Assignment 12 Name: Wendy Number: 100501042 Real Life vs Virtual Life For many‚ the first thing they do to start a day is logging into their Facebook account to check out news feeds. After catching up with all their friends’ updates‚ they go to the virtual farm or restaurant that they are running and begin the works. Meanwhile‚ they are preparing for their real-life exam or meeting. But things used to be a lot easier when there were no Facebook and Farm Ville. With the popularity of social
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“The Arrow impossibility theorem and its implications for voting and elections” Arrow’s impossibility theorem represents a fascinating problem in the philosophy of economics‚ widely discussed for insinuating doubt on commonly accepted beliefs towards collective decision making procedures. This essay will introduce its fundamental assumptions‚ explain its meaning‚ explore some of the solutions available to escape its predictions and finally discuss its implications for political
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Chinese remainder theorem The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by Chinese mathematician Sun Tzu. In its basic form‚ the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders. For example‚ what is the lowest number n that when divided by 3 leaves a remainder of 2‚ when divided by 5 leaves a remainder
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Real Life versus Perfect Life Have you ever thought about how your real life would compare to your perfect life? Seven years ago I actually thought about this. When I was 21 years old I had my first child‚ a son Jayson Alexander Raney. I was working as a cashier at Food Lion‚ and my boyfriend was working at Advance Auto Parts. Our home was a two bedroom apartment that we shared with his mother. I knew that we weren’t financially prepared to provide for our son. I enrolled at Robeson Community College
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LIMITS AND CONTINUITY 1. The concept of limit x2 − 4 . Examine the behavior of f (x) as x approaches 2. Example 1.1. Let f (x) = x−2 Solution. Let us compute some values of f (x) for x close to 2‚ as in the tables below. We see from the first table that f (x) is getting closer and closer to 4 as x approaches 2 from the left side. We express this by saying that “the limit of f (x) as x approaches 2 from left is 4”‚ and write x→2− lim f (x) = 4. Similarly‚ by looking at the second table
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The Pythagorean theorem (A^2 + B^2 = C^2) has been impacting all types of people and careers since it was first realized during Ancient Greece times. It is one of the most widely recognized theorems in the mathematics community‚ and used much more than the average person knows: whether you need need to know the dimensions of a bag or you need find the distance from location to another‚ the Pythagorean theorem can be used. Everyone who was taught this theorem in their first year of algebra continues
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1 10/10/01 Fermat’s Little Theorem From the Multinomial Theorem Thomas J. Osler (osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2
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Kirchhoff’s Law Kirchhoff’s current law (KCL) imposes constraints on the currents in the branches that are attached to each node of a circuit. In simplest terms‚ KCL states that the sum of the currents that are entering a given node must equal the sum of the currents that are leaving the node. Thus‚ the set of currents in branches attached to a given node can be partitioned into two groups whose orientation is away from (into) the node. The two groups must contain the same net current. In general
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A Brief History of the Pythagorean Theorem Just Who Was This Pythagoras‚ Anyway? Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece‚ and did much traveling through Egypt‚ learning‚ among other things‚ mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group‚ the Brotherhood of Pythagoreans‚ which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols‚ rituals and prayers. In addition
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a NOR gate. DeMorgan’s theorems state the same equivalence in "backward" form: that inverting the output of any gate results in the same function as the opposite type of gate (AND vs. OR) with inverted inputs De Morgan’s theorem is used to simplify a lot expression of complicated logic gates. For example‚ (A + (BC)’)’. The parentheses symbol is used in the example. _ The answer is A BC. Let’s apply the principles of DeMorgan’s theorems to the simplification of
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