Wednesday, 27 September 2017

puzzle game

1.What number should replace the question mark?

 2.What number should replace the question mark?



ANSWERS:
1) 17: it is the sum of the two digits (9 + 8) in the quadrant
directly opposite.
2)55: each number indicates its position in the grid. 55 indicates
row 5 column 5.

Sunday, 24 September 2017

புள்ளியியலில் மிகச்சிறப்பு வாய்ந்த துறைகள்

புள்ளியியலில் மிகச்சிறப்பு வாய்ந்த துறைகள்

சில துறைகள் பயன்பாட்டுப் புள்ளியியல் ஆராய்ச்சிகளை பரவலாக மேற்கொள்வதால், அவற்றிற்கு மிகச்சிறப்பு வாய்ந்த பெயர்களும் உள்ளன. கீழே வழங்கிய துறைகள் அவற்றை சார்ந்தவை:
·         உண்மையுரிமை அறிவியல்
·         பயன்பாட்டுத் தகவல் பொருளாதாரம்
·         உயிரிபுள்ளியியல்
·         காலணி நூல் மற்றும் மாலுமிக்கத்தி மறு மாதிரிமுறை
·         வணிகவியல் புள்ளியியல்
·         வேதியியல் புள்ளியியல் (வேதியியல்சம்பந்தப்பட்ட தரவுகளுக்கான புள்ளியியல் ஆய்வு)
·         தரவுகளை சுரண்டி எடுத்தல் (புள்ளியியல் மற்றும் கோலப்பாங்குகளை அடையாளம் காணுதல் மூலமாக தரவுகளில் இருந்து அறிவாற்றலை கண்டெடுத்தல்)
·         மக்கள்தொகையியல்

     
வணிகவியல் மற்றும் உற்பத்தித்துறையிலும் புள்ளியியல் ஒரு முக்கிய அடிப்படைக்கருவியாக விளங்குகிறது. அதை வைத்துக்கொண்டு அளவுமானிகளின் மாறுபடும் தன்மையை அறிந்துகொள்ளவும், செய்முறைகளை கட்டுப்படுத்தவும், (புள்ளியியல் செயல்முறை கட்டுப்பாடு போன்ற (SPC), தரவுகளை தொகுப்பதற்காகவும், மற்றும் தரவுகளை சார்ந்த முடிவுகளை எடுப்பதற்காகவும் பயன்படுகிறது. இதுபோன்ற பணிகளில், இது ஒரு முக்கியமான கருவியாகும், மற்றும் நம்பத்தகும் ஒரே கருவியாகவும் இது இருக்கலாம்.


Saturday, 23 September 2017

புள்ளியியலின் வரலாறு

சில அறிஞர்கள் புள்ளியியல் முதல் முதலாக 1663 ஆண்டில் தோன்றியதாக சுட்டிக்காட்டுகின்றனர், ஜான் கிரான்ட் என்பவர் அவ்வாண்டு நாச்சுரல் அண்ட் பொலிடிகல் ஓப்செர்வேசன்ஸ் அபான் தி பில்ஸ் ஒப் மோர்டாலிடி என்ற கட்டுரையை வெளியிட்டார். நாட்டின் மக்கள் தொகை மற்றும் பொருளாதார தேவைகளின் அடிப்படையில் முந்தைய சிந்தனையாளர்கள் நாட்டிற்கான கொள்கைகளை உருவாக்க நினைத்ததால், ஆங்கிலத்தில் தொடக்கத்தில்ஸ்டேட் - என்ற சொல்தோற்றத்திற்கு காரணமாக அமைந்தது. புள்ளியியல் என்ற பிரிவின் நோக்கெல்லை 19 ஆம் நூற்றாண்டில் மேலும் விரிவடைந்தது மேலும் பொதுவாக தரவுகளை சேகரிப்பது மற்றும் தரவுகளை ஆராய்ந்து பார்ப்பதையும் அத்துடன் இணைத்துக் கொண்டது. இன்றுபுள்ளியியல் மிகவும் பரவலாக அரசு, தொழில் அல்லது வணிகம், இயற்கை அறிவியல் மற்றும் சமூக அறிவியல் போன்ற துறைகளில் பயன்பட்டு வருகிறது.
அனுபவபூர்வமான ஆதாரங்களை அடிப்படையாக கொண்டதாலும், மற்றும் அதன் குவிமையம் பயன்பாட்டில் வேரூன்றியதாலும்புள்ளியியல் என்பது கணிதத்தின் ஒரு கிளையாக அல்லாமல், பொதுவாக ஒரு தனிப்பட்ட கணித அறிவியலாக கருதலாம். 17 ஆம் நூற்றாண்டில் பிளைஸ் பாஸ்கல் மற்றும் பிஎர்ரே தே பெர்மாத் ஆகிய இருவரும் நிகழ்ச்சித்தகவு கொள்கை என்ற பகுப்பை மேலும் மேம்படுத்தினார்கள் மற்றும் அதனுடைய கணிதத்திற்குரிய அடித்தளத்தையும் அமைத்தார்கள். நிகழ்ச்சித்தகவு கொள்கை என்ற பிரிவானது வாய்ப்புகளுக்கான விளையாட்டுக்களை பயிலும் போது ஏற்பட்டது. முதன் முதலாக குறைந்த வர்க்க முறை (method of least squares) கார்ல் பிரீட்ரிச் காஸ் (Carl Friedrich Gauss) என்பவர் 1794 ஆண்டுகளில் விவரித்தார். இன்றைய நவீன கணினிகளின் பயன்பாடு மிகையான அளவிலான புள்ளிவிவரங்கள் சார்ந்த கணக்கிடுதல் முறைகளை துரிதப்படுத்தியுள்ளது மேலும் மனிதனால் இயலாத சில புதிய முறைகளை செயல்படுத்தவும் அதன் மூலம் சாத்தியமாகி உள்ளது.
தி அமெரிக்கன் ஸ்டட்டடிக்கல் அசோசியேஷன் (American Statistical Association) என்ற அமைப்பு டெமிங் (Deming), பிஷேர் (Fisher), மற்றும் சி ஆர் ராவ் (CR Rao) போன்றவர்களை எக்காலத்தையும் சார்ந்த மிகவும் மகத்தான புள்ளியியல் வல்லுனர்களாக தரவரிசைப்படுத்தியுள்ளது.


Friday, 22 September 2017

Probability


                                 Probability


 Probability:
   It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knoweldge.

Randam Experiment
A Randam experiment is one in which the  exact outcome cannot be predicated before conducting the experiment . However, One can list out all possible outcomes of the experiment.

Sample Space:
                    The set of all possible outcomes of a Randam experiment is called its same space. It is denoted by the letter 8.
Trial:              
Each repetition of the experiment is called a trail.
 Event :
A subject of the sample space “s” is called an event.

Tuesday, 19 September 2017

MATHS PUZZLE GAME

1.What number should replace the question mark?






2.What number should replace the question mark?

ANSWERS:
1)5: (8 + 7) × 5 = 75
2) 4: looking across at the three circles, the number in the
middle is the product of the two numbers in the same
segment in the other two circles. Thus, 3 × 2 = 6, 7 × 3 =
21 and 4 × 4 = 16.

Monday, 18 September 2017

INDIAN MATHEMATICS - BRAHMAGUPTA


                                 BRAHMAGUPTABrahmagupta (598–668 CE)

The great 7th Century Indian mathematician and astronomer Brahmagupta wrote some important works on both mathematics and astronomy. He was from the state of Rajasthan of northwest India (he is often referred to as Bhillamalacarya, the teacher from Bhillamala), and later became the head of the astronomical observatory at Ujjain in central India. Most of his works are composed in elliptic verse, a common practice in Indian mathematics at the time, and consequently have something of a poetic ring to them.
                 It seems likely that Brahmagupta's works, especially his most famous text, the “Brahmasphutasiddhanta”, were brought by the 8th Century Abbasid caliph Al-Mansur to his newly founded centre of learning at Baghdad on the banks of the Tigris, providing an important link between Indian mathematics and astronomy and the nascent upsurge in science and mathematics in the Islamic world.
        In his work on arithmetic, Brahmagupta explained how to find the cube and cube-root of an integer and gave rules facilitating the computation of squares and square roots. He also gave rules for dealing with five types of combinations of fractions. He gave the sum of the squares of the first n natural numbers as n(n + 1)(2n + 1)⁄ 6 and the sum of the cubes of the first n natural numbers as (n(n + 1)⁄2)².
             Brahmagupta’s rules for dealing with zero and negative numbers.  Brahmagupta’s genius, though, came in his treatment of the concept of (then relatively new) the number zero. Although often also attributed to the 7th Century Indian mathematician Bhaskara I, his “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.
      .



Sunday, 17 September 2017

Babbage, Charles

                           Babbage, Charles
                                                 (1792–1871) British,Analysis



The name of Charles Babbage is associated with the early computer. Living during the industrial
age, in a time when there was unbridled optimism in the potential of machinery to improve
civilization, Babbage was an advocate of mechanistic progress, and spent much of his lifetime
pursuing the invention of an “analytic engine.” Although his ambitious project eventually ended
in failure, his ideas were important to the subsequent develop of computer logic and technology.
Born on December 26, 1792, in Teignmouth, England, to affluent parents, Babbage exhibited
great curiosity for how things worked. He was educated privately by his parents, and by the
time he registered at Cambridge in 1810, he was far ahead of his peers. In fact, it seems that he
knew more than even his teachers, as mathematics in England had lagged far behind the rest
of Europe. Along with George Peacock and John Herschel, he campaigned vigorously for the resuscitationof English mathematics.

Friday, 15 September 2017

Democritus of Abdera

Democritus of Abdera

(ca. 460 B.C.E.–ca. 404 B.C.E.)Greek Geometry


           Democritus is numbered among the very early Greek mathematicians who influenced the later
development of geometry. Although his mathematical works have not survived, it is clear that
Democritus possessed an extensive interest in conics and other aspects of solid geometry. The
great Greek geometers APOLLONIUS OF PERGA and ARCHIMEDES OF SYRACUSE came much later,
but even they studied some of the problems investigated by Democritus.
Information on Democritus’s life is distorted by several unverifiable accounts. One chronology
places his birth after 500 B.C.E. and his death about 404 B.C.E., and represents him as the
teacher of Protagoras of Abdera; another version frames his life much later, depicting him as a
contemporary of Socrates, being born around460 B.C.E. and dying in about 404 B.C.E. Most
scholars accept the latter dates.
         

Thursday, 14 September 2017

MATHS GAME


1.Which number is the odd one out?
       
       9654 4832 5945 7642 7963 8216 3649
2.Find five consecutive numbers below that total 23.
   
          6 2 9 3 4 7 2 9 3 2 6 4 9 1 2
3.What number should replace the question mark?


ANS:

1.3649: in all the others multiply the first two digits togetherto produce the number formed by the last two digits..2.72932

3.1417: 42 ÷ 3 = 14, 51 ÷ 3 = 17

Wednesday, 13 September 2017

Archimedes of Syracuse


Archimedes of Syracuse(ca. 287 B.C.E.–212 B.C.E.)Greek Geometry 

MechanicsOf the mathematicians of Greek antiquity,
Archimedes should be considered the greatest.
His contributions to geometry and mechanics,
as well as hydrostatics, place him on a higher
pedestal than his contemporaries. And as his
works were gradually translated and introduced
into the West, he exerted as great an influence
there as his thought already had in Byzantium
and Arabia.

Tuesday, 12 September 2017

Ramanujan, Srinivasa Aiyangar

Ramanujan, Srinivasa Aiyangar

                                                            (1887–1920)Indian                                                                                                                                      Number Theory
  1. The Indian mathematician Ramanujan led a short life full of mathematics. From a highly disadvantageous background, he was able to make substantial contributions to number theory. His feverish preoccupation with mathematics, bordering on obsession, is remarkable for its intensity and devotion. He is remembered as one of India’s greatest mathematical geniuses.
  2. Srinivasa Aiyangar Ramanujan was born in Erode, Madras Province, India, on December 22,1887. Although descended from the Brahman caste, his family was quite poor, as his father was a bookkeeper for a local cloth merchant. He excelled in his early education, and in 1900 he began his own investigations of mathematics. In 1903 he borrowed G.S. Carr’s Synopsis of Pure Mathematics, which contained thousands of theorems. Ramanujan quickly devoured this book,and mathematics became his sole interest.
  3. It is said of Ramanujan that he was quiet and meditative, with a fondness for numerical calculations and an unusual memory. In 1904 he won a fellowship at Government College, but failed to graduate due to his neglect of English.For a time he was without a definite occupation;he spent his time jotting down results and computations in a little notebook. In 1909, at age 22, he married, at the arrangement of his mother,a 9-year old girl. Shortly thereafter he secured a job as a clerk, and in 1912 worked at the Madras Port Trust. At this time, his first publication appeared, titled Some Properties of Bernoulli Numbers (1911), a communication on series, infinite products, and a geometric approximate construction of pi. In the Madras area, he was increasingly recognized for his brilliant work.

Monday, 11 September 2017

Pythagoras of Samos

                      Pythagoras of Samos

                     ca. 569 B.C.E.–ca. 475 B.C.E.
                   Greek Number Theory, Geometry
Pythagoras of Samos was one of the earliest Greek
mathematicians, and is certainly one of the most
famous of all time due to the well-known
Pythagorean theorem. However, very little is
known of his life, and what details exist are reconstructed
from several secondary sources. He
left no writings of his own behind him.
Pythagoras of Samos was born around 569
B.C.E. on the island of Samos, Greece. His father,
Mnesarchus, was a Phoenician merchant who
earned citizenship at Samos by delivering a
shipment of grain during a time of famine.
His mother was Pythais, a native of Samos.
 [Pythagoras was a philosopher who believed numbers
had personalities. His cult formulated and proved the
Pythagorean theorem.]
Pythagoras received the best education, being
trained in poetry and music, and later in philosophy.
He had two brothers, and the family
traveled extensively during Pythagoras’s youth,
visiting Italy and Tyre.
        Pythagoras was later taught by THALES OF
MILETUS and his pupil Anaximander; from
Thales he gained an appreciation for geometry,
and he traveled to Egypt in 535 B.C.E. to further
his studies. Before he left, the tyrant Polycrates
took over Samos, and Pythagoras’s friendship
with him facilitated his introduction into
Egyptian society, since Polycrates had an alliance
with Egypt. Pythagoras visited with the
priests there, but was admitted only to the temple
of Diospolis, where he was inducted into the
religious mysteries. It seems that many of
Pythagoras’s later beliefs, as well as the rites of
the cult he would later found, were drawn from
his time among the Egyptian clerics for instance,
his vegetarianism and stress on ethical
purity can be traced to his time in Egypt. In
terms of mathematics, it is not likely that he
learned much more there than Thales would
have taught him.