Thursday, 10 November 2016

Game Theory And Chance Of Life

     Chance and probability plays a great role in shaping our day to day life. Followings are main concepts of probability in our life.
Game Theory Exposed


  1. Game theory is a tool for making decision.

  2. Life at every instance is uncertain and what we are doing in life, we can either get success or failure.

  3. From birth to death is the journey of life.

  4. Life of a person is fixed and within that period of time he/she has to achieve or loss in this materialistic world.

  5. Life on intermediate journey can change path, but birth and death are fixed.

  6. Happiness and sorriness on intermediate journey depends on the success and failure respectively.

  7. The probability of success and failure is applicable everywhere.

  8. Game is zero-sum if during game wealth is neither created nor destroyed.

  9. So gambling is a zero-sum game. One person wins then other person must have to lose the game.

  10. A million dollar person (million-er) can take $1000 risk, but a common man only having $1000 can not take that risk. This is the reason, why rich grow richer and poor grow poorer.

  11. Game having negative average return attracts more player. One suitable example is lottery.


Key Highlights:
What is your chance of winning the game?
Why to take risk in zero-sum game?
Gambling and probability
जुआ में जितने की संभावना






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Wednesday, 9 November 2016

Woman Mathematician

1. Hypatia of Alexandria (AD 350 or 370-AD 417,Egyptian)
Woman Mathematician Hypatia of Alexandria
Woman Mathematician
     She was the daughter of a mathematician called Theon. Hypatia brilliance in astronomy, philosophy and mathematics made her the first and last greatest female thinker of ancient Alexandria located in Egypt.

2. Maria Agnesi (1718-1799, Italian)

Woman Mathematician Maria Agnesi
Woman Mathematician
     Maria Agnesi was an Italian philosopher and mathematician, most known for being the first female to be appointed as a mathematics professor. She wrote a book on math that still survives, (i.e, Analytical Institutions) for the Use of Italian Youth in English. Another pioneering contribution was the Witch of Agnesi- a curve that she wrote the equation for.

3. Émilie du Châtelet (1706-1749, French)
Woman Mathematician Emilie du Chatelet
Woman Mathematician

     She was a physicist, mathematician and writer during the Enlightenment era in Europe. She commented on Newton’s Principia Mathematica which is its best known translation in French even today.

4. Sophie Germain (1776-1831, French)
Woman Mathematician Sophie Germain
Woman Mathematician

     Sophie Germain’s paper on elasticity theory made her the first woman to be awarded from the Paris Academy of Sciences in 1816 and first unmarried woman to attend sessions at the Academy of Sciences and the Instit de France. She was also a major contributor in proving Fermat’s Last Theorem.

5. Ada Lovelace (1815-1852, British)
Woman Mathematician Ada Lovelace
Woman Mathematician

     When asked to translate the memoir of Charles Babbage, the Analytical Engine, Lovelace went ahead and added her own comments and notes about a method of calculating a sequence of Bernoulli numbers: what is today known as the world’s first ever computer program subsequently making Lovelace renowned as the world’s first computer programmer.
6. Sofia Kovalevskaya (1850-1891, Russian)
Woman Mathematician Sofia Kovalevskaya
Woman Mathematician

     Kovalevskaya’s biggest achievement was becoming the first woman in Europe to receive full professorship at the University of Stockholm.

 Contributions:
  • She gave the Cauchy-Kovalevskaya Theorem its end result in 1875.
  • worked on a paper in which she invented the Kovalevskaya Top and published ten papers based on mathematics and mathematical physics.

7. Emmy Noether (1882-1935, German)
Woman Mathematician Emmy Noether
Woman Mathematician
     Emmy Noether is famous for coining the Noether’s Theorem that clarifies the relationship between conservation laws and symmetry, as well as Noether’s Ring that changed the basics of abstract algebra.

 Contributions:
  • Theories for non-commutative algebras
  • hyper-complex numbers
  • commutative rings.

 Awards and Recognition:
  • She received the Ackermann-Teuber Memorial Award for her input in the field of mathematics.
8. Mary Cartwright (1900-1998, British)
Woman Mathematician Mary Cartwright
Woman Mathematician

     Cartwright was the first female selected as a Fellow for the Royal Society of England.

 Contributions:
  • She authored over a 100 papers which include her work on level curves, functions in the unit disk, topology and ordinary differential equations among others.
Awards and Recognition:
  • Received the De Morgan Medal from the London Mathematical Society
  • Received Sylvester Medal of the Royal Society

 9. Julia Robinson (1919-1985, American)
Woman Mathematician Julia Robinson
Woman Mathematician

     Though she suffered from ill-health throughout her short life, Robinson made it as the first female mathematician elected by the National Academy of Sciences. 

 Contributions:
  • She is well regarded for her work on Hilbert’s Tenth problem and decision problems.
Awards and Recognition:
  • President of the American Academy of Arts and Sciences.

10. Shafi Goldwasser (1958 - Till Date, American)
Woman Mathematician Shafi Goldwasser
Woman Mathematician
     Goldwasser is an American professor teaching mathematics at Weizmann Institute of Science and computer science at  and MIT.

 Contributions:
  • Zero-knowledge proof
  • Complexity theory
  • Computation number theory
  • Cryptography.
Awards and Recognition:
  • Gödel Prize twice for her work on theoretical computer science
Key Highlights:
woman mathematician of all times
woman and their contribution in mathematics
महिला गणितज्ञ की योगदान




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Sunday, 6 November 2016

Mathematics and Fictions

     Mathematical fictions exists since ancient times. In mathematical fictions visionary philosopher and mathematician express their views about the futures of mathematics. This area now becoming very popular in academics.

Mathematical Fiction
Mathematics & Fiction

     In mathematics whatever was fiction earlier has now become a reality. Followings are some mathematical fictions of past and now a reality today.


  1. Concept of real number and its well established theory.

  2. Concept of imaginary number. 

  3. Concept of calculus and its use in various field. 

  4. Proof of Fermat's last theorem.

  5. Efficient method for calculating prime number.

  6. Number theory and encryption security.

  7. Efficient algorithm and advancement in computation accuracy.

Some important references:
  • Film "A Beautiful Mind", based on life of John Forbes Nash mathematician.
  • The Mathematical Fiction Homepage, maintained by Dr. Alex Kasman of the College of Charleston, - See more at: http://blogs.ams.org/mathgradblog/2012/09/30/stories-mathematicians-mathematical-fiction-homepage/#sthash.n38JuZlU.dpuf
  •  Website maintained by Dr. Alex Kasman of the college of Charleston





Key Highlights:
What is mathematical fiction?
How mathematical fiction has helped mankind?
गणित और उपन्यास एवम् उनका योगदान





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Lost Mathematics


     History of mathematics is since mankind came out of cave age. Certain assumptions of mathematics keeps changing over time. But progress of mathematics has never been stopped. Old assumptions are validated with new concepts and ideas. But Concept of Mathematics has never been lost.

Lost Math
     No one is father of mathematics. Mathematics has contribution from different countries and civilizations. Some time its progress is slow and some times its progress is exponential.
     One idea is validated by many branches of mathematics. Mathematical progress is very dynamic and random since time immemorial.

      Followings are brief description of examples of lost mathematics work in past.

  1. Math will be lost if company maintain them does not exists.

  2. It has happened in past and will also happen in future.

  3. Archimedes (ca. 287-212 BC) description of 13 Archimedean solids which was mentioned by Pappus was in past and it was Kepler (1619) who discover it again known as 13 semiregular polyhedra.

  4. Ramanujan lost diary had many new discoveries that are now lost.

  5. The algorithm for calculating FFT, described in Cooley and Tukey's landmark 1969 paper, was known to Gauss and appears among his unpublished works (around 1805).

  6. Archimedes' discovery of (at least parts of) integral calculus was found in a Byzantine manuscript.

  7. The Rogers-Ramanujan identities have a similar story. They were discovered and proved by Leonard James Rogers in 1894 and then promptly forgotten. Later Ramanujan discovered them in 1913.

  8. The number theory work of Fermat is other example. Much of Fermat number theory work was rediscovered later by Euler. This includes Fermat's two-square theorem: It was first mentioned by Fermat as a theorem in a 1640 letter to Mersenne and also analogous statements about primes numbers of the form x2 + 2x2y2 + 2y2 & x2 + 3y2x2 + 3y2 were made in a 1654 letter to Pascal.

Key Highlights:
Mathematics that is lost
History of lost mathematics
Lost mathematics boon or curse
गम हो गया गणित

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Mathematics and Humanity


"Mathematics is the most beautiful and most powerful creation of the human spirit”------ Stefan Banach


"Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country" ----- David Hilbert


     Mathematics has played a great role in nurturing humanity. Mathematics has provided tools to mankind to do analysis of events with reasoning. Mathematics has helped to prove reasoning with scientific evidence.

Mathematics and Humanity
Mathematics & Humanity
     Correct use of Mathematics is crucial for the progress of humanity. Humanity has flourished with the help of mathematics. Mathematics can be used for betterment of humanity. Followings are some of the example of correlation of mathematics and humanity.


  1. Use mathematics to remove gender biasness. For a post what is probabilities of a woman and man. In an institution, how many men and women get promotion every year?

  2. To reduce death due to home violence.

  3. To calculate chance of outbreak of an disease.

  4. Simulation of success rate of events.

  5. To develop new techniques in mathematics so that new scientific research can be done. This can improve life of human mankind.
Key Highlights:
What is mathematics and humanity relation?
How mathematics has helped humanity?
गणित और मानवता 
मानवता के लिए गणित का योगदान



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Mathematics and Science Relationship

“Mathematics is queen of science”---- Carl Friedrich Gauss

Mathematics and Science Relationship
Mathematics & Science

  1. One of the first analyses of the relationship between mathematics and other sciences was done by ancient Greek philosopher Aristotle. He mentioned about the interdependence of mathematics and other sciences in his work.

  2. By using statistics, scientists can use data as evidence to either support or dispute scientific theories.

  3. Calculus and differential equations are used to study complex relationships between one property and another in physics.

  4. Science applies both simple and complex mathematical concepts for studying science. Famous example is measurement of amount of chemicals to be used in a solution or figuring out the velocity required in order for the Mars Curiosity to safely land on Mars.

  5. Algebra deals with general statements of relations, uses letters and other symbols to represent different values.  It is used in science to develop formulas to find an unknown value.

  6. Calculus used to find volume and area using complicated surfaces.  It is used in most branches of science to derive answers that cannot be measured directly.

  7. Geometry deals with properties of points, lines, angles, and figures in space. This is very helpful in scientific study.

  8. Trigonometry deals with the relationship between angles and sides.  Used in science to locate events like earthquakes, fires, tsunami, tornado, planets, stars, and many other things that we cannot directly measure.

  9. Euclidean geometry deals with a flat world (stating that parallel lines are always parallel and never intersect).  It is used in measuring things on earth surface.

  10. Riemannian Geometry deals with a spherical world (stating that parallel lines will intersect).  This is used throughout the Universe.

Key Highlights:
What is mathematics and science relationship?
Mathematics contribution in science?
गणित और विज्ञान का सम्बन्ध
गणित का विज्ञान में योगदान

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Mathematics of Alien


     Alien's mathematics and our mathematics may be slightly different, but there must be some overlap.
Mathematics and Alien
Alien Life & Mathematics
     Physics law of nature will be same in alien's world. Mathematics is like tool that provides analysis of things in most scientific way. Alien's way of performing mathematics may be slightly different. They may have different ways of proving and stating Pythagoras theorem, but end result will be same. They may have different number system and different ways of performing computation, but end result of mathematical computation will be same as ours.

     What will happen if alien comes in contact with us. It will be really an exciting moments for us. Both humans and alien can benefit with each other's knowledge if both work together for a better world without any conflict. Each of them can gain and exchange knowledge for betterment of this universe.

     Alien's mathematics can be advance or at par with us. This will be interesting to interact with alien's and have access to their way's of interacting with wonder's of this universe.
     Following major benefit to the math may take place when we interact with alien.

  1. Many new branches to both our and alien mathematics will start.

  2. New algorithm and concept will come to existence.

  3. We and alien will be solving each others unsolved mathematical jargon.

  4. we and alien will take benefit of each other mathematics.


Key Highlights:
What is alien mathematics?
Difference between our and alien mathematics
विदेसी संसार के प्राणी का गणित और हमारा गणित
क्या हमारा गणित विदेसी ग्रह के गणित से अलग है





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