Sunday 6 November 2016

Challenges In Mathematics


     Followings are major challenges in teaching mathematics to students and hence for the popularity and development of mathematics.

  • Challenges in Mathematics
    Challenge of Mathematics

  1. Availability of good teacher.

  2. Availability of good quality of reference text books.

  3. Availability of best quality teaching aids and environment setup.

  4. Proper motivation to young generation to take up research activity.


Key Highlights:
What is challenges in mathematics?
How to overcome mathematical challenges?
गणित की चुनौतियाँ
गणित की चुनौतियों का निपटारा 
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Futuristic Math

     Future of mathematics is bright. Mathematics best future is good for mankind. Mathematics has made yesterday's wonders a reality today. Mathematics is present everywhere. It has made possible today's reality a possibility. Mathematics is available in astronomy, electronics, biological computation and modelling, economics etc.
Mathematics in Future
Futuristic Math

     From 17th century onward mathematics has progressed a lot. Mankind should keep mathematical progress at the current level. For bright future of mathematics, we need bright mathematician. we need lots more Newton, Fermat, Gauss, Leibnitz to launch mathematics in new orbits.

     The dark side of story is that very few young mind are getting attraction towards mathematics. Every countries should encourage new vibrant and young blood in mathematic's beautiful world.

      A glimpse of future of mathematical advancement and computational power of mankind is given below.


  1. We will carry 100X times more computatonal power in our pocket after 10 years down the line.

  2. Current financial encryption security will be at risk and some more advanced encryption methods will be used.

  3. New starts, planets and galaxies will be discovered due to increase in computational power.

  4. Quantum mathematics will gain prominence.

  5. Visualisation and feel of math will be easy due to smart phone penetration and other devices popularity. This will elliminate math phobia from student.

Key Highlights:
What is math future?
How future math is different than present math?

भविष्य का गणित
गणित का भविष्य

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Lost Mathematicians


Takeo Nakasawa (1913 - 1946)
Lost Mathematician Takeo Nakasawa
Lost Mathematician-Takeo Nakasawa

     Matroid theory was invented in the middle of the 1930s independently by two great mathematicians ---- Hassler Whitney in the USA and Takeo Nakasawa in Japan. Whitney became famous for his work, but Nakasawa remained anonymous for almost two decades. He published  four papers of his work. His work was not recognised when he was alive. World recognised his contribution only after two decade.
Key Highlights:
Who are lost mathematicians?
How is contribution of lost mathematician?
गुमनाम गणितज्ञ
गुमनाम गणितज्ञ का योगदान





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Indian Mathematician


1. Aryabhata (476–550 CE)
Indian Mathematician Aryabhata
Indian Mathematician

Contributions:
  • Continued fraction in arithmetic
  • Quardatic equation and sum of power series in algebra
  • Sine table in plane trigonometry
  • Treatises on spherical trigonometry
  • Treatises on Astronomy


2. Bhaskara I (600–680 CE)
Indian Mathematician Bhaskara-I
Indian Mathematician

I is appended to his name to distinguish him from a 12th-century Indian astronomer of the same name. He was the first to write numbers in the Hindu decimal system with a circle for the zero.

Contributions:
  • Disseminate the mathematical work of Aryabhata
  • Mahabhaskariya (“Great Book of Bhaskara”) on astronomy
  • Laghubhaskariya (“Small Book of Bhaskara”) on astronomy 
  • Ryabhatiyabhashya  prose commentary on the Aryabhatiya of Aryabhata
3. Brahamgupta (598-665)
Indian Mathematician Brahamgupta
Indian Mathematician

Contributions:
  • Method to find cube and cube-root of an integer
  • Rules facilitating the computation of squares and square roots
  • Provided formula for the sum of the squares of the first n natural number
  • Provided formula for the sum of the cube of the first n natural number
  • His book "Brahmasphutasiddhanta” is probably the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit as was done by the Babylonians, or as a symbol for a lack of quantity as was done by the Greeks and Romans.


4. Srinivasa Ramanujan (1887-1920)
Indian Mathematician Srinivasa Ramanujan
Indian Mathematician

 Contributions:
  • Compiled nearly 3,900 results (mostly identities and equations)
  • His legendry work such as Ramanujan prime and the Ramanujan theta function, have inspired a vast amount of further research
5. Prasanta Chandra Mahalanobis(1893-1972)
Indian Mathematician Prasanta Chandra Mahalanobis
Indian Mathematician

Contributions:
  • Mahalanobis distance, a statistical measure
  • One of the members of the first Planning Commission of free india
  • Founder of Indian Statistical Institute, and contribution to the design of large-scale sample surveys
Awards and Recognition:
  • Fellow of the Royal Society, London (1945)
  • President of Indian Science Congress (1950)
  • Fellow of the American Statistical Association (1961)
6. Calyampudi Radhakrishna Rao(1920-Till date)
Indian Mathematician Calyampudi Radhakrishna Rao
Indian Mathematician

Contributions:
  • Estimation theory
  • Statistical inference and linear models
  • Combinatorial design
  • Orthogonal arrays
  • Biometry
  • Statistical genetics
  • Multivariate analysis
  • Generalized matrix inverses
  • Functional equations
Awards and Recognision:
  • Sardar Patel Lifetime Achievement Award (Sardar Ratna) of the Sardar Patel Foundation India (2015)
  • India Science Award 2010
  • International Mahalanobis Prize (2003) of the International Statistical Institute
  • Padma Bhushan (1968)
  • Megnadh Saha Medal (1969) of the Indian National Science Academy
  • JC Bose Gold Medal of the Bose Institute
  • Gold Medal of the University of Calcutta


7. D. R. Kaprekar(1905-1986)
Indian Mathematician D.R.Kaprekar
Indian Mathematician

Kaprekar constant is his one of the most famous contribution. Let's start with any four-digit number, not all the digits being equal. Suppose we choose 4637. Rearrange the digits to form the largest and smallest numbers with these digits, namely 7643 and 3467, and subtract the smaller from the larger to obtain 4167. Continue the process with this number - subtract 1467 from 7641 and we obtain 6174, Kaprekar's constant.

Contributions:
  • Kaprekar constant (6174)
  • A Kaprekar number n is such that n2 can be split into two so that the two parts sum to n. For example 7032 = 494209. But 494 + 209 = 703. 
  • Many other contributions in number theory.
8. Satyendranath Bose(1894-1974)
Indian Mathematician Satyendranath Bose
Indian Mathematician

Contributions:
  • Paper on Statistical mechanics
  • Work on quantum mechanics


9. Narendra Karmarkar(1957-Till date)
Indian Mathematician Narendra Karmarkar
Indian Mathematician

Contributions:
  • Invented a polynomial algorithm for linear programming also known as the interior point method
  • Karmarkar's algorithm to solve linear programming problems in polynomial time



Key Highlights:
Indian mathematician and their contribution
भारतीय गणितज्ञ
गणित में भारतीय गणितज्ञ का योगदान




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Greatest Mathematician of All Time


1. John Forbes Nash Jr.
Great Mathematician John Forbes Nash Jr.
Contributions:
  • Game Theory
  • Differential Geometry
  • partial differential equation
Award & Recognition:
  • got Nobel Prize for Economics in 1994
  • In 2015, he got Abel Prize for his work on nonlinear partial differential equations.
In 1959, Nash mental illness deteriorated and he spent several years at psychiatric hospitals being treated for paranoid schizophrenia. After 1970, his condition slowly improved and he returned to academic work by the mid-1980. His struggles with his illness and his recovery became the basis for Sylvia Nasar's biography, A Beautiful Mind, as well as a film of the same name starring Russell Crowe. On May 23, 2015, Nash and his wife, were killed in a car crash while riding in a taxi on the New Jersey.


2. Pythagoras of Samos (570BC - 495BC, Greek)


Great Mathematician Pythagoras


    Contributions:
    • Pythagoras Theorem
    • Number Theory
    • Concept of geometrical figure (triangle, rectangle) and related theorem


    3. Andrew Wiles (1953-till today, Great Britain)
    Great Mathematician Andrew Wiles
    Contributions:
    He provided proof of Fermat’s last theorem. No positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula).




    4. Isaac Newton (1642-1727)
    Great Mathematician Isaac Newton
    Contributions:
    • Inventor of calculus
    • Binomial Theorem


    5. Leonardo Pisano Blgollo (1170-1250)



    Blgollo is also known as Leonardo Fibonacci.

    Contributions:
    • Fibonacci Series
    •  Introduction of the Arabic numbering system

    6. Alan Turing (1912-1954)
    Great Mathematician Alan Turing
    He is regarded as one of the greatest mind of 20th Century. He was computer scientist and crypt-analyst. He has written many brilliant papers that are still relevant today.

    Contributions:
    • Formulated the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general purpose computer
    • Considered the father of theoretical computer science and artificial intelligence


    7. René Descartes (1596 - 1650)
    Great Mathematician Rene Descartes
    • He developed Cartesian Geometry.


    8. Euclid (300BC)
    Great Mathematician Euclid
    • He is considered father of geometry. 

    9. G. F. Bernhard Riemann (1826-1866)
    Great Mathematician Bernhard Riemann
    The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers.


    10. Carl Friedrich Gauss
    Great Mathematician Carl Friedrich Gauss


    • He introduced Gaussian gravitational constant in physics.



    11. Leonhard Euler (1707 - 1783)
    Great Mathematician Leonhard Euler


    he is regarded as the greatest mathematician to have ever walked this planet. In his day he was ground breaking and on par with Einstein in genius. 



    Key Highlights:
    World mathematician
    Contribution of mathematician
    महान्तम गणितज्ञ एवं उनका योगदान






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