1. Engineering and Mathematics – A historical Overview

2. Welcome As a Senior Lecturer in the Department of Mathematics, I warmly welcome you to our Department.

3. Congratulations on your success in gaining admissions into a prestigious Engineering Faculty in the country.

4. Best wishes for continued success in all your future endeavors too.

5. We are proud to have you here as the best students in our country in the Mathematics stream

6. You can be proud too For having an opportunity to learn both Engineering and Mathematics

7. Throughout history Mathematics has been one of the most prominent subjects of human learning

8. It is unfortunate that some people don’t like Mathematics !!

9. Why do they hate Mathematics?

10. The mistake is not in Mathematics!. It is in the way some people look at Mathematics!!.

11. Mathematics only as a subject for an examination Some people look at

12. So, they see only as a collection of Mathematics Theorems, Proofs and Formulas

13. Then they say, theorems are hard to understand proofs are boring to read and formulas are difficult to remember

14. Mathematics Appear to be For them, difficult, uninteresting and useless.

15. Mathematics But there are others who look at as the most beautiful and useful subject

16. It is remarkable that the Famous mathematician Mathematics is the Queen of the Sciences. Carl Friedrich Gauss (1777 - 1855) once said:

17. mathematics Why did Gauss compare to the Queen?

18. Because, both have two important attributes in common:

19. Beauty and Power

20. In fact, the of Mathematics are the two important factors that attracted people towards Mathematics throughout history. Beauty and Power

21. Aesthetic pleasure derived from looking at beautiful patterns and relationships in numbers and geometrical shapes encouraged people to sacrifice their time and energy to develop subjects like NUMBER THEORY and GEOMETRY.

22. Power of Mathematics On the other hand, to solve their day to day problems encouraged them to develop subjects like ALGEBRA and TRIGONOMETRY

23. The Power and Beauty of Mathematics Today, has increased manifold

24. scientific and technological developments In fact, the astonishing of the present day world are mainly due to the advancement in the mathematical knowledge

25. Influence of Mathematics Chemistry, Physics, Medicine, Economics, Social Sciences etc. has now penetrated into almost every other field like

26. Engineering in particular, depends heavily on Mathematics

27. Your success as an engineering student will mostly depend on the Quality of Mathematics that you learn.

28. Our Department is responsible for teaching you the Essentials of Mathematics that are needed for a successful engineering education

29. We shall try to make learning Mathematics Fruitful and enjoyable.

30. as engineering students, You should have the correct attitude towards Mathematics. Before beginning to learn Advanced Mathematics

31. and enjoy the beauty We should learn to appreciate the power of Mathematics.

32. The purpose of this presentation is to give you few glimpses of the history, power and beauty of mathematics

33. Important Milestones in the History of Mathematics

34. Why should we learn History?

35. Earliest Branch of Mathematics:

36. Earliest Branch of Mathematics: Arithmetic

37. Counting and measuring has been an essential activity in human life from ancient times.

38. When people of early civilizations began to do, farming and agriculture a basic need in their life was to count or measure their belongings like Number of animals Sacks of Grain Area of Land

39. This inevitably led them to discover numbers

40. Earliest type of numbers introduced by ancient people were the integers: one, two, three, four, … and so on.

41. They also used various objects like fingers, pebbles and sticks to represent these numbers.

42. The Oldest Counting Machine

43. As Agriculture and Commerce expanded between communities, they had the problem of recording and communicating numbers in written form

44. symbols and notations They solved this problem by introducing various which varied from civilization to civilization

45. In about 1500 B.C., Egyptians were using the following symbols:

47. At that time they did not have instruments like paper and pencil to write these numbers.

48. They had to inscribe them on materials like stones, wood, leather etc.

50. An ancient mathematical text

51. The Romans were active in trade and commerce, and the numeral system they developed lasted many centuries.

52. Roman Numerals 1510501005001000 IVXLCDM

53. CCLXXVI 276

54. Much later, in the period 50 – 550 A.D., Indian and Arabic mathematicians introduced the Arabic Numeral System that we use today.

55. As trade and commerce expanded between communities, people began to perform simple arithmetical operations like addition and multiplication

56. The discovery of the Arabic numeral system made application of arithmetical operations very easy for them.

57. By 1600 years B.C., arithmetic was being used for a number of practical purposes like agriculture, farming and trade and architecture

58. They also discovered several devices to perform such operations.

59. The oldest adding machine.

60. Later in about 300 B.C., the Babylonians invented the earliest calculator the abacus. Astonishingly, the abacus was in use in many parts of the world, even during the last century.

61. THE ONLY CALCULATING DEVICE THEY HAD WAS THE ABACUS A ROMAN ABACUS A CHINESE ABACUS

62. It is remarkable that even before paper and pencil were discovered, people were able to compute an expression like using an abacus. But, it would have consumed a tremendous amount of time.

63. IT IS REMARKABLE THAT WITH SUCH PRIMITIVE DEVICES THEY WERE ABLE TO PERFORM MARVELOUS ENGINEERING FEATS LIKE ….

64. PYRAMIDS OF EGYPT (2000 B.C.)

65. BRIDGES OF ROME (2000 YEARS OLD)

66. GREAT WALL OF CHINA (200 B.C)

67. For the next few centuries, Mathematics evolved into various fields like ALGEBRA NUMBER THEORY GEOMETRY AND TRIGONOMETRY

68. During the 17 th and 18 th century a revolutionary change took place in the History of Mathematics

69. Paradoxes When mathematicians were trying to study quantities which are infinitely large or infinitely small, they faced with apparent contradictions called

70. Bertrand Russel Mathematics is the Science in which we do not know what we are talking about, neither what we are saying is true

71. Newton and Leibniz discovered Calculus independently

72. Set Theory Was established giving definitions of LIMIT, DIFFERENTIATION and INTEGRATION Formal

73. These concepts had lots of applications in Physics, Chemistry, Engineering and Economics which involved more and more complicated calculations that could not be done with fingers or abacus

74. So, people were trying to invent easier and faster ways of calculating

75. In 1614, Scotsman John Napier discovered logarithm. Napier also invented an ingenious system of moveable rods (referred to as Napier's Rods or Napier's bones). These allowed the operator to multiply, divide and calculate square and cube roots by moving the rods around and placing them in specially constructed boards.

76. NAPIERS’ BONE John Napier (1550-1617),John Napier

77. The Slide Rule was invented by William Oughtred in 1625. The slide rule is based on Napier's ideas about logarithms - it has logarithmic scales that can be slid past each other to allow approximations to multiplication to be carried out quickly and easily.

78. SLIDE RULE John Napier (1550-1617),John Napier

79. Slide Rules

80. Slide rules were in continual use by scientists and mathematicians right up until to the introduction of the first handheld calculator by Hewlett Packard in 1972.

81. THE PASCALINE Blaise Pascal (1623-1662)Blaise Pascal

82. Leibniz Stepped Drum Wilhelm Von Leibniz (1646-1716),Wilhelm Von Leibniz (a)The Difference Engine (1822) British mathematician Charles Babbage designed this mechanical device. It was able to calculate up to a precision of 31 digits (a)The Analytical Engine (1830) 1.IBM introduced the first mainframe computer. These computers enabled users to perform thousands of arithmetical operations in a fraction of a second. In 1970 there were only three or four such computers in whole of Sri Lanka. Two of them were at the Universities of Moratuwa and Peradeniya. 1967 A team of three engineers from Texas Instruments, Inc. invented the electronic pocket calculator. The invention of the pocket calculator was a great leap forward in the history of computational mathematics. With calculators, performing arithmetical operations became an instantaneous task. As engineering students you should be thorough in using facilities available in a calculator. The most simple tasks are to evaluate arithmetical expressions..

83. The Difference Engine (1822) British mathematician Charles Babbage designed this mechanical device. It was able to calculate up to a precision of 31 digits

84. Analytical Engine(1830)

85. Electrical and Electronic devices: The following is a summary of remarkable events with regard to computational devices.

86. 1906 birth of electronics.

87. 1940 Electronic computers were invented. This invention made arithmetical computations very fast and accurate. But early computers were the size of houses and were very expensive. Even though the actual computation took very minute time, writing computer programs and feeding them into the computer involved considerable amount of time. The only way of communication with these giant computers was through punch cards, tapes and print-outs only. There were no keyboards, mouses or video screens

91. 1964 IBM introduced the first mainframe computer. These computers enabled users to perform thousands of arithmetical operations in a fraction of a second. In 1970 there were only three or four such computers in whole of Sri Lanka. Two of them were at the Universities of Moratuwa and Peradeniya.

93. 1967 A team of three engineers from Texas Instruments, Inc. invented the electronic pocket calculator. The invention of the pocket calculator was a great leap forward in the history of computational mathematics. With calculators, performing arithmetical operations became an instantaneous task. As engineering students you should be thorough in using facilities available in a calculator. The most simple tasks are to evaluate arithmetical expressions

94. THIS CENTURY WE SAW ANOTHER IMPORTANT MILESTONE IN THE HISTORY OF MATHEMATICS: THE DISCOVERY OF ELECTRONIC CALCULATORS AND THE COMPUTERS

95. THIS HAS MADE MATHEMATICS EVEN MORE POWERFUL AND AN INDISPENSABLE TOOL OF AN ENGINEER

96. THESE DEVELOPMENT BROUGHT ABOUT A REVOLUTIONARY ADVANCEMENT IN THE FIELDS OF SCIENCE, ENGINEERING AND TECHNOLOGY.

97. ONE EXAMPLE IS THE MOST WONDERFUL ENGINEERING FEAT OF HUMAN HISTORY: THE PANAMA CANAL

98. PANAMA

100. THEY WERE FASCINATED BY THE BEAUTIFUL INTRINSIC MATHEMATICAL RELATIONSHIPS THAT EXIST BETWEEN NUMBERS, GEOMETRICAL SHAPES AND IN NATURE.

101. FOR EXAMPLE, WHILE ENGINEERS IN EGYPT WERE DOING CALCULATIONS ON BUILDING PYRAMIDS PEOPLE IN CHINA SPENT THEIR TIME AND ENERGY DISCOVERING THINGS LIKE …

102. MAGIC SQUARES 37141625 11202329 22461518 101317241 19215812

103. While serious mathematicians were working on theory of numbers, some others derived pleasure constructing anagrams like the following

104. A decimal point What is

105. I'm a dot in place !

106. Is pity love?

107. Positively !

108. WHILE ENGINEERS ARE REJOICING OVER THE ACHIEVEMENT OF CONSTRUCTING PANAMA CANAL SOME OTHER MATHEMATICAL MIND HAS CONSTRUCTED A FASCINATING SENTENCE IN HONOUR OF THE PERSON WHO PLANNED IT

109. A MAN, A PLAN, A CANAL, PANAMA

110. WE SHOULD LEARN MATHEMATICS WITH THIS SPIRIT. THEN, LEARNING MATHEMATICS WILL BE AN INTERESTING EXPERIENCE