A nice and well organized format made to help others in need

1.  NATURE OF MATHEMATICS
 OBJECTIVE OF MATHEMATICS
 CHRACTERISTICS OF MATHEMATICS
 MATHEMATICS AND PHYSICAL WORLD
 HISTORY OF MATHEMATICS USEFUL FOR TEACHER
 CONTRIBUTION OF INDIAN MATHEMATICIAN
 CONCLUSION
 BIBLIOGRAPHY

2.  Is a science of number and space.
 Own language-signs, symbols, terms and operations.
 Involves man’s high cognitive powers.
 Has own tools like intuition, logic, reasoning, analysis, etc.
 Helps in drawing conclusions and interpreting various ideas.
 The tool specially suited for dealing with abstract ideas.
 It helps in solving the problems of our life.

3.  Knowledge and understanding objectives.
 Skill objectives.
 Application objectives.
 Attitude objectives.
 Appreciation and interest objectives.

4.  It is the science of measurement, quantity and magnitude.
 It is the systematized, organized and extract branch of science.
 It is the science of calculations.
 It deals with quantitative facts and relationships.
 It is the abstract form of science.
 It is a science of logical reasoning.
 It is an inductive and experimental science.

5. If we take physics we see that its study requires the knowledge of
mathematics at every point. All the physical laws, laws of motion,
laws of lever, etc can only be understood and applied with the help
of the understanding of mathematics. The need of the numerical
calculations in dealing with the problems in physics clearly reveals
the value of mathematics in learning physics.

6.  Role of mathematics in various walks of life.
 Shows the correlation of mathematics.
 Brings out significant developments.
 Makes mathematics teaching effective.
 Easier to understand.
 Helps in gradation.
 Helps in enhancing the reputation.
 Better understanding of the subject.

7.  RAMANUJAN
 He was born on 22naof December 1887 in a small village
of Tanjore district, Madras.He failed in English in Intermediate,
so his formal studies were stopped but his self-study of
mathematics continued.
He sent a set of 120 theorems to Professor Hardy of Cambridge.
As a result he invited Ramanujan to England.
Ramanujan showed that any big number can be written as sum of
not more than four prime numbers.
He showed that how to divide the number into two or more
squares or cubes.

8.  ARYABHATTA
Aryabhatta was born in 476A.D in Kusumpur, India.
He was the first person to say that Earth is spherical and it
revolves around the sun.
He gave the formula (a + b)2 = a2 + b2 + 2ab
He taught the method of solving the following problems:
14 + 24 + 34 + 44 + 54 + …………+ n4 = n(n+1) (2n+1) (3n2+3n-1)/30

9.  BRAHMA GUPTA
Brahma Gupta was born in 598A.D in Pakistan.
He gave four methods of multiplication.
He gave the following formula, used in G.P series
a + ar + ar2 + ar3 +……….. + arn-1 = (arn-1) ÷ (r – 1)
He gave the following formulae :
Area of a cyclic quadrilateral with side a, b, c, d= √(s -a)(s- b)(s -
c)(s- d) where 2s = a + b + c + d

10.  SHAKUNTALA DEVI
She was born in 1939
In 1980, she gave the product of two, thirteen digit numbers within 28 seconds,
many countries have invited her to demonstrate her extraordinary talent.
In Dallas she competed with a computer to see who give the cube root of
188138517 faster, she won. At university of USA she was asked to give the 23rdroot
of9167486769200391580986609275853801624831066801443086224071265164279
346570408670965932792057674808067900227830163549248523803357453169351
119035965775473400756818688305620821016129132845564895780158806771.She
answered in 50seconds. The answer is 546372891. It took a UNIVAC 1108
computer, full one minute (10 seconds more) to confirm that she was right after
it was fed with 13000 instructions. Now she is known to be Human Computer.

11.  BHASKARACHARYA
 He was born in a village of Mysore district.
He was the first to give that any number divided by 0 gives
infinity (00).
He has written a lot about zero, surds, permutation and
combination.
He wrote, “The hundredth part of the circumference of a circle
seems to be straight. Our earth is a big sphere and that’s why it
appears to be flat.”
He gave the formulae like sin(A ± B) = sinA.cosB ± cosA.sinB

12.  MAHAVIRA
Mahavira was a 9th-century Indian mathematician from Gulbarga who asserted
that the square root of a negative number did not exist. He gave the sum of a
series whose terms are squares of an arithmetical progression and empirical
rules for area and perimeter of an ellipse. He was patronised by the great
Rashtrakuta king Amoghavarsha. Mahavira was the author of Ganit Saar
Sangraha. He separated Astrology from Mathematics. He expounded on the
same subjects on which Aryabhata and Brahmagupta contended, but he
expressed them more clearly. He is highly respected among Indian
Mathematicians, because of his establishment of terminology for concepts such
as equilateral, and isosceles triangle; rhombus; circle and semicircle. Mahavira’s
eminence spread in all South India and his books proved inspirational to other
Mathematicians in Southern India.

13.  PYTHAGORAS
This eventually led to the famous saying that “all things are numbers.”
Pythagoras himself spoke of square numbers and cubic numbers, and we still
use these terms, but he also spoke of oblong, triangular, and spherical numbers.
He associated numbers with form, relating arithmetic to geometry. His greatest
contribution, the proposition about right-angled triangles, sprang from this line
of thought:
From Pythagoras we observe that an answer to a problem in science may give
raise to new questions. For each door we open, we find another closed door
behind it. Eventually these doors will be also be opened and reveal answers in a
new dimension of thought. A sprawling tree of progressively complex
knowledge evolves in such manner. This Hegelian recursion, which is in fact a
characteristic of scientific thought, may or may not have been obvious to
Pythagoras. In either way he stands at the beginning of it.

14.  ARYABHATTA I
Quadratic equations
Trigonometry
The value of π, correct to 4 decimal places.
Arithmetic
Algebra
Mathematical astronomy
Calculus

15.  VARAHAMIHIRA
Varahamihira (505-587) produced the Pancha Siddhanta (The Five
Astronomical Canons). He made important contributions to
trigonometry, including sine and cosine tables to 4 decimal places
of accuracy and the following formulas relating sine and cosine
functions:
sin2(x) + cos2(x) = 1

16.  NIELS HENRIK ABEL
Niels Henrik Abel (August 5, 1802 – April 6, 1829) was a noted
Norwegian mathematician[1] who proved the impossibility of
solving the quintic equation in radicals.

17.  CARL FRIEDRICH GAUSS
Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a
German mathematician and scientist who contributed significantly to
many fields, including number theory, statistics, analysis, differential
geometry, geodesy, geophysics, electrostatics, astronomy and optics.
Sometimes known as the Princeps mathematicorum and “greatest
mathematician since antiquity”, Gauss had a remarkable influence in
many fields of mathematics and science and is ranked as one of history’s
most influential mathematicians. He referred to mathematics as “the
queen of sciences.”
He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at
the age of 21, though it would not be published until 1801. This work was
fundamental in consolidating number theory as a discipline and has
shaped the field to the present day.

18.  LEONHARD EULER
 Leonhard Paul Euler (15 April 1707 – 18 September 1783) was a pioneering Swiss
mathematician and physicist who spent most of his life in Russia and Germany.
 Euler made important discoveries in fields as diverse as infinitesimal calculus and
graph theory. He also introduced much of the modern mathematical terminology and
notation, particularly for mathematical analysis, such as the notion of a mathematical
function. He is also renowned for his work in mechanics, fluid dynamics, optics, and
astronomy.
 Euler is considered to be the preeminent mathematician of the 18th century and one of
the greatest of all time. He is also one of the most prolific; his collected works fill 60–80
quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler’s
influence on mathematics: “Read Euler, read Euler, he is the master [i.e., teacher] of us
all.” Euler was featured on the sixth series of the Swiss 10-franc banknote and on
numerous Swiss, German, and Russian postage stamps. The asteroid 2002 Euler was
named in his honor. He is also commemorated by the Lutheran Church on their
Calendar of Saints on 24 May – he was a devout Christian (and believer in biblical
inerrancy) who wrote apologetics and argued forcefully against the prominent atheists of
his time.

19.  DAVID HILBERT
David Hilbert (January 23, 1862 – February 14, 1943) was a German
mathematician, recognized as one of the most influential and universal
mathematicians of the 19th and early 20th centuries. He discovered and
developed a broad range of fundamental ideas in many areas, including
invariant theory and the axiomatization of geometry. He also formulated the
theory of Hilbert spaces one of the foundations of functional analysis.
Hilbert adopted and warmly defended Georg Cantor‘s set theory and transfinite
numbers. A famous example of his leadership in mathematics is his 1900
presentation of a collection of problems that set the course for much of the
mathematical research of the 20th century.
Hilbert and his students contributed significantly to establishing rigor and
some tools to the mathematics used in modern physics. He is also known as one
of the founders of proof theory, mathematical logic and the distinction between
mathematics and metamathematics.

20.  BERNHARD RIEMANN
Georg Friedrich Bernhard Riemann (help·info) (German
pronunciation: [ˈriË•man]; September 17, 1826 – July 20, 1866)
was an influential German mathematician who made lasting
contributions to analysis and differential geometry, some of them
enabling the later development of general relativity.

21.  EUCLID
Euclid of Alexandria, was a Greek mathematician and is often
referred to as the “Father of Geometry.” He was active in
Hellenistic Alexandria during the reign of Ptolemy I (323–283 BC).
His Elements is the most successful textbook and one of the most
influential works in the history of mathematics, serving as the
main textbook for teaching mathematics (especially geometry)
from the time of its publication until the late 19th or early 20th
century. In it, the principles of what is now called Euclidean
geometry were deduced from a small set of axioms. Euclid also
wrote works on perspective, conic sections, spherical geometry,
number theory and rigor.

22. Thus the contributions of these mathematicians are
tremendous in the field of mathematics. They gave a new era
to the modern mathematics. Their methods are still around
us and we are applying it. They gave some unique view to the
world of mathematics which is unforgettable. If we compare
of the situation under which they worked all and achieved
this we come to realize that it is a great achievement for
them.

23. Bourbaki, Nicolas (1998), Elements of the History of Mathematics, Berlin,
Heidelberg, and New York: Springer-Verlag, 301 pages, ISBN 3-540-64767-8.
Boyer, C. B.; Merzback (fwd. by Isaac Asimov), U. C. (1991), History of
Mathematics, New York: John Wiley and Sons, 736 pages, ISBN 0-471-54397-7.
Bronkhorst, Johannes (2001), "Panini and Euclid: Reflections on Indian
Geometry", Journal of Indian Philosophy, (Springer Netherlands) 29 (1–2): 43–
80, doi:10.1023/A:1017506118885.
Burnett, Charles (2006), "The Semantics of Indian Numerals in Arabic,
Greek and Latin", Journal of Indian Philosophy, (Springer-Netherlands) 34 (1–
2): 15–30, doi:10.1007/s10781-005-8153-z.
Burton, David M. (1997), The History of Mathematics: An Introduction, The
McGraw-Hill Companies, Inc., pp. 193–220.
Cooke, Roger (2005), The History of Mathematics: A Brief Course, New York:
Wiley-Interscience, 632 pages, ISBN 0-471-44459-6.
Dani, S. G. (25 July 2003), "Pythogorean Triples in the Sulvasutras" (PDF),
Current Science 85 (2): 219–224.
Datta, Bibhutibhusan (Dec 1931), "Early Literary Evidence of the Use of the
Zero in India", The American Mathematical Monthly 38 (10): 566–572,
doi:10.2307/2301384, JSTOR 2301384.