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Indian-origin mathematician Manjul Bhargava wins Fields Medal

Dear Reader,

Manjul Bhargava, a Canadian mathematician of Indian origin, has been awarded the prestigious 2014 Fields Medal at the International Mathematical Union’s (IMU) International Congress of Mathematicians held in Seoul. Bhargava, 40, is the first person of Indian origin to receive the prestigious medal, which has been awarded since 1936 and recognizes outstanding mathematical achievement for existing work and the “promise of future achievement”. Known to colleagues as a gifted mathematician who would devise new and simple methods to prove centuries-old theorems in number theory, Bhargava’s work has been described by IMU as based both on a deep understanding of the representations of arithmetic groups and a unique blend of algebraic and analytic expertise. Bhargava was awarded the medal “for developing powerful new methods in geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves”, IMU said. One of Bhargava’s most prominent discoveries was a thesis that threw a new light on Gauss’s Law for the composition of two binary quadratic forms. When Bhargava was a graduate student, he read Disquisitiones Arithmeticae, where Gauss developed his composition law which gives a method for composing two binary quadratic forms to obtain a third one. According to IMU’s description of his work, Bhargava one day came up with the idea that if he cut off the Rubik’s mini-cube into half and labelled each corner of the cube with two sets of numbers, that would lead to a cubic analogue of the Gauss Composition. After being cut, a Rubic’s mini-cube could generate three quadratic forms. From the three ways of slicing the cube, three binary forms emerged, and so Bhargava had discovered a simple way to prove the law. “It’s all about contributing to the understanding of ourselves and the world around us. One of the keys to understanding mathematical problems that people have been thinking about for years is to think about them in a totally different way,” said Bhargava in an interview with Simons Foundation and IMU. He went on to discover 12 other analogues of Gauss compositions over the years. He received his Ph.D in 2001 from Princeton University for a thesis that has been described as “stunning” and a “breakthrough”. It generalized the classical Gauss composition law for quadratic forms to many other situations, according to the Tata Institute of Fundamental Research. By 2003, Bhargava had become a professor at Princeton . Born in 1974 in Canada, Manjul Bhargava grew up in the US and often visited Jaipur to stay with his grandparents. His grandfather was a professor in Sanskrit from whom Bhargava learnt Sanskrit poetry, while his mother was a mathematics professor who allowed Bhargava to attend her college-level classes as a child, according to interviews. “He is an extremely original mathematician, who has developed a style which is distinctly his own,” said Benedict Gross, professor of mathematics at Harvard University, who has known Bhargava since his days as a Harvard undergraduate. “His method—combining the arithmetic interpretation of integral orbits with their enumeration, using the geometry of numbers—has led to the solution of a large number of problems in number theory. I think his mathematical work is tremendously important, and has changed the face of the subject,” added Gross, who himself is a renowned mathematician for his work on the Gross-Zagier Theorem that won him the Cole Prize along with his collaborators. Bhargava has also collaborated with mathematicians to increase the understanding of elliptic curves, which are one of the fundamental objects in number theory with applications in the fields of cryptography and data security. Describing the uniqueness of his work, Gross said, “He obtains results ‘on average’ that we can’t obtain in individual cases. For example, for a cubic equation (an elliptic curve), it is quite difficult to determine the size of the group of rational solutions. Bhargava determines an upper bound on the average size, over all cubic equations with rational coefficients.” Bhargava is an accomplished tabla player, having trained under Ustad Zakir Hussain, one of the greatest exponents of the percussion instrument. He is also an impressive and lucid orator. “He is a very kind person, who shares his ideas freely with others. He is also a talented tabla player, who loves music and other arts,” said Gross. Peter Sarnak, professor in the department of mathematics at Princeton University, said, “Bhargava has developed fundamental new tools geometric and diophantine, to count objects in algebraic number theory, that before his work seemed hopeless. His work reminds me of the great German mathematician Hermann Minkowski’s work in number theory: it is brilliant, clear and beautiful and has reshaped the landscape.” Three others received the Fields medal—Maryam Mirzakhani, the first Iranian and the first woman to be awarded the medal; Artur Avila, the first Brazilian to be awarded, and Martin Hairer, the first Austrian to win the medal. Subhash Khot, an Indian-origin scientist from New York University, was awarded the Nevanlinna Prize in Seoul for his prescient definition of the “Unique Games” problem, and his efforts to understand its role in the study of efficient approximation of optimization problems, which have produced breakthroughs in algorithmic design and approximation hardness, according to ICM.



Weekly Test XI and XII Class - Paper and Solution Key

Dear Reader,
Weekly test was held in the classes XI and XII. Hope that all the students have performed well. Here is the test paper and its answer key.
Class XI : Test Paper     Solution Key
Class XII : Test Paper     Solution Key
In case any doubt, kindly drop a small email at amitbajajcrpf@gmail.com
Amit Sir

Do you know what’s special about today, 22 July?

Dear Reader,


Well, today is Pi Approximation Day.
Pi Approximation Day celebrates the mathematical constant π (pi). It is observed on July 22, due to π being roughly equal to 22/7.
The fractional approximation of π ,22⁄7, resembles the date July 22 in the day/month format, where it is written 22/7. Pi Approximation Day is therefore celebrated on July 22.
In geometry, pi is defined as the ratio of a circle's circumference to its diameter. July 22, often written as 22/7, is an appropriate day to explore pi, since 22 divided by 7 is an approximation of pi.
Pi Approximation Day is celebrated in a number of ways, including contests to memorize pi to the most decimal places, solving math problems involving pi, discovering the history of pi, ruminating on how life would be different without pi and—of course—eating pie.
So, enjoy this mathematical day ...
Amit Sir

THREE DAYS MATH'S WORKSHOP CONDUCTED BY ME AT SAINIK SCHOOL, TILAIYA

Dear All

I am delighted to share with you all that I was invited by Sainik School,Tilaiya, Jharkhand to conduct a three days workshop for teachers from all the 24 Sainik Schools across the country. 
In those three days I along with another Math’s expert Mrs. Shuchi Goyal discussed Mathematics beyond Curriculum, Problem Solving, Model Making, and various Hands-on-activities etc.
It was really a fun-filled great learning and sharing experience. All the participants enjoyed the sessions and took part in each activity enthusiastically. It is obvious that if teachers of any age or many years experience can enjoy this Mathematics, I am certain the students will also enjoy the same with more zeal and enthusiasm. The only pre-requisite condition is that as a Mathematics teacher we are passionate learner, flexible, ready to change for betterment and have will and desire to do best for the students.
It is hoped that all the teachers who attended these sessions are now ready to create fun based mathematical classroom where no student is phobic towards Mathematics.
As promised during the sessions I am providing the photographs of all the sessions day-wise.

MEDIA COVERAGE
DAY 1
DAY 2
DAY 3


Happy Learning!

MCQ TEST - INVERSE TRIGONOMETRY

Dear class XII students,

A multiple choice questions based test was held in all the sections of XII. Hope you have performed well in the same.
Here is the test paper and its answer key.
In case any doubt, kindly drop a small email at amitbajajcrpf@gmail.com

Next scheduled test: Continuity and Differentiation on 19 May (Monday)

Amit Sir

MCQ BASED TEST MATRICES AND DETERMINANTS

Dear class XII students,

A multiple choice questions based test was held today in the classes. Hope you have performed well in the same.
Here is the test paper and its answer key.
These files are password protected which was shared with the students in the classroom.
In case any other person wishes to see the paper, kindly drop a small email at amitbajajcrpf@gmail.com
I will share the password with you.

Next scheduled test: Inverse Trigonometry on 25 April (Friday)

Amit Sir

Change in Pattern of CBSE XII Maths Paper for session 2014-15

Dear All,

I hope that most of you are aware of certain changes in the pattern of CBSE math's paper class XII from this session onward. For your ready reference I am providing the same.


(click on images to enlarge)

Download curriculum for class XI and XII from here.

For Class XII Mathematics Students

Dear class XII Students,

Hope you have done well in your exams held till date. I am providing links of previous year's papers held in school for past 4-5 years (with solutions). I hope it will help you to prepare better for the examination.
All the best!

Links for All helpful Resources for class XII Mathematics
Value based:
Latest Sample Paper by CBSE:
Sample Papers by Directorate of Education (given to every Government School Students): http://amitbajajcrpf.files.wordpress.com/2013/12/12_math_english_2013-page-136-172-for-sp.pdf
(Also check two Sample papers from page number 136 onward)
Previous year’s papers (held in School)