Basic Introduction to mathematics

Lesson: 1 Newton Spectra @Extramural Academy

BASIC INTRODUCTION TO MATHEMATICS

Instructional resources: YouTube, google, Text books & whiteboards •Vocabularies ••HHiissttoorryy ••MMaatthheemmaattiiccss ••BBrraanncchh ••SScchhoollaarr ••RReeaall lliiffee ••AApppplliiccaattiioonn

Instructional techniques / Methods: Explanatory, discussion, demonstration. Entry behavior: The pupils are familiar with Mathematics in their daily activities. Behavioral Objectives: At the end of this lesson, the learners should be able to: •Narrate the history of mathematics •Define mathematics •List and explain the branches of mathematics •Identify and state some scholars and their contribution in the field of mathematics. •Enumerate the application of mathematics in our daily activities.

•STEP 1: HISTORY OF MATHEMATICS •Mathematics is a historical subject. It has been explored by various mathematicians across the world since centuries, in different civilizations. Archimedes, from the BC century is known to be the Father of Mathematics. He introduced formulas to calculate surface area and volume of solids. •In the 6th century BC, the study of mathematics began with the Pythagoreans, as a “demonstrative discipline”.

•The word mathematics originated from the Greek word “mathema”, which means “subject of instruction”.History of Mathematics has been an ancient study and is described by each part of the world, in a varying method. There were many mathematicians who have given different theories for many concepts, which we are applying in modern mathematics.

MATHEMATICS •Mathematics is a branch of science that deals with the study of numbers shapes, data, measurements and logical activities. WHO IS A MATHEMATICIAN ? Someone with the knowledge of mathematics is called MATHEMATICIAN





BRANCHES OF MATHEMATICS

What is Algebra? •Algebra is a branch of Mathematics that is useful for the purpose of expressing a mathematical equation through the development of relationships with the use of letters or other symbols to represent the entities. The equation's unknown quantities can be solved using algebra. BRANCHES OF ALGEBRA •elementary, advanced, abstract, linear, and cumulative.

•What is Calculus? •Calculus is the branch of mathematics that deals with continuous change. Calculus is also called infinitesimal calculus or “the calculus of infinitesimals”. The meaning of classical calculus is the study of continuous change of functions. •CALCULUS •Limits,Differential calculus (Differentiation),Integral,calculus (Integration), Multivariable calculus (Function theory).

•What is Measurement? •Measurement is a technique in which the properties of an object are determined by comparing them to a standard quantity. Also, measurement is the essential metric to express any quantity of objects, things and events. •MEASUREMENT •Time, Length/ Distance, Weight/Mass, Volume, Temperature

•What is Geometry? •Geometry is the branch of mathematics that deals with shapes, angles, dimensions and sizes of a variety of things we see in everyday life. Geometry is derived from Ancient Greek words – ‘Geo’ means ‘Earth’ and ‘metron’ means ‘measurement’ •GEOMETRY •Lines,Shapes,Angles,Triangles,Quadrilaterals,Coordinate Plane,Area and Perimeter,Volume and Surface Area,Trigonometry,Circles,Pythagorean Theorem

•What is Probability ? •Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. •PROBABILITY •Theoretical Probability, Experimental Probability, Axiomatic Probability

•What is Statistics ? •Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. •STATISTICS •Descriptive Statistics & Inferential Statistics

What is Computation & Estimation? Estimation of numbers is the process of estimating/approximating or rounding off the numbers in which the value is used for some other purpose in order to avoid complicated calculations. •COMPUTATION & ESTIMATION •Rounding off, Place value, Use of compatible numbers, addition and subtraction, multiplication, division operations.

•SCHOLARS AND THEIR CONTRIBUTIONS IN MATHEMATICS •Euclid : •Euclid was one among the famous mathematicians, and he was known as the ‘Father of Geometry.’ His famous Geometry contribution is referred to as the Euclidean geometry, which is there in the Geometry chapter of class IX. He spent all his life working for mathematics and set a revolutionary contribution to Geometry. •Pythagoras •‘Pythagoras theorem’ is very popular and an important mathematical formula to solve mathematical problems. Since childhood, all of us have struggled to solve mathematical problems applying the Pythagoras theorem. Pythagoras discovered this prominent theorem and he became the father of ‘Pythagoras theorem.’ Pythagoras was from Greece, but he fled off to India in the latter part of his life.

•Archimedes •Archimedes was a Greek Scientist, a great mathematician, and a Physicist. He also worked his entire life in search of discovering mathematical formulas that are related to Physics. The best contribution of Archimedes in mathematics is known as the invention of compound pulleys, antiquity, and screw pump. •‘Hero of Alexandria.’ •Heron’s formula in mat•Blaise Pascal •Blaise Pascal, a French philosopher, mathematician, and physicist. He contributed to several areas of mathematics, but he is widely known for Pascal’s triangle. Its common use is in probability, where it can be used to find combinations.

•Aristotle •Aristotle was a great scholar and he had vast knowledge in various areas, including Physics, mathematics, geology, metaphysics, medicine, biology, and psychology. He was a student of Plato, and both of them together discovered many philosophical theories and contributed to mathematics and Platonism. He combines mathematics and philosophy and in his treaties, and uses mathematical science in three principal ways. •Diophantus •His algebraic equations are quite easy and unique, so he was popularly known as the ‘Father of Algebra.’ He wrote a series of books on Algebra. He later gained popularity for his book Arithmetic, where a brief description with examples was given on the best solution for all the algebraic equations and the theory related to the number.

•Ptolemy •Ptolemy was a mathematician; he was also a geographer, musician, writer, and astronomer. His contributions to mathematics were incredible. He wrote about mathematics, and among them, his best treaty was called Almagest. He also believed that in the Universe, the position of the Earth was in the center. •Antiphon •Antiphon discovered the value of Pi. This renowned mathematician was the first one who calculated the upper bound and lowers bound values of Pie by inscribing and circumscribing around a circle, the polygon, and processed finally to calculate the areas of the polygon. His idea of calculating a polygon area became very famous, and it changed mathematics for the world.

•‘Hero of Alexandria.’ •Heron’s formula in mathematics is applied by students from class VI onwards. Yes, he was the one who discovered the square root of numbers. In today’s mathematics, his formula is known as Heron’s formula. So, he gained popularity and became known as the ‘Hero of Alexandria.’ •Sir Isaac Newton •Sir Isaac Newton was one of the greatest contributors in the field of maths and physics. His works are spread in almost every field. He developed Calculus, both differential and integral, that are still the most important aspects of higher mathematics. Using Calculus, he made it easier to find the area bounded by closed curves. In physics, his most world-changing work was the discovery of existence of gravitational force in our surrounding.

Application of mathematics •Communication Everyone has a cell phone which requires basic knowledge of skills and mathematics. He needs to know the numbers and how they work on the cell phone. •Computer science Mathematics helps learn data entry in many functions (such as engineering, science, computer programming, accounting, and banking) that rely entirely on mathematics. Mathematics is a fundamental intellectual tool in computing. •Banking and Finance Mathematics is the most important part of banking and financial matters. It is necessary to be accurate in the accounts to be able to maintain the money in an optimal manner.

•Sport •Mathematics is an important part of the sports field. It plays a big role in the efficiency of sports. Mathematics improves a person's cognitive and decision-making skills. These skills are very important for a sportsperson because they help him to make the right decisions for his team. Engineering and trigonometry help the player determine the way and the angle that the ball hits to achieve the goal. •Population •Mathematics is used to study the extent of population growth by environmental scientists, and the extent of population density.

•In the kitchen •Mathematics also plays a major role in the kitchen. Baking and cooking require some mathematical skills. Every ingredient must be measured and sometimes we need to multiply or divide to get the exact amount we need. •Mathematics helps to estimate the quantity of food and bread to be prepared. •Music: •Mathematics and music are already connected and we usually use numbers and mathematics to describe and teach music. Understanding fractions and ratios helps to understand the rhythm of musical notes.

•Agriculture: •Mathematics is also important in the field of agriculture. Farmers must have sufficient knowledge of mathematical knowledge that makes them progress. The important benefits of mathematics in agriculture are. Mathematics accurately describes weather conditions and analyzes acidity in the soil, allowing the identification of crops that can be grown in these soils.

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