Why is Mathematics Important

Published on May 2016 | Categories: Types, School Work, Essays & Theses | Downloads: 62 | Comments: 0 | Views: 1036
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HY IS MATHEMATICS IMPORTANT? In this note we excerpt some of the highlights of Professor Arnold's May 2003 commencement address, titled "Doing the Math and Making an Impact", and given by him for the mathematics and statistics graduation at the University of Illinois in Urbana-Champaign. Professor Arnold is the Director of the Institute for Mathematics and its Applications which is associated with our department. The full text of this interesting and inspiring talk is online at http://www.ima.umn.edu/newsltrs/updates/summer03 Asking "What makes the math sciences so central?", he answers by quoting Galileo: "The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics.", adding "Math is the way to understand all sorts of things in the world around us." To elaborate on this point he gives some well-chosen examples, beginning with some insightful comments on the Swiss victory in the 2003 America's Cup. "...you know that Switzerland is a small, mountainous, land-locked country. So how did the Swiss pull this upset off?" While acknowledging that a number of diverse factors had to come together, he makes his point: " Well Switzerland may not have a great sailing tradition (at least until now!) but it does have a very strong tradition in mathematics--Euler's picture appeared on a Swiss 10 franc note--and the Swiss team wisely brought this strength in math to bear on the America's Cup challenge. They enlisted a group of mathematicians specializing in mathematical modeling and numerical computation led by Professor Alfio Quarteroni at the national polytechnical university in Lausanne. The mathematicians used partial differential equations to model the flow of the sea around the hull, the dynamics of the air and the sails, and the turbulent interaction of the ocean, wind, and boat. They then applied advanced numerical algorithms to solve these equations on high performance computers. This allowed them to optimize such things as hull and keel design, sail geometry and placement, and so forth. Their work was essential to the design of the Alinghi, and so to the Swiss victory. They did the math and made a big impact." ("Alinghi" was the name of the Swiss boat.) On the increasing role of mathematics in biological sciences he comments as follows: "Increasingly math is making an impact in the life sciences as well, prompting biologist Rita Colwell, director of the National Science Foundation, to observe that "mathematics is biology's next microscope--only better." In their recent bio textbook Keener and Sneyd wrote that "teaching physiology without a mathematical description of the underlying dynamical processes is like teaching planetary motion to physicists without mentioning...Kepler's laws;" He then mentions still other areas of applications: "And math increasingly reaches outside the sciences, to economics, sociology, and business for example. ...Illinois's new Applied Mathematics Program ...involves no less than 22 departments from bioengineering to linguistics. ...Problems which need mathematics for their solution also arise throughout industry." To underline how seriously this is taken worldwide, he cites a strategic plan published by the British government in 2003, seeking to exploit mathematical research to improve the competitiveness of industry in the UK: ""Mathematics is the most versatile of all the sciences. It is uniquely well placed to respond to the demands of a rapidly changing economic landscape...Mathematics now has the opportunity more than ever before to under-pin quantitative understanding of industrial strategy and processes across all sectors of business. Companies that take best advantage of this opportunity will gain a significant competitive advantage:

mathematics truly gives industry the edge." He also notes that British government policy in dealing with the hoof-and-mouth disease outbreak a few years ago relied heavily on studies based on mathematical epidemiology. He states that a major current challenge we face is how to get the most out of all the data that has been accumulated thanks to the modern technology: "For example, how can we exploit the world-wide network of seismic sensors to predict earthquakes? How can we mine the vast genomic databanks to advance biology and medicine? How can we sift through the massive amounts of text, video, web, and satellite data to detect terrorist events before they happen? Well, data means big collections of numbers--remember that text and images are digitized and stored as numbers--and data mining means discovering the patterns and structures hidden in those collections. That's practically a definition of mathematics: the study of structures and patterns in large numerical sets. So you can be sure that in the 21st century--the century of data--math will again have a huge impact." In conclusion he exhorts the graduates to cultivate and apply logical, mathematical and quantitative thinking even if they do not become research mathematicians.

FACT: The Bermuda Triangle is NOT a triangle; it’s a trapezoid. DEPOTA. That’s exactly how I vented my disgust for my Engineering Mechanics professor after he uttered these words ad nauseam: Mathematics is the language of the universe.

I’m not good in math. Those basic stuff, sure, I get them. But when it comes to the more complicated details (e.g. derivatives, integrals, limits, etc.), that’s when my nose bleeds. I suddenly remembered something that happened during my initial year in college. It was 3 or 4 in the afternoon; our Trigonometry professor was discussing something about some trigo-function crap, when I saw something on my notebook. There was a big red dot on the page. So I instinctively touched my upper lip, it was wet. For Christ’s sake it was not snot. Then there was blood.

How poetic, my nose LITERALLY bled during a math subject. I did not want to cause a commotion so I kept it to myself and covered my nose with tissue. (It was my freshman year; I was ready as a boy scout back then.) After a while, it eventually stopped. Thank god I was the only one who actually noticed. I passed the subject though, but by far, my final grade in Trigonometry is the lowest for all of my subjects, ever. The prospectus of my course, which is Electronics and Communications Engineering, mainly projects electronics and math— the two topics I loathe the most. You might ask me how I get by with a course that is totally beyond my comfort zone without flunking any subjects. I ask myself the same thing. Hakhak. I’ll share something harsh about my scholarship. So you probably realize by now that I’m an SM Scholar—ehem, a PROUD SM Scholar. Thanks to Henry Sy, Sr., I do not have to cash-out a single centavo for my tuition. And the best part is they even pay me. But there is a catch. If ever I fail a subject, I’ll have to pay for that subject only. But if I do not reach the required Graded Point Average, I’ll have to pay for the full tuition fee next term, and that’s a whopping 40,000 pesos! I certainly cannot afford that so I do my darn hardest to

pass my calculus quizzes, even if that means not sleeping for two days. I hate equations. I mean come on, in real life, no one actually uses derivatives. Okay, so there may be a few who do. But the point is, math should have never been invented—and in effect computers could have not been invented, too. And in turn, this amazing (?) blog could not have existed. Okay, I take back my statement. I love math.

The Importance of Mathematics
From the National Curriculum for Mathematics, website: "Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decisionmaking. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy. Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of pleasure and wonder for all pupils when they solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Pupils who are functional in mathematics and financially capable are able to think independently in applied and abstract ways, and can reason, solve problems and assess risk. Mathematics is a creative discipline. The language of mathematics is international. The subject transcend cultural boundaries and its importance is universally recognised. Mathematics has developed over time as a means of solving problems and also for its own sake."

So that's why maths is important! Try explaining that to 11-16 year olds.... I have highlighted in red the part about creativity, for that is all that I have been going on about this past week at this school. (By the way I haven't looked at anything else on the site, because I have to eat now and wanted to post this before doing so.) Today, I tried my creativity "bull" (as named by someone) past a few students. Some gave me "the look" but to one student I ended up using Harry Potter and The Goblet of Fire as an example. Well the final task for the Tri-wizard tournament to be precise, and how Harry didn't give up when he came across challenges in the maze. Lame I know, but I was trying to tell this student that the wrong answer shouldn't stop him. Since he was a Harry Potter fan he seemed to like the maze, but more on this in my "journal post" coming up later. So how would you "summarise" them three long paragraphs to a secondary school student, especially when they cry: "I hate Maths--why do we have to learn this? How is it going to help me?" Oh, and they don't give a damn about the future but the here and now.

1 Plato’s View on the Importance of Mathematics Plato (427-347 B.C.) is considered to be one of the great philosophers who contributed much in shaping western philosophy. He was born from an aristocratic family. His early interests were in poetry and politics. He learned philosophy from Socrates, the famous Greek philosopher. As a consequence of the political unrest in Athens that in turn led to the execution of his teacher, Socrates, he abandoned temporarily his political interests and left Athens. In his travels, he got acquainted with the Pythagoreans. From the Pythagoreans, he gained the interest in the study of Mathematics. He then returned to Athens about 385 B.C. and founded his Academy where he was lecturing for the rest of his life. The Academy was considered one of the main centers of intellectual life at the time. The topics of study in the Academy included philosophy, mathematics and law. The Academy attracted many talented people in Greece. One student of the Academy was Eudoxus of Cindus. He became one of the most able mathematicians at the time. Eudoxus gained fame from his work on the theory of proportions. He is also considered by many as the one behind the idea of the method of exhaustion. Plato’s contributions to mathematics were focused on the foundations of mathematics. He discussed the importance of examining the hypotheses of mathematics. He also drew attention toward the importance of making mathematical definitions clear and precise as these definitions are fundamental entities in mathematics. Another indirect contribution of Plato was the important role he played in encouraging and inspiring people to study mathematics. In the Academy, he proposed many mathematical problems and encouraged the students of the Academy to investigate. This led to the appearance of many mathematicians, like Eudoxus, who contributed in the progress of mathematics. But why did Plato stress on the study of mathematics. One can find the answer in the seventh book of his masterpiece, The Republic, where he stated some of his views on the importance of mathematics. To Plato, the idea of good is the ultimate objective of philosophy. He thinks that “in the world of knowledge the idea of good appears last of all, and is seen only with an effort; and, when seen, is also inferred to be the universal author of all things beautiful and right.”[4, p. 179] To help in understanding and attaining the idea of good, one has to study arithmetic and geometry. These two subjects have two important characteristics that make them valuable in comprehending the idea of good. The first characteristic that arithmetic and geometry have is that they invite thought and lead the mind to reflect and hence enabling the mind to reach truth. The second characteristic is that the advanced parts of arithmetic and geometry have the power to draw the soul from becoming to beings. To Plato, this is “the true use of arithmetic.” And the easiest way for the soul to go from becoming to being is to pursue the study of arithmetic until one is able to see 2

“the natures of numbers with the mind only.” Also, “arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number and repelling against the introduction of visible or tangible objects into the argument.”[4, p.188] He also thinks that studying arithmetic as an amateur or like a merchant with a view to buying or selling will not help the soul to make this transition from becoming to being. In addition to these two criteria, Plato thinks that people who are good in mathematics will do well in any other field of knowledge: “those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been” and “any one who has studied geometry is infinitely quicker of apprehension than one who has not.”[4, pp. 188-189]. One of the topics of mathematics that Plato drew much attention to was that of irrationals. Plato strongly encouraged the students of the Academy to pursue the study of irrationals. His opinion was that science is incomplete without them and that a comprehensive study of irrationals is necessary to build “a coherent and universal philosophy free of the difficulties that wrecked the Phythagorean system.”[3, p.95]. One, thus, observes that, in Plato’s view, mathematics has a philosophical importance. Mathematics is a tool that helps and trains the mind to think. This process of thinking will then help the mind to understand and acquire the idea of good, which is the ultimate aim of philosophy. Plato did not deny the important applications of mathematics in people’s daily life. But, to Plato, the philosophical importance of mathematics is more important and more rewarding as it may affect one’s understanding of his being. References: 1. Boyer, Carl C. and Merzbach, Uta C. A History of Mathematics. Second edition, 1989, John Wiley &Sons, Inc. New York. 2. Heath, Thomas. A History of Greek Mathematics. Vol. 1. 1965. Oxford university press. Oxford. 3. Maziarz, Edward A. and Greenwood, Thomas. Greek Mathematical Philosophy. 1968. Frederick Ungar Publishing Co., Inc. New York. 4. Plato. The Republic. Translated by B. Jowett. 2000. Dover Publications, Inc. New York. March 14, 2005 (4 Safar, 1426)

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