MATHEMATICS AND WE…

TOPIC

PRESENTED BY:

• RISHABH AGARWAL 13\IT\061• HIMANSHU VYAS 13\IT\062• ABHISHEK DWIVEDI 13\IT\064• AKASH PRAJAPATI 13\IT\066• ANKIT RAJ 13\IT\067• RISHABH KAMAL 13\IT\068

“IN THIS PRESENTATION WE ARE AIMING TO SHOW THE IMPORTANCE OF MATHEMATICS IN OUR LIFE.”

• The word “MATHEMATICS” comes from the Greek word mathema, which means “that which is learnt”.

• ARISTOTLE defined mathematics as “the science of quantity and figures”.

• Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement and later astronomy; today, all sciences suggest problem studied my mathematician.

INTRODUCTION

• Galileo Galilei said , “The universe cannot be read until we have learned the language and become familiar with the characters which is written in mathematical language.”

• Maths has been defined in many ways throughout the ages . Today , maths is an inevitable part of life. Applied maths has always been leading to important discoveries and giving birth to new disciplines.

Mathematics

Arithmetic

Algebra

Geometry

TrigonometryCalculus

Probability

Set Theory

CLASSIFICATION OF MATHEMATICS

CONTRIBUTION OF INDIA

Aryabhata was the one who added ‘0’ to maths.

He also gave the accurate value of pi up to 8 digits.

Aryabhata, an Indian mathematician living in the 6th century, discovered, or perhaps rediscovered, the formula for the area of an isosceles triangle between the 4th and 13th centuries other Hindus and Muslims used their geometric knowledge to establish and make advances in the field of trigonometry.

• Bhaskara supplied the correct answer for division by zero as well as rules for operating with irrational numbers.

• In the 9th century, Jain mathematician Mahavira stated rules for operations with zero.

• Napier gave the Logarithmic table after

having a deep study of mathematics of

Indian system.

• Carl Friedrich Gauss

German mathematician Carl Friedrich Gauss contributed to many areas of mathematics, including probability theory, algebra, and geometry. In his doctoral thesis he proved that every polynomial has at least one root, or solution; this theory became known as the fundamental theory of algebra. Gauss also applied his mathematical work to theories of electricity and magnetism. The magnetic unit of intensity is named in his honor.

Euclid

Euclid was a Greek mathematician who lived around 300 BC . He wrote Elements, a 13-volume work on the principles of geometry and properties of numbers.

Sir Isaac Newton and Gottfried Wilhelm Leibniz

• Their work ranks as the crowning achievement of 17th-century mathematics. Calculus allowed the solution of many problems that had been previously insoluble, including the determination of the laws of motion and the theory of electromagnetism.

• Srinivasa Ramanujan (1887 - 1920)

Famously known as “A MAN WHO NEW INFINITY”.Once the mathematician G. H. Hardy had referred to the number—1729—on the back of a taxi cab, as "dull”.But he said,” No, it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways.The two ways are 1³+ 12³ or 9³ + 10³.

• She was an Indian writer and mental calculator thus Also known as ‘Human Computer’ .

• She was asked to give the 23rd root of a 201-digit number; she answered in 50 seconds. Her answer—546,372,891—was confirmed by calculations done at the U.S. Bureau of Standards by the UNIVAC 1101 computer, for which a special program had to be written to perform such a large calculation.

• She demonstrated the multiplication of two 13-digit numbers—7,686,369,774,870 × 2,465,099,745,779.She correctly answered 18,947,668,177,995,426,462,773,730 in 28 seconds.

This event is mentioned in the 1982 Guinness Book of Records.

Shakuntala Devi

INVOLVEMENT OF

MATHEMATICS

IN OUR DAILY LIFE…

Math is everywhere and yet, we may not recognize it because it doesn't look like the math we did in school. Math in the world around us sometimes seems invisible.But math is present in our world all the time--in the workplace, in our homes, and in life in general.

Lets see how much it is involved in per day to day life……

Maths in Commercial Usage

• Discount

• Banking

• Foreign Exchange

• Stock and Share

Discount

> Offers during festival seasons .> If you buy Many, get one free/two free.

>If you buy for more amount, more discount.

Banking Transaction in Maths

Stocks and Bonds

All these are nothing but Maths!!

Foreign Exchange Market What are the rates of each currency when compared to Indian Rupees?

Stock and Share

Stocks are sold by Brokers. CP = Market value + Brokerage

To be more précised letsSee the uses of different Fields of mathematics in

Our life…

How Algebra is Useful?

To understand the important of algebra in our life,lets take a example….

Suppose we appoint a person for some work we give him 2 options: Say :

i. Rs 100/- per day

ii.Rs 50/- per first day, then increase of Rs 5/-per the summing days.

Which is better ????

How the concept of Mean, Median & Mode are used in daily life?

A shopkeeper keeps more stock of a particular type of shoe which has more sale. Here the concept of MODE applies.

The average daily expenditure in a month of a family gives the concept of MEAN.

If 15 people of different heights are standing height-wise, then the middle man’s height is the MEDIAN height.

Calculus

It is the study of change.

It includes limits, derivatives, integrals and infinite series.

It helps us to find the area of figures, to know the acceleration of a car moving in a highway with a uniform speed. Also, the movement of an artificial satellite, ship etc.

Newton and Gottfried Leibniz are usually credited with the invention of calculus. Newton used calculus in his laws of motion and gravitational attraction.

Application of probability

Aristotle said, “The probable is what usually happens.” You can’t predict the future,

but you can use mathematical probability to determine how likely it is that something will – or won’t -- happen.

We talk about the probability/chance of getting a certain result everyday. E.g., we say, "There is 90% chance (probability) that there will be rain today.“here we are using probability.

Casino owners aren’t in the business to lose money. The odds are in their favor. Gamblers play the games, in hopes of defying those odds. In the game of blackjack, a player has a 1 in 20 chance of getting 21, a "blackjack." The probability is 5 percent.again probability.

The Canadian 6/49 Lottery has 6 numbers drawn from a total of 49 balls with the numbers 1 through 49 on them. You must use the formula for permutations and combinations to figure out the probability of getting all 6 numbers in the correct order. The answer would be that the number of ways of choosing 6 numbers from 49 is49C6 = 13, 983, 816 . Therefore the probability of winning the lottery is 1/13983816 = 0.000 000 071 5 (3sf), which is about a 1 in 14 million chance!

In field of chemistry while balancing the Chemical equation ,mathematical concept of ratios and proportion is utilized.

In field of Physics again like Mechanics ,mathematics Faciliates the conversion Of physical principle into relations To derive result and proofs.

In field of computer, the Binary language ,the only one computer understand ,comprises of 0 and 1.Moreover ,some logics of mathematics are utilized in programming.

Mathematics serves as a important Tool in making calculations in Field of Astromomy,Astrophysics,Astrology Etc.

Uses of Mathematics In other subjects

Use of Mathematics in Mechanics.

Mechanics is a branch of physics which deals with study , concerned with the behaviour of physical bodies Subjected to forces or displacements .

Mathematics provide a aid to transform concept of Mechanics in equations and notation to derive results.

.For example: Maximum distance a football can go when kicked by the goal keeper at an angle of 45°.This is derived By combine utilization of Mathematics and mechanics.

Mathematics In Projection• For accurate delineation of large areas on a

small scale, a number of called projections have been developed mathematically. Maps based on mathematical computation represent the entire earth in circles, ovals, or other shapes. Mathematical Techniques are used by Google Earth to represent 3-dimensional objects on a 2-dimensional screen.

Mathematics in Astronomy The journey to the Moon is shown as a yellow

line, while the return trip is indicated by a blue line. Space travel would be impossible without precise mathematical calculations of acceleration, distance, gravitational pull, friction.

INVOLVEMENT OF MATHEMATICS IN DAY TO DAY LIFE

At Home While making food or other dishes ratio is involved. Eg- 1/2 cup water +1/2 cup milk+

1 teaspoon sugar +1teaspoon tea= 1 cup tea

In TravelTravellers often consider their miles-per-gallon when fuelling up for daily trips, but they might need to calculate a new when faced with obstructionist detours and consider the cost in miles, time and money

Conclusion

As we come to the end of our presentation we have seen the origin of maths and its versatile involvement in our daily life. Through this we may conclude that mathematics is required for literate as well as for illiterate persons. The former one uses in the field of research whereas later one uses it for simple daily calculations.

• From the ancient times Indians like Aryabhata, Bhaskara etc played a crucial role in the field of mathematical research and statistics.Even in the present age the people like Narendra Karmakar, C.S. Sheshadri are still contributing so it is our sole duty to take this prestige heritage to a higher level.

• Mathematics is a subject that not only develops the aptitude or thinking ability of a person but also it helps in boosting up his confidence and personality.

• At last but not the least………………

So, lets us thanks mathematics for making our life simpler and easy……………