Author Archives: nkpithwa

I am a DSP Engineer and a mathematician working in closely related areas of DSP, Digital Control, Digital Comm and Error Control Coding. I have a passion for both Pure and Applied Mathematics.

Make reading a part of your daily routine

Reference: The DNA newspaper, Mumbai print edition, June 25 2017, Sunday. (Rya Jetha: (The writer is a 17 year old Indian-American, currently studying at Bombay International School)

Note: Although this article may not be directly to the topics of this blog, namely, math or the kinds of levels of concentration, memory power and retention required for intensely competitive Math exams like IITJEE, RMO/INMO (of Homibhabha/TIFR), it certainly suggests the benefits of good reading habits, which directly impact the development of the intellect and overall personality of a person/student of any age. I only mean to share this “feeling” or “opinion” of mine…) – Nalin Pithwa.


What’s In It for you:

  • Reading facilitates interaction between our own experiences and the world beyond our own.
  • Reading allows us to create an image for ourselves that is intimate and personal.
  • Reading gives us the opportunity to rekindle the bond with ourselves that is neglected and wilting.


Our brains are perpetually fed with images. Images of skyscrappers billowing flames, images of celebrities strutting down the red carpet, images of scrumptious Mediterranean food platters. Images, images, images. Everywhere. On billboards as we navigate through the intersections and flyovers of our city, on our social media feeds, on television, on newspapers covers. With the tentacles of the media being ever more agile and developing finer capillaries by the second, nothing is left to imagination.

What about creating the image? What about allowing our brains to somersault, cartwheel, and back flip once in a while? How do we periodically escape the reality impressed upon us, where our brains are spoon fed and mollycoddled by our circumstances? How do we give ourselves the space to be active creators, and not dormant receivers?

The answer is reading. Fellow teenagers, I bet you just rolled your eyes, thinking “easier said than done!” I couldn’t agree more. Who has the time or inclination to read when there are standardized tests to rigorously practise for, laps to swim, tracks to run around, places to be and people to meet? It doesn’t strike me as particularly surprising when teenagers regards reading as a pastime belonging to a previous era, a time when minutes elapsed slower and free time was available in enviable abundance.

Apart from the obvious advantage of reading —- expanding our vocabularies and knowledge, improving focus and enhancing writing and comprehension skills —- I see another benefit to reading critical for teenagers in the 21st century. Reading facilitates interaction between our own experiences and the world beyond our own. Reading allows us to create an image for ourselves that is intimate and personal —- an ability we have lost as thousands of visuals assault us on a daily basis. Sidetracked by the hyperactivity of the world we live in, we lack a connection with our own experiences  and creativity, and reading gives us the opportunity to rekindle the bond with ourselves that is neglected and wilting.

Teenagers are both victims and beneficiaries of the overwhelming bombardment of the 21st century. Instead of suffering from the onslaught of sensational news and enduring the blitzkrieg of our social media feeds, how about we acclimatize ourselves to a different kind of bombardment…of suspense, of plots, of twists, of complex characteers and vibrant settings! The possibilities are endless, and I assure you, the vibrancy and exhilaration is unparalleled by any Snapchat filter, Buzzfeed article or Trump meme. How about exploring the Taliban agenda in A Thousand Splendid Suns, or viewing the world through the lens of a migrant in The Sympathizer, and Americanal, or experience the trauma of World War II through the perspective of a blind French girl in All The Light We Cannot See, or delving into the history of The Gene, or exploring British occupied Burma in The Glass Palace, or living the psychological tension in The Girl on the Train. Take your pick!


On my part, if you are interested in Math and Physics, you can try reading some of the following books:

  1. The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel,
  2. Men of Mathematics by E. T. Bell, this is the book which had inspired (to some extent) John Nash, Jr., as a boy, and he later on became a Nobel Laureate, an Abel Laureate, whose life inspired the Hollywood movie, A Beautiful Mind. The movie in turn is based on the biography ” A Beautiful Mind” by Sylvia Nasar; you can buy these books also from Amazon India or some other place.
  3. Taming the Infinite: The Story of Mathematics by Ian Stewart.
  4. A Brief History of Time: From Big Bang to Black Holes by Stephen Hawking.
  5. The Physics of Superheroes by James Kakalios.
  6. Physics for Entertainment by Ya. Perelman;
  7. Surely, you are joking, Mr. Feynman!
  8. Sherlock Holmes, (Unabridged complete works) by Sir Arthur Conan Doyle,
  9. Super Memory: it can be yours by Shakuntala Devi,
  10. P. G. Wodehouse ! (This is, of course, for light reading and besides, who can forget The Inimitable Jeeves, the Empress of Blandings, and Bertie Wooster? 🙂 🙂 🙂 )
  11. S. Chandrasekhar, Man of Science, by Radhika Ramnath,

(I will try to suggest more such literature later, although, you can find many many like these on your own…)

– shared by Nalin Pithwa.

Maths in a minute! Thanks to PlusMath!

All 30 candidates of Patna’s Super 30 crack IITJEE Advanced 2017!

(This piece of news is also a bit dated, but v v inspirational)

(Reference: DNA newspaper, print edition, Mumbai, June 17 2017, Education section)

Patna: Mathematician Anand Kumar’s Super 30 has once again created a record as its 30 out of 30 candidates cracked the IITJEE Advanced Examination (2017) results which were announced last Sunday.

“I am happy that my 30 out of 30 candidates have cracked IITJEE Advanced this year. Now time has come to give Super 30 some much needed expansion. We will now organize tests for selecting students in different parts of the country and give all the details on the website,” the Super 30 founder said.

Talking to media persons after the results, Kumar attributed his yet another success story of Super 30 to the hard work and perseverance of his students and said that its time to expand his famous Super 30 in the country.

Kumar’s Super 30 provides free coaching along with lodging to students of underprivileged sections of the society.

Super 30 has completed its 15 years of journey during which it has sent 396 out of 450 candidates to IIT. Kumar said adding that it coached 450 candidates in 15 years, 30 candidates every year.

Among the 30 students of Super 30 who have cracked prestigious IITJEE Advance 2017, there are wards of landless farmer, egg seller, unemployed father.

There are several inspiring tales that have emerged from the Super 30 coaching institute this year too.

Be it the story of Kevlin, son of an unemployed father, or roadside egg seller’s son Arbaaz Allam, a farm labourer’s son Abhishek, they all stand tall having overcome the stiff odds of poverty and deprivation to make it to IIT and become an inspiration for several others like them.

Kevlin’s father Deepak is unemployed. He teaches yoga to people, but still his earning is not enough to make both ends meet. But Deepak knew that the only way to get out of the life of poverty is through education. Tears of joy continue to roll down his cheeks as he sits with mathematician Anand Kumar.

“I had heard of Super 30 almost 10 years ago and since that day I dreamt of seeing my son here to realize my dream. Today my son has realized it,” said Deepak.

Arbaaz’s father sells eggs in Bihar’s Biharsharief district. But he never lost heart. He always aspired to be at the top to change the course of his life.

“Anand Sir made me feel confident about my abilities. He boosted my confidence. Now, I think it is a matter of a few years when my father will not have to sell eggs braving the chilly winds of winter nights. I will also have a house where I will live with my father and mother,” said Arbaaz.

Kaushlendra Kumar of Nalanda is a landless farm labourer. Kaushlendra is proud of his son Arjun Kumar and Super 30. Arjun proudly recounts how his journey from a village school devoid of even basics took him to Super 30 and now he plans to step into IIT. “It is due to programmes like Super 30 that make even students from underprivileged sections dream of IIT. Now after engineering, I plan to go in for UPSC,” Arjun said.


Hats off to Prof. Anand Kumar and his team !!! From Nalin Pithwa.

Petronet Kashmir Super 30: Nine crack IITJEE 2017 exams

(This news is a bit delayed here on this blog, nevertheless, inspirational.)

Reference: DNA, Mumbai print edition, June 15 2017:

Srinagar: Petronet LNG Ltd. (PLL), which started its CSR voyage from western India and traversing South and East, have now reached Northern state of Jammu and Kashmir.

Considering the lack of facilities/faculty in J and K to impart coaching for Engineering Entrance Examination to facilitate admissions to IITs/NITs/other institutions of repute, Petronet LNG Ltd. sponsored 40 underprivileged students in 2016-17 to fulfill their dream of higher engineering education (35 boys and 5 girls) under Petronet Kashmir Super 30 programme in association with Indian Army, CSRL. This 11 months’ residential programme was attended by 40 students (kargil 7, Pulwama 5, Bandipura 6, Baramulla 4, Anantnag 7, Ganderbal 4, Kulgam 1, Tangmarg 2, Ramban 1, Shopian 1, Sopora 1, Nagrota 1).

Despite hardships in Kashmir and educational institutions being closed last year, the project continued with its mission. The declaration of IITJEE results on April 27 2017 saw selection of 28 students (including 2 girls) who were coached under Petronet Kashmir Super 30 cracking the IITJEE mains exams. Six other students will join Regional Engineering Colleges.

Shri Dharmendra Pradhan, Hon’ble Minister of State (I/C) Petroleum and Natural Gas and Mr. Chowdhary Zulfkar Ali ji, Hon’ble Minister for Dept. of Food, Civil Supplies and Consumer Affairs and Information Dept., J and K, interacted with students of Petronet Kashmir Super 30 at Delhi and felicitated them for their hard work and achievement.

Shri Pradhan expressed happiness that students from underprivileged backgrounds from places like Kupwara, Pulwama, Anantnag, Shopian etc. have shown their determination and got selected in prestigious institutes. He also announced on behalf of Petronet LNG Ltd. that 100 students will be sponsored from Kashmir for engineering entrance next year.


🙂 🙂 🙂 Congratulations to Petronet (Kashmir) LNG Team including their faculties and the students from Nalin Pithwa !

Who wants to be a mathematician

I wish that there were official programmes like the following in India too:

Something Cute I Never Noticed Before About Infinite Sums

Source: Something Cute I Never Noticed Before About Infinite Sums

Arithmetic Puzzle


Following is a very common arithmetic puzzle that you may have encountered as a child:

Express any whole number $latex n&bg=ffffff$ using the number 2 precisely four times and using only well-known mathematical symbols.

This puzzle has been discussed on pp. 172 of Graham Farmelo’s “The Strangest Man“, and how Paul Dirac solved it by using his knowledge of “well-known mathematical symbols”:

$latex displaystyle{n = -log_{2}left(log_{2}left(2^{2^{-n}}right)right) = -log_{2}left(log_{2}left(underbrace{sqrt{sqrt{ldotssqrt{2}}}}_text{n times}right)right)}&bg=ffffff$

This is an example of thinking out of the box, enabling you to write any number using only three/four 2s. Though, using a transcendental function to solve an elementary problem may appear like an overkill.  But, building upon such ideas we can try to tackle the general problem, like the “four fours puzzle“.

This post on Puzzling.SE describes usage of following formula consisting of  trigonometric operation $latex cos(arctan(x)) = frac{1}{sqrt{1+x^2}}&bg=ffffff$ and $latex tan(arcsin(x))=frac{x}{sqrt{1-x^2}}&bg=ffffff$ to obtain the square…

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APJ Abdul Kalam : How to manage success and failure

It is examinations &/or results of examinations time in India. Especially, the ruthlessly, mercilessly competitive, intense IITJEE Advanced…

So, here is some advice for a life time from our revered, adored APJ Abdul Kalam. Actually, this advice applies to all adult stages in life…

Three in a row !!!

If my first were a 4,

And, my second were a 3,

What I am would be double,

The number you’d see.

For I’m only three digits,

Just three in a row,

So what must I be?

Don’t say you don’t know!


Nalin Pithwa.

Follow Descartes’ Historically Famous Problems !

Problem 1:

Three circles touching one another externally have radii r_{1}, r_{2} and r_{3}. Determine the radii of the two circles that can be drawn touching all the three circles.

Problem 2:

Consider a circle, say (numbered 1) of unit radius 1. Inside this circle, two circles are drawn (say, numbered 2 and 3), each of radius \frac{1}{2}, which touch each other externally and the first circle internally. Determine the radius of the fourth circle, which touches circles 2 and 3 externally and circle 1 internally. Determine the radius of the fifth circle, which touches each of the circles 2, 3, and 4 externally. Determine the radius of the sixth circle, which touches circles 2 and 4 externally and circle 1 internally. One might notice that curvature of all such circles drawn within the first circle has integer curvature!

It is such historically famous problems (within scope of IITJEE Mains and IITJEE Advanced Maths) which all students should try to internalize all the concepts of Math for IITJEE. Also, in a similar vein, you should practice deriving all basic formulae, relationships of co-ordinate geometry.

More later,

Nalin Pithwa.