
Pages

Categories
 algebra
 applications of maths
 Basic Set Theory and Logic
 calculus
 careers in mathematics
 Cnennai Math Institute Entrance Exam
 coordinate geometry
 combinatorics or permutations and combinations
 Complex Numbers
 Fun with Mathematics
 geometry
 IITJEE Advanced
 IITJEE Advanced Mathematics
 IITJEE Foundation Math IITJEE Main and Advanced Math and RMO/INMO of (TIFR and Homibhabha)
 IITJEE Foundation mathematics
 IITJEE Mains
 IMO International Mathematical Olympiad IMU
 Inequalities
 Information about IITJEE Examinations
 INMO
 ISI Kolkatta Entrance Exam
 KVPY
 mathematicians
 memory power concentration retention
 miscellaneous
 motivational stuff
 physicisrs
 PreRMO
 probability theory
 pure mathematics
 RMO
 RMO Number Theory
 Statistics
 time management
 Trigonometry

Archives
 March 2021
 January 2021
 November 2020
 October 2020
 September 2020
 August 2020
 July 2020
 June 2020
 May 2020
 April 2020
 March 2020
 February 2020
 January 2020
 December 2019
 November 2019
 October 2019
 September 2019
 August 2019
 June 2019
 May 2019
 March 2019
 February 2019
 January 2019
 November 2018
 October 2018
 September 2018
 August 2018
 July 2018
 June 2018
 May 2018
 April 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 October 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 April 2017
 March 2017
 February 2017
 January 2017
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 August 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
Category Archives: miscellaneous
Annual Essay Contest: Mentoris Project: Aug 2021
Express a given integral number in any scale (radix)
Several scales (radix) have been used by mathematicians. Binary (2), Ternary (3), Quaternary (4), Quinary (5), Senary (6), Septenary (7), Octenary(8), Nonary (9), Denary (10/Decimal), Undenary(11), Duodenary (12) and of course, hexadecimal (16). Note that in any scale the base radix is “10”. Thus, “10” stands for 2 in “binary”, “ten” in “decimal”, 8 for “octal” radix respectively, etc.
Let the digits used in a proposed scale(radix r) be . Let us express an integer in this scale. Let be unit’s digits. Analagous to the place value system (in decimal):
Now, let us say we want to express this number N in terms of these digits s.
Dividing N by , we get the unit’s digit as the remainder; and the quotient is:
.
Dividing the above quotient by r, we get as the remainder and the quotient as:
, and so on.
Example: Express the denary number 5213 in the scale of seven.
Solution: gives 5 as remainder and as quotient.
gives 2 as remainder and as remainder.
Continuing this way, we are able to express:
. That is . You can check the equivalence by converting both to decimal values.
Cheers,
Nalin Pithwa.
STEM for Australia
Wisdom of George Polya
A great discovery solves a great problem. But there is a grain of discovery in the solution of any problem.
— George Polya, How to Solve it
To balance, to focus, for inner calm and concentration
Happiness Chemicals and how to hack them:
I) DOPAMINE: The reward chemical:
 Completing a task
 Doing selfcare activities
 Eating food
 Celebrating little wins
II) SEROTONIN: The mood stabilizer:
 Meditating
 Running
 Sun exposure
 Walk in nature
 Swimming
 Cycling
III) OXYTOCIN: The love hormone
 Playing with a dog
 Playing with a baby
 Holding hand
 Hugging your family
 Give compliment
IV) ENDORPHIN: The pain killer
 Laughter exercise
 Essential oils
 Watch a comedy
 Dark chocolate
 Exercising
The City with a large heart : Bombay/Mumbai
Mumbai is rich,
Mumbai is poor,
Mumbai is fast,
Mumbai is slow.
Little bit sweet,
and little bit sour.
Sometimes its hot,
but not too cold.
Mornings r energetic
& evenings are electric.
Noons r lazy but
Nights are crazy.
And anyone U ask,
he always says “M busy”
Dude, life in Mumbai
Is not so easy…!
There is lot of Masti with
little bit of Maska…
Welcome to the city that
can’t live without our Bollywood Chaska!
Sev puri, Vada Pav and bhel puri
are all Mumbai chaat.
Relishing it with spicy chutney is no easy art
From popcorn to icecream, all sold
on cart
Mumbai o Mumbai you’re always
close to my heart!
Where local trains
usually run on time
And violently rushing
for a seat is not a crime.
Here 3 PM for lunch and
12AM to dine,
People face hardships,
but still say, “It’s fine”!
From Siddhivinayak in Dadar
to Woodhouse Cathedral in Town,
And ISKCON in Juhu to Haji Ali in
Mumbai’s Crown,
Marathi, Malayalee, Christian to
Gujarati,
Everyone together celebrate
Christmas and Diwali,
Holi is colourful and Diwali is cheerful,
Spend some time here and your life
will be unforgetful!
Billionaires to beggars,
all found in this city,
Be careful dude,
this place is a bit witty…
Overall this dream world
is huge but pretty
Mumbai Mumbai,
you’re wonderful city
After all a mother is called
MUM in English
BA in Gujarati &
Ai in Marathi
That’s My Mumbai
Dedicated to all Mumbaikars !!
Some thoughts on teaching
If you learn you teach, but if you teach you learn. (Bertrand Russell) Teaching is like gardening. To teach is to teach to learn to think deep. To teach is to uncover a subject or rediscover a subject rather than to finish the syllabus. To teach is to prepare for the uncertain future. To teach is to gradually emerge the potential and motivation of the student. To teach is to impart a love for lifelong learning of the subject. To teach is to impart intellectual clarity. Passion is the key. To teach is to assume that the students are bright, hard working and motivated. To teach is to Kindle curiosity. In my mother tongue it is said the following are the pillars of teaching : prayatna ( to try ), protsahan ( to encourage ), prashansha ( to praise), and pralobhan ( some fantastic tangible motivation). In education, there is a wise quote : we go from the known to the unknown. From darkness to the light of knowledge. Knowledge means understanding not rote memorization of the subject. …To teach is to teach the art of problem solving.
Regards
Nalin Pithwa
Wisdom of Yajurveda
As are the crests on the crowns of peacocks,
As are the gems on the hoods of cobras,
So is mathematics at the helm of all Sciences.
— Yajurveda circa 400 BC