethics, and justice and specifically rejects rituals and ceremonies as a means to affirm their life stance. Another synonym is scientific humanism, which the biologist Edward O. Wilson termed "the only worldview compatible with science's growing knowledge of the real world and the laws of nature". Secular humanism advocates secularism but is a broader concept. Secularism has a number of usages but generally emphasize limits on the role of religious or supernatural considerations in the affairs of society or government. Secular humanism adds to these positions a comprehensive perspective on life, including affirmation of human dignity and the importance of ethics.

Incidentally, though I have seen the movie, Passage to India, based on Forster's book, (don't think I have seen the movies, Howards End and A Room with a View based on books by Forster), I had no idea what relation he had to India which made him write a book based in India. The wiki article on him mentions:

He travelled in Egypt, Germany, and India with the classicist Goldsworthy Lowes Dickinson in 1914. He spent a second spell in India in the early 1920s as the private secretary to the Maharajah of Dewas. The Hill of Devi is his non-fictional account of this trip. After returning from India he completed A Passage to India (1924) which became his most famous, most widely-translated, and last novel. Forster wrote little more fiction apart from short stories intended only for himself and a small circle of friends. Some critical debate has concerned the question of why he gave up writing novels.

Everyone's read doomsday forecasts about how the aging population in Europe is going to doom them ....but a sign of the times to come for Europe as Italy votes to possibly elect a 87 year old as Senate Leader?!!! My granddad is 89 and I cannot imagine anyone 85+ being a leader of anything!! These guys are in trouble...

'Italy is a phallic gerontocratic society' ....

'What future for youth in a country where a man of 87 is being proposed as the next leader of the Senate, an 85-year-old may be re-elected president, and the prime minister-elect is one of the few major world leaders born before the outbreak of World War II? Fueling the debate are statistics released this week showing that the elderly form an increasingly large slice of the population: Nearly 20 percent of Italians are over 65, with that figure projected to rise to 34 percent by 2050. Still more strikingly, nearly two-fifths of the population is older than 50.'

Book by Kaavya Viswanathan faces plagiarism controversy - contains similarities to other works - apparently 29 to 40 passages of her book were straight straight from books by author Megan Mcafferty, who Kaavya admits to have read voraciously as a teenager and been influenced by.

Update: The book has been withdrawn from bookstores by its publisher. Mcafferty has said she is not pressing any charges and just wants to forget this whole episode and move on.)

Can't help but opine here...
(damn.. sound like Bill OReilly...he really loves the word, opine..doesn't he use it at the end of his show every time when he asks for viewers..his faithful 'opine'? I havent seen his show in ages..but when I had seen it, he said that word almost every the end..)... since this one particularly bothers me maybe because she is Indian..maybe because she writes chic-lit, which I deem inane (see rant below), or maybe because there was a hint of jealousy in reading that even a 17-year old could get a book contract - although to be fair I have also been riled up by other cases of plagiarists - Indian as well as Non-Indian. Cheating, by any other name, is cheating and its NOT COOL in my book (pun unintended.)

Surely Kaavya will recieve a lot of flak in the next few days and months for what she has called a
"unintentional and unconscious" infringement (implausible, I say! Influenced in style is one thing - copying entire paragraphs is not unconscious!! See these examples - Unpardonable, IMO) from many online like us who do not even know her nor will ever read her books to others in the publishing world as well as people she knows! She was on a high with some big contracts, making newspaper articles locally and maybe internationally...and probably enjoying the positive attention. How she handles the negative press and criticism is unknown but given that in todays world, in the US but more and more in India too maybe, notoreity is not a bad thing , she just might be ok - if, as a 17 year old, she can handle the pressure of this "infamy" and learn how to use it to her advantage. No big $$ contracts or fame like a vikram seth or vikram chandra maybe but she'll continue to write pulp novels like she does.. and nothing dishonorable in doing that - IF SHE LEARNS NOT TO PLAGIARISE/GET INSPIRED/WHATEVER U WANT TO CALL IT....

Without reading her book, one last comment on the general genre of writing - I had no idea when I had initially
blogged about her on my Indian Subcontinent Literature thread that she was a chic-lit writer -
to each their own..what can i do if people want to read nonsense like a book titled ' How Opal Mehta Got Kissed, Got Wild and Got a Life ' - what kind of a book title is that?!! uugggh... Is it a play on 'How Stella got her groove back', a book whose popularity with women has really ended up in more and more of this chicklit garbage ending up on bookstore shelves. Can understand it though - women are a big target market-group and maybe there was a unmet need for a Mills-n-boons for the cynical relationship-jaded women of our generation? (I am posing these as questions as I have not read them and so do not know if my bias against them is justified)... if people want to read such garbage on how someone got their groove back, or kissed, or cuddled or got wild and got married instead of reading great authors of the day like Ishiguro, Mcewan, or even a Vikram Seth - let alone going back to classics from the past like Turgenev or Balzac or Proust or...heck, even a Chaucer or a Shakespeare...then so be it! I myself have no time for such much to read little time... too many distractions..too many books...too many interests....

enuf said..

Others have also opined ;) and she's been already added to the blacklist on the Plagiarism entry at wiki.

Plagiarism and punishment - We should find a way to treat Kaavya Viswanathan and William H Swanson as we do our errant students.

29 to 40 passages of her book were lifted straight from author Megan Mcafferty’s books.

Falstaff 1 and 1, Sepia Mutiny 1 and 2 - links I found via Amit Varma's post at India Uncut who writes about an interesting aspect of this unseemly affair - something I had not read about before...
But this isn't all that is unpalatable in this episode. Apparently a 'book-packager' called Alloy Entertainment helped put this book together, as also many others in its genre. The more I read about them, the more the lines blur between the author and her 'consultants,' whose role seems similar, as Manish Vij speculates here, to the music industry guys who manufacture boy bands.
Another unrelated article in the NY Times on the competitiveness for college admissions has another interesting tidbit about an interesting consulting outfit she used in getting into Harvard as an example of students going to extremes and possibly even cheating to get a leg up. She is called the 'Barry Bonds' of today's college crowd....

Kaavya Viswanathan.., a
Harvard sophomore won admission to the university partly through the ministrations of a consulting outfit named IvyWise, which charges $10,000 to $30,000 for its services. Then she wrote a roman à clef about the process, How Opal Mehta Got Kissed, Got Wild and Got a Life. Now, Miss Viswanathan has been accused of plagiarism, and, in an interview with The New York Times, has acknowledged an "unintentional and unconscious" pattern of appropriation from two other books. Of course, Barry Bonds has insisted that all he ever knowingly took were nutritional supplements.

UPDATE- May 2, 2006
She really thought she would get away with it....aaj ke duniya mein!!??

Sepia Mutiny, a blog I sometimes read (the guy who had the great pictures from Bandra recently), is mentioned in this Outlook article.

What is significant is that almost all the new "revelations" seem to have been the results of close readers posting their comments on various blogs and sharing their findings with each others or mainstream media.
The similarities in passages with Rushdie's Haroun and the Sea of Stories (HATSOS) were brought out on the weblog where it was pointed out how the passage in Rushdie's book where his hero, Haroun, enters a bus depot and passes by several admonitions written on the walls surrounding the depot's courtyard found its echoes in Viswanathan's book where her protagonist, Opal Mehta, helps another student place posters on a wall that discourage drug and alcohol use.

On page 35 of Rushdie's HATSOS, one of the warnings reads: "If from speed you get your thrill / take precaution ”make your will."
On page 118 of Viswanathan's HOMGKGWAGAL, one of the posters reads: "If from drink you get your thrill, take precaution ”write your will."
On page 31 of Rushdie's HATSOS, another warning reads: "All the dangerous overtakers / end up safe as undertaker".
On page 119 of Viswanathan's HOMGKGWAGAL, another poster reads: "All the dangerous drug abusers end up safe as total losers."

And so on forth...!!

Guilty Kaavya hopefully survives: Rushdie Financial Express, India
Rushdie enters row over young author's 'plagiarism' Scotsman
Salman Rushdie: 'Kaavya a victim of her own ambition' Hindustan Times
Salman has no sympathy for Kaavya CNN-IBN

Chernobyl - 20 years later

on April 27, 2006 with 0 comments »

Listen to BBC's Chernobyl: the lessons learned - What is the truth behind the Chernobyl? And why, on the 20th anniversary of the disaster, is the nuclear industry seeing an upturn in its fortunes?

News articles on the 20th anniversary:
20 years on: the horrors of Chernobyl still linger
Measuring Chernobyl's Fallout
Farms still affected by Chernobyl
UK farmers face Chernobyl horror - 20 years on
Chernobyl's Tiniest Victims
Chernobyl: the final word is yet to be said
Lukashenko equates material losses from Chernobyl, World War II
Normalcy coming back to Chernobyl-hit Belarus areas 20 years on
Survivors struggle with sickening legacy

Chernobyl: wet rugs and a run on vodka - oped piece a IHT, where the writer, Schmemann, writes: 'The greatest catastrophes take on a personality, a name: Bhopal, Oklahoma City, Sept. 11, the tsunami. These names and others have entered the language as symbols of apocalyptic tragedies. Each disaster has its own unique attributes. Chernobyl, for me, stands for a fear that many have described in recent days, a fear of an evil that cannot be seen or fathomed. I was a reporter in Moscow at the time and lived through the anxiety and questions that gripped us all in the hours, days, weeks and even months after we got the first word of the disaster - one paragraph from Tass that still ranks as one of the great understatements of all time: "An accident has occurred at the Chernobyl nuclear power plant as one of the reactors was damaged." That's all. Unlike most of the natural or manmade threats we confront, this one had no face, no presence, no visible menace. There was no black thundercloud firing bolts of lightning, no powerful wind bending trees to the ground, no huge building disappearing into a vast cloud of dust. There was only the knowledge that a great, invisible, mysterious killer had been loosed on the world.' .....

And finally, President Gorbachev marks 20th Anniversary of Chernobyl
Meanwhile, a Russian newspaper has published transcripts of a politburo meeting during which the Soviet leader Mikhail Gorbachev suggested covering up the real circumstances of the accident.

Chernobyl Here and Now: Global Engagement, Local Encounter To listen to speakers and find out more about this important conference which took place in Madison Wisconsin in March 2006. Two other conferences recently concluded in countries affected the most by the disaster include:

International Conference “20 Years after Chernobyl: Strategy for Recovery and Sustainable Development of the Affected Regions” (19-21 April 2006, Belarus)

International Conference “Twenty Years after Chernobyl Accident. Future Outlook” (24-26 April 2006, Ukraine)

Other Online Resources and Information:
Greenpeace report says Chernobyl death toll has been

The United Nations and Chernobyl

The Lesson Of Chernobyl

Chernobyl Disaster - Information about the Chernobyl accident. Includes causes, sequence of events, health consequences, and social, economic, political and environmental consequences

The Report on Chernobyl An independent scientific evaluation of the health and environmental effects of the Chernobyl nuclear disaster with critical analyses of recent reports by the International Atomic Energy Agency (IAEA) and the World Health Organisation (WHO)

Chernobyl Pictures Collection of photos of the Chernobyl area including walkdown comments, accident information and radioactivity data measurements. Also see Ghost Town chronicling Elena's motor cycling through the Chernobyl "dead zone". Provides her pictures, maps and stories.

Chernobyl Page


Chernobyl: A Nuclear Disaster

360 Degrees Leader

on April 24, 2006 with 0 comments » |

Reading The 360 Degree Leader - Developing Your Influence from Anywhere in the Organization by John C. Maxwell

Probaby be good to simultaneously go through The 360 Degree Leader Workbook

Other related books by John Maxwell:

Other good books to read:
Revolutionary Wealth by Alvin Toffler, Heidi Toffler
Creating the Good Life :Applying Aristotle's Wisdom to Find Meaning and Happiness by James O'Toole
The Highest Goal: The Secret That Sustains You in Every Moment by Michael Ray, Jim Collins
Change Your Questions, Change Your Life: 7 Powerful Tools for Life and Work by Marilee G. Adams, Berrett-Koehler

Estranged partners Leander Paes and Mahesh Bhupathi had contrasting fortunes in the ATP doubles rankings released on Monday, and while the former dropped down two places to 10th spot, the latter climbed up six rungs to 23rd on the leaderboard. In the ATP doubles race, Leander and his Czech partner Martin Damm are at sixth position with the Bryan brothers — Bob and Mike — from the US up at the mound. Bhupathi and Radek Stepanek, also from Czech Republic, who lost in the semifinals at Monte Carlo Masters on Saturday, are way down at 26th position.
In the singles rankings, Prakash Amritraj slipped 12 places to 248th position allowing, in the process, Rohan Bopanna to become the highest-ranked Indian on the leaderboard. Big-serving Bopanna gained a place to sit at 243rd position. Meanwhile, Karan Rastogi gained 47 places to 385th while Harsh Mankad slipped 56 spots to 341st position.
Some good performances by the Indian women in the Federation Cup where they blanked both Phillipines and Chinese Taipei 2-0 (the inconsequential doubles match was not played in both series) and then beat New Zealand 2-1 to meet Australia in the finals. However, Australia defeated India 2-1 to advance to the Fed Cup World Group play-offs while India was left rueing more bad news for Sania Mirza comes out of this tournament nursing elbow and wrist injuries, which her doctor claims are 'not serious'.
Sania is now seeded 40 and can be expected to go lower if injuries keep her out for long. 'Among other Indians, US-based Shikha Uberoi maintained her 183rd spot while Ankita Bhambhri gained two places to 336th position, according to information received here. Meanwhile, veteran Rushmi Chakravarthi suffered a free fall in the rankings dropping a whopping 92 rungs down the ladder to 459th spot. Isha Lakhani (368) and Sanaa Bhambri (462), both climbing down four spots, were other Indians in the top 500.'
Meanwhile: Belgium to meet US in Fed Cup semis after Belgium beat Russia, following victories by Justine Henin-Hardenne (6-2, 6-0 win against Elena Dementieva) and Kim Clijsters (61, 6-4 win over Maria Kirilenko.) Russia, who had been aiming to win the Fed Cup for the third year in succession, had lost to Belgium in the 2001 final too, following which the Russians won 3 in a row.
Spanish teenage tennis star, Rafael Nadal, retained his Monte Carlo Masters title with a 6-2 6-7 (2) 6-3 7-6 (5) victory over Roger Federer, his fourth win over the world number one in five meetings. It was also his 42nd successive win on clay and he is now third on the all-time list behind Guillermo Vilas (53) and Bjorn Borg (46) for consecutive match wins on clay. Sunday's success marked only the second defeat for world number one Federer this season - both at the hands of Nadal who also beat Federer in last month's Dubai Open final. Federer now has a 33-2 win-loss record in 2006. The reigning Roland Garros champion, the world number two, and winner of eight clay crowns in 2005, beat Federer for the second time on clay after ousting him in the French Open semi-final last year.