Wednesday, August 03, 2011

Precalculus by Askey and Wu

Many years back, Professor Richard Askey sent me hard copies of some notes he had made, with a supplement by  H. Wu. I think these notes are just wonderful, and am placing them here.

Review of Pre-Calculus by Richard Askey and H. Wu
Precalculus - Further Notes by Richard Askey

Wednesday, April 27, 2011

Punya - A nearly Palindromic poem


your palindromes,
the poetry,
ambigrammed symmetry.
An inspiration-
your blog.
Hope you keep up with
your slog.
the perspiration:
programmed asymmetry,
but palindromes!


This was inspired by a blog post by Punya, about an 8th grader who loved his palindromic poetry. The associated facebook page attracted some comments admiring Punya, including a little palindromic poem by me. 

While I am not an 8th grader anymore, I do feel many times that I am still in 12th grade. 
So, I thought of a  
nearly-palindromic poem. 

So near a palindromic poem, yet far from it. The first of its kind. Enjoy. Or not.

Monday, April 25, 2011

Identities and Mathematical Intuition: Talk in DPS - Dwarka to DPS Math Teachers

On April 18th, I gave a talk on Identities to Delhi Public School (DPS) Math teachers  attending a training conference/workshop. The teachers were from DPSs all over the country and teach in senior school (XIth-XIIth).

The overall idea of the talk was to organize information about identities according to the three kinds of mathematical intuition I have spoken about earlier. The three kinds of mathematical intuition are: Symbolic, graphical or physical intuition, and structural intuition. These are motivated by the following quote:
…some mathematicians are more endowed with the talent of making pictures, others with that of juggling symbols and yet others with the ability of picking a flaw in an argument.
~Gian Carlo Rota 

Tuesday, March 08, 2011

Sunil Mittal

A schoolboy, named Sunil Mittal,
What goes through 
his adolescent mind?

Here's a clue:

The movies playing in his brain
and the color of his uniform,
are both the same.

They are Blue!

Sunil is a friend from modern school. This one came up on FB as a comment on a discussion. 

Wednesday, February 09, 2011

In Praise of an Elementary Identity of Euler

After many years, a new math paper. Its mostly a survey of my favorite identities, but has some new identities too. The new results have been checked (as typeset in the paper) using Maxima.  I have tried to write the first few sections so that  anyone can read and appreciate it.
I would appreciate any comments, typos, etc.

Update (March 16, 2011):
Presentation from: Georgia Southern q-Series conference, March 15. Here is a link.

Update (June 11, 2011): The paper is published by the Electronic J. of Combinatorics, Vol 18 (2), P13 44 pp. Download.

Telescoping, Fibonacci Numbers,  Pell Numbers, Derangements, Hypergeometric Series, Fibonacci Polynomials,  q-Fibonacci Numbers,  q-Pell numbers, Basic Hypergeometric Series, q-series, Binomial Theorem, q-Binomial Theorem, Chu--Vandermonde sum, q-Chu--Vandermonde sum, Pfaff--Saalschutz sum, q-Pfaff--Saalschutz sum, q-Dougall summation, very-well-poised 6 phi 5 sum, Generalized Hypergeometric Series, WZ Method

Sunday, February 06, 2011

My Mathematical Forefathers

From time to time, I look at the Mathematics Genealogy Project, and search for my own mathematical tree. I was happy to note that I am a direct descendant of Gauss and of Leibnitz. What I noticed today, was that I am a mathematical cousin of Saroj Malik, my teacher in Hindu College, who taught me abstract algebra and elementary number theory. We branch out at Gauss.

Here is the complete list of my mathematical forefathers.

  • Friedrich Leibnitz
  • Jakob Thomasius
  • Otto Mencke
  • Johann Christoph Wichmannshausen
  • Christian August Hausen
  • Abraham Gotthelf Kästner
  • Johann Friedrich Pfaff
  • Carl Friedrich Gauß
  • Christoph Gudermann
  • Karl Theodor Wilhelm Weierstraß
  • Leo Königsberger
  • Georg Alexander Pick
  • Charles Loewner
  • Adriano Mario Garsia
  • Stephen Carl Milne
  • Gaurav Bhatnagar

Monday, August 02, 2010

Math Problem Book - Grade 6

Here is a book made from some problem sets I used to give Tejasi and her friends in my garage. The explanations have been added later on. Most of the kids who took these problem sets the sense that they began doing well in exams. Here is a collection of the problem sets for grade 6.

Click here to download/view Math Problem Book - Grade 6

Sunday, August 01, 2010

Experience Mathematics

A book I wrote long ago. Recently, I re-edited it based on comments made by Professor Dick Askey. Looking for a publisher, but meanwhile here it is for my friends and their kids...

Click here to view the PDF File

Friday, June 04, 2010

The q-disease

Special Functions,
by Andrews, Askey and Roy.
Here's a belated review,
and a thank you.


Beauty in mathematics,
said Polya,
is seeing the truth
without effort.

in The Book
is as elegant,
as could be.

as simple,
as effortless,
as should be.

as beautiful,
as it is.


Thursday, May 14, 2009

Design II

Design II
Ambigram by punyamishra

A great design:
Everything fits in nicely
into one complete whole.

Not a hair out of place,
and not one thing
than what is

The form
and the function,
made for each other.

GB #32

Sunday, April 05, 2009


Ambigram by punyamishra

All Cretans are liars
said Epiminedes,
a Cretan,
a classic Paradox.

If Epiminedes tells the truth
then he must be lying.
And if he is lying,
he is telling the truth.

Saturday, April 04, 2009


Ambigram by punyamishra

Watson and Crick
what fun it is
to be
a scientist.

What fun it is
to discover
something new.

What fun it is
to compete
with the best
and win.

Watson and Crick
the secret of life
GB #30

Friday, February 27, 2009


Ambigram by punyamishra

The Internet
inking pacts
across the world.

and connecting
all humanity.

all the dots
into one
continuous whole.

GB #29

Internet II

Internet II
Ambigram by punyamishra

Small knots
woven together
become a net.
Flexible, stable,
and very strong.

Small computers
become the Net.

the power
of communication,
of creativity,
of community.

Small individuals,
linked together
become the

GB #28

Friday, February 20, 2009

Douglas R Hofstadter

Ambigram by punyamishra

Douglas R Hofstadter
sides reversed is
Retdatsfoh R Salgoud
sides reversed is
Douglas R Hofstadter
is one Strange Loop.

Hofstadter wrote
Godel, Escher and Bach:
An eternal golden braid.

A personal review follows.