Introduction
Mathematical reasoning that to nowadays represents more essential to said verbal reasoning, plays a fundamental role in the development of our life and the progress of humanity. Areas such as, physics, social sciences, management and computer science. But in computing, we need more of a particular branch of the so-called mathematics: discrete mathematics. Discrete mathematics has become popular thanks to their applications in computer science. Notations and concepts of discrete mathematics are used to study problems in algorithmic and programming.
Development
From the historical point of view, computing has roots dating back to the mathematics of antiquity, through two main currents: algorithms, which systematizes the notion
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These are intended for a human calculator, but their systematic nature already foreshadows what will serve to lay the first foundations of computer science. In parallel, at the turn of the 20th century, the axiomatic current conquers many branches of mathematics, with for corollary of the methodological questions giving rise to a new discipline - mathematical logic. This current will be issues in particular a general theory of computability (Post, Turing, Kleene, and Church) and several theories of the demonstration (Gentzen, Herbrand, and Heyting). These theories are the second basis of computing: as soon as it will be necessary to formalize the notion of defining languages of programming specific to the unambiguous expression of algorithms, algorithm to verify the consistency of languages and programs, they will prove particularly valuable.
The discrete mathematics provides a rich and varied source of problems for exploration and communication. Discrete mathematics also helped to analyse and have several types of reasoning such as logical thinking (logic used in mathematics statements and arguments), relational thinking (solving a mathematical problem and describe the relationships), quantitative thinking (counting the element), analytical thinking (algorithms) and recursive
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As in other areas, progress is based on number of clever and innovative ideas, an abstraction of mathematical nature, and relative distancing with respect to the technology of the moment. It 's the kind that could hatch most of the major innovations that have shaped the computer landscape. It should be noted that the fact that several branches 'unnecessary ' long considered pure mathematics but at least recognised as having some "depth", found unexpected applications in computer science. A historical source consists of very theoretical needs of understanding of formal calculations underlying mathematical analysis. It is thanks to these achievements that the public can now have the Internet, the Web, DVD, mobile phone,
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.
This essay will consist in an exposition and criticism of the Verification Principle, as expounded by A.J. Ayer in his book Language, Truth and Logic. Ayer, wrote this book in 1936, but also wrote a new introduction to the second edition ten years later. The latter amounted to a revision of his earlier theses on the principle.It is to both accounts that this essay shall be referring.
Math is the universal language, encoded at the molecular level. For this reason, the very understanding of this subject allows us to have a better understanding in how we, as humans, fit into the larger universal picture. This universal language is taken for granted by most people because they do not see how math interconnects, not only in their daily lives, but how it interconnects the actual atoms and atomic structures that make up literally everything in their daily life.
There are many different beginnings to the origins of computers. Their origins could be dated back more than two thousand years ago, depending on what a person means when they ask where the first computer came from. Most primitive computers were created for the purpose of running simple programs at best. (Daves Old Computers) However, the first ‘digital’ computer was created for the purposes of binary arithmetic, otherwise known as simple math. It was also created for regenerative memory, parallel processing, and separation of memory and computing functions. Built by John Vincent Atanasoff and Clifford Berry during 1937-1942, it was dubbed the Atanasoff Berry Computer (ABC).
Computer engineering started about 5,000 years ago in China when they invented the abacus. The abacus is a manual calculator in which you move beads back and forth on rods to add or subtract. Other inventors of simple computers include Blaise Pascal who came up with the arithmetic machine for his father’s work. Also Charles Babbage produced the Analytical Engine, which combined math calculations from one problem and applied it to solve other complex problems. The Analytical Engine is similar to today’s computers.
Mathematics is everywhere we look, so many things we encounter in our everyday lives have some form of mathematics involved. Mathematics the language of understanding the natural world (Tony Chan, 2009) and is useful to understand the world around us. The Oxford Dictionary defines mathematics as ‘the science of space, number, quantity, and arrangement, whose methods, involve logical reasoning and use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis of mathematical operations or calculations (Soanes et al, Concise Oxford Dictionary,
Logos is the logic of arguments which makes sense from the readers’ view. A good persuasion must follow some rules which make the thesis relates to the readers’ view. The interesting of math games and the logical similarity between recreational math and advanced mathematics are strong arguments to conclude that, recreational math is important to lead intro level math lovers into the gate of high level mathematics. Suri lists many recreational math problems in the editorial to embody the interesting. “Make a plane with eight pentagonal shapes” and “Hexaflexagons” (Suri, 1) are two enjoyable examples he mentions at the beginning. By using specific instances of problems instead of explaining why recreational math is important in cold words, he makes the readers to feel the interesting by participating them in the solving process, thereby further inspiring readers’ desire to more recreational math problems. Sequentially, let the readers understand that interesting is the most powerful energy of learning. Therefore, we can say that, interesting of recreational math is an important element in stimulating people’s interest in advanced mathematics. However, interesting cannot fully explain the importance of recreational math. As a rigorous science, logical thinking capability is another important element in studying of mathematics. Certainly, Suri also demonstrated that recreational math can also educate players
Mathematics is part of our everyday life. Things you would not expect to involve math
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.
The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...
This means that math work with numbers, symbols, geometric shapes, etc. One could say that nearly all human activities have some sort of relationship with mathematics. These links may be evident, as in the case of engineering, or be less noticeable, as in medicine or music. You can divide mathematics in different areas or fields of study. In this sense we can speak of arithmetic (the study of numbers), algebra (the study of structures), geometry (the study of the segments and figures) and statistics (data analysis collected), between
The history of the computer dates back all the way to the prehistoric times. The first step towards the development of the computer, the abacus, was developed in Babylonia in 500 B.C. and functioned as a simple counting tool. It was not until thousands of years later that the first calculator was produced. In 1623, the first mechanical calculator was invented by Wilhelm Schikard, the “Calculating Clock,” as it was often referred to as, “performed it’s operations by wheels, which worked similar to a car’s odometer” (Evolution, 1). Still, there had not yet been anything invented that could even be characterized as a computer. Finally, in 1625 the slide rule was created becoming “the first analog computer of the modern ages” (Evolution, 1). One of the biggest breakthroughs came from by Blaise Pascal in 1642, who invented a mechanical calculator whose main function was adding and subtracting numbers. Years later, Gottfried Leibnez improved Pascal’s model by allowing it to also perform such operations as multiplying, dividing, taking the square root.
After my twelfth grade, the inherent ardor I held for Computer Sciencemotivated 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. I still vividly remember the time during my graduation,when I was successful in creating a simple calculator application as a class assignment.The joy I derived from creating something that is used by a lot of people to help them perform complex calculations,made me realize the power of computing in its true sense.It was also in my graduation that I developed an immense interest in programming languages such as Java, C++ an...
It was pure joy to learn how the Boolean logic makes computers work. In my undergraduate study I had taken up courses on Software Engineering, Computer Networks, Data Structures, JAVA, Operating Systems, Computer Graphics, Design and Analysis of Algorithms, Database Management, Web Technology and Mobile Application Development. Practical application aspects were introduced to me through laboratories correspond...
The Nature of Mathematics Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its basic interest. The essence of mathematics lies in its beauty and its intellectual challenge. This essay is divided into three sections, which are patterns and relationships, mathematics, science and technology and mathematical inquiry. Firstly, Mathematics is the science of patterns and relationships. As a theoretical order, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world.