2. For more than two thousand years, mathematics has been a part of the human
search for understanding. Mathematical discoveries have come both from the
attempt to describe the natural world and from the desire to arrive at a form of
inescapable truth from careful reasoning. These remain fruitful and important
motivations for mathematical thinking, but in the last century mathematics has
been successfully applied to many other aspects of the human world: voting
trends in politics, the dating of ancient artifacts, the analysis of automobile
traffic patterns, and long-term strategies for the sustainable harvest of
deciduous forests, to mention a few. Today, mathematics as a mode of thought
and expression is more valuable than ever before. Learning to think in
mathematical terms is an essential part of becoming a liberally educated
3. Mathematics first arose from the practical need to measure time and to
count. The earliest evidence of primitive forms of counting occurs in
notched bones and scored pieces of wood and stone. Early uses of
geometry are revealed in patterns found on ancient cave
As civilisations arose in Asia and the Near East, sophisticated number
systems and basic knowledge of arithmetic, geometry, and algebra began
4. The ancient Egyptians (3rd millennium BC), Sumerians (20001500 BC), and Chinese (1500 BC) had systems for writing
down numbers and could perform calculations using various
types of abacus.
The Egyptians were able to solve many different kinds of practical mathematical problems, ranging
from surveying fields after the annual floods to making the intricate calculations necessary to build
the pyramids. Egyptian arithmetic, based on counting in groups of ten, was relatively simple. This
Base-10 system probably arose for biological reasons, we have 8 fingers and 2 thumbs. Numbers
are sometimes called digits from the Latin word for finger. Unlike our familiar number
system, which is both decimal and positional (23 is not the same as 32), the Egyptians' arithmetic
was not positional but additive.
Unlike the Egyptians, the Babylonians of ancient Mesopotamia (now Iraq) developed a more
sophisticated base-10 arithmetic that was positional, and they kept mathematical records on clay
tablets. The most remarkable feature of Babylonian arithmetic was its use of a sexagesimal (base
60) place-valued system in addition to a decimal system. Thus the Babylonians counted in groups
of sixty as well as ten. Babylonian mathematics is still used to tell time - an hour consists of 60
minutes, and each minute is divided into 60 seconds - and circles are measured in divisions of 360
5. The Greeks were the first to develop a truly
mathematical spirit. They were interested not only in
the applications of math's but in its philosophical
The Greek philosopher Pythagoras, explored the nature
of numbers, believing that everything could be
understood in terms of whole numbers or their ratios.
Ancient knowledge of the sciences was often wrong
and wholly unsatisfactory by modern standards.
However, the math's of Euclid, Apollonius of
Perga, and Archimedes--the three greatest
mathematicians of antiquity--remains as valid today as
it was more than 2,000 years ago.
Roman mathematicians, in contrast to the
Greeks, were renowned for being very practical. The
Romans cared for the usefulness of math in measuring
6. Indian mathematicians were especially skilled in arithmetic, methods of calculation, algebra, and trigonometry. Their
decimal place-valued number system, including zero, was especially suited for easy calculation. Aryabhata (476-550?)
an Indian astronomer and the earliest Hindu mathematician was one of the first to use algebra. Aryabhata calculated
pi to a very accurate value of 3.1416.
When the Greek civilization declined, Greek mathematics (and the rest of Greek science) was kept alive by the Arabs.
The Arabs also learned of the considerable scientific achievements of the Indians, including the invention of a system
of numerals (now called `arabic´ numerals) which could be used to write down calculations instead of having to resort
to an abacus.
One of the greatest scientific minds of Islam was al-Khwarizmi, who introduced the name (al-jabr) that became known
as algebra. By the end of the 8th century the influence of Islam had extended as far west as Spain. It was
there, primarily, that Arabic, Jewish, and Western scholars eventually translated Greek and Islamic manuscripts into
By the 13th century, original mathematical work by European authors had begun to appear. It was the demands of
commerce which gave the major impetus to mathematical development and north Italy, the centre of trade at the
time, produced a succession of important mathematicians beginning with Italian mathematician Leonardo Fibonacci
who introduced Arabic numerals. The Italians made considerable advances in elementary arithmetic which was
needed for money-changing and for the technique of double-entry book-keeping invented in Venice.
7. During the 1400's and
1500's, European explorers sought new
overseas trade routes, stimulating the
application of Mathematics to
navigation and commerce.
The invention of printing in the
mid 1400's resulted in the speedy and widespread communication of
8. Mathematics received considerable stimulus
in the 17th century from astronomical
problems. The astronomer Johannes
Kepler, for example, discovered the elliptical
shape of the planetary orbits.
The greatest achievement of the 17th century
was the discovery of methods that applied
mathematics to the study of motion. An
example is Galileo's analysis of the parabolic
path of projectiles, published in 1638.
The greatest development of mathematics in
the 18th century took place on the
Continent, where monarchs such as Louis
XIV, Frederick the Great, and the Empress
Catherine the Great of Russia provided
generous support for science, including
9. The 19th century witnessed tremendous change
in maths with increased specialization and new
theories of algebra and number theory. Public
education expanded rapidly, and mathematics
became a standard part of University Education.
Mathematicians in England slowly began
to take an interest in advances made on
the Continent during the previous century.
The Analytic Society was formed in 1812
to promote the new notation and ideas of
the calculus commonly used by the
10. In the 20th century, mathematics has become much more diversified. Each specialist
subject is being studied in far greater depth and advanced work in some fields may be
unintelligible to researchers in other fields. Mathematicians working in universities have
had the economic freedom to pursue the subject for its own sake. Nevertheless, new
branches of mathematics have been developed which are of great practical importance
and which have basic ideas simple enough to be taught in secondary schools. Probably
the most important of these is the mathematical theory of statistics in which much
Another new development is operations research, which is concerned with finding
optimum courses of action in practical situations, particularly in economics and
As in the late medieval period, commerce began to emerge again as a major impetus for
the development of mathematics. Higher mathematics has a powerful tool in the highspeed electronic computer, which can create and manipulate mathematical `models´ of
various systems in science, technology, and commerce.
11. It's really a great question, and not particularly an easy one to answer.
It's a big enough thing that you can describe it in a lot of different
ways, depending on your perspective.
Maths is the study of how to create, manipulate, and understand abstract
structures. Abstract structures are the heart of it. Math can work with
numbers: the various different sets of numbers are examples of one of the
kinds of abstract structures that we can work with. But math is so much
more than just numbers. It's numbers, and sets, and categories, and
topologies, and graphs, and much, much more.
12. The topics which are mainly useful in daily life are :
13. COMMERCIAL MATHEMATICS
This include the following topics :
Stock and Share
Arithmetic ( Profit & Loss, Percentage, Ratio and Proposition , Time
Discount : Reduction from the full amount of a price .
The following are the six types of discounts which we see are
Simple Discount. Offer a price reduction on a product by a
percentage. For example, buy a shirt and receive 25 % off the original
Minimum Purchase Discount. Offer a price reduction on a minimum
quantity purchase. For example, buy two shirts and receive 20 % off
Buy N, Get one Free. Offer a free gift with a minimum quantity purchase. For example, buy
two shirts and receive a third shirt for free.
Paired Discount. Offer a price reduction on a product if another
product is purchased. For example, buy a shirt and receive Rs.10 off a
pair of jeans.
Paired Set Discount. Offer a price reduction on an item if a certain quantity of another item is
purchased. For example, buy three shirts and receive 30 % off a pair of jeans.
Order Discount. Offer a price reduction or free shipping on the order
total, if a certain amount is purchased. For example, buy Rs. 5000
worth of merchandise, and receive 10 % off the total order.
Banking : A system of trading in money which involved safeguarding
deposits and making funds available for borrowers.
What is the use of mathematics in Banking ?
Bank is full of transactions. In turn the transaction is nothing but
Banks are also involved in stocks and bonds. Bond
calculations are mathematical. Stock options are
also quite mathematical.
16. Foreign Exchange Market
The foreign exchange (currency)
market refers to the market for
currencies. Transactions in this
market typically involve one
party purchasing a quantity of
one currency in exchange for paying a
quantity of another.
What are the rate of exchange of
different counties w.r.t.
17. Stock and Share
Stock and Share :In business and finance, a share (also referred to
as equity share) of stock means a
share of ownership in a corporation (company). In the
plural, stocks is often used as a synonym for shares
A stock is at a premium ( above par) , at par or at a discount (below par )
according as its market value is greater than , equal to or less than the face
Generally stocks are sold and purchased through brokers. The amount paid
to them in selling and purchasing stocks are called Brokerage.
so ,C.P.=M.V. + Brokerage
Arithmetic ( Profit & Loss, Percentage, Ratio and Proposition , Time related
problems): The word refers to a branch of mathematics which records
elementary properties of certain operations on numbers.
The traditional arithmetic operations are addition, subtraction, multiplication
and division, although more advanced operations (such as manipulations of
percentages, square root, exponentiation, and logarithmic functions) are also
sometimes included in this subject.
Algebra : It is a branch
structure, relation, and quantity.
Classification :Algebra may be divided into the following categories:
Elementary algebra, in which the properties of operations on the real number
system are recorded using symbols as "place holders" to denote constants and
variables, and the rules governing mathematical expressions and equations involving
these symbols are studied
Abstract algebra, sometimes also called modern algebra, in which algebraic
structures such as groups, rings and fields are axiomatically defined and investigated.
Linear algebra, in which the specific properties of vector spaces are studied (including
Universal algebra, in which properties common to all algebraic structures are studied.
Algebraic number theory, in which the properties of numbers are studied through
algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic geometry in its algebraic aspect.
20. How Algebra is useful in daily life ?
Suppose , we are to appoint a person for some domestic purpose .We give
him two option for salary per month as :
(1)Rs. 25 daily
(2)Rs.5 for the first day and keep on increasing Rs. 2 to the pervious days for
the next day
Which option will be better for him ?
(2) option is better:
As in the (1) option he will get only25 30 = Rs. 750
And in the (2) option he will get = 5 +7+9 +...+ upto 30 terms
= Rs. 1020. ( sum of 30 terms)
Statistics: It is a mathematical science pertaining to the
collection, analysis, interpretation or explanation, and presentation of
data. Also with prediction and forecasting based on data.
Statistics form a key basis tool in business and manufacturing as well. It is
used to understand measurement systems variability, control processes
for summarizing data, and to make data-driven decisions. In these roles, it
is a key tool, and perhaps the only reliable tool.
22. Some fields of inquiry use applied statistics so
extensively that they have specialized terminology. These
Applied information economics
Chemometrics (for analysis of data
Structured data analysis (statistics)
Statistics in various sports, particularly
baseball and cricket
Geography and Geographic Information
23. How the concept of mean, mode and median is used
in daily life ?
A shopkeeper, selling shirts, keeps more stock of that size of shirt which has
more sale. Here the size of that shirt is the mode among other .
If in a tour, the total money spent by10 students is Rs. 500. Then the
average money spent by each student is Rs. 50. Here Rs. 50 is the mean.
If you have 25 people lined up next to each other by age, the median age
will be the age of the person in the very middle. Here the age of the middle
person is the median.
Calculus: It is the study of change, in the same way that geometry is the
study of space. It includes the study of limits, derivative , integrals, and
Calculus has widespread applications in science and engineering and is
used to solve problems for which algebra alone is insufficient. Calculus
builds on algebra, trigonometry, and analytic geometry and includes two
major branches, differential calculus and integral calculus, that are
related by the fundamental theorem of calculus.
25. How is Integral and differential calculus useful in daily
Integration is used to find areas of figures which are not geometric. Suppose
you spill water on the floor and want to find out what area the water has
covered, you can do so by integration. What it does is that it breaks up the
non-geometric shape into a number of tiny geometric shapes. It then
calculates the area of each of the tiny figures and adds them up. This of
course gives only an approximation to the actual area.
Let us consider the movement of a car on a highway. Here we can clearly
visualize that if the highway is clear the driver would look forward to increase
the speed to an optimum level after which he will drive with the same speed.
With the help of calculus we can easily estimate the car's acceleration if we
know the initial speed and the speed when he settled.
Acceleration is therefore defined as the first order derivative of
velocity, which in turn is the first order derivative of displacement.
figures and with properties of space.
How Is Geometry Used In Our Daily Life?
Geometry is especially useful in home building or improvement projects. If
you want to find the floor area of a house, you use geometry. This
information is useful for laying carpet or tiles and for telling an estate agent
how big your house is when you want to put it on the market. If you want to
reupholster a piece of furniture, you have to estimate the amount of
fabric you need by calculating the
surface area of the furniture.
Geometry: It a part of mathematics concerned with questions of
size, shape, and relative position of
Mechanics : It is concerned with the behaviour of physical bodies when
subjected to forces or displacements, and the subsequent effect of the
bodies on their environment.
Covering a long horizontal distance while making a long jump , the angle of
elevation should be 45°.
Riding a bicycle round and round a globe, head downward
aths is unavoidable. It's a deeply fundamental thing. Without
math, there would be no science, no music, no art. Maths is part of all of
those things. If it's got structure, then there's an aspect of it that's