Mean value theorem Essays

  • Public Schools and Education - It's Time for Education Reform

    972 Words  | 2 Pages

    system. There is quite a bit of bureaucracy and conformity to overcome. The education system is profoundly skewed and this is the second time I have experienced its most significant problem: placement and grading. Most educators place too much value on inflexible systems for identifying proper places for students and estimate their comprehension of the material; there are many factors that may aid or hinder a student's performance on such tests. Yet, even excusing poor test score(s) is not my

  • Fermat’s Little Theorem

    864 Words  | 2 Pages

    1. Introduction: As I was looking for a theorem to prove for my Mathematics SL internal assessment, I couldn’t help but read about Fermat’s Little Theorem, a theorem I never heard of before. Looking into the theorem and reading about it made me develop an interest and genuine curiosity for this theorem. It was set forth in the 16th century by a French lawyer and amateur mathematician named Pierre de Fermat who is given credit for early developments that led to infinitesimal calculus. He made significant

  • The Evolution of Differential Calculus

    2665 Words  | 6 Pages

    process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables

  • Mathematical Exploration: Exploring the Proofs of Fermat's Little Theorem

    1381 Words  | 3 Pages

    Fermat's Little Theorem came about. INTRODUCTION OF FERMAT'S LITTLE THEOREM Pierre de Fermat was a French mathematician whose contribution to analytic geometry and calculus are duly noted. But, what made him and still makes him a relevant mathematic figure is one of his well and widely known theorem; Fermat's Little Theorem. This theorem was first stated by him in a letter to a fellow friend on October 18, 1640, but what made it interesting is that he gave no proof of this theorem. This is how the

  • Importance Of Bayes Theorem In Law And Courtrooms

    1101 Words  | 3 Pages

    D. How is Bayes theorem important in avoiding fallacies commonly made in law and courtrooms? I. Base rate fallacy If presented with related generic, general information and specific information (information pertaining only to a certain case), the mind tends to ignore the former and focus on the latter. This can be avoided using Bayes’ Theorem, as it takes into account prior probability (which is the probability assessed before making reference to certain relevant observations, especially subjectively

  • Measures Of Spread And Dispersion

    1221 Words  | 3 Pages

    Chebyshev theorem applies to all kinds of distribution regardless of their shape. It can be used in scenarios where the shape of the distribution is not known or not normal. Chebyshev Theorem states at least 1-(1/k2) values will fall within (+/- )k standard deviations of the mean regardless of the shape of the distribution. Within k standard deviations of the mean μ (+/- )kσ lie at-least 1-(1/k2) Proportion of values. Assumption : k>1 Coefficient of variation

  • Theorem Of Pythagorean Theorem

    1937 Words  | 4 Pages

    YTHAGOREAN THEOREM 3 Pythagorean Theorem Introduction The purpose of this paper is for grade 9 and grade 10 students in Ontario high schools to know a brief history about the development of the Pythagorean theorem, write a proof of the theorem, solve problems using the Pythagorean theorem, and calculate primitive Pythagorean triples with one odd and one even number. The theorem is called by di erent names: Pythagoras' theorem, the hypotenuse theorem or Euclid I 47, so called because it is listed

  • Fermat’s Last Theorem

    2222 Words  | 5 Pages

    Fermat’s Last Theorem The year is 1637. Pierre de Fermat sits in his library, huddled over a copy of Arithmetica written by the Greek mathematician Diaphantus in the third century A. D. Turning the page, Fermat comes across the Pythagorean equation: x 2 + y 2 = z 2. He leans back in his chair to think and wonders if this property is limited to the power of two only. He bends over the book again, scanning ahead through the pages to look for any clues. Suddenly, he begins writing intensely

  • Binomial Theorem Essay

    1796 Words  | 4 Pages

    Binomial Theorem is one such phenomenon, which was founded by the combined efforts of Blaise Pascal, Isaac Newton and many others. This theorem is mainly algebraic, which contains binomial functions, arithmetic sequences and sigma notation. I chose the Binomial Theorem because of its complexity, yet simplicity. Its efficiency fascinates me and I would like to share this theorem that can be utilized to solve things in the Mathematical world that seem too daunting to be calculated by normal means. In 1665

  • The Importance Of Logic And Mathematics

    1191 Words  | 3 Pages

    When we talk about topics such as Logic and Mathematics, we tend to think of certain, only abstract concepts. The word ‘Logic’ in this title can mean an analysis of a hidden structure associated with syntax of propositions, while the word ‘Mathematics’ can be defined as a specialized kind of abstract language. The title itself follows the concept of opinion and proposition that states both Logic and Mathematics are nothing but specialized linguistic structures, meaning these topics are considered

  • Book Review Of Ian Ayres's 'Super Crunchers'

    951 Words  | 2 Pages

    organization. To be competent in number crunching, we need to feel comfortable about using two quantitative tools: 2SD Rule and Bayes Theorem. The 2SD Rule, to use this rule, you start by estimating what the mean or average value is and what the standard deviation is. The 2SD Rule then gives you a way to translate those statistics into numbers people will relate to. Bayes Theorem, allows you to combine two or more probabilities into a single number. To come up with a combined probability, multiply the initial

  • Greek Geometry Essay

    988 Words  | 2 Pages

    geometry and also to have a mathematical discovery attached to their name. Thales theorem states that an inscribed angle in a semicircle is a right angle. One interesting Pythagoras and his followers held the belief that “all things are numbers”. He also thought the designs of buildings should include ratios. One building that used geometry was the Parthenon in Greece. The ratio of the width to length is the same value of the ratio of height to width. Making a ratio with the height, width, and length

  • Essay On Gaussian Distribution

    827 Words  | 2 Pages

    probability density function of a normal (or Gaussian) distribution is defined as Where the parameters μ is the mean or expectation of the distribution σ is the Standard deviation of the distribution σ 2 is the variance of the distribution. And is represented as The normal distribution is very utilizable because of the central limit theorem, which states that, under mild conditions, the mean of many arbitrary variables independently drawn from the same distribution is distributed approximately customarily

  • Median Voter Theorem

    850 Words  | 2 Pages

    Median Voter Theorem On the spectrum of politics (or any other ideologically-based matter), personal opinions will inevitably vary from one extreme on the left to the opposite on the right. In a governing system such as that of the United States, where the population directly elects representatives to govern, the position a candidate holds on the spectrum pertaining to certain issues in relation to other candidates becomes increasingly important. Theoretically, two people coming from different

  • Ancient Greek Contributions To Western Civilization

    923 Words  | 2 Pages

    What does it mean to contribute? By dictionary definition contribute means give in order to help achieve or provide something. Contribute is exactly what the Ancient Greeks did. The Ancient Greeks works have greatly contributed to the development of the Western Civilization. The Ancient Greeks works in mathematics contributed to the development of Western civilizations developments in mathematics. The Ancient Greeks development in the government system democracy is a very important contribution to

  • Mathematics And Mathematics: Fermat's Contribution To Mathematics

    1742 Words  | 4 Pages

    Fermat’s Last Theorem--which states that an + bn = cn is untrue for any circumstance in which a, b, c are not three positive integers and n is an integer greater than two—has long resided with the collection of other seemingly impossible proofs. Such a characterization seems distant and ill-informed, seeing as today’s smartphones and gadgets have far surpassed the computing capabilities of even the most powerful computers some decades ago. This renaissance of technology has not, however, eased this

  • Computational Complexity and Philosophical Dualism

    3243 Words  | 7 Pages

    a new revised version of the Lucas-Penrose position in light of physical a priori limitations of computing machines. Finally, the last part derives some epistemological/philosophical implications of the relationship between Gödel's incompleteness theorem and Complexity Theory for the mind/brain problem in Artificial Intelligence and discusses the compatibility of functionalism with a materialist theory of the mind. This paper purports to re-examine the Lucas-Penrose argument against Artificial

  • Pythagora's Contributions to Math

    1075 Words  | 3 Pages

    on other historical events. Whatever we know about him is information learned after his death. Most of his writings were not published so we do not have many of his personal notes. Pythagoras is popularly known for his ligating the Pythagorean theorem used in geometry. It is reported that Pythagoras was born anywhere between 520 to 570 on the Samos island, which was part of Greece . His father's name was Mnesarchus, and he was a merchant while his mother's name was Pythias(School of Mathematics

  • Gauss Essay

    1168 Words  | 3 Pages

    world-renowned mathematician. He has contributed to some of the most influential and fundamental theories and concepts in mathematics including geometry, probability theory, number theory, the theory of functions, planetary astronomy and most importantly the theorem of algebra. Being born into a underprivileged family, Gauss was fortunate enough to have his mother and uncle recognise his genius abilities for mathematics and thus, provided him with education to further his gift. Gauss attended college, devoting

  • The Importance Of Morse Theory

    967 Words  | 2 Pages

    middle of paper ... ...such abrupt changes in a system’s behavior is that we usually observe a dynamical system when it’s at or near its steady-state, or equilibrium, position (Casti, 1996, p. 116). When critical points are non-degenerate, Morse’s Theorem applies (Casti, 1996, p. 108). There are a number of classical applications of Morse theory, including counting geodesics on a Riemann surface and determination of the topology of a Lie group (Bott 1960, Milnor 1963) (Eric W). Morse theory has received