Mathematics in modern World, Lecture notes of Mathematics

Download Mathematics in modern World and more Lecture notes Mathematics in PDF only on Docsity! ~ DE SAN FRANCISCO JAVIER - MATHEM TS IN THE MODERNZ~- AX SOLE | i ALTHEA D. ONDAC You can message me on my Gmail account/phone number / 09618280996 1] MATHEMATICS IN THE MODERN WORLD ALTHEA D. ONDAC, a licensed professional teacher and currently a faculty of Colegio De San Francisco Javier of Rizal Incorporated in Junior High school Department in Rizal, Zamboanga del Norte. She is also a part-time College instructor at the College of Social Work and Development Studies in this institution. She obtained her Bachelor of Secondary Education major in Mathematics, year 2019 at Jose Rizal Memorial State University, Main Campus, Dapitan City. She was a former President of Euclidean Circle, the official Mathematics Club in the said institution. 2|MATHEMATICS IN THE MODERN WORLD TABLE OF CONTENT COVER PAGE ABOUT THE AUTHOR MODULAR ONLINE CLASSROOM POLICIES COURSE REQUIREMENTS COURSE EXPECTTATIONS OBJECTIVE CONTENT * INTRODUCTION * CONTENT DISCUSSION * ASSESSMENT * RUBRICS * VIDEO WATCHING * REFERENCE 5|MATHEMATICS IN THE MODERN WORLD COLEGIO DE SAN FRANCISCO JAVIER COLLEGE OF SOCIAL WORK AND DEVELOPMENT STUDIES MATHEMATICS IN THE MODERN WORLD Module 1-l THE NATURE OF MATHEMATICS I Math in the Modern World *Sd OBJECTIVES > 0 Atthe end of this module, the student would be able to: 1. Identify patterns in nature and regularities in the world. 2. Argue about the nature of mathematics what it is, how it is expressed, represented, and used. 3. Articulate the importance of mathematics in one’s life. 4. Express appreciation for mathematics as a human endeavor. rw _ © | INTRODUCTION We live in a universe of patterns. Human mind and culture have developed a formal system of thought for recognizing, classifying, and exploiting patterns. We call it mathematics. By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes. Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems. As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but numbers, chance, form, algorithms, and change. As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs observation, simulation, and even experimentation as means of discovering truth. The special role of mathematics in education is a consequence of its universal applicability. The results of mathematics--theorems and theories--are both significant and useful; the best results are also elegant and deep. Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty. In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols. Experience with mathematical modes of thought builds mathematical power--a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives. Mathematics empowers us to understand better the information-laden world in which we live. KS) content > | CONTENT WHAT IS MATHEMATICS? + Mathematics is the study of pattern and structure. Mathematics is fundamental to the physical and biological sciences, engineering and information technology, to economics and increasingly to the social sciences. Mathematics is a useful way to think about nature and our world. Mathematics is a tool to quantify, organize and control our world, predict phenomena and make life easier for us. WHERE IS MATHEMATICS? * Many pattems and occurrences exists in nature, in our world, in our life. Mathematics helps makes sense of these patterns and occurrences. WHAT ROLE DOES MATHEMATICS PLAY IN OUR WORLD? * Mathematics helps organize patterns and regularities inn our world. * Mathematics helps predict the behavior of nature phenomena in the world. * Mathematics helps control nature and occurrences in the world for our own ends, * Mathematics has numerous application in the world making it indispensable. 6|MATHEMATICS IN THE MODERN WORLD Patterns and Numbers in Nature and the World Patterns in nature are visible regularities of form found in the natural world and can also be seen in the universe. Nature patterns which are not just to be admired, they are vital clues to the rules that govern natural processes. Patterns can be observed even in stars which move in circles across the sky each day. The weather season cycle each year. All snowflakes contain six fold symmetry which no two are exactly the same. s.0rg/2020/01/19/wilson-bentley-snowflakes/ Patterns can be seen in fish patterns like spotted trunkfish, spotted puffer, blue spotted stingray, spotted moral eel, coral grouper, redlion fish, yellow boxfish and angel fish. These animals and fish stripes and spots attest to mathematical regularities in biological growth and form. https://www.scribd.com/document/413135891/mathematics-in-the-modern-world Zebras, tigers, cats and snakes are covered in patterns of stripes; leopards and hyenas are covered in pattem of spots and giraffes are covered in pattem of blotches. https://www.scribd.com/document/413135891/mathematics-in-the-modern-world Natural patterns like the intricate waves across the oceans; sand dunes on deserts; formation of typhoon; water drop with ripple and others. These serves as clues to the rules that govern the follow of water, sand and air. https://www.scribd.com/document/41313589 1/mathematics-in-the-modern-world We are still learning to recognize new kinds of pattern. Only within the last thirty years has humanity become explicitly aware of the two types of pattem now known as fractals and chaos. Fractals are geometric shapes that repeat their structure on ever-finer scales. It is a never-ending pattern. Fractals are infinitely complex patterns that are self- similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems — the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since 7\