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Happy Birthday to Srinivasa Ramanujan, the great Indian mathematician


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 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 33. Today, his home state of Tamil Nadu 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.

Ignited Minds of Mathematics (IMM) CONCLAVE 2018


Ignited Minds of Mathematics (IMM), a voluntary group of Mathematics teachers , has organized its second conclave, supported by International Council for school leadership (ICSL), in Modern School Barakhamba Road, New Delhi. The theme of the conclave was “ From rote learning to thinking Mathematically”. Chief guest of the conclave was Dr. Vijay Datta, Principal Modern School Barakhamba Road. It was attended by about 140 Mathematics associates who have come on their own to be the part of this conclave. There were presentations and panel discussions by eminent Mathematicians, Principals and Mathematics enthusiasts.

The group has launched a platform” Ignited Minds Foundation Olympiads” to boost the thinking process and to search and support the talented and deserving students by organizing Olympiads across the country and contributing the right kind of questions which are apt for the the cause “ thinking mathematically”.


Dr. Sanjeev Verma and Mr. Amit Bajaj,  members of the core group has reiterated the  need of organizing such conclaves in other parts of India to spread the message and to improve the way Mathematics has been taught and learned.

All Photos at https://www.facebook.com/amitbajajcrpf/media_set?set=a.10161007489070367&type=3

XII CLASS CBSE MATHEMATICS: CH 13 PROBABILITY MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

  

XII CLASS CBSE MATHEMATICS CH 11 THREE DIMENSIONAL GEOMETRY MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

   

XII CLASS CBSE MATHEMATICS: CH 10 VECTOR ALGEBRA MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

  

XII CLASS CBSE MATHEMATICS: CH 9 DIFFERENTIAL EQUATIONS MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

   

XII CLASS CBSE MATHEMATICS: CH 8 AREA UNDER CURVE MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

  

XII CLASS CBSE MATHEMATICS: CH 7 DEFINITE INTEGRAL MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

  

XII CLASS CBSE MATHEMATICS: CH 7 INTEGRAL CALCULUS MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

XII CLASS CBSE MATHEMATICS: CH 6 APPLICATIONS OF DERIVATIVES MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

XII CLASS CBSE MATHEMATICS: CH 5 DIFFERENTIATION MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

  

XII CLASS CBSE MATHEMATICS: CH 4 DETERMINANTS MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)


XII CLASS CBSE MATHEMATICS: CH 3 MATRICES MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

   

XII CLASS CBSE MATHEMATICS : CH 2 INVERSE TRIGONOMETRY MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)

   

XII CLASS CBSE MATHEMATICS Ch 1 RELATIONS AND FUNCTIONS MULTIPLE CHOICE QUESTIONS (WITH ANSWERS)


HAPPY PI DAY


Dear All,
Pi Day is held to celebrate the mathematical constant π (pi). Pi Day is observed on March 14 (3/14) ,due to π being approximmately equal to 3.14.
Pi Minute is also sometimes celebrated on March 14 at 1:59 p.m. If π is truncated to seven decimal places, it becomes 3.1415926, making March 14 at 1:59:26 p.m., Pi Second (or sometimes March 14, 1592 at 6:53:58 a.m.).
The Pi Day celebration includes public marching, consuming fruit pies and playing pi games... The founder of Pi Day was Larry Shaw, a now retired physicist at the Exploratorium who still helps out with the celebrations.
Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits.

HAPPY PI DAY :)

Excellent Maths Video by Sarvjeet Arora


Dear all,
Please watch free online videos for classes XI and XII mathematics including questions of NCERT, REFERENCE BOOKS, HOTS, VALUE BASED and TEN YEARS BOARD QUESTIONS by my friend SARVJEET ARORA.
https://www.youtube.com/channel/UC3ohUuLBae-gt_lmn8jGqPQ

Largest Prime Number M77232917 discovered on January 4 , 2018

Largest Prime Number M77232917 discovered on January 4 , 2018

A FedEx employee Jonathan Pace ,an engineer by profession has discovered the largest prime Number. According to GIMPS’s (Great Internet Mersenne Prime Search) website, the newly discovered prime number is calculated by raising 2 to the 77,232,917th power and subtracting 1.

M77232917 itself is reportedly 23 million digits long. According to New Scientist, it is one million digits longer than its predecessor, which clocked in at 22 million digits.

The greatest prime number discovered before M77232917 was found in 2015, and was 5 million digits longer than the one that came before it in 2013. 

Although Euclid proved that if 2^P-1 is prime, then 2^P-1*(2^P-1) is a perfect number in 350 BC, the French monk Marin Mersenne was honored with the name for his conjecture of which prime numbers could be used for P to produce larger primes. Although written in the early 17th Century, the conjecture took 300 years to prove. Meanwhile, Euler also got in on the act, proving that all even perfect numbers are formed this way.

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form of 2^p − 1 for some integer p.