In only 45 years, computers have premiered every aspect of people’s life. Computers serving as a multifunctional machine changes the way people live. People use it for pleasure, for study, for work. Surprisingly, digital computers were invented mainly for arithmetic only first. People who invented the first “computer” would never imagine how this could change the world. The magical combination of 0 and 1 has leaded the world into a new era. This paper focuses on the relationship between math and digital computers; how mathematics triggers the invention of digital computers and how digital computers change the way of math development.
Looking back the history, it is the computation demands motivate the invention of the digital computers. Before people did the all complicated computation mainly by hands. Inevitably, there would be many errors due to carelessness or different accuracy. Then calculating devices like slide rules were invented to simply the calculations in the seventh century. Slide rules were mainly used for multiplications and divisions based on the concept of logarithm. But they weren’t very accurate. Thus some people had to rely on tables in order to have higher accuracy. The problem is that whenever there was a new version of table published, errors would happen. For instance, in nineteenth century an English teacher Shanks spent 28 years to calculate π to 707 places. Sadly, it was only correct up to the 〖527〗^(th) place. Shanks could make mistakes anywhere. Probably he copied the wrong number from the tables. Probably the new tables caused the errors. At the same time of Shanks, the industrial revolution was underway with booming development of machines. Engineers need accurate numbers to build the bridges, to na...
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...n programing. These punched cards are “orders” for the machine or in modern concept, they are software for the hardware machine. However, the machine requires the space as large as a football field and he ended up with only a small model. Thus “Babbage fell from the status of national celebrity to that of a national joke in a matter of a few years, and he died a bitter, unheralded man”. (2) The invention for digital computers then suspended for nearly 100 years.
After a hundred years, technology has changed from steam engine to oil burner, from vehicles to planes, from letters to telephones. But there is little progress in the calculating devices. Most of the calculations are performed by “teams of human computers equipped with desk-top calculating machines”. (3) In 1939, the World War two started. Different than the ancient wars, World War Two was a scientific war
Over the past few decades technology has advanced quite a bit. The use of calculators, computers, and other techniques in many fields has increased significantly. In a large scale, technology is replacing the method of instruction in the field of education. Many people believe that adopting technology in learning process can increase productivity. However, David Gelernter, who is a professor at Yale University as well as a leading figure in the field of technology, suggests to limit the use of technology in the classroom in his article “Unplugged: The Myth of Computers in the Classroom” which was published in the New Republic magazine in 1994. In this article he offers well illustrated analysis which makes the readers to regulate the use of technology in the classroom. He thinks that the technology comes in a way of building strong foundation of basic skills. He insists that computers should be used to aid the learning process, not to replace cognitive thinking.
The Web. The Web. 04 Feb. 2010. http://www.shmoop.com/wwi/science-technology.html>. "
Thesis: Though many argue that World War 2 was an unnecessary show of violence that benefitted no one, World War 2 uniquely and critically revolutionized the world in science, technology, and medicine.
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
When World War II broke out in 1939 the United States was severely technologically disabled. There existed almost nothing in the way of mathematical innovations that had been integrated into military use. Therefore, the government placed great emphasis on the development of electronic technology that could be used in battle. Although it began as a simple computer that would aid the army in computing firing tables for artillery, what eventually was the result was the ENIAC (Electronic Numerical Integrator and Computer). Before the ENIAC it took over 20 hours for a skilled mathematician to complete a single computation for a firing situation. When the ENIAC was completed and unveiled to the public on Valentine’s Day in 1946 it could complete such a complex problem in 30 seconds. The ENIAC was used quite often by the military but never contributed any spectacular or necessary data. The main significance of the ENIAC was that it was an incredible achievement in the field of computer science and can be considered the first digital and per...
If the nineteenth century was an era of the Industrial revolution in Europe, I would say that computers and Information Technology have dominated since the twentieth century. The world today is a void without computers, be it healthcare, commerce or any other field, the industry won’t thrive without Information Technology and Computer Science. This ever-growing field of technology has aroused interest in me since my childhood. After my twelfth grade, the inherent ardor I held for Computer Science motivated me to do a bachelors degree in Information Technology. Programming and Math, a paragon of logic and reasoning, have always been my favorite subjects since childhood.
As everyone grows up, everyone has to take a Math class from Kindergarten to twelfth grade. At the early stage of math classes, most of the problems were solved by using pencil and paper. Eventually, calculators took over the method of using pencil and paper. Calculators were first made in 1642 by a French mathematician, Blaise Pascal. According to the article, “Who Made the First Calculator,” calculators were created for the usage of helping a person add and subtract numbers without using their hands (“Who made the first calculator”). However, they were not introduced into classrooms due to the cost, size, and appearance of the calculator. Eventually they became sleeker and less expensive. Ever since then students started to use them in and out of classrooms. However, the practice of using calculators in the classroom has been a continuing debate since the introduction of calculators. There are many advantages and disadvantages to allowing educators and students to use calculators within the classroom. However, calculators should not be used in class rooms unless it is necessary, due to the student becoming dependent on the calculator.
However, technology should never substitute the fundamental learning in our educational systems. Specifically, in primary school, building a firm fundamental education is crucial. Seeing children still using fingers to do simple math in second grade is not a good sign of academic improvement. Though the students may easily figure out the answers by using a calculator, before letting the children get any closer to these technical gadgets, they have to first learn to figure out the answers themselves.... ... middle of paper ... ...
So what does all of this have to do with computers? Well without numbers computers wouldn’t exist or have any reason to exist. The whole point of a computer is to perform mathematical computations. Computers weren’t the first to do these mathematical calculations though. In 1623 AD Wilhelm Schickard invented “The Calculating Clock” which would perform operations like addition, subtraction, multiplication, and division. In the year 1801 Jacquard Loom devised a punch card system with a power loom and an automatic card reader. Later that century in 1890 Herman Hollerith invented a census calculator that put each person’s information on a punch card and sent it through an electrical/mechanical tabulating machine. This sped up the process from about 7 years to 2 years making this a very efficient method of performing a census, which in turn helped spread it around the world (History of Computers).
After viewing the video by Wolfram (2010), I believe that as teachers we need to prepare more for using computers. Most of my students have a smartphone. And they use it for almost everything, including using the calculator. “Using new technologies involves time, effort, and a rethinking of instructional approaches.” (Sousa. 2015, p. 129). I learned math in a paper, and I love it, but I feel that today that is not enough for our students. Our students get bored about doing calculation the whole time on a piece of paper. Wolfram (2010) questioned, “Do we really believe that the math that most people are doing in school practically today is more than applying procedures to problems they don 't really understand, for reasons they don 't get?”
Charles Babbage was born at Walworth, Surrey England in December 26,1791. He achieved many great feats and belonged to many very distinguished groups before he died in October 18, 1871. Many people consider him to be the grandfather of computer science due to his great works with his Difference Engine (1821), which printed tables of polynomials, and his Analytical Engine (1856), which was intended as a general symbol manipulator. These inventions were far more complex than the work of any of his fellow inventors. Although there is no evidence that the computers of today are direct descendants of his work. He grew up with a passion for how mechanical objects worked. He also was an excellent mathematician. This was discovered at an early age when he employed a tutor only to find out he knew more about math than the tutor did. He was home schooled for a good many years before entering Cambridge University in 1810 an institution where he would later hold the position of Lucasian chair of mathematics from 1828 to 1839. His home schooling was in direct result of poor health in his youth. He was involved in many different fields of science. He was the first person to be presented the Gold Medal award given by the Astronomical Society. He was also a key figure in the founding of the Astronomical Society in 1820, the British Association for the Advancement of Science in 1831 and the Statistical Society of London in 1834. He is also the author of the very influential book On the Economy of Machinery and Manufactures. He also wrote a series of papers on many different topics such as optics and cryptology. Babbage excelled in many categories but being a politician wasn’t one of them. As a result he would not be able to persuade the government in England to give him a grant on working on the analytical engine. In Babbages early years he was quite social an pleasant to have around. In fact he was notorious for excellent dinner parties where many famous and prominent people would be in attendance. Although over the years and believed by some as a result from the death of his daughter Shelley, who drowned near La Spezia in July of 1822 and 5 years later the death of his 35-year-old wife Georgiana in August 1827 he became a very bitter old man.
Computers have been in the schools since the 1960s, but they were not used in the same capacity as they are used today. The use of computers is still expanding, and the future of education is very exciting when the full extent of this revolutionary phenomena is realized. In the 1960s computers were not widespread and most people who were educated during this decade hardly remember them at all. In the 1970s computers became smaller and less expensive, but the schools still did not use them much throughout most of the decade. By the end of the seventies, computer use in the schools started to increase. Students began to have hands-on experience.
Technology continued to prosper in the computer world into the nineteenth century. A major figure during this time is Charles Babbage, designed the idea of the Difference Engine in the year 1820. It was a calculating machine designed to tabulate the results of mathematical functions (Evans, 38). Babbage, however, never completed this invention because he came up with a newer creation in which he named the Analytical Engine. This computer was expected to solve “any mathematical problem” (Triumph, 2). It relied on the punch card input. The machine was never actually finished by Babbage, and today Herman Hollerith has been credited with the fabrication of the punch card tabulating machine.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
The fist computer, known as the abacus, was made of wood and parallel wires on which beads were strung. Arithmetic operations were performed when the beads were moved along the wire according to “programming” rules that had to be memorized by the user (Soma, 14). The second earliest computer, invented by Blaise Pascal in 1694, was a “digital calculating machine.” Pascal designed this first known digital computer to help his father, who was a tax collector. Pascal’s computer could only add numbers, and they had to be entered by turning dials (Soma, 32). It required a manual process like its ancestor, the abacus. Automation was introduced in the early 1800’s by a mathematics professor named Charles Babbage. He created an automatic calculation machine that was steam powered and stored up to 1000 50-digit numbers. Unlike its two earliest ancestors, Babbage’s invention was able to perform various operations. It relied on cards with holes punched in them, which are called “punch cards.” These cards carried out the programming and storing operations for the machine. Unluckily, Babbage’s creation flopped due to the lack of mechanical precision and the lack of demand for the product (Soma, 46). The machine could not operate efficiently because technology was t adequate to make the machine operate efficiently Computer interest dwindled for many years, and it wasn’t until the mid-1800’s that people became interested in them once again.