Mathematics : Mathematical Reasoning And Logic Essay examples

Mathematics : Mathematical Reasoning And Logic Essay examples

Length: 1013 words (2.9 double-spaced pages)

Rating: Strong Essays

Open Document

Essay Preview

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 of computation and logic that formalizes the notion of demonstration. These two aspects are already strongly present in Greek science: Archimedes and Diophantus 'calculate ' the area under a parable and solutions of systems of equations in integers, while Euclid has the notion of axiomatic system for elementary geometry, and Aristotle of speech abstract propositional logic. It is piquant to note that these two fundamental currents still constitute the basis of modern computing.

Until the 19th century great mathematicians such as Newton, Leibniz, Euler or Gauss, invented original methods of numerical and symbolic computation. 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...


... middle of paper ...


...echnology, we illustrated the fact that the discrete mathematics is a science widely included in the tradition of other sciences. 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, etc.

Reference



Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »

Essay on Aristotle 's Contributions On Mathematics

- 6.1 Mathematical Objects and Truths Even though Aristotle’s contributions to mathematics are significantly important and lay a strong foundation in the study and view of the science, it is imperative to mention that Aristotle, in actuality, “never devoted a treatise to philosophy of mathematics” [5]. As aforementioned, even his books never truly leaned toward a specific philosophy on mathematics, but rather a form or manner in which to attempt to understand mathematics through certain truths. To better attempt to understand Aristotle’s view on mathematical truths, further inquiry will be made in regards to a fictionalist versus a literalist view point of mathematical objects....   [tags: Mathematics, Logic, Philosophy of mathematics]

Strong Essays
1005 words (2.9 pages)

Logic And Its Effect On Our Lives Essay

- After, one semester trying to understand what is logic about and how it works, finally, I understood that Logic is always present in our life. The logic used to explain miracles of everyday life, thinking logically helps man to question the functioning of everything around us, the logic used to argue and is somehow a thought an idea that influences us for an action we do in our daily lives. Used to think properly about what is and what happens in reality, to act in a reasonable manner at all times of our lives....   [tags: Logic, Reasoning, Critical thinking, Psychology]

Strong Essays
964 words (2.8 pages)

Theory Of Knowledge : Mathematics Essay

- Kelsey Amadeo-Luyt Theory of Knowledge September 2, 2014 Prompt: To understand something you need to rely on your own experience and culture. Does that mean this it is impossible to have objective knowledge. As children we are immersed in our communities in which we are fed predisposed knowledge that has been passed down and developed within our communities or families for numerous generations. Not until we begin primary, or even secondary school do we start to formulate ideas and opinions of our own....   [tags: Logic, Mathematics, Axiom, Scientific method]

Strong Essays
1084 words (3.1 pages)

Methods of Instruction for Teaching Mathematics Essay

- Mention the word math and a considerable number of people are sure to express their aversion to the subject. To illustrate: Raytheon Corporation surveyed approximately 1,000 adulterants whether they would prefer to eat broccoli or to work on a problem in mathematics. The preponderance of the students picked broccoli. The terror of math encompasses into later life. According to research by the non-profit institute Change the Equation in 2010, nearly one-third of Americans would rather clean an unsanitary bathrooms than do a mathematics assignment....   [tags: Mathematics, Education, Schools]

Strong Essays
1881 words (5.4 pages)

Mathematics and Art Essay

- Mathematics and art are two areas of knowledge that demonstrate different degrees of interaction between critical and creative thinking. Whether considering mathematics or art, creative thinking evaluates a new or original idea containing some degree of value. Critical thinking examines assumptions and challenges a current belief or theory that has previously assumed to be true. Although general assumptions and creativity may be considered separately when considering extreme examples of concrete ideas and abstract ideas, the interplay of critical and creative thinking is one method in which new and validated knowledge is attained....   [tags: Logic, Creativity, Philosophy]

Strong Essays
1590 words (4.5 pages)

George Boole's Impact on Mathematics Essay

- “He had a better mind and a more rigorous temperament than me; he thought logically, and then acted on the conclusion of logical thought. Whereas most of us, I suspect, do the opposite: we make an instinctive decision, then build up an infrastructure of reasoning to justify it. And call the result common sense.” This quote, by Julian Barnes, embodies the reason George Boole was my choice for my mathematician. I have always been fascinated by logic and reasoning, possibly because I constantly find myself in arguments which I prefer to call friendly debates....   [tags: logic, award, computers]

Strong Essays
723 words (2.1 pages)

Essay on The Theory Of Numeracy And Numeracy

- Task 1 To investigate the notion of numeracy, I approach seven people to give their view of numeracy and how it relates to mathematics. The following is a discussion of two responses I receive from this short survey. I shall briefly discuss their views of numeracy and how it relates to mathematics in the light of the Australian Curriculum as well as the 21st Century Numeracy Model (Goos 2007). Note: see appendix 1 for their responses. What is numeracy. Both A and B’s answers appear to equate numeracy to math, which contradicts Australian curriculum’s definition, but, in a small way, fulfils the 21st century model’s (appendix 2) first requirement, that “a numerate person requires mathematical...   [tags: Mathematics, Logic, 21st century, Reasoning]

Strong Essays
1041 words (3 pages)

Essay on Boolean Logic

- Boolean Logic Many of our computer databases utilize boolean logic as the basis of querying the database. Boolean logic has a much older history than most computer users imagine. It is helpful to understand the background and theory behind this concept, because this theory is the foundation on which contemporary computer science and information technology has been built. George Boole was an English mathematician. Born in 1815, he had no formal higher education, but had a natural gift for mathematics....   [tags: Mathematics George Boole Statistics Essays]

Strong Essays
1564 words (4.5 pages)

Essay on The Benefits of Learning Mathematics

- When I graduated from high school, forty years ago, I had no idea that mathematics would play such a large role in my future. Like most people learning mathematics, I continue to learn until it became too hard, which made me lose interest. Failure or near failure is one way to put a stop to learning a subject, and leave a lasting impression not worth repeating. Mathematics courses, being compulsory, are designed to cover topics. One by one, the topics need not be important or of immediate use, but altogether or cumulatively, the topics provide or point to a skill, a mastery of mathematics....   [tags: Math Education]

Strong Essays
929 words (2.7 pages)

Fuzzy Logic Essay

- Fuzzy Logic "So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality." -Albert Einstein, Geometry and Experience “It’s funny how when we’re the recipients of pain we’re clear that it’s black and white. But when we’ve got something to gain there are shades of gray.” – Dr. Laura Schlessinger Fuzz adds extreme choices of black and white, between shades of gray. Claim ness is given with fuzz; it does not make us choose....   [tags: Essays Papers]

Free Essays
768 words (2.2 pages)