Nature of Mathematics PDF

NATURE OF MATHEMATICS MATHEMATICS OF OUR WORLD  NATURE OF MATHEMATICS Mathematics is a formal system of thought that was gradually developed in the human mind and evolved in the human culture. Thus, in the long course of human history, our ancestors at a certain point were endowed with insight to...

NATURE OF MATHEMATICS MATHEMATICS OF OUR WORLD  NATURE OF MATHEMATICS Mathematics is a formal system of thought that was gradually developed in the human mind and evolved in the human culture. Thus, in the long course of human history, our ancestors at a certain point were endowed with insight to realize the existence of “form” in their surroundings. From their realization, a system of thought further advanced their knowledge into understanding measures. They were able to gradually develop the science of measures and gained the ability to count, gauge, assess, quantify, and size almost everything.  NATURE OF MATHEMATICS From our ancestor’s realization of measures, they were able to notice and recognize some rudiment hints about patterns. Thus, the concept of recognizing shapes made its course towards classifying contour and finally using those designs to build human culture: an important ingredient for a civilization to flourish. we made use of mathematics as a brilliant way to understand the nature by comprehending the structure of its underlying patterns and regularities. Mathematics is present in everything we do; it is all around us and it is the building block of our daily activities.  MATHEMATICS AS A TOOL Mathematics, as a tool, is immensely useful, practical, and powerful. It is not about crunching numbers, formulas, and symbols but rather, it is all about forming new ways to see problems so we can understand them by combining insights with imagination. It also allows us to perceive realities in different contexts that would otherwise be intangible to us. It can be likened to our sense of sight and touch. Mathematics is our sense to decipher patterns, relationships, and logical connections. It is our whole new way to see and understand the modern world. It is asserting that mathematics is a powerful tool in decision- making and it is a way of life MATHEMATICS AS A TOOL  MATHEMATICS AS A TOOL is stated that mathematics is a set of problem-solving tools. It provides answers to existing questions and presents solutions to occurring problems. It has the power to unveil the reasons behind occurrences and it offers explanations. Moreover, mathematics, as a study of patterns, allows people to observe, hypothesize, experiment, discover, and recreate. On the other hand, mathematics is an art and a process of thinking. For it involves reasoning, which can be inductive or deductive, and it applies methods of proof both in fashion that is conventional and unventional.  MATHEMATICS IS EVERYWHERE We use mathematics in their daily tasks and activities. It is our important tool in the field of sciences, humanities, literature, medicine, and even in music and arts; it is in the rhythm of our daily activities, operational in our communities, and a default system of our culture. There is mathematics wherever we go. It helps us cook delicious meals by exacting our ability to measure and moderately control of heat. It also helps us to shop wisely, read maps, use the computer, remodel a home with constrained budget with utmost economy. ESSENTIAL ROLE OF MATHEMATICS Mathematics has countless hidden uses and applications. It is not only something that delights our mind but it also allows us to learn and understand the natural order of the world. Science would definitely agree that when it comes to discovering and unveiling the truth behind the inherent secrets and occurrences of the universe, nothing visual, verbal, or aural come close to matching the accuracy, economy, power, and elegance of mathematics. Mathematics helps us to take the complex processes that is naturally occuring in the world around us and it represents them by utilizing logic to make things more organized and more efficient. MATHEMATICAL LANDSCAPE The human mind and culture developed a conceptual landscape for mathematical thoughts and ideas to flourish and propagate. There is a region in the human mind that is capable of constructing and discerning the deepest insights being perceived from the natural world. This landscape claimed complex numbers as the firmament and even asserted that imaginary numbers also exist. To the low state negative numbers relentlessly enjoying recognition as existent beings MATHEMATICAL LANDSCAPE The wind in this landscape is unpredictable that the rate of change of the rate of change of weather is known as calculus. And beneath the surface of this mathematical landscape are firmly- woven proofs, theorems, definitions, and axioms which are intricately “fertilized” by reasoning, analytical, critical thinking and germicide by mathematical logic that made them precise, exact and powerful The numbers in mathematics is not a "thing" but a process. HOW MATHEMATICS IS DONE? Math is a way of thinking, and it is undeniably important to see how that thinking is going to be developed rather than just merely see face value of the results. For others, this discipline is so complex and they have to understand the confusing symbols, the difficult procedures, and the dreaded graphs and charts. For most, mathematics is just nothing but something to survive, rather than to learn. HOW MATHEMATICS IS DONE? If you come across a mathematical problem that you cannot solve, the first thing to do is to identify the components or the operations that it wants you to carry out, and everything follows. Doing and performing mathematics is not that simple. It is done with curiosity, with a penchant for seeking patterns and generalities, with a desire to know the truth, with trial and error, and without fear of facing more questions and problems to solve. (Vistru-Yu) MATHEMATICS IS FOR EVERYONE The relationship of the mathematical landscape in the human mind with the natural world is so strange that in the long run, good math provides utilization and usefulness in the order of things. Perhaps, for most people, they simply need to know the basics of the mathematical operations in order to survive daily tasks; but for the human society to survive and for the human species to persistently exist, humanity needs, beyond rudiment of mathematics. To safeguard our existence, we already have delegated the functions of mathematics across all disciplines. MATHEMATICS IS FOR EVERYONE There is mathematics we call pure and applied, as there are scientists we call social and natural. There is mathematics for engineers to build, mathematics for commerce and finance, mathematics for weather forecasting, mathematics that is related to health, and mathematics to harness energy for utilization. To simply put it, everyone uses mathematics in different degrees and levels. Everyone uses mathematics, whoever they are, wherever they are, and whenever they need to. From mathematicians to scientists, from professionals to ordinary people, they all use mathematics. For mathematics puts order amidst disorder. It helps us become better persons and helps make the world a better place to live in. IMPORTANCE OF MATHEMATICS Why do we want to observe and describe patterns and regularities? Why do we want to understand the physical phenomena governing our world? Why do we want to dig out rules and structures that lie behind patterns of the natural order? It is because those rules and structures explain what is going on. It is because they are beneficial in generating conclusions and in predicting events. It is because they provide clues. The clues that make us realize that interference in the motion of heavenly bodies can predict lunar eclipse, solar eclipse as well as comets’ appearances.  IMPORTANCE OF MATHEMATICS That the position of the sun and the moon relative to the earth can predict high tide and low tide events affecting human activities. And that human activities need clues for the human culture to meaningfully work. Mathematical training is vital to decipher the clues provided by nature. But the role of mathematics goes clues and it goes beyond prediction. Once we understand how the system works, our goal is to control it to make it do what we want. We want to understand the mathematical pattern of a storm to avoid or prevent catastrophes. We want to know the mathematical concept behind the contagion of the virus to control its spread. We want to understand the unpredictability of cancer cells to combat it before it even exists