also introduced characters used to describe the numbers 10 and 100‚ making it easier to describe larger numbers. Geometry started to receive great attention and served in surveying land‚ cities and streets. The Babylonians discovered the Pythagorean theorem. They understood it before Pythagoras was even born. The Babylonians also found out the approximate value of r^2. In India‚ Aryabhata calculated the number p to its fourth decimal point‚ managed to correctly forecast eclipses and‚ when solving astronomical
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Licensed to: iChapters User PRINCIPLES OF MICROECONOMICS: A G U I D E D T O U R PART ONE: INTRODUCTION Chapter 1 Chapter 2 Chapter 3 Ten Principles of Economics Thinking Like an Economist Interdependence and the Gains from Trade The study of economics is guided by a few big ideas. Economists view the world as both scientists and policymakers. The theory of comparative advantage explains how people benefit from economic interdependence. PART TWO: SUPPLY AND DEMAND I: HOW MARKETS
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References: Internet Encyclopedia of Philosophy‚ Last updated: April 21‚ 2001 | Originally published: April/21/2001. Retrieved from http://www.iep.utm.edu/pythagor/ Fey‚ James. Looking for Pythagoras: The Pythagorean Theorem. (1997). White Plains‚ NY: Dale Seymour Publications‚. O ’Connor‚ J. J.‚ Robertson‚ E. F. January (1999). Pythagoras‚ Phoenician/Greek Mathematician. Retrieved from: http://phoenicia.org/pythagoras.html Pythagoras of Samos. Retrieved from http://www-groups
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David Hilbert was born around 1682 in Konigsberg in East Prussia‚ which comprised a section of Germany and modern day Kaliningrad Russia. His father was a judge and his mother an amateur mathematician. He became known because of the contribution he made in mathematics and physics in the twentieth century. Hilbert is well remembered for landmark researches he conducted in algebra. He also left an indelible mark in axiomatic geometry and mathematics. Hilbert also profoundly contributed in other areas
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they also learned how to determine they lengths of objects from the Babylonians by using Pythagorean theorem. Building upon what they learned from the Egyptians and Babylonians they found fundamental truths in geometry‚ and from these truths they mad propositions called axioms‚ through deductive reasoning the Greeks would use these axioms to find new theorems that could be proven. These theorems would be used to find solutions of both practical and abstract nature. 2. Thales: Thales of Miletus
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Ancient Greece influenced Western Civilization in many ways. Many ideas of the Ancient Greeks came from the city-state of Athens. The Greek culture has had a very large impact on the way people have lived. The Ancient Greek civilization made significant contributions to western civilization in the areas of government‚ philosophy‚ and math. The Ancient Greeks made many contributions to Western Civilization in the area of Government. Government is a system of control citizens‚ societies
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this work‚ he described the known results in probability theory and in enumeration‚ often providing alternative proofs of known results. This work also includes the application of probability theory to games of chance and his introduction of the theorem known as the law of large numbers. The terms Bernoulli trial and Bernoulli numbers result from this work. The lunar crater Bernoulli is also named after him jointly with his brother Johann. John Craig (1663 – October 11‚ 1731) was a Scottish mathematician theologist
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sum of the area of squares of its adjacent and opposite sides.) Then let’s look at the famous Pythagoras theorem: “The square on the hypotenuse of a right angled triangle is equal to the sum of squares of its sides” The Sulba sutra was written on 12th century B.C. but the Pythagoras theorem was introduced on 6th century B.C‚ 600 years after Sulba sutra. That is‚ most of the works‚ theorems and concepts of mathematics existed in India on its own form even before in other countries. Let’s look at
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detectors‚ including the direct-matrix-inversion (DMI) blind linear minimum mean square error (MMSE) detector‚ the subspace blind linear MMSE detector‚ and the form-I and form-II group-blind linear hybrid detectors‚ are analyzed. Asymptotic limit theorems for each of the estimates of these detectors (when the signal sample size is large) are established‚ based on which approximate expressions for the average output signal-to-interderence-plus-noise ratios (SINRs) and bit-error rates (BERs) are given
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Central Limit Theorem The key to the behavior of x-bar is the central limit theorem. It says: Suppose the population has mean‚ m‚ and standard deviation s. Then‚ if the sample size‚ n‚ is large enough‚ the distribution of the sample mean‚ x-bar will have a normal shape‚ the center will be the mean of the original population‚ m‚ and the standard deviation of the x-bars will be s divided by the square root of n. Probability and statistics - Karol Flisikowski Central Limit Theorem If the
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