Ramanujan’s mathematical ideas‚ I will not go very deep into them. This I will do in the second section in which I will focus on a few of Ramanujan’s mathematical ideas. In the last section‚ I will use Mathematica to compute and verify some of Ramanujan’s theorems from the second section. Ramanujan’s Life Ramanujan was born on the 22nd of December‚ 1887 in his Maternal grandmother’s house in Erode. Erode is a small town approximately 250 miles south west of Madras (see map). At the age of 1‚ Ramanujan’s
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to Algebra Instructor Yvette Gonzalez-Smith August 04‚ 2013 Pythagorean Quadratic The Pythagorean Theorem is an equation that allows a person to find the length of a side of a right triangle‚ as long as the length of the other two sides is known. The theorem basically relates the lengths of three sides of any right triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs. It also can help a person to figure out whether or
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of statistics. The Central Critical Theorem is able to draw somewhat precise conclusions from small amounts of data. The Central Critical Theorem is the power source for many of the statistical activities that involve using a sample to make inferences about a large population. Wheelan dissects the theorem by using multiple examples to support the claim that the theorem only works if large samples of data are collected. Wheelan starts off breaking down the theorem with a city hosting a marathon for
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CHAPTER 1 INTRODUCTION 1.1 Introduction Geometry is one of the most interesting fields of mathematics. From the ancient times of the Greeks up to now‚ it has held captive the imagination of many mathematicians‚ artists‚ scientists‚ engineers and architects. Its application to modernization and technological advancement cannot be denied. Thus‚ it must be given emphasis in educational institutions particularly in secondary schools. The low achievement test results in mathematics of high
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1 Gauss’ theorem Chapter 14 Gauss’ theorem We now present the third great theorem of integral vector calculus. It is interesting that Green’s theorem is again the basic starting point. In Chapter 13 we saw how Green’s theorem directly translates to the case of surfaces in R3 and produces Stokes’ theorem. Now we are going to see how a reinterpretation of Green’s theorem leads to Gauss’ theorem for R2 ‚ and then we shall learn from that how to use the proof of Green’s theorem to extend it
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1. Gradient of a scalar field function Scalar Function: Generally‚ What Is Scalar Function? The Answer Is that a scalar function may be defined as A function of one or more variables whose range is one-dimensional‚ as compared to a vector function‚ whose range is three-dimensional (or‚ in general‚ -dimensional). Scalar Field When We Talk about Scalar Field‚ We Are Talking about the Scalar Function Being Applied to a Space (More like Euclenoid Space etc) or‚ a scalar field associates
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Gauss-Markov Theorem The Gauss-Markov Theorem is given in the following regression model and assumptions: The regression model (1) Assumptions (A) or Assumptions (B): Assumptions (A) Assumptions (B) E( If we use Assumptions (B)‚ we need to use the law of iterated expectations in proving the BLUE. With Assumptions (B)‚ the BLUE is given conditionally on Let us use Assumptions (A). The Gauss-Markov Theorem is stated below
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Pierre de Fermat was born August 17‚ 1601 in Beaumont- Lomagne‚ France. Pierre was born into a Catholic family and was baptized August 20‚ 1601. He was one of four children‚ three boys and one girl. Pierre’s father was a leather merchant and the second consul of his hometown. His mother was a parliamentary noblesse de la robe. He began his secondary schooling at Cordeliers. Then it was said he went to the University of Toulouse. He acquired his degree of Bachelor of Civil Laws from the University
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Analytic Functions Edwin G. Schasteen⇤ June 9‚ 2008 Abstract We prove a theorem that relates non-zero simple zeros z1 and z2 of two arbitrary analytic functions f and g‚ respectively. 1 Preliminaries Let C denote the set of Complex numbers‚ and let R denote the set of real numbers. We will be begin by describing some fundamental results from complex analysis that will be used in proving our main lemmas and theorems. For a description of the basics of complex analysis‚ we refer the reader
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Summary of the Article‚ ”Why do firms exist”……….. Ronald Coase may not be as famous as other economists due to his non-recognisable status but at the turn of the century ‚ he was able to achieve a recognisable status by applying practical theories on pre- existing economic theories. Highlights Deregulation revolution of 1980s Re-surfacing the pin factory which was the foundation of division of labour criticism of earlier economics theories of Adam Smith and others. Bureacracy in modern
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