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Words 908

Pages 4

MTH/110

March 14, 2011

The Concept of Prime Numbers and Zero Have you ever wondered about the origins of prime numbers or the numeral zero? The ancient philosophers and mathematicians from such early civilizations in Egypt, Greece, Babylon, and India did. Their efforts have provided the basic fundamentals for mathematics that are used today.

Prime Numbers A prime number is “any integer other than a 0 or + 1 that is not divisible without a remainder by any other integers except + 1 and + the integer itself (Merriam-Webster, 1996). These numbers were first studied in-depth by ancient Greek mathematicians who looked to numbers for their mystical and numerological properties, seeking perfect and amicable numbers. (O’Connor & Robertson, 2009) In 300 BC, Greek mathematician, Euclid of Alexandria proved and documented in his Book IX of the Elements that prime numbers were infinite. He started with what he believed to be a comprehensive list of prime numbers, created a new number, N, by multiplying all of the prime numbers together and adding 1. This resulted in a number not on his list and not divisible by any of his prime numbers. N therefore had to be either prime itself or be a composite number that was a product of at least two other prime numbers not on his list. In 1747, a mathematician named of Euler demonstrated that all even numbers were perfect numbers. However, one hundred years later in 200 BC, Eratosthenes of Cyrene, a famous Greek mathematician known for his studies regarding prime numbers as well as for measuring the diameter of the earth, devised a procedure or algorithm for calculating prime numbers called the Sieve of Eratosthenes (O’Connor & Robertson, 2009). The study of prime numbers seemingly ceased to exist during the period of time known as the Dark Ages. Studies on the subject…...

...say whether I was able to learn how to be a better teacher and what the teacher did that I could possibly use in the future. While analyzing and going through the process of this assignment it is helping realize how to become a better teacher as well. I would also like to get more comfortable and experience on using this template of the paper. Memories Of A Teacher My teacher, Mr. G, used many different instructional techniques and approaches to his lessons. Mr. G had taught me math for three years in a row, so I think that I have a good grasp on his approaches to the lessons that he would teach. He would assign many homework assignments, as well as in-class assignments, which helped me and other students understand and get practice with the lesson that we were learning. I think that with math having a lot of homework is a good thing. In my mind, the only way to learn how to do math is plenty of practice. The more you practice, the easier it will be. Mr. G would also have the students do some math problems on the chalk board or smart board to show the class and go over the corrections with the whole class so that everyone would understand the problem. Playing “racing” games also helped and added fun to the class. With the “racing” games, the students would get into groups and have to take turns doing problems on the chalk board and see who could get the correct answer first. It added fun and a little friendly competition to the class. It also helped the students want to......

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...Diana Garza 1-16-12 Reflection The ideas Stein presents on problem saving and just math in general are that everyone has a different way of saving their own math problems. For explains when you’re doing a math problem you submit all kinds of different numbers into a data or formula till something works or maybe it’s impossible to come up with a solution. For math in general he talks about how math is so big and its due in large measure to the wide variety of situations how it can sit for a long time without being unexamined. Waiting for someone comes along to find a totally unexpected use for it. Just like has work he couldn’t figure it out and someone else found a use for it and now everyone uses it for their banking account. For myself this made me think about how math isn’t always going to have a solution. To any math problem I come across have to come with a clear mind and ready to understand it carefully. If I don’t understand or having hard time taking a small break will help a lot. The guidelines for problem solving will help me a lot to take it step by step instead of trying to do it all at once. Just like the introduction said the impossible takes forever. The things that surprised me are that I didn’t realize how much math can be used in music and how someone who was trying to find something else came to the discovery that he find toe. What may people were trying to find before Feynmsn....

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...STAT2011 Statistical Models sydney.edu.au/science/maths/stat2011 Semester 1, 2014 Computer Exercise Weeks 1 Due by the end of your week 2 session Last compiled: March 11, 2014 Username: mac 1. Below appears the code to generate a single sample of size 4000 from the population {1, 2, 3, 4, 5, 6}. form it into a 1000-by-4 matrix and then ﬁnd the minimum of each row: > rolls1 table(rolls1) rolls1 1 2 3 4 5 6 703 625 679 662 672 659 2. Next we form this 4000-long vector into a 1000-by-4 matrix: > four.rolls=matrix(rolls1,ncol=4,nrow=1000) 3. Next we ﬁnd the minimum of each row: > min.roll=apply(four.rolls,1,min) 4. Finally we count how many times the minimum of the 4 rolls was a 1: > sum(min.roll==1) [1] 549 5. (a) First simulate 48,000 rolls: > rolls2=sample(x=c(1,2,3,4,5,6),size=48000,replace=TRUE) > table(rolls2) rolls2 1 2 3 4 5 6 8166 8027 8068 7868 7912 7959 (b) Next we form this into a 2-column matrix (thus with 24,000 rows): > two.rolls=matrix(rolls2,nrow=24000,ncol=2) (c) Here we compute the sum of each (2-roll) row: > sum.rolls=apply(two.rolls,1,sum) > table(sum.rolls) sum.rolls 2 3 4 5 6 7 8 9 10 11 742 1339 2006 2570 3409 4013 3423 2651 1913 1291 1 12 643 Note table() gives us the frequency table for the 24,000 row sums. (d) Next we form the vector of sums into a 24-row matrix (thus with 1,000 columns): > twodozen=matrix(sum.rolls,nrow=24,ncol=1000,byrow=TRUE) (e) To ﬁnd the 1,000 column minima use > min.pair=apply(twodozen,2,min) (f) Finally compute......

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...Jasmine Petersen Dr. Abdeljabbar MAT 1111 April 23, 2014 Algebra is one of the most important subjects someone can learn. It is a subject that transfers into daily life. A lot of people do not realize that they are using algebra. Algebra can be anything from calculating the amount of money you’ve spent on your grocery shopping, designing structural plans for a building, and keeping track of the calories you have in your diet. Our professor told us that in every subject, we use math. My major is chemistry and mathematics is used widely in chemistry as well as all other sciences. Mathematical calculations are absolutely necessary to explore important concepts in chemistry. You’ll need to convert things from one unit to another. For example, you need to convert 12 inches to feet. Also, we use simple arithmetic to balance equations. A lot of things I’ve had learned from this course and one of them was that we use Math for everyday life. I’ve also learned many ways how to solve equations such as linear, quadratic, exponential, and logarithmic equations. All the material that we did learn was all easy to learn and understand. I believe that the instructor did a good job explaining on how to solve problems. If my friend was asking me how to determine the differences between the equation of the ellipse and the equation of the hyperbola, I would first give he or she the definition of the two words ellipse and hyperbola. An ellipse is a set of all points in a plane such that the......

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...Analytical summary on the following reading: Edwards, Paul and Wajcman, Judy in Edwards, P. and Wajcman, J., 2005, The Politics of Working Life, Oxford University Press, Oxford, pp. 19-43. What is Happening to Jobs? The main theme in which Edwards et al. portrays within the chapter of ‘What is Happening to Jobs?’ in ‘The Politics of Working life is what individuals expect from work and how those prospects are formed. Through work we can establish our ambitions and our talents and advance our social selves, where as individual and communal work is a vital foundation of meaning and satisfaction in our lives. Conversely, work can therefore create dissatisfaction for individuals. The key points of the chapter are market individualism, alienation and the division of labour, the changing character of labour, and subjectivity, status and satisfaction. Market individualism is created by the negotiation between employers and employees of a labour contract of an employee’s labour for a wage in return, along with which the wages are spent on supplies suited to an individual’s needs. The notion of ‘consumer sovereignty’ conveys that the individual is the best judge of their preferences and therefore individuals are able to enter into contracts to give away his or her labour. Alienation and the division of labour demonstrate that ‘structured antagonism’ (Edwards 1986) is implanted within employment relationship, meaning that is characterised by the potential for conflict as well as......

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...This article is about the study of topics, such as quantity and structure. For other uses, see Mathematics (disambiguation). "Math" redirects here. For other uses, see Math (disambiguation). Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1] Mathematics is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8] Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become......

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...Dec 4 | 11.5: Alternating Series | | 12 | Dec 7 – Dec 11 | 11.6: Absolute Convergence and the Ratio and Root Tests Review for Midterm Exam 2Midterm Exam 2 | Exam 2 : Wed, Dec 10, 5:30-7:00pm Sections: 10.1-10.4, 11.1-11.5 | 13 | Dec 14 – Dec 18 | 11.8: Power Series11.9: Representation of Functions as Power Series | | 14 | Jan 4 – Jan 8 | 11.10: Taylor and Maclaurin Series 11.11: Applications of Taylor PolynomialsComplex Numbers | | 15 | Jan 11 – Jan 15 | Review for Final Exam | Final Exam (comprehensive) | Math Learning Center (NAB239) The Department of Mathematics and Statistics offers a Math Learning Center in NAB239. The goal of this free of charge tutoring service is to provide students with a supportive atmosphere where they have access to assistance and resources outside the classroom. No need to make an appointment-just walk in. Your questions or concerns are welcome to Dr. Saadia Khouyibaba at skhouyibaba@aus.edu or cas-mlc@aus.edu Math 104 Suggested Problems TEXTBOOK: Calculus Early Transcendentals, 7th edition by James Stewart Section | Page | Exercises | 7.1 | 468 | 3, 4, 7, 9, 10, 11, 13, 15, 18, 24, 26, 32, 33, 42 | 7.2 | 476 | 3, 7, 10, 13, 15, 19, 22, 25, 28, 29, 34, 39, 41, 55 | 7.3 | 483 | 1, 2, 3, 5, 8, 9, 13, 15, 23, 24, 26, 27 | 7.4 | 492 | 1, 3, 6, 7, 9, 11, 15, 17, 22, 23, 31, 43, 45, 47, 49, 54 | 7.5 | 499 | 3, 7, 8, 15, 17, 33, 37, 41, 42, 44, 45, 49, 58, 70, 73, 76, 80 | 7.8 | 527 | 1, 2, 5, 7, 10, 12, 13, 17, 19, 21, 25,......

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...Math 1P05 Assignment #1 Due: September 26 Questions 3, 4, 6, 7, 11 and 12 require some Maple work. 1. Solve the following inequalities: a) b) c) 2. Appendix D #72 3. Consider the functions and . a) Use a Maple graph to estimate the largest value of at which the graphs intersect. Hand in a graph that clearly shows this intersection. b) Use Maple to help you find all solutions of the equation. 4. Consider the function. a) Find the domain of. b) Find and its domain. What is the range of? c) To check your result in b), plot and the line on the same set of axes. (Hint: To get a nice graph, choose a plotting range for bothand.) Be sure to label each curve. 5. Section 1.6 #62 6. Section 2.1 #4. In d), use Maple to plot the curve and the tangent line. Draw the secant lines by hand on your Maple graph. 7. Section 2.2 #24. Use Maple to plot the function. 8. Section 2.2 #36 9. Section 2.3 #14 10. Section 2.3 #26 11. Section 2.3 #34 12. Section 2.3 #36 Recommended Problems Appendix A all odd-numbered exercises 1-37, 47-55 Appendix B all odd-numbered exercises 21-35 Appendix D all odd-numbered exercises 23-33, 65-71 Section 1.5 #19, 21 Section 1.6 all odd-numbered exercises 15-25, 35-41, 51, 53 Section 2.1 #3, 5, 7 Section 2.2 all odd-numbered exercises 5-9, 15-25, 29-37 Section 2.3 all odd-numbered exercises 11-31...

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...can see how to split up the original equation into its factor pair, this is the quickest and allows you to solve the problem in one step. Week 9 capstone part 1 Has the content in this course allowed you to think of math as a useful tool? If so, how? What concepts investigated in this course can apply to your personal and professional life? In the course, I have learned about polynomials, rational expressions, radical equations, and quadratic equations. Quadratic equations seem to have the most real life applications -- in things such as ticket sales, bike repairs, and modeling. Rational expressions are also important, if I know how long it takes me to clean my sons room, and know how long it takes him to clean his own room. I can use rational expressions to determine how long it will take the two of us working together to clean his room. The Math lab site was useful in some ways, since it allowed me to check my answers to the problems immediately. However, especially in math 117, it was too sensitive to formatting of the equations and answers. I sometimes put an answer into the math lab that I knew was right, but it marked it wrong because of the math lab expecting slightly different formatting Week 9 capstone part 2 I really didn't use center for math excellence because i found that MML was more convenient for me. I think that MML reassures you that you’re doing the problem correctly. MML is extra support because it carefully walks you through the problem visually......

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...AD P1). GCC is happening. P2). We will have economic catastrophes. P3). We will have disease epidemics. P4). The government will collapse. CC). Something needs to be done to stop GCC. When listening to this argument the arguer commits several fallacies. The first fallacy that was committed was appeal to unqualified authority. He is a science teacher not someone who specializes in GCC, so how can he know if any of these events will happen? This is not his area of specialty. The second fallacy that was committed was appeal to ignorance. I chose this fallacy because he has presented no evidence besides his chart with the columns and rows. This is not enough information to go on to say that GCC is happening or not. The third fallacy committed was false cause. I say he committed this fallacy because what does GCC have to do with bread baskets of the USA and Russia turning to dust bowls causing catastrophic famines, or sea levels rising 10-20 feet. How can he be sure of this kind of catastrophes? Another fallacy that is committed is slippery slope. This fallacy is committed when the arguer commits this fallacy by saying of we don’t take action against GCC the end results are negative or undesirable. Basically a cause and effect event. The arguer has no evidence that GCC is happening or will happen so how can he be sure that it will or won’t happen. I also would say that the arguer is using the fallacy of appeal to emotion. I say this fallacy is being used because he asks...

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...Sample Exam 2 - MATH 321 Problem 1. Change the order of integration and evaluate. (a) (b) 2 0 1 0 1 (x y/2 + y)2 dxdy. + y 3 x) dxdy. 1 0 0 x 0 y 1 (x2 y 1/2 Problem 2. (a) Sketch the region for the integral f (x, y, z) dzdydx. (b) Write the integral with the integration order dxdydz. THE FUNCTION f IS NOT GIVEN, SO THAT NO EVALUATION IS REQUIRED. Problem 3. Evaluate e−x −y dxdy, where B consists of points B (x, y) satisfying x2 + y 2 ≤ 1 and y ≤ 0. − Problem 4. (a) Compute the integral of f along the path → if c − f (x, y, z) = x + y + yz and →(t) = (sin t, cos t, t), 0 ≤ t ≤ 2π. c → − → − → − (b) Find the work done by the force F (x, y) = (x2 − y 2 ) i + 2xy j in moving a particle counterclockwise around the square with corners (0, 0), (a, 0), (a, a), (0, a), a > 0. Problem 5. (a) Compute the integral of z 2 over the surface of the unit sphere. → → − − → − → − − F · d S , where F (x, y, z) = (x, y, −y) and S is → (b) Calculate S the cylindrical surface deﬁned by x2 + y 2 = 1, 0 ≤ z ≤ 1, with normal pointing out of the cylinder. → − Problem 6. Let S be an oriented surface and C a closed curve → − bounding S . Verify the equality → − → − → → − − ( × F ) · dS = F ·ds − → → − if F is a gradient ﬁeld. S C 2 2 1 ...

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...and solve problems in everyday life”. In my everyday life I have to keep the balance in my check book, pay bills, take care of kids, run my house, cook, clean etc. With cooking I am using math, measuring how much food to make for four people (I still haven’t mastered that one). With bills I am using math, how much each company gets, to how much money I have to spare (which these days is not much). In my everyday life I do use some form of a math. It might not be how I was taught, but I have learned to adapt to my surroundings and do math how I know it be used, the basic ways, none of that fancy stuff. For my weakest ability I would say I fall into “Confidence with Mathematics”. Math has never been one of my favorite subjects to learn. It is like my brain knows I have to learn it, but it puts up a wall and doesn’t allow the information to stay in there. The handout “The Case for Quantitative Literacy” states I should be at ease with applying quantitative methods, and comfortable with quantitative ideas. To be honest this class scares the crap out of me, and I am worried I won’t do well in this class. The handout also says confidence is the opposite of “Math Anxiety”, well I can assure you I have plenty of anxiety right now with this class. I have never been a confident person with math, I guess I doubt my abilities, because once I get over my fears and anxiety I do fine. I just have to mentally get myself there and usually it’s towards the end of the class. There are......

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...dose 500mg amoxicillin; 4 year old child |300mg adult, 100mg child | |U or F |adult dose 1000mg acetaminophen; 3 year old child |75mg adult, 12.5mg child | |W or D |adult dose 75mg Tamiflu; 5 year old child |1200mg adult, 300mg child | |Y or B |adult dose 400mg ibuprofen; 2 year old child |400mg adult, 50mg child | • Explain what the variables in the formula represent and show all steps in the computations. • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): o Literal equation o Formula o Solve o Substitute o Conditional equation...

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...Running head: SOMETHING HAPPENING HERE There’s Something Happening Here: Occupying Wall Street Mindy Newell, R.N., CNOR Grand Canyon University NRS – 432V Teresa Ortner, RNC, MSNEd October 8, 2011 There’s Something Happening Here: Occupying Wall Street The Plan of Action On September 17, 2011, nearly 1,000 protesters gathered around the symbolic sculpture of a charging bull that is the focal point of Bowling Green Park, which is in the financial district of downtown Manhattan, to say to the kings of Wall Street “Enough! No more! You will not continue to profit on the broken backs and weary shoulders of we, the people! You will not destroy the American dream with your greed!” They did not leave, but hoisted tents and unrolled sleeping bags to “Occupy Wall Street” (Smith, 2011). Since that day, the movement has spread across the country, from New York up the coast to Boston, down the coast through Washington to Miami, and across the country through Chicago and St. Louis all the way to Los Angeles, from large metropolises to small towns across America. It has become a genuine social and political movement, utilizing both old media such as newspapers and television news and new media such as Facebook, Twitter, and Youtube (Ellis, Raja & Follman, 2011). Major labor unions, such as National Nurses United, the AFL-CIO, the Communications Workers of America, the United Auto Workers, the United Federation of Teachers, the Writers......

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...Mathematical Happenings Egypt is one of the advanced civilizations in the ancient world. If it was not for them and their advancements in mathematics, the world we live in now would be a very different place. They paved the way for the Greeks and other ancient civilizations to continue improving not only the world of math but also most other industries. One of the first people to start writing down anything were the Ancient Egyptians. They needed to keep track of the days for planting and harvesting, they needed geometry to build things, and arithmetic for trading purposes. It paved the way for the barter system. They needed a way to figure out how much of something else they would get for their product. The members of the Egyptian society that were in charge of numbers and keeping track of the surplus of good were priests. Their jobs besides their religious duties were in charge of creating a writing system, keeping records, create a calendar, watch the sky for astrological events and other intellectual endeavors. The number system for Ancient Egypt was called hieroglyphics. The system is based on groupings of 10. The numbers each have a name. The number 1 is called the stick, the number 10 is called the heel bone, the number 100 is called the scroll, the number 1,000 is called the lotus flower, the number 10,000 is called the bent finger or snake, the number 100,000 is called the burbot fish or tadpole and the number 1,000,000 is called the astonished man.......

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