The document discusses the history and origins of mathematics. It notes that mathematics originated from practical needs like measurement and counting, with early forms found on notched bones and cave walls. Over thousands of years, mathematics has developed from attempts to describe the natural world and arrive at logical truths. Today, mathematics is highly specialized but also applied in diverse fields from politics to traffic analysis. The document also provides examples of how concepts in commercial mathematics, algebra, statistics, geometry are useful in daily life.
4. Mathematics
•Mathematics is a study of quantity, structure and space.
•It is a science dealing with logic of quantity, shape and
arrangement.
Origin
The word mathematics originated from Greek word
‘Mathematika’ which means learning
5. 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. 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. Learning to think in mathematical
terms is an essential part of becoming a liberally educated
person.
6. 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 walls and pottery.
As civilisations arose in Asia and the Near East,
sophisticated number systems and basic knowledge
of arithmetic, geometry, and algebra began to develop.
7. 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
mathematics.
8. 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 French.
9. 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. 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 pioneering work
was done by Karl Pearson.
Higher mathematics has a powerful tool in the high-speed
electronic computer, which can create and manipulate
mathematical `models´ of various systems in science, technology,
and commerce.
10. The topics which are mainly useful in daily life are :
Commercial Mathematics
Algebra
Statistics
Geometry
11. This include the following topics :
Discount
Arithmetic ( Profit & Loss, Percentage, Ratio and
Proposition , Time problems)
COMMERCIAL MATHEMATICS
12. Discount
Discount : Reduction from the full amount of a price .
The following are the four 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
price.
• Minimum Purchase Discount. Offer a price reduction on a minimum
quantity purchase. For example, buy two shirts and receive 20 % off
each shirt.
• Buy ONE, 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.
13. 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.
Arithmetic operations:
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.
ARITHMETIC
14. Algebra
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 of A.P.)
15. STATISTICS
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.
16. 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.
17. Geometry: It a part of mathematics concerned with questions of
size, shape, and relative position of 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
