Uses of Mathematics in daily life

The topics which are mainly useful in daily life are : • • • • • • • •

Commercial Mathematics Algebra Statistics Calculus Number Theory Graph Theory Geometry Mechanics

 Commercial Mathematics This include the following topics • Discount • Banking • Foreign Exchange • Stock and Share • Arithmetic ( Profit & Loss, Percentage, Ratio and Proposition , Time problems)

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.

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.

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 ?

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

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.

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. • Algebraic combinatorics, in which abstract algebraic methods are

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 : (2) Rs. 25 daily (3) 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 only 25 × 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.)

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. • Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include:

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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

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, derivatives, 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.

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.

Number Theory :Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers. • The term "arithmetic" is also used to refer to number theory but Number theory used to be called the higher arithmetic . • The Social Insurance Number (SIN) was created in 1964 to serve as a client account number in the administration of the Canada Pension Plan and Canada's varied employment insurance programs. In 1967, what is now Canada Revenue Agency (CRA) started using the SIN for tax reporting purposes. • Number theory is used in Cryptography (study of hiding information) for creating codes for ATM/Credit cards.

Graph Theory: graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. • A problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian circuit a salesman can take through each of cities. No general method of solution is known, and the problem is NP-hard. Solution to the traveling salesman problem is implemented as Traveling Salesman.

• The arrow marked path is the best path to follow by the travelling sale man to cover all the cities without going back to any city again

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.

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.