- 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