Category Archives: IITJEE Foundation Math IITJEE Main and Advanced Math and RMO/INMO of (TIFR and Homibhabha)

Going Negative, part 3

Let’s start with a joke:

A physicist, a biologist and a mathematician are sitting in a street café one morning watching an empty store on the other side of the street.They see someone unlock the store and go in.Time passes.Someone else goes in. More time passes. Then three people come out.

The physicist says, “Our measurements weren’t accurate.” The biologist says, “The two people who went in must have reproduced.” The mathematician says, “If one more person enters the store, it will be empty.”

Of course the joke here is that the mathematician is holding the absurd belief that there are a negative number of people in the store.1 The joke is built on our shared knowledge that although negative numbers make sense in some contexts, they aren’t sensible in the present context. But the knowledge that negative numbers do make sense in some contexts shouldn’t be taken for…

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IITJEE Mains or Advanced Maths Doubt Solving Tutorials

Any maths questions from any where or any other branded class problems sets.

Contact Nalin Pithwa

Eugenia Cheng: When 1 + 1 = 3: (En)Lightning Talks Chicago

Four Basic Proof Techniques Used in Mathematics by patrickJMT

Probability by 2 Great Friends

Folium of Descartes & Fermat

Maths will rock your world — a motivational article

keep dreaming the applications of math…try to count every thing….

Mathematics Hothouse

Math will rock your world

BusinessWeek

Jan 23 2006

A generation ago, quants turned finance upside down. Now they’re mapping out ad campaigns and building new businesses from mountains of personal data

 

Neal Goldman is a math entrepreneur. He works on Wall Street, where numbers rule. But he’s focusing his analytic tools on a different realm altogether: the world of words.

Goldman’s startup, Inform Technologies LLC, is a robotic librarian. Every day it combs through thousands of press articles and blog posts in English. It reads them and groups them with related pieces. Inform doesn’t do this work alphabetically or by keywords. It uses algorithms to analyze each article by its language and context. It then sends customized news feeds to its users, who also exist in Inform’s system as — you guessed it — math.

How do you convert written words into math? Goldman says it takes a…

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A motivation for Math and some Math competitive exams in India

what motivates you to keep going in math?

Mathematics Hothouse

Sometime back, there was a tremendous publicity in the Indian media to two Fields medallists of Indian origin. They also talked about what motivated them towards Math when they were young. One should  not do Math just lured by its glamorous applications in IT or other engineering disciplines. But, one can develop both aptitude and attitude  towards it if one works from a young age.

What you need is intrinsic motivation. In this context, I like to quote the following words of a famous mathematician:

“And, a final observation. We should not forget that the solution to any worthwhile problem very rarely comes to us easily and without hard work; it is rather the result of intellectual effort of days or weeks or months. Why should the young mind be willing to make this supreme effort? The explanation is probably the instinctive preference for certain values, that is, the attitude…

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Skill Check I: IITJEE Foundation Maths

  1. Simplify: (+1) \times (-1) + (+1) \div (-1) -()-1 +(-1) \div (-1) \times (-1) +(-1)
  2. Simplify: \{ 7 \hspace{0.1in} of \hspace{0.1in} 6  \div 2 - 4(8 \times 12 \div 3 + \overline{-3 \hspace{0.1in} of \hspace{0.1in}+6 -2 })\} \div (-3)
  3. Simplify: 24 \div (-8) + 3 \times (-3)
  4. Simplify: (+7) - (-3) + (+4) \times (-3) \div (+3) of (-2)
  5. Simplify: (-3) of (-5) \div (-3) \times (-2) + (-5) - (-2) \div (+2)
  6. Simplify: (-7) + (-8) - (-3) \hspace{0.1in} of \hspace{0.1in} (-6) \div (+2) - (-4) \times (-4) \div (+2)
  7. Simplify: (+24) \div (-3) \hspace{0.1in} of \hspace{0.1in} (+4)  - (-25) \times (-6) \div (-3) + (-15) \div (-3) \times (-10)
  8. Simplify: (-3) \hspace{0.1in} of \hspace{0.1in} (-8) \div (-6)  - (-8 +4-3)
  9. Simplify: (-5) [ (-6) - \{ -5 + (-2 + 1 - \overline{3-2})  \} ]
  10. Simplify: (-3) [ (-8) - \{ +7 - (4-5 - \overline{2-5-1})\}] \div (-11)
  11. Simplify: (+8) \times (-3) \times (+2) \div [ -1 - \{ -3 + 8 - (6 -2 - \overline{3+5-4}) \} ]
  12. Simplify: (+32) \div (+2) of (-4) \div [(-7) of 3 \div \{4 - 5(3 - \overline{4 of 2 - 2 of 5}) \}]
  13. Simplify: (-30) + (-8) \div (-4) \time 2
  14. Simplify: (-3) \times (-6) \div (-2) + (-1)
  15. Simplify: 56 \div (16 + \overline{4-6}) + (6-8)
  16. Simplify: (7+6) \times [19 + \{ (-15) + \overline{6-1}\}]

Regards,

Nalin Pithwa

Purva building, 5A
Flat 06
Mumbai, Maharastra 400101
India

Math Basics Division by Zero

the eleventh commandment of Moses: Though shall not divide by zero !!

Mathematics Hothouse

Let’s pause Geometry for a little time and start thinking of some basic rules of the game of Math. Have you ever asked “why is division by zero not allowed in Math?” Try to do 1/2 in a calculator and see what you get!!

This was also a question an immortal Indian math genius, Srinivasa Ramanujan had asked his school teacher when he was a tiny tot. Note the following two arguments against the dangers of division by zero:

(a) Suppose there are 4 apples and two persons want to divide them equally. So, it is 4/2 apples per person, that is, 2 apples per person. But, now consider a scenario in which there are 4 apples and 0 persons. So, how can you divide 4 apples amongst (or by) 0 persons? You can think of any crazy answer and keep on arguing endlessly about it!!!!

(b) The cancellation law…

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