Elements of Mathematics for Economists Bernard Cornet January 18‚ 2011 Contents Notation 1 Euclidean Spaces 1.1 Scalar Product and Associated Norm . . . . . . . . . . . . 1.1.1 Scalar Product . . . . . . . . . . . . . . . . . . . . 1.1.2 Norm Associated to a Scalar Product . . . . . . . . 1.1.3 Convergence in a Normed Space . . . . . . . . . . . 1.1.4 Euclidean Spaces and Hilbert Spaces . . . . . . . . 1.2 Matrices and Scalar Product . . . . . . . . . . . . . . . . . 1.2.1 Generalities on Matrices
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13 March 2014 Early Philosophers “Pre-Socratic” or “Mythopoeic” thinkers? The Ancient Greek philosophers played a pivotal role in the shaping of the western philosophical tradition. The Ancient Greek philosophical tradition broke away from a mythological approach to explaining the world‚ and it initiated an approach based on reason and evidence. Initially concerned with explaining the entire cosmos (the universe seen as a well-ordered whole)‚ the Pre-Socratic philosophers strived to identify its
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Jonald Atienza February 3‚ 2015 MT32-C11 C/M Ronel Almacen Finals Activity 2: Channeling Introduction On February 2‚ 2015‚ C/M Almacen discussed about channeling. He showed us the famous channel in the world the Istanbul‚ Turkey. He shared his experiences in navigating in this channel. He taught us the Traffic Separation Scheme (TSS). It has the north bound and south bound just like the road in land. Counter flowing is not allowed also in narrow channeling. When joining the Traffic
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2000-1800 BC) and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem‚ which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans‚ who coined the term "mathematics" from the ancient Greek μάθημα (mathema)‚ meaning "subject of instruction". Greek mathematics
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math teacher shows their students how to do math‚ you were the first teacher who taught us what the math meant‚ what people actually used it for. I came out of algebra‚ geometry‚ and pre-calculus with knowledge of how to factor‚ how to use the Pythagorean Theorem‚ and how to find a function’s horizontal asymptotes‚ but after your calculus class I had a deeper understanding of the topics you taught us. And‚ since in your class I began to understand the usefulness of things like related rates or integration
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In ancient Mesopotamia‚ we introduce the concept of reciprocal‚ plus solutions to different logarithmic problems‚ progress was such that it created algorithms for calculating sums of progressions. In geometry‚ it is believed that they knew the Pythagorean Theorem‚ though not as a general theorem. With no doubt‚ China played a big role in mathematical progress. However‚ it was in Greece‚
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The Stoics and Socrates The question of the reality of the soul and its distinction from the body is among the most important problems of philosophy‚ for with it is bound up the doctrine of a future life. The soul may be defined as the ultimate internal principle by which we think‚ feel‚ and will‚ and by which our bodies are animated. The term "mind" usually denotes this principle as the subject of our conscious states‚ while "soul" denotes the source of our vegetative activities as well. If
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equal to numbers (square root of x = 2)‚ squares and roots equal to number (x2+3x = 25)‚ squares and numbers equal to roots (x2+1 = 9)‚ and roots and numbers equal to squares (3x+4 = x2). One of the more complex equations Al-Khwarizmi used was the quadratic equation. This equation is used to solve for the unknown which in this equation would be x (ax2+bx+c=0). When in that specific form‚ Al-Khwarizmi is asking‚ what is x when the function is equal to zero? Al-Khwarizmi’s theory was that when you take
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east to acquire knowledge. Little is known about his life because records were not kept. all we know are some major discoveries that were recovered. Demoritus was born in Abdera‚ Thrace about 460B.C. and died about 370 B.C. He was schooled at Pythagorean but traveled to Athens to visit Anaxagoras‚ a great mathematician that wanted nothing with Democritus. His father was from a noble family and of great wealth‚ which Democritus inherited and decided to travel to but not limited to Egypt‚ India‚ Etheopia
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www.jntuworld.com www.jwjobs.net 1 Code: 9A05603 III B. Tech II Semester (R09) Regular Examinations‚ April/May 2012 OPTIMIZING TECHNIQUES (Common to Computer Science & Engineering & Computer Science & Systems Engineering) Time: 3 hours Max Marks: 70 1 (a) (b) 2 Answer any FIVE questions All questions carry equal marks ***** State the necessary and sufficiency conditions for the minimum of the single variable function f ( x ) . Find the minimum of the function: f
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