Formal Mathematical Methods And Hardware Systems

Mathematical activities at Ysgol Dolafon are delivered in accordance with pupil’s individual needs and great deal of emphasis is given to continuity of learning. Ample opportunity is provided for pupils to discuss their understanding of concepts as they progress and teachers are aware of the importance of eliminating any gaps in the children’s mathematical knowledge. The Welsh Assembly Government guideline for Mathematical Development maintains that: ‘It is crucial that gaps in children’s mathematical learning are avoided, so that children do not miss out on essential elements in their understanding of mathematical concepts’ (WAG 2008) and Ysgol Dolafon fully agrees with that statement.

Mathematics is a logical and precise subject. Without precision in math everything is imprecise. A modest inaccuracy can produce a catastrophe. For example, if a doctor fails to calculate the correct amount of medicine to give a patient, it could result in a serious complication, such as death. A further example is the logic and precision it takes to construct a building. If there is one minor miscalculation the whole building could collapse, causing mass destruction.

Geometry and Algebra are so crucial to the development of the world it is taught to every public high school in the United States, around 14.8 million teenagers each year (National Center for Education Statistics). Mathematics is the engine powering our world; our stocks, economy, technology, and science are all based off from math. Math is our universal and definite language “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings.” (Rene Descartes, 1637).

In Rene Descartes’ Discourse on Method he expresses his disappointment with traditional philosophy and with the limitations of theology; only logic, geometry and algebra hold his respect, because of the utter certainty which they can offer us. Unfortunately, because they depend on hypotheses, they cannot tell us what is real, i.e. what the world is really like. Therefore Descartes suggests a method of thought combining the consistency of mathematics but based on natural truths about what is real, basic knowledge which could not be wrong (like the axioms of geometry). He calls into question everything that he thinks he has learned through his senses but rests his entire system on the one truth that he cannot doubt, namely, the reality of his own mind and the radical difference between the mental and the physical aspects of the world.

We use mathematics to our great advantage to explain many things. Although Pythagoras, applied A^2+B^2=C^2, he did not create the substance of the equation, this theorem is timeless, he only brought it to our attention.

He then goes on to talk about math as an example of a certain and simple concept that is also true and important to him.

Although it is irrefutable that both Aristotle and Isaac Newton are great scientists and have made phenomenal contributions to scientific development, their scientific methods vary to a large extent. With reference to Scientific Method in Practice, Aristotle investigated the world by using inductions from observations to infer general principles and deductions from those principles to conduct further observational research (Gauch, 2003), while in Isaac Newton's Scientific Method, the author describes Newton’s method as aiming to turn theoretical questions into ones which can be explained by mathematical ideas and measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally guides to further research

When teaching mathematical concepts it is important to look at the big ideas that will follow in order to prevent misconceptions and slower transformation

In today’s society mathematics is a vital part of day-to-day life. No matter what a person is doing at home or at the workplace, he/she is constantly using different mathematics skills to simply function. Then what does this mean for mathematics education? When someone needs to utilize a skill every day then he/she needs a strong background in the skill. Therefore, today’s students need more than a just a working knowledge of mathematics or enough knowledge to pass a test. Today’s students need to understand how mathematics works and how to utilize mathematics skills in the best way possible.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Maths is a subject that has always interested me, but looking at the roots of it is an aspect that I have never explored. I always knew that it is very open to debate, with various different opinions but I have always been intrigued by it, so I have decided to use it as the subject of my Extended Project.

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

Mathematics is a type of reasoning. Thinking mathematically includes thinking in a rational way, developing and checking conjectures, understanding things, and forming and validating judgments, reasoning, and conclusions. We show mathematical habits when we acknowledge and explain patterns, build physical and theoretical models of sensations, develop sign systems to assist us stand for, control, and review concepts, and create treatments to address issues (Battista, 1999).

Mathematics is the one of the most important subjects in our daily life and in most human activities the knowledge of mathematics is important. In the rapidly changing world and in the era of technology, mathematics plays an essential role. To understand the mechanized world and match with the newly developing information technology knowledge in mathematics is vital. Mathematics is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the world. The world cannot progress without mathematics. Mathematics fulfills most of the human needs related to diverse aspects of everyday life. Mathematics has been accepted as significant element of formal education from ancient period to the present day. Mathematics has a very important role in the classroom not only because of the relevance of the syllabus material, but because of the reasoning processes the student can develop.

The purpose of this report is to give information on the subject known as Logical reasoning and its use in Computer Science and computers in general. A historical background behind logic and Logical reasoning is firstly given, followed by an overview of the modern subject and the types it’s divided into. The types are then explained. The overlap between the field of logic and that of computer science is also given an explanation. The report ends with a brief overview on the subject and its tie to computer science and computing.