The document discusses how mathematics is commonly misunderstood as merely formulas and computations, when it is in fact about concepts and problem solving. It then lists several topics in mathematics that are useful in daily life, including commercial mathematics, algebra, statistics, calculus, number theory, graph theory, geometry, and mechanics. It provides examples of how each of these topics applies to real-world situations and challenges the misconception that mathematics is just about memorizing formulas.

3. The great misconception about mathematics -- and it stifles and
thwarts more students than any other single thing -- is the notion
that mathematics is about formulas and cranking out computations.
It is the unconsciously held delusion that mathematics is a set of
rules and formulas that have been worked out by God knows who
for God knows why, and the student's duty is to memorize all this
stuff. Such students seem to feel that sometime in the future their
boss will walk into the office and demand "Quick, what's the
quadratic formula?" Or, "Hurry, I need to know the derivative of
3x^2 - 6x + 7." There are no such employers.

4. The topics which are mainly useful in daily life are :
 Commercial Mathematics
 Algebra
 Statistics
 Calculus
 Number Theory
 Graph Theory
 Geometry
 Mechanics

5. COMMERCIAL MATHEMATICS
This include the following topics :
Discount
Banking
Foreign Exchange
Stock and Share
Arithmetic ( Profit & Loss, Percentage, Ratio and
Proposition , Time problems)

6. Discount
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
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 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.

7. BANKING
 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 mathematics
 Banks are also involved in stocks and bonds. Bond
calculations are mathematical. Stock options are
also quite mathematical.

8. 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 currencies of
different counties w.r.t.
Indian currencies?

9. 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 value .
 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

10. ARITHMETIC
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.

11. ALGEBRA
Algebra : It is a branch of mathematics concerning the study of 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
matrices);
 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.

12. 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.)

13. 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.
 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.

14. Some fields of inquiry use applied statistics so
extensively that they have specialized terminology. These
disciplines include:
 Actuarial science
 Applied information economics
 Biostatistics
 Business statistics
 Data mining
 Engineering statistics
 Environmental Statistics
 Epidemiology
 Geography and Geographic Information Systems
 Psychological statistics
 Quality
 Social statistics
 Statistical literacy
 Statistical modeling
 Statistical surveys
 Chemometrics (for analysis of data from chemistry)
 Structured data analysis (statistics)
 Statistics in various sports, particularly baseball and cricket

15. 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.

16. CALCULUS
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 infinite series.
 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.

17. How is Integral and differential calculus useful in daily
life ?
 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.

18. GEOMETRY
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.

19. MECHANICS
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

20. Maths 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 mathematical.