Mathematics is possibly one of the most underappreciated sciences. It everywhere in our lives, mathematics runs our computers, flies our aircraft, and protects our information. But for such a major part of our lives, very few people can say that they know how it is done, how the RSA encryption protects their e-mail, or even that 21 squared is 441 without going into tedious mental calculations or reaching for their calculator.
Contrary to popular belief, mathematics has a wide range of useful applications. Those who would ask whenever they would need algebra, both linear algebra and calculus is used extensively in computer programming and engineering. The fact is that mathematics is integrated into almost every profession, and every aspect of your life.
During world war two, number theory, a highly theoretical branch of mathematics focusing on the properties of integers, found new applications in the field of cryptography. Both the allies and the axis sent encoded message over airways that both sides had access to. Obviously they didn’t want the other side to know what they were up to, so they both sent encoded messages. Mathematics served a primary role in the cracking of these codes, most notably the enigma code used primarily by Nazi Germany.
The problem with an encoded message though, is that historically, a code needed to be prearranged along with some sort of decryption key, between the two parties wishing to communicate. This led to the field of public key cryptography.
Imagine that two people want to send messages through the postal service, but they want to make sure no one reads it. Person A puts a lock on their package, which both Person A and Person B has a key to. This allows person B to remove the lo...
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...nown for his creation of the Mandelbrot set fractal, which is also in appendix a, he created the fractal using computer software.
Fractals can be used to store pictures. The idea is to take a few colored pixels, and create a fractal generator program that would result in the picture. Storing a simple fractal generation program and a few pixels, would be infinitely more efficient than storing an entire .JPG image.
In conclusion, Mathematics can and does have many applications outside of the theoretical. Whether it is playing the odds by counting cards, or analyzing a new road plan mathematics does have applications. Mathematics is also integral to everyday life, it protects our data, and allows for the operation of the electronics and computers which allow us to live our way of life. Whether we like it or not, mathematics is a fundamental part of our lives.
The sender would type the message in plaintext (not encrypted) and the letters would be illuminated on a glass screen. With the press of each typewriter key the rotor would shift 1/26 of a revolution giving each letter a different encryption each time, which made the code so difficult to crack. Due to the complexity of the code the enigma became very useful for the Germans for radioing messages to u-boats. The cipher was finally broken when the British were able to capture some key documents from a German warship.
Math is everywhere when most people first think of math or the word “Algebra,” they don’t get too excited. Many people say “Math sucks” or , “When are we ever going to use it in our lives.” The fact is math will be used in our lives quite frequently. For example, if we go watch a softball game all it is, is one giant math problem. Softball math can be used in many
Enigma machines were built to make coding and decoding messages easier. As explained by Andrew Hodges, a mathematician and author, “The basic principle of using an Enigma machine was that its rotors and rings and plug board would be set up in some particular way, and then the message would be encrypted, the rotors automatically stepping round as this was done,” (171). So after the initial state of the machine was decided normal by the cipher clerk, the message would be typed on a message going out into a “26 letter keyboard,” stated by William Jacobs a writer and producer, encrypting it causing the rotors to move as he typed the message (1). During this part of the process the machine encodes the message by replacing the words with random groupings of letters. An electrical signal is sent through a maze of wires and every time a key is pressed the rotating wheels turned lighting up a specific bulb showing an encrypted letter. Upon receiving the code, the decipher would need to know the machine’s initial state to be able to use the message he received in any means of communication. He would then take the encrypted code and decipher it using an Enigma Machine. Although it seemed to be a very simple process Carol Marshall, Computer Science Manager states, “… the Germans refined and improve their encryption tool so that it was used constantly throughout the war,”
I also learned that mathematics was more than merely an intellectual activity: it was a necessary tool for getting a grip on all sorts of problems in science and engineering. Without mathematics there is no progress. However, mathematics could also show its nasty face during periods in which problems that seemed so simple at first sight refused to be solved for a long time. Every math student will recognize these periods of frustration and helplessness.
Mathematics is used to pay bills and to cook to give a few examples. It is also used to figure out different formulas for space. Mathematics is used for computing
Math is a very important subject because not only does it improve your learning skills but it also improves your problem solving and creative techniques as well.
Throughout my past and current educational experiences I have excelled in math and biology. These subjects have appealed to me ever since I was a kid, I used to spend most of my free time reading about the history of math, learning about our body and learning how scientists like Isaac Newton and Euler derived formulas that that have been used in mechanics, fluid dynamics, optics, differential calculus and are used to build technology i.e. Rockets, jet engines and Tow missile etc. that has transformed human life . My understanding of these subjects has developed over the years because of our daily interaction with them, we use math from calculating the cost of an item on sale, to making budgets and biology from our circulation of blood, to respiration and the complex process of sexual reproduction involving meiosis. These interactions have helped me realize the importance of math and biology in our daily life.
There are many reasons why Algebra matters in life. One reason that comes to mind is from an early age, your understanding and success in algebra can help build math confidence, notable achievements in high school coursework and college readiness, and more importantly help predict one’s salary earnings on so many levels. As one would know that nearly all sports statistics are produced using algebraic equations. Average points per game are used to determine the Most Valuable Player. Winning percentages are used to determine top rankings. These are calculated with concepts learned in Algebra. Formulas are a part of our lives, whether we drive a car and need to calculate the distance, or need to work out our food volume intake for dieting; algebraic formulas are used every day without us even realizing it.
Mathematics is everywhere we look, so many things we encounter in our everyday lives have some form of mathematics involved. Mathematics the language of understanding the natural world (Tony Chan, 2009) and is useful to understand the world around us. The Oxford Dictionary defines mathematics as ‘the science of space, number, quantity, and arrangement, whose methods, involve logical reasoning and use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis of mathematical operations or calculations (Soanes et al, Concise Oxford Dictionary,
Fibonacci Numbers originated from India hundreds of years ago. Though Fibonacci Numbers came from India, Leonardo of Pisa, better known as Fibonacci, made it known to the world. Leonardo came from a wealthy Italian family and traveled to North America to join his father. He was educated by the Moors and sent on business trips. “After returning to Pisa around 1200, Leonardo wrote his most famous literature, Liber Abaci” (Pearson). Leonardo featured a rabbit question in the book. The question was asked in a mathematical competition, he appeared in when he was young. Leonardo Fibonacci used the Fibonacci Numbers to solve it. Fibonacci Numbers is now used throughout our society.
Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in the early twentieth century. Although it appears simple, the Sierpinski Triangle is actually a complex and intriguing fractal. Fractals have been studied since 1905, when the Mandelbrot Set was discovered, and since then have been used in many ways. One important aspect of fractals is their self-similarity, the idea that if you zoom in on any patch of the fractal, you will see an image that is similar to the original. Because of this, fractals are infinitely detailed and have many interesting properties. Fractals also have a practical use: they can be used to measure the length of coastlines. Because fractals are broken into infinitely small, similar pieces, they prove useful when measuring the length of irregularly shaped objects. Fractals also make beautiful art.
It is constructed by taking an equilateral triangle, and after many iterations of adding smaller triangles to increasingly smaller sizes, resulting in a "snowflake" pattern, sometimes called the von Koch snowflake. The theoretical result of multiple iterations is the creation of a finite area with an infinite perimeter, meaning the dimension is incomprehensible. Fractals, before that word was coined, were simply considered above mathematical understanding, until experiments were done in the 1970's by Benoit Mandelbrot, the "father of fractal geometry". Mandelbrot developed a method that treated fractals as a part of standard Euclidean geometry, with the dimension of a fractal being an exponent. Fractals pack an infinity into "a grain of sand".
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
...re encompassing way, it becomes very clear that everything that we do or encounter in life can be in some way associated with math. Whether it be writing a paper, debating a controversial topic, playing Temple Run, buying Christmas presents, checking final grades on PeopleSoft, packing to go home, or cutting paper snowflakes to decorate the house, many of our daily activities encompass math. What has surprised me the most is that I do not feel that I have been seeking out these relationships between math and other areas of my life, rather the connections just seem more visible to me now that I have a greater appreciation and understanding for the subject. Math is necessary. Math is powerful. Math is important. Math is influential. Math is surprising. Math is found in unexpected places. Math is found in my worldview. Math is everywhere. Math is Beautiful.
As mathematics has progressed, more and more relationships have ... ... middle of paper ... ... that fit those rules, which includes inventing additional rules and finding new connections between old rules. In conclusion, the nature of mathematics is very unique and as we have seen in can we applied everywhere in world. For example how do our street light work with mathematical instructions? Our daily life is full of mathematics, which also has many connections to nature.