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### P1_224

Course: MATH 331, Fall 2008
School: CSU Channel Islands
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Word Count: 747

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1 224 224 Professor Roybal History of Mathematics 10/21/08 History of Mathematics Project 1 This is an example of corresponding angles. In the diagram, the two horizontal lines are parallel to each other, and are crossed by a sloping straight line, causing angles to be formed. (Everett) A proof is how to do a problem a proof will walk you through each step and elaborates on how to do the step or how to solve the...

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1 224 224 Professor Roybal History of Mathematics 10/21/08 History of Mathematics Project 1 This is an example of corresponding angles. In the diagram, the two horizontal lines are parallel to each other, and are crossed by a sloping straight line, causing angles to be formed. (Everett) A proof is how to do a problem a proof will walk you through each step and elaborates on how to do the step or how to solve the problem. A proof is made so that everyone can read it and understand how to do the problem. It makes it so that someone can pick up the proof and know how to go through the steps to solve it. This makes it so that through the years everyone can learn the way the problem was meant to be solved. Proof based mathematics compared to non-proof based mathematics allows the student to get a step-by-step learning if the problem. This also gives a student another 224 2 way of learning the math if they are not a certain type of a learner. With non-proof mathematics you just have one way of learning how to do the problem. However, some student cant understand a non-proof way a little more. An example of the difference between proof and non-proof mathematics is how Greek mathematics was helped by proofs because it allowed the mathematician to get their work out of their mind and on to something to help teach it to others. Once the work was out in writing and explanations, others could go over the work and revise it or add to it. Because of the proofs being recorded on how they did it and how they understood the problems it allowed the world across all centuries to observe the work and learn from it and develop our understandings of the problems as well as adding a new since of how to solve the problem or make it easer to understand. The Greek mathematicians were also hindered by the proofs because it caused for questioning of their beliefs on how to do the problem. For example, some of the proofs were written for the problem long after the original thinker had passed on. For a typical text, the earliest copy was probably written one thousand years or so after the text. (Emerson handout) This creates a major because problem we dont know how the original mathematician really solved the problem. Some of the proofs like Euclids could be questioned. Some of the proofs could be discredited for example Proposition I 47 is the Pythagorean theorem, with a proof universally credited to Euclid himself, and the final proposition, I 48, is the converse of the Pythagorean theorem. The material of this book was developed by the early Pythagoreans. (Eves) If these proofs went unpublished then the wrong person was given credit for achievement that had already been done. The problem that I did was 5.8 the proof is as followed: 224 3 224 4 224 5 The advantage of doing this problem with a proof is that it will help get real detail into the problem and understand it a little better. If you do this proof by intuition you might miss certain aspect of the problem causing you to do it all wrong. For example, you might get that the line would not be all three angles adding up to the line to equal the triangle. For a typical student there it would probably be better to solve the problem by the proof. The proof would make it easier to understand and would confuse the student less and help them really understand and take the concept in and learn how to solve the problem. However, there are o...

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CSU Channel Islands - MATH - 331
History of Math Number: 369Math 331Project 1- Proofs GaloreA proof is a combination of statements and ideas that can be put together to prove a mathematical idea. Proofs can be long and complicated, but sometimes they are not nearly so long or c
CSU Channel Islands - MATH - 331
Math 331 ID# 268 Project 1 A proof is an ingenious way of solving difficult problems with simple algebra and geometry. You take a hard problem for example: 13 + 23 + . + n3 = (1 + 2 + . + n)2, and solve it using basic algebraic functions such as mult
CSU Channel Islands - MATH - 331
Math # 303 Proof: Proofs are used to help solve problems by taking step-by-step procedures. Each step is taken to show the reason why the answer for the problem is what it is. A proof illustrates why a problem would come to the conclusion that it doe
CSU Channel Islands - MATH - 331
Sam Levison 000296128 October 19, 2008 Math 331 Project #1Since humans in the 21st century where born they have always been taught the fundamentals of mathematics. As young children before any organized education we have been able to tell who has m
CSU Channel Islands - MATH - 331
314 Project1 Theconceptbehindaproofisthatwearetryingtoshowandvalidatea statementusingthecharacteristicsanddefinitionsofelementsrelatedtothe conceptwewanttoconfirm.Wethenmanipulatethosedefinitionsand characteristicsusingdeductivereasoning,untilweare
CSU Channel Islands - MATH - 331
Katie Gills Automathography!Hi Math 331 Classmates! So I have to admit, Math is not really my strong suit. I struggled with Math all through High School. Although back in Elementary school I liked it. Anyway, I always seemed to have really awesome
CSU Channel Islands - MATH - 331
CSU Channel Islands - MATH - 140
Math 140 Final Review Solutions Tuesday Dec. 9 4:00-6:00 for 4:30 class Thursday 7:00-9:00 for 6:00 class 1. Find all local and absolute minima/maxima for the function f (x) = x2 x . +9This function is dierentiable everywhere and has domain all of
CSU Channel Islands - MATH - 331
Project 1, History of math History of math number 167 A proof, is a demonstration that some statement logically follows from the definitions and axioms (&quot;givens&quot;) of the world in question. For example, to prove that 1+1 &lt;&gt; 1 [1+1 is not equal 1] one
CSU Channel Islands - MATH - 331
Hello fellow Math 331 classmates. My name is Laura Cordero and I am currently taking my last two classes in order to graduate with my business degree. The only other math class I have taken here at CSU Channel Islands was Statistics. I have alwa
CSU Channel Islands - MATH - 331
Shahab Lashkari's AutomathographyGrowing up, I have always liked Math. Having been into computer programming since elementary school, I used Math and Logic quite often. I liked being able to describe things mathematically, and grew up experimenting
CSU Channel Islands - MATH - 331
(On vacation in Sonoma Jack London State Historical Park)Kims Authomathography Well, back in the covered wagon days when I went to high school, Algebra was not a requirement for graduation, and as a habitual D student in math, in my infinite wisdo
CSU Channel Islands - MATH - 331
Bryan Podgorny Project #1 Math 331 Due: 3/26/08Proof Explain in clear, ordinary language the concept of proof. A proof is a detailed and organized way to show that something is true or a fact. The way to show that something is true is to compare i
CSU Channel Islands - MATH - 331
Project 1: Proof and Greek Mathematics A proof is merely a justification for a conclusion, showing how the conclusion was obtained using logically true statements as steps. A proof can use deductive reasoning or inductive reasoning to obtain the conc
CSU Channel Islands - MATH - 331
#406 Math 331 Roybal 3/26/08Project 1What is the purpose of a proof? In mathematics a proof is used to prove a problems solution to be true; its made up of steps that are specifically used to come to a conclusion. But to a non-mathematician, a pro
CSU Channel Islands - MATH - 331
History of Math # 415 03/24/2008 Math 331 History of MathematicsA proof is a use of known theorems and basic algebra to show through a logical succession of steps that a mathematical problem is either true or false. Basically you start with a math
CSU Channel Islands - MATH - 331
280 Dr. Richard Roybal Math 331 24 March 2008 The Mathematical Proof Math is unique in many ways but one thing that makes it extremely unique is that it can also be categorized as a language. A language is usually defined as a tool that it is used to
CSU Channel Islands - MATH - 331
Project 1 #971 Q.E.D. Does not Stand for Quite Easily DemonstratedIn order to completely understand mathematics, you must understand the method of using proofs. Proof-based mathematics is paramount in providing evidence for a certain theorem or rul
CSU Channel Islands - MATH - 331
Project1-370 March 26, 2008 Proofs Why? As children, it was the one question we were really good at asking. Whysomething was the way it was. Children want to know the essence of an object and understand its existence. Conceptually, proofs work in
CSU Channel Islands - MATH - 140
Math 140 Final Review Monday May 12 1:00-3:00 for 12:00 class Friday May 16 4:00-6:00 for 3:00 class The final will be comprehensive over the material in class. This review is designed to be an aid in study for the final. It is not designed to mimic
CSU Channel Islands - MATH - 331
Stacys automathographyI love numbers. Math is my favorite subject; it always has been and always will be. When I was in elementary school I always did well in Math. In the second grade my entire class made number scrolls. We were each given paper of
CSU Channel Islands - MATH - 140
Math 140 Midterm 2 Review Midterm 2 - Wednesday April 9 The midterm will cover the sections 3.1-3.6. This review is designed to be an aid in study for the midterm. It is not designed to mimic exactly what will be on the exam. The problems on the exam
CSU Channel Islands - MATH - 208
Math 208: Reective Writing Assignment 1 Mathematizing is solving problems, posing problems, playing with patterns and relationships, and proving their thinking to fellow mathematicians. We constantly mathematize physical and social phenomena and use
CSU Channel Islands - MATH - 208
Math 208: Reflective Writing Assignment 2 From Alternate Algorithms by Michael Naylor: Learning a variety of algorithms that focus on number sense will help kids develop a better understanding of number operations. An algorithm is a step-by-step &quot;rec
CSU Channel Islands - MATH - 140
CSU Channel Islands - MATH - 208
Math 208 Review 21. Dene the following terms: prime number, composite number. Which positive integer is neither prime nor composite? 2. Use the Sieve of Erastothenes to nd all the primes up to 200. (You may start sieving at 101, if you desire so.) 3
CSU Channel Islands - MATH - 208
Math 208, First Exam Review 1. What are the four steps to Polyas problem solving process? 2. What are some problem solving strategies? 3. Show why 3 always divides evenly into the sum of any three consecutive whole numbers. (Hint: What are the possib
CSU Channel Islands - MATH - 140
CSU Channel Islands - MATH - 331
The concept of &quot;proof&quot; is taking an abstract problem and explaining step by step why it is true. Proof based mathematics differs from non-proof based mathematics in many ways. Proof based math deals with using logic while non-proof based math is stra
CSU Channel Islands - MATH - 331
Pythagorean theoremThe concept of proof is an argument that is used to show the truth of a mathematical assertion. In modern mathematics, a proof begins with one or more statements called premises and demonstrates, using the rules of logic, that if
CSU Channel Islands - MATH - 95
Math Lab Syllabus Math 94 and Math 95 Lab assistant: Jaimee Morrison Email: jaimee.morrison191@dolphin.csuci.edu Lab assistant: Melinda Sherman Email: melinda.sherman049@dolphin.csuci.edu Lab hours: Monday OH 1964 1:30-3pm OH 1964 6-8pm Tuesday Wedne
CSU Channel Islands - MATH - 331
Project 1 What exactly is a mathematical proof? The concept of a proof is a way to communicate the steps you have taken to justify why your answer is right or to prove that it is right. I took a Logic class last semester and all we did were proofs. W
CSU Channel Islands - MATH - 331
Project 2 Unquestionably, calculus was the most remarkable mathematical achievement of the seventeenth century because creative mathematics passed to an advanced level. Calculus also led to, essentially, the termination of the history of elementary m
CSU Channel Islands - MATH - 331
Project OneA proof is a way of showing why an equation or a set of steps works and will give the correct answer. It follows through every step showing why each jump of logic is true and valid. Proof based mathematics differ from non-proofed mathema
CSU Channel Islands - MATH - 331
Project 1 History of Math Number: 772 In mathematics, a proof is a formalized, expository technique for demonstrating the validityor invalidityof a proposition. As such, proofs rely upon detailed, logical steps that can not only be followed by the re
CSU Channel Islands - MATH - 331
#380 Math 331 Project 2 European Mathematics began to develop after the fall of the Roman Empire. Three main mathematicians during the Dark Ages were: Boethius of Rome, Bede and Alcuin of Britain, and Gerbert of France. Boethius incorporated statemen
CSU Channel Islands - MATH - 331
545 Math 331 Project 2 Astronomy European mathematics in the seventeenth century made quite a lot of advances. Astronomy was certainly a field of study that progressed greatly during this time. Astronomy relies heavily on mathematics. Because of this
CSU Channel Islands - MATH - 331
#160 Project 1 A proof is the mathematical version of a literal map of how you got to a conclusion. Basically you start with a bunch of things that are given to you in math, and you know them to be true. These are called postulates or you could use p
CSU Channel Islands - MATH - 331
Once Upon A Greek Proof Open a High School Mathematics textbook and look to the beginning of each chapter. One will find that the book explains the methods and theories that it wishes to teach in what we can understand to be todays modern proof. Proo
CSU Channel Islands - MATH - 331
Roybal Math 331 11/23/2007 Development of Algebra A true knowledge of algebra is an invaluable attribute in the world of mathematics. Algebra has been defined as the branch of mathematics in which letters are used to represent basic arithmetic relati
CSU Channel Islands - MATH - 331
677 History of MathThe Development of ZeroThe development of zero was one of the most important mathematical developments in all of human history. It signified a change in the ways in which we think mathematically, and it opened new doors for us t
CSU Channel Islands - MATH - 95
Math 95 Week 8 1. a. b. c. d. e. 2. a. The _ is the part of the quadratic formula that is under the square root. b. If the discriminant is equal to 0, then there is a _ solution. c. Solve by using the quadratic formula: 2x2 + 4x 3 d. Solve by using
CSU Channel Islands - MATH - 331
History of Math number # 560Project 1Prove it! How do we know that these mathematical statements are correct that we find in are textbooks? They are proven facts. As the name implies, a proof is proving some statement is true. This is formed by co
CSU Channel Islands - MATH - 331
In the following pages I will be discussing the rise of algebra in Europe spanning from the thirteenth through the sixteenth century. I will be discussing the beginning of Europeans using Hindu-Arabic numeral systems to the eventual solving of the ge
CSU Channel Islands - MATH - 331
P2-470 Astronomy in Mathematics The study of mathematics has proven to be imperative throughout history. It is a broad, interdisciplinary subject that has ties to many other fields of study, especially astronomy. Many mathematicians, however, could n
CSU Channel Islands - MATH - 331
Roybal Math 331 10/26/2007 Proofs and Mathematics Proofs are integral to the history and development of mathematics. They help to form a firm foundation upon which mathematical advancements can develop. In general terms, the proof of a concept is the
CSU Channel Islands - MATH - 331
Math #761 Math331 Essay3The first evidence of a zero in mathematics was found 5000 years ago in Mesopotamia. It was represented in cuneiform symbols and displayed as two small triangle wedges in between other cuneiform symbols. This representation
CSU Channel Islands - MATH - 331
History of Math number: 545 Math 331 A mathematical proof is a way to show that some mathematical thing is true by using other things that are understood to be true. A proof relies only on things that have already been proven. This is what makes them
CSU Channel Islands - MATH - 331
Proofs and Mathematical Understanding A proof is a formal method of showing that a statement is either true or false, using logical reasoning to follow through a sequence of statements that can be derived from the previous ones. There are many differ
CSU Channel Islands - MATH - 331
Astronomy in MathematicsGalileo had a big impact on astronomy; in the early 1600s he discovered a lens that magnified things used in childrens toys and converted it into a superior lens. He then went on to use his creations as telescopes, gazing ou
CSU Channel Islands - MATH - 331
Math 331 Project 2 November 20, 2007 Development of Algebra Algebra is one of the most common practiced forms of mathematics. Algebra is used to study structure, and relation; three areas of study that we find very valuable in every day mathematics.
CSU Channel Islands - MATH - 331
MATH331 In modern mathematics, as in the time of the ancient Greeks, mathematical proofs provide a means to determine the truth of generalized mathematical principles. But what is a proof? Simply put, a proof is a series of logically valid steps that
CSU Channel Islands - MATH - 331
Project 2 131 The Development of Calculus Calculus is a type of mathematics that some high school and many college students learn every year. It, most importantly, involves the ideas of differentiation and integration. Integration was discovered firs
CSU Channel Islands - MATH - 95
Math 94 Week 8 1. a. When multiplying polynomials, you should multiply each term of the first polynomial to each term of the second polynomial and then _. b. If P is equal to a second degree polynomial and Q is equal to a third degree polynomial, wha
CSU Channel Islands - MATH - 331
Project 2: The Rise of Hindu-Arabic Numerals History of Math Number 772 November 21, 2007It was, according to Eves [1], circa 766 that Indian texts by Brahmagupta were brought to Baghdad and translated into Arabic. In this way, Hindu numerals were
CSU Channel Islands - MATH - 331
MATH331 Today, the language of mathematics is well established. The symbols used to denote a particular operation are standardized such that any mathematician can read an equation and understand what is supposed to be done. Modern mathematics relies
CSU Channel Islands - MATH - 331
Project1 HistoryofMathNumber579 Inmathematics,itisusefultohaveaformulaoraproperty,orarulethatwecanuseforgeneralcases, notonlyforspecificones.Evenifeveryexamplethatwetrytheformulaongivestherightresult,we stillwanttobesurethatitwillworkforallthevalues.
CSU Channel Islands - MATH - 331
P1-277.pdfpage 1Mathematics today is a logical science based on a foundation of proof. A mathematical proof is a logical argument designed to persuade another mathematician of the veracity of a statement. Proofs are expositions that demonstrate a
CSU Channel Islands - MATH - 331
Student #663 The concept of proof is a simple and complex explanation. It validates a theory, experiment, formula, etc. It gives a reason to justify why things have happened, will happen, why things work or dont work. Without proof we would not know
CSU Channel Islands - MATH - 331
379 Chinese Mathematics Early Chinese mathematics can be similar to how we teach math in modern times from time to time. They memorized multiplication tables up to nine times nine, and had a system of physical rods to solve longer multiplication very
CSU Channel Islands - MIS - 310
Operations Research Management Science - Software ReviewPage 1 of 17OR/MS Today - June 2008 Software ReviewAnalytica 4.1User examines modeling environment and takes a few irreverent pokes at spreadsheets.By Robert D. Brown III&quot;The purpose o