Pick a number and try it.

You can see what is going on if you let x be your original number, and follow the steps to make a formula for the number you end up with.

Have fun !!!

Shared by Nalin Pithwa,

Ref: Calculus and Analytic Geometry by G B Thomas, 9th edition.

]]>So we often use the equations of lines (called linear equations) to study such motions.

Many important quantities are related by linear equations. Once we know that a relationship between two variables is linear, we can find it from any two pairs of corresponding values just as we find the equation of a line from the coordinates of two points.

Slope is important because it gives us a way to say how steep something is (roadbeds, roofs, stairs, banking of railway tracks). The notion of a slope also enables us to describe how rapidly things are changing. (To philosophize, everything in the observable universe is changing). For this reason, slope plays an important role in calculus.

More later,

Nalin Pithwa.

PS: Ref: Calculus and Analytic Geometry by G B Thomas and Finney; or any other book on calculus.

PS: I strongly recommend the Thomas and Finney book : You can get it from Amazon India or Flipkart:

or Flipkart:

[contact-form] ]]>Shared by Nalin Pithwa — for spreading awareness in India also about career opportunities in maths/mathematics

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Happy problem solving ! Practice makes man perfect.

Cheers,

Nalin Pithwa.

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http://www.nesinkoyleri.org/eng/

https://www.ams.org/notices/201506/rnoti-p652.pdf

https://en.wikipedia.org/wiki/Nesin_Mathematics_Village

https://interestingengineering.com/nesin-mathematics-village-learn-enjoy-math

http://mathematics-in-europe.eu/?p=1568

http://www.hurriyetdailynews.com/a-brief-introduction-to-turkeys-mathematics-village-70193

I can’t help myself noticing similarities between Prof Anand Kumar of India’s Super 30 http://www.super30.org and Prof Ali Nesin

Regards,

Nalin Pithwa

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Maths and the bomb Sir Michael Atiyah at 80

The Times

April 21 2009

When, five years ago, he shared the £480,000 Abel Prize, the equivalent of a Nobel prize in the world of mathematics, Sir Michael Atiyah might have listened to his wife’s urgings to put his feet up and settle into a comfortable life. But that would not have been his style. “Some mathematicians retire,” he concedes with a smile. “I don’t think I have.”

This week, Sir Michael’s 80th birthday and a life dedicated to science and political activism is celebrated in a series of events. A three-day conference celebrating his contribution to geometry and physics, at the University of Edinburgh Informatics Forum, ends today, his birthday. Tomorrow and on Friday his Sir Michael’s role in promoting disarmament is recognised with readings and lectures dedicated to exposing the folly of nuclear weapons.

Much has been achieved at an age when contemporaries might have settled for a quiet life. In 1995, as president of the Royal Society and aged 67, Sir Michael made a stinging attack on Britain’s nuclear weapons policy.

Subsequently he accepted the presidency of the influential Pugwash disarmament conferences, which unite scientists in opposition to the arms race.

**He still believes passionately in the cause, which, he says, is more important to the world than maths, “because if we blow ourselves up, there will be no mathematics anyway”. **

Sir Michael discovered his aptitude for mathematics during his boyhood in the Sudan. His Lebanese father was an Oxford graduate and a civil servant, his mother was Scottish and he grew up regarding himself as British, studying at Manchester Grammar School and Cambridge University.

The key professional encounters in his life came in the United States in the 1950s, when he joined the Institute for Advanced Study, at Princeton University, a gathering place for the world’s most brilliant mathematical minds. Here he forged relationships which have endured, and much of his greatest work has come from what he calls the “dialogues of ideas” established there.

His greatest achievement has been the Atiyah-Singer theorem, which secured his fame and prize money, shared with his collaborator, Isadore Singer, of the US. At the time, he said he couldn’t think what to do with his share; the sporty red Lexus parked outside the Informatics building suggests he has since given it more thought.

In simple terms, the theorem provided a kind of analytical bridge which could be shifted between disciplines. “The theorem technique enables you to get to an answer by-passing all the intervening calculations,” he says. The idea “was something where you could calculate numbers of solutions by very indirect methods which applied in a very wide range of situations: geometry, algebra, physics…”

**Maths, he says, is something he plays out in his mind as he walks around his flat and his garden, and he jots things down – “the dull stuff” – only when he has to check something. **

**“Walking helps the physiological process. You have to maintain a very high pitch of concentration when you do mathematics. It’s illumination – shining the mind’s eye on a problem and really seeing through it. **

**“The old clichés about the beauty of maths are true. It has beauty within it, but not all parts are equally beautiful. Beauty in mathematics is the thing that helps you in the search for truth.” **

Some people, he believes, are born with mathematical brains, although they might choose other careers. One former student won the Nobel Prize for Economics, another is the best-paid hedge fund manager in the US. So was Sir Michael never tempted to use his mathematical skill in a wider world? Could he have solved the global financial crisis?

“Economics is a combination of gambling, psychology and who knows what,” he says. “The current crisis? I think people made a bloody mess. You can foretell that the bubble will burst – the question is when. If you gambled on it you might win or lose a lot of money. I just didn’t gamble.”

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Regards,

Nalin Pithwa.

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The above references are a must. Best time to start is from standard VII or standard VIII.

-Nalin Pithwa.

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