Sunday, January 10, 2021

NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)

Dear all,

Please do watch my latest video (dated 10-01-2021) on the topic “NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)”


VIDEO LINK HERE

In case you have missed watching Part -1, please do watch it at https://youtu.be/CtKVq7VxS7s

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Amit Bajaj

Saturday, January 9, 2021

NUMBER OF TRAILING ZEROES IN A PRODUCT (Part - 1)

 Dear all,

Please do watch my latest video on the topic *“NUMBER OF TRAILING ZEROES IN A PRODUCT”*, a topic covered in *Non-Routine and Recreational Mathematics*.

Number of trailing zeroes

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https://www.youtube.com/MakingMathematicsMeaningful

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Amit Bajaj

Tuesday, December 22, 2020

Celebrating the birth anniversary and legacy of Srinivasa Ramanujan on National Mathematics Day 2020

“An equation for me has no meaning unless it expresses a thought of God.”



Today is the birthday of Srinivasa Ramanujan, the great Indian mathematician who studied number theory, mastered modular and partition functions, and designed summation formulas.

Ramanujan was born on December 22, 1887, in Erode, a city along the banks of the Cauvery River in the southern state of Tamil Nadu. He enrolled in a local high at the age of 10 but learned more about mathematics from the college students who boarded in his parents' home. According to Robert Kanigel, Ramanujan's biographer and author of The Man Who Knew Infinity, the young mathematician was deeply influenced by two borrowed books: S.L. Loney's Plane Trigonometry and George Shoobridge Carr's Synopsis of Elementary Results in Pure Mathematics. Carr's work, a list of 5000 mathematical formulas, inspired Ramanujan to develop his own proofs for these theorems. By the age of 17, Ramanujan had calculated Euler's constant to 15 decimal places and proposed a new class of numbers. Although his peers "stood in respectful awe of him", said one contemporary, "we, including his teachers, rarely understood him".

Like Albert Einstein, Srinivasa Ramanujan struggled with school and even failed his high school exams because of difficulties concentrating. In 1909, the 22-year old college dropout moved from Erode to Madras and found work as a clerk in the Accountant General's Office. Ramachandra Rao, an Indian mathematician who helped Ramanujan obtain the clerkship, encouraged the young man to publish papers and seek broader support for his work. In 1911, Ramanujan's 17-page paper about Bernoulli numbers appeared in the Journal of the Indian Mathematical Society. Two years later, the young mathematician wrote a 10-page letter with over 120 statements of theorems on infinite series, improper integrals, continued fractions, and number theory. The letter's recipient, a Cambridge mathematician named G.H. Hardy, had ignored previous communications from Ramanujan, but shared this latest letter with J.E. Littlewood, a university colleague. According to Hardy, the English mathematicians concluded that Ramanujan's results "must be true because, if they were not true, no one would have the imagination to invent them."

With Hardy's help, Ramanujan was named a research scholar at the University of Madras, a position that doubled his clerk's salary and required only the submission of quarterly reports about his work. In March 1914, Ramanujan boarded a steamship for England and, upon his arrival at Cambridge University, began a five-year collaboration with G.H. Hardy. Together, the scholars identified the properties of highly composite numbers and studied the partition function and its asymptotics. They also identified the Hardy-Ramanujan number (1729), the smallest number expressible as the sum of two positive cubes in two different ways. Individually, Ramanujan made major breakthroughs with gamma functions, modular forms,

divergent series, hypergeometric series, and mock theta functions. He also developed closed-form expressions for non-simple continued fractions (Ramanujan's continued fractions) and defined a mathematical concept known as the Ramanujan prime. "I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people," Hardy later wrote, "'Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.'"

Srinivasa Ramanujan received an honorary bachelor's degree from Cambridge University in 1916 and was later appointed a Fellow of Trinity and a Fellow of the Royal Society. Despite his professional accomplishments, Ramanujan suffered from poor health and was eventually diagnosed with tuberculosis and amoebiasis, a parasitic infection of the liver. A vegetarian, he also suffered from a severe vitamin deficiency that may have been due to the shortage of fresh fruits and vegetables in wartime England. Srinivasa Ramanujan died on April 26, 1920, at the age of 32. Today, the whole of India celebrates his birthday, December 22, to memorialize both the man and his achievements.

G. H. Hardy liked to rank mathematicians on a scale of 1 to 100, and he gave himself 25, Littlewood 30, David Hilbert 80, and Ramanujan 100, which shows just how great Ramanujan was.

Thursday, December 10, 2020

Linear Programming Problem : Class XII MATHEMATICS

Linear Programming Problem: Class XII MATHEMATICS
Online classroom teaching notes/videos/assignments etc
https://wke.lt/w/s/CtLCe6

Saturday, October 31, 2020

POLYMINOES - Non-Routine and Recreational Mathematics

 Dear all,

Please do watch my latest video (dated 31/10/2020) on the topic “POLYMINOES”, a topic covered in “Non-Routine and Recreational Mathematics”.

POLYMINOES


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Regards

Amit Bajaj

Saturday, August 15, 2020

Four Colour Theorm | Non-Routine Mathematics

 Dear all,

HAPPY INDEPENDENCE DAY TO ALL

Please do watch my latest video (dated 15/08/2020) on the topic “COLOURING PROBLEM”. You may like to use this mathematical idea in Art Integration (especially in classes VI-X).


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Regards

Amit Bajaj

Sunday, August 9, 2020

Four 4’s Game | Non-Routine Mathematics

 Dear all,

Please do watch my latest video (dated 09/08/2020) on the topic “Four 4’s Game”.

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Regards

Amit Bajaj

NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)

Dear all, Please do watch my latest video (dated 10-01-2021) on the topic “NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)” VIDEO LINK HERE...