Macroeconomics Assignment Example | Topics and Well Written Essays - 250 words - 4

Macroeconomics - Assignment Example The government therefore has to increase their purchases of these products to the same amount as that planned for reduction in the investment spending. c. A change in taxes can produce the same result. This is because taxes affect the production of companies. When taxes are reduced, companies can use that money elsewhere such as for investment purposes, they will also be motivated to increase their production as they will be paying lower taxes. d. In a balanced budget economy law makers have to be very keen on the fiscal policies that they put in place so as to restore the economy to full employment. The most feasible way this can be done is by taking of loans to invest in other areas that will be repaid over time. The blue line in the graph represents the total demand. The red line in the graph represents the total supply of goods and services. The black line represents the economy’s capacity in the long run. The equilibrium where they intersect is the potential output. a) When people buy goods and services using money the money is handed over to the stores who in turn pay their suppliers. The money circulates in the economy and is used by various people. The money supply is therefore maintained. When people use credit banks to pay for their shopping, there is no money that exchanges hands. This leads to a decrease in the money supply in the economy. b) To reduce money supply the bank should increase lending rates. Higher rates mean that fewer people will be willing to borrow money from the bank and over time, there will be a decrease in the money supply within the economy. A. i) The purchasing power parity theory is concerned with the exchange rates (Blaug, 2006). Therates of exchange between two currencies are at equilibrium as long as their domestic purchasing power at a given exchange rate is equal. In this case, Gold should cost the same in both Mexico and U.S after taking into account the interest

Donatello Essay Example | Topics and Well Written Essays - 1500 words

Donatello - Essay Example Biography: Donatello Italy is world renowned for Renaissance art and Donatello (Florence) is one of the best examples of the same. Besides, his birth was in the year 1386. After formal education, Donatello decided to be a goldsmith and underwent training. Besides, the training at the studio of Lorenzo Ghiberti helped him to realize that his field is art, not the work of a goldsmith. But he did not neglect the work as a goldsmith because it helped him to keep himself away from poverty. His deep interest in Roman architecture, especially the works by Filippo Brunelleschi, gradually attracted him towards sculpture. One can easily identify that both the artists (Donatello and Filippo Brunelleschi) revolutionized the field of sculpture and architecture in the 15th century. Donatello’s relationship with Lorenzo Ghiberti was so helpful to develop his interest in sculpture. For instance, Donatello worked as Lorenzo Ghiberti’s assistant at Florence Baptistery. Kleiner stated tha t â€Å"Donatello was also a pioneer in relief sculpture, the first to incorporate the principles of linear and atmospheric perspective, devices also employed brilliantly by Lorenzo Ghiberti in his Gates of Paradise for the Florence baptistery† (577). Lorenzo Ghiberti’s guidance helped Donatello to be free from the influence of Gothic Mannerism and to develop his own style in sculpture. Gradually, Donatello began to undertake independent works. For instance, Donatello work, bronze David proves his creativity in sculpture. Besides, this work helped Donatello to be famous in the field of sculpture, especially Renaissance sculpture. In the year 1450, Donatello completed another work in Padua, which is known as Gattamelata. This work is in the form of a statue, which deeply influenced the artists in Europe. Later in the year 1453, Donatello returned to his birthplace and began to undertake other works. His later works include St. John the Baptist and Martyrdom of St. Lawre nce. Donatello passed away in the year 1466. His body was buried in a large church in Florence, namely Basilica of San Lorenzo. Britannica Educational Publishing stated that â€Å"A good deal is known about Donatello’s life and career, but little is known about his character and personality, and what is known is not wholly reliable† (31). To be specific, Donatello’s deep interest and passion towards sculpture helped him to be one of the pioneers of early Renaissance in Italian sculpture. Ghiberti’s training helped Donatello to learn the basics of sculpture but he developed his own style in sculpture. For instance, Donatello developed his own style in sculpture, namely relief sculpture. His passion towards sculpture forced him to be in Rome and other places like Siena and Padua. This helped him to lead more about the scope of sculpture in Europe. Besides, Donatello was able to keep himself free from the influence of Gothic style of Mannerism. Within the co ntext of early Renaissance in Italian sculpture, Donatello’s name is most memorable because his sculptures represent the Renaissance spirit of the age. Analysis 1: Equestrian statue of Gattamelata The Equestrian statue of Gattamelata (see appendix-1) is a statue in Bronze by Donatello, which was commissioned in the year 1453. This sculpture, which acts the role of a landmark, is situated in Padua. This sculpture is interconnected with the history of Padua, especially the life history of condottiero Erasmo

Big Data in Companies Essay Example for Free

Big Data in Companies Essay Big data (also spelled Big Data) is a general term used to describe the voluminous amount of unstructured and semi-structured data a company creates data that would take too much time and cost too much money to load into a relational database for analysis. Although Big data doesnt refer to any specific quantity, the term is often used when speaking about petabytes and exabytes of data. A primary goal for looking at big data is to discover repeatable business patterns. It’s generally accepted that unstructured data, most of it located in text files, accounts for at least 80% of an organization’s data. If left unmanaged, the sheer volume of unstructured data that’s generated each year within an enterprise can be costly in terms of storage. Unmanaged data can also pose a liability if information cannot be located in the event of a compliance audit or lawsuit. Big data analytics is often associated with cloud computing because the analysis of large data sets in real-time requires a framework like MapReduce to distribute the work among tens, hundreds or even thousands of computers. Big data is data that exceeds the processing capacity of conventional database systems. The data is too big, moves too fast, or doesn’t fit the strictures of your database architectures. To gain value from this data, you must choose an alternative way to process it. The hot IT buzzword of 2012, big data has become viable as cost-effective approaches have emerged to tame the volume, velocity and variability of massive data. Within this data lie valuable patterns and information, previously hidden because of the amount of work required to extract them. To leading corporations, such as Walmart or Google, this power has been in reach for some time, but at fantastic cost. Today’s commodity hardware, cloud architectures and open source software bring big data processing into the reach of the less well-resourced. Big data processing is eminently feasible for even the small garage startups, who can cheaply rent server time in the cloud. The value of big data to an organization falls into two categories: analytical use, and enabling new products. Big data analytics can reveal insights hidden previously by data too costly to process, such as peer influence among customers, revealed by analyzing shoppers’ transactions, social and geographical data. Being able to process every item of data in reasonable time removes the troublesome need for sampling and promotes an investigative approach to data, in contrast to the somewhat static nature of running predetermined reports. The past decade’s successful web startups are prime examples of big data used as an enabler of new products and services. For example, by combining a large number of signals from a user’s actions and those of their friends, Facebook has been able to craft a highly personalized user experience and create a new kind of advertising business. It’s no coincidence that the lion’s share of ideas and tools underpinning big data have emerged from Google, Yahoo, Amazon and Facebook. The emergence of big data into the enterprise brings with it a necessary counterpart: agility. Successfully exploiting the value in big data requires experimentation and exploration. Whether creating new products or looking for ways to gain competitive advantage, the job calls for curiosity and an entrepreneurial outlook. What does big data look like? As a catch-all term, â€Å"big data† can be pretty nebulous, in the same way that the term â€Å"cloud† covers diverse technologies. Input data to big data systems could be chatter from social networks, web server logs, traffic flow sensors, satellite imagery, broadcast audio streams, banking transactions, MP3s of rock music, the content of web pages, scans of government documents, GPS trails, telemetry from automobiles, financial market data, the list goes on. Are these all really the same thing? To clarify matters, the three Vs of volume, velocity and variety are commonly used to characterize different aspects of big data. They’re a helpful lens through which to view and understand the nature of the data and the software platforms available to exploit them. Most probably you will contend with each of the Vs to one degree or another. Volume The benefit gained from the ability to process large amounts of information is the main attraction of big data analytics. Having more data beats out having better models: simple bits of math can be unreasonably effective given large amounts of data. If you could run that forecast taking into account 300 factors rather than 6, could you predict demand better? This volume presents the most immediate challenge to conventional IT structures. It calls for scalable storage, and a distributed approach to querying. Many companies already have large amounts of archived data, perhaps in the form of logs, but not the capacity to process it. Assuming that the volumes of data are larger than those conventional relational database infrastructures can cope with, processing options break down broadly into a choice between massively parallel processing architectures — data warehouses or databases such as Greenplum — and Apache Hadoop-based solutions. This choice is often informed by the degree to which the one of the other â€Å"Vs† — variety — comes into play. Typically, data warehousing approaches involve predetermined schemas, suiting a regular and slowly evolving dataset. Apache Hadoop, on the other hand, places no conditions on the structure of the data it can process. At its core, Hadoop is a platform for distributing computing problems across a number of servers. First developed and released as open source by Yahoo, it implements the MapReduce approach pioneered by Google in compiling its search indexes. Hadoop’s MapReduce involves distributing a dataset among multiple servers and operating on the data: the â€Å"map† stage. The partial results are then recombined: the â€Å"reduce† stage. To store data, Hadoop utilizes its own distributed filesystem, HDFS, which makes data available to multiple computing nodes. A typical Hadoop usage pattern involves three stages: * loading data into HDFS, * MapReduce operations, and * retrieving results from HDFS. This process is by nature a batch operation, suited for analytical or non-interactive computing tasks. Because of this, Hadoop is not itself a database or data warehouse solution, but can act as an analytical adjunct to one. One of the most well-known Hadoop users is Facebook, whose model follows this pattern. A MySQL database stores the core data. This is then reflected into Hadoop, where computations occur, such as creating recommendations for you based on your friends’ interests. Facebook then transfers the results back into MySQL, for use in pages served to users. Velocity The importance of data’s velocity — the increasing rate at which data flows into an organization — has followed a similar pattern to that of volume. Problems previously restricted to segments of industry are now presenting themselves in a much broader setting. Specialized companies such as financial traders have long turned systems that cope with fast moving data to their advantage. Now it’s our turn. Why is that so? The Internet and mobile era means that the way we deliver and consume products and services is increasingly instrumented, generating a data flow back to the provider. Online retailers are able to compile large histories of customers’ every click and interaction: not just the final sales. Those who are able to quickly utilize that information, by recommending additional purchases, for instance, gain competitive advantage. The smartphone era increases again the rate of data inflow, as consumers carry with them a streaming source of geolocated imagery and audio data. It’s not just the velocity of the incoming data that’s the issue: it’s possible to stream fast-moving data into bulk storage for later batch processing, for example. The importance lies in the speed of the feedback loop, taking data from input through to decision. A commercial from IBM makes the point that you wouldn’t cross the road if all you had was a five-minute old snapshot of traffic location. There are times when you simply won’t be able to wait for a report to run or a Hadoop job to complete. Industry terminology for such fast-moving data tends to be either â€Å"streaming data,† or â€Å"complex event processing. This latter term was more established in product categories before streaming processing data gained more widespread relevance, and seems likely to diminish in favor of streaming. There are two main reasons to consider streaming processing. The first is when the input data are too fast to store in their entirety: in order to keep storage requirements practical some level of analysis must occur as the data streams in. At the extreme end of the scale, the Large Hadron Collider at CERN generates so much data that scientists must discard the overwhelming majority of it — hoping hard they’ve not thrown away anything useful. The second reason to consider streaming is where the application mandates immediate response to the data. Thanks to the rise of mobile applications and online gaming this is an increasingly common situation. Product categories for handling streaming data divide into established proprietary products such as IBM’s InfoSphere Streams, and the less-polished and still emergent open source frameworks originating in the web industry: Twitter’s Storm, and Yahoo S4. As mentioned above, it’s not just about input data. The velocity of a system’s outputs can matter too. The tighter the feedback loop, the greater the competitive advantage. The results might go directly into a product, such as Facebook’s recommendations, or into dashboards used to drive decision-making. It’s this need for speed, particularly on the web, that has driven the development of key-value stores and columnar databases, optimized for the fast retrieval of precomputed information. These databases form part of an umbrella category known as NoSQL, used when relational models aren’t the right fit. Microsoft SQL Server is a comprehensive information platform offering enterprise-ready technologies and tools that help businesses derive maximum value from information at the lowest TCO. SQL Server 2012 launches next year, offering a cloud-ready information platform delivering mission-critical confidence, breakthrough insight, and cloud on your terms; find out more at www. microsoft. com/sql. Variety Rarely does data present itself in a form perfectly ordered and ready for processing. A common theme in big data systems is that the source data is diverse, and doesn’t fall into neat relational structures. It could be text from social networks, image data, a raw feed directly from a sensor source. None of these things come ready for integration into an application. Even on the web, where computer-to-computer communication ought to bring some guarantees, the reality of data is messy. Different browsers send different data, users withhold information, they may be using differing software versions or vendors to communicate with you. And you can bet that if part of the process involves a human, there will be error and inconsistency. A common use of big data processing is to take unstructured data and extract ordered meaning, for consumption either by humans or as a structured input to an application. One such example is entity resolution, the process of determining exactly what a name refers to. Is this city London, England, or London, Texas? By the time your business logic gets to it, you don’t want to be guessing. The process of moving from source data to processed application data involves the loss of information. When you tidy up, you end up throwing stuff away. This underlines a principle of big data: when you can, keep everything. There may well be useful signals in the bits you throw away. If you lose the source data, there’s no going back. Despite the popularity and well understood nature of relational databases, it is not the case that they should always be the destination for data, even when tidied up. Certain data types suit certain classes of database better. For instance, documents encoded as XML are most versatile when stored in a dedicated XML store such as MarkLogic. Social network relations are graphs by nature, and graph databases such as Neo4J make operations on them simpler and more efficient. Even where there’s not a radical data type mismatch, a disadvantage of the relational database is the static nature of its schemas. In an agile, exploratory environment, the results of computations will evolve with the detection and extraction of more signals. Semi-structured NoSQL databases meet this need for flexibility: they provide enough structure to organize data, but do not require the exact schema of the data before storing it.

Importance of Discrete Mathematics in Computer Science

Importance of Discrete Mathematics in Computer Science Computer science is the study of problems, problem solving and the solutions that come out of the problem solving process, B. Miller and D. Ranum (2013). A computer scientist goal is to develop an algorithm, a step by step list of instructions in solving a problem. Algorithms are finite processes that if followed will solve the problem Discrete mathematics is concerned with structures which take on a discrete value often infinite in nature. Just as the real-number system plays a crucial role in continuous mathematics, integers are the cornerstone in discrete mathematics. Discrete mathematics provides excellent modelling tools for analysing real-world phenomena that varies in one state or another and is a vital tool used in a wide range of applications, from computers to telephone call routing and from personnel assignments to genetics, E.R. Scheinerman (2000) cited in W. J. Rapaport 2013). The difference between discrete mathematics and other disciplines is the basic foundation on proof as its modus operandi for determining truth, whereas science for example, relies on carefully analysed experience. According to J. Barwise and J. Etchemendy, (2000), a proof is any reasoned argument accepted as such by other mathematicians. Discrete mathematics is the background behind many computer operations (A. Purkiss 2014, slide 2) and is therefore essential in computer science. According to the National Council of Teachers of Mathematics (2000), discrete mathematics is an essential part of the educational curriculum (Principles and Standards for School Mathematics, p. 31). K. H Rosen (2012) cites several important reasons for studying discrete mathematics including the ability to comprehend mathematical arguments. In addition he argues discrete mathematics is the gateway to advanced courses in mathematical sciences. This essay will discuss the importance of discrete mathematics in computer science. Furthermore, it will attempt to provide an understanding of important related mathematical concepts and demonstrate with evidence based research why these concepts are essential in computer science. The essay will be divided into sections. Section one will define and discuss the importance of discrete mathematics. The second section will focus on and discuss discrete structures and relationships with objects. The set theory would be used as an example and will give a brief understanding of the concept. The third section will highlight the importance of mathematical reasoning. Finally, the essay will conclude with an overview of why discrete mathematics is essential in computer science. Discrete Mathematics According to K. H. Rosen, (2012) discrete mathematics has more than one purpose but more importantly it equips computer science students with logical and mathematical skills. Discrete mathematics is the study of mathematics that underpins computer science, with a focus on discrete structures, for example, graphs, trees and networks, K H Rosen (2012). It is a contemporary field of mathematics widely used in business and industry. Often referred to as the mathematics of computers, or the mathematics used to optimize finite systems (Core-Plus Mathematics Project 2014). It is an important part of the high school mathematics curriculum. Discreet mathematics is a branch of mathematics dealing with objects that can assume only distinct separated values (mathworld wolfram.com). Discrete mathematics is used in contrast with continuous mathematics, a branch of mathematics dealing with objects that can vary smoothly including calculus (mathworld wolfram.com). Discrete mathematics includes graph theory, theory of computation, congruences and recurrence relations to name but a few of its associated topics (mathworld wolfram.com). Discrete mathematics deals with discrete objects which are separated from each other. Examples of discrete objects include integers, and rational numbers. A discrete object has known and definable boundaries which allows the beginning and the end to be easily identified. Other examples of discrete objects include buildings, lakes, cars and people. For many objects, their boundaries can be represented and modelled as either continuous or discrete, (Discrete and Continuous Data, 2008). A major reason discrete mathematics is essential for the computer scientist, is, it allows handling of infinity or large quantity and indefiniteness and the results from formal approaches are reusable. Discrete Structures To understand discrete mathematics a student must have a firm understanding of how to work with discrete structures. These discrete structures are abstract mathematical structures used to represent discrete objects and relationships between these objects. The discrete objects include sets, relations, permutations and graphs. Many important discrete structures are built using sets which are collections of objects K H Rosen (2012). Sets As stated by Cantor (1895: 282) cited in J. L. Bell (1998) a set is a collection of definite, well- differentiated objects. K. H Rosen (2012) states discrete structures are built using sets, which are collections of objects used extensively in counting problems; relations, sets of ordered pairs that represent relationships between objects, graphs, sets of vertices and edges that connect vertices and edges that connect vertices; and finite state machines, used to model computing machines. Sets are used to group objects together and often have similar properties. For example, all employees working for the same organisation make up a set. Furthermore those employees who work in the accounts department form a set that can be obtained by taking the elements common to the first two collections. A set is an unordered collection of objects, called elements or members of the set. A set is said to contain its elements. To denote that a is an element of the set A, we write a â‚ ¬ A. For example the set O of odd positive integers less than 10 can be expressed by O = {1, 3, 5, 7, 9}. Another example is, {x |1 ≠¤ x ≠¤ 2 and x is a real number.} represents the set of real numbers between 1 and 2 and {x | x is the square of an integer and x ≠¤ 100} represents the set {0. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100}, (www.cs.odu.edu). Mathematical Reasoning Logic is the science for reasoning, Copi, (1971) and a collection of rules used in carrying out logical reasoning. The foundation for logic was laid down by the British mathematician George Boole. Logic is the basis of all mathematical reasoning and of all automated reasoning. It has practical applications to the design of computing machines, to the specification of systems, to artificial intelligence, to computer programming, to programming languages and to other areas of computer science, K H Rosen, (2012 page 1). Mathematical logic, starts with developing an abstract model of the process of reasoning in mathematics, D. W. Kucker page 1. Following the development of an abstract model a study of the model to determine some of its properties is necessary. The aim of logic in computer science is to develop languages to model the situations we encounter as computer science professionals, in such a way that we can reason about them formally. Reasoning about situations means constructing arguments about them; we want to do this formally, so that the arguments are valid and can be defended rigorously, or executed on a machine. In understanding mathematics we must understand what makes a correct mathematical argument, that is, a proof. As stated by C. Rota (1997) a proof is a sequence of steps which leads to the desired conclusion Proofs are used to verify that computer programs produce the correct result, to establish the security of a system and to create artificial intelligence. Logic is interested in true or false statements and how the truth or falsehood of a statement can be determined from other statements (www.cs.odu.edu). Logic is represented by symbols to represent arbitrary statements. For example the following statements are propositions â€Å"grass is green† and â€Å"2 + 2 = 5†. The first proposition has a truth value of â€Å"true† and the second â€Å"false†. According to S. Waner and S. R Constenoble (1996) a proposition is any declarative sentence which is either true or false. Many in the computing community have expressed the view that logic is an essential topic in the field of computer science (e.g., Galton, 1992; Gibbs Tucker, 1986; Sperschneider Antoniou, 1991). There has also been concern that the introduction of logic to computer science students has been and is being neglected (e.g., Dijkstra, 1989; Gries, 1990). In their article â€Å"A review of several programs for the teaching of logic†, Goldson, Reeves and Bornat (1993) stated: There has been an explosion of interest in the use of logic in computer science in recent years. This is in part due to theoretical developments within academic computer science and in part due to the recent popularity of Formal Methods amongst software engineers. There is now a widespread and growing recognition that formal techniques are central to the subject and that a good grasp of them is essential for a practising computer scientist. (p. 373). In his paper â€Å"The central role of mathematical logic in computer science†, Myers (1990) provided an extensive list of topics that demonstrate the importance of logic to many core areas in computer science and despite the fact that many of the topics in Myers list are more advanced than would be covered in a typical undergraduate program, the full list of topics covers much of the breadth and depth of the curriculum guidelines for computer science, Tucker (1990). The model program report (IEEE, 1983) described discrete mathematics as a subject area of mathematics that is crucial to computer science and engineering. The discrete mathematics course was to be a pre or co requisite of all 13 core subject areas except Fundamentals of Computing which had no pre requisites. However in Shaw’s (1985) opinion the IEEE program was strong mathematically but disappointing due to a heavy bias toward hardware and its failure to expose basic connections between hardware and software. In more recent years a task force had been set up to deve lop computer science curricula with the creation of a document known as the Denning Report, (Denning, 1989). The report became instrumental in developing computer science curriculum. In a discussion of the vital role of mathematics in the computing curriculum, the committee stated, mathematical maturity, as commonly attained through logically rigorous mathematics courses is essential to successful mastery of several fundamental topics in computing, (Tucker, 1990, p.27). It is generally agreed that students in undergraduate computer science programs should have a strong basis in mathematics and attempts to recommend which mathematics courses should be required, the number of mathematics courses and when the courses should be taken have been the source of much controversy (Berztiss, 1987; Dijkstra, 1989; Gries, 1990; Ralston and Shaw, 1980; Saiedian 1992). A central theme in the controversy within the computer science community has been the course discrete mathematics. In 1989, the Mathematical Association of America published a report about discrete mathematics at the undergraduate level (Ralston, 1989). The report made some recommendations including offering discrete mathematics courses with greater emphasis on problem solving and symbolic reasoning (Ralston, 1989; Myers, 1990). Conclusion The paper discussed the importance of discrete mathematics in computer science and its significance as a skill for the aspiring computer scientist. In addition some examples of this were highlighted including its usefulness in modelling tools to analyse real world events. This includes its wide range of applications such as computers, telephones, and other scientific phenomena. The next section looked at discrete structures as a concept of abstract mathematical structures and the development of set theory a sub topic within discrete mathematics. The essay concluded with a literature review of evidence based research in mathematical reasoning where various views and opinions of researchers, academics and other stakeholders were discussed and explored. The review makes clear of the overwhelming significance and evidence stacked in favour for students of computer science courses embarking on discrete mathematics. Overall, it is generally clear that pursuit of a computer science course w ould most definitely need the associated attributes in logical thinking skills, problem solving skills and a thorough understanding of the concepts. In addition the review included views of an increased interest in the use of logic in computer science in recent years. Furthermore formal techniques have been acknowledged and attributed as central to the subject of discrete mathematics in recent years. References A. Purkiss 2014, Lecture 1: Course Introduction and Numerical Representation, Birkbeck University. B. Miller and D. Ranum 2013. Problem Solving with Algorithms and Data Structures: accessed on [18.01.15] Berztiss, A. (1987). A mathematically focused curriculum for computer science. Communications of the ACM, 30 (5), 356–365. Copi, I. M. (1979). Symbolic Logic (5th ed.). New York: Macmillan Core-Plus Mathematics Project 2014: Discrete Mathematics available at http://www.wmich.edu/cpmp/parentresource/discrete.html [accessed on 25.01.14] 6. D W Kucker Notes on Mathematical Logic; University of Maryland, College Park. Available at http://www.math.umd.edu/~dkueker/712.pdf Accessed on [24.01.15] Denning, P. J. (chair). (1989). Computing as a discipline. Communications of the ACM, 32 (1), 9–23. Dijkstra, E. W. (1989). On the cruelty of really teaching computing science. Communications of the ACM, 32 (12), 1398–1404. Discrete and Continuous Data, (2008). Environmental Systems Research Institute, Inc. Available at http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=Discrete%20and%20continuous%20data [accessed on 18.01.15]. Discrete Structures (2010) available at http://www.cs.odu.edu/~toida/nerzic/content/schedule/schedule.html#day3 [accessed on 25.01.15] Edward R. Scheinerman (2000), Mathematics, A Discrete Introduction (Brooks/Cole, Pacific Grove, CA, 2000): xvii–xviii. Cited in W. J. Rapaport (2013). Discrete Structures. What is Discrete Maths? available from http://www.cse.buffalo.edu/~rapaport/191/whatisdiscmath.html-20130629 accessed on [25.01.2015] Galton, A. (1992). Logic as a Formal Method. The Computer Journal 35 (5), 431–440 Gibbs, N. E., Tucker, A. B. (1986). A model curriculum for a liberal arts degree in computer science. Communications of the ACM 29 (3), 202–210 Goldson, D., Reeves, S., Bornat, R. (1993). A review of several programs for the teaching of logic. The Computer Journal, 36 (4), 373–386. Gries, D. (1990). Calculation and discrimination: A more effective curriculum. Communications of the ACM. 34 (3). 44–55. 16. http://www.cs.odu.edu/~toida/nerzic/content/intro2discrete/intro2discrete.html : Introduction to Discrete Structures What’s and Whys IEEE Model Program Committee. (1983). The 1983 IEEE Computer Society Model Program in Computer Science and Engineering. IEEE Computer Society. Educational Activities Board J. Barwise and J. Etchemendy, Language, Proof and Logic, Seven Bridges Press, New York, 2000, ISBN 1-889119-08-3. J. L. Bell Oppositions and Paradoxes in Mathematics and Philosophy available at http://publish.uwo.ca/~jbell/Oppositions%20and%20Paradoxes%20in%20Mathematics2.pdf accessed on [25.01.2015] 20. K. H Rosen 2012 Discrete Mathematics and its Applications, 7edn, Monmouth University. Myers, Jr. J. P. (1990). The Central role of mathematical logic in computer science. SIGCSE Bulletin, 22 (1), 22–26. Ralston, A. (Ed.) (1989). Discrete Mathematics in the First Two Years. MAA Notes No. 15. The Mathematical Association of America. Ralston, A., Shaw, M. (1980). Curriculum 78 Is computer science really that unmathematical? Communications of the ACM, 23 (2), 67–70. Rota, G.-C. (1997). The phenomenology of mathematical proof. Syntheses, 111:183-196. S. Waner S. R. Costenoble (1996) Introduction to Logic. Saiedian, H. (1992). Mathematics of computing. Computer Science Education, 3 (3), 203-221. Shaw, M. (Ed.) (1985). The Carnegie-Mellon Curriculum for Undergraduate Computer Science. New York: Springer-Verlag Sperschneider, V., Antoniou, G. (1991). Logic: A foundation for computer science International Computer Science Series. Reading, MA: Addison- Wesley The National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Tucker, A. B. (Ed.) (1990). Computing Curricula 1991: Report of the ACM/IEEE-CS Joint Curriculum Task Force Final Draft, December 17. ACM Order Number 201910. IEEE Computer Society Press Order Number 2220

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All-star football player, Lieutenant Commander, University of Michigan graduate, Yale graduate, adopted, and also the thirty-eighth president of the united states? These are all some ways that you could describe a man by the name of Leslie King Jr. You may be wondering who that is, but he is a president of these United States of America. Leslie King Jr. is the original name of Gerald Rudolph Ford. I am going to tell you all about his childhood, his high school experience, his college experience, his whole election process, his presidency, and his post-presidency experience. Gerald Ford was born July 14, 1913 in Omaha, Nebraska. His parents, Dorothy Ayer Gardner and his father Leslie Lynch King Sr. separated just sixteen days after Ford was born. His father was a wool trader and also was the son of a banker. They were officially divorced in December 1913, where Fords mother Dorothy was granted full custody. Soon after, Ford and his mother moved to Grand Rapids, Michigan to live with Fords grandparents. (Dorothy’s parents) Fords grandfather (Leslie Sr.’s father) paid child support until his death. In Ford’s biography, written by a member of his administration, Ford said that his biological father was known to get physical with his mother. He also stated that the main reason for their divorce was a few days after Ford’s birth his father threatened his mother with a butcher knife. In the biography it said that his father first hit his mother on their honeymoon, for smiling at another man. In 1916 Dorothy remarried a salesman by the name of Gerald Rudolph Ford. Gerald then went on to adopt Leslie, later renaming him Gerald Rudolph Ford Jr. Ford grew up with three younger half-brothers from his mother’s second marriage. Thomas ... ... for the vice presidency. That one time in 1960 he almost became the vice president, but the Republican nominee Richard Nixon chose Massachusetts senator Henry Cabot Lodge instead of Ford. Ford continued to run for Congress and continually got reelected. The Fifth District constituents liked ford a lot. They always gave Ford at least sixty percent of their votes. Later in 1963 Ford was named Republican conference Chairman, and two years later was named House Minority Leader. Ford was not commonly known by very many Americans except those from Michigan and those who are part of Congress. This all changed when Ford and Senate Minority Leader Everett Dirksen talked together at some press conferences, criticizing the â€Å"Great Society Programs† of President Lyndon B. Johnson. These press conferences were known to many as â€Å" The Ev and Jerry Show† (Frank N. Magill, 791) Essay examples -- All-star football player, Lieutenant Commander, University of Michigan graduate, Yale graduate, adopted, and also the thirty-eighth president of the united states? These are all some ways that you could describe a man by the name of Leslie King Jr. You may be wondering who that is, but he is a president of these United States of America. Leslie King Jr. is the original name of Gerald Rudolph Ford. I am going to tell you all about his childhood, his high school experience, his college experience, his whole election process, his presidency, and his post-presidency experience. Gerald Ford was born July 14, 1913 in Omaha, Nebraska. His parents, Dorothy Ayer Gardner and his father Leslie Lynch King Sr. separated just sixteen days after Ford was born. His father was a wool trader and also was the son of a banker. They were officially divorced in December 1913, where Fords mother Dorothy was granted full custody. Soon after, Ford and his mother moved to Grand Rapids, Michigan to live with Fords grandparents. (Dorothy’s parents) Fords grandfather (Leslie Sr.’s father) paid child support until his death. In Ford’s biography, written by a member of his administration, Ford said that his biological father was known to get physical with his mother. He also stated that the main reason for their divorce was a few days after Ford’s birth his father threatened his mother with a butcher knife. In the biography it said that his father first hit his mother on their honeymoon, for smiling at another man. In 1916 Dorothy remarried a salesman by the name of Gerald Rudolph Ford. Gerald then went on to adopt Leslie, later renaming him Gerald Rudolph Ford Jr. Ford grew up with three younger half-brothers from his mother’s second marriage. Thomas ... ... for the vice presidency. That one time in 1960 he almost became the vice president, but the Republican nominee Richard Nixon chose Massachusetts senator Henry Cabot Lodge instead of Ford. Ford continued to run for Congress and continually got reelected. The Fifth District constituents liked ford a lot. They always gave Ford at least sixty percent of their votes. Later in 1963 Ford was named Republican conference Chairman, and two years later was named House Minority Leader. Ford was not commonly known by very many Americans except those from Michigan and those who are part of Congress. This all changed when Ford and Senate Minority Leader Everett Dirksen talked together at some press conferences, criticizing the â€Å"Great Society Programs† of President Lyndon B. Johnson. These press conferences were known to many as â€Å" The Ev and Jerry Show† (Frank N. Magill, 791)

Gender Stereotypes in Media Essay example -- Media Stereotyping of Me

The judgments we make about people, events or places are based on our own direct impressions. But for most of the knowledge, we rely on media. The media actually re-present the world to us. However, the media only shows us some aspects of the world, ignoring the rest. So basically, the media chooses what is to be shown and what is to be discarded (Andrew Pilkington and Alan Yeo (2009)). . In this essay, I will explain what stereotypes are and primarily give an example of a famous men’s magazine called ‘nuts’ and explain how these stereotypes are created by print and the digital media and what are their impacts on people. Stereotypes can be defined as an exaggerated belief about an individual or a group based on their appearance, behavior or beliefs. Though our world seems to be improving in many other ways, it seems almost impossible to emancipate it from stereotypes. Today, the media is so powerful that it can make or break an image of a person and also can change the views of the audience. ‘Gender refers to the cultural nature of the differences between the natural biological sexes of male and female’ (Long, P & Wall, T (2009)). Gender is perhaps the basic category we use for sorting human beings. The media mostly portrays men as strong, masculine, tough, hard and independent while women are shown as fragile, soft, clean and mostly 'sexy'. Whatever the role, television, film and popular magazines are full of images of women and girls who are typically white, desperately thin, and tailored to be the perfect woman. The representation of women on the print and the visual media mostly tend to be stereotypical, in terms of societal expectations (mediaknowall.com). These days, most of the fashion magazines are full of white ... ...ogy in focus for AQA A2 Level. 2nd ed. Britain: Causeway Press.p99-112. Branston, G & Stafford, R (2010). The Media Students Book. 5th ed. London: Natalie Fenton, Goldsmiths, University of London, UK. 22. Harper, S. (2008). Stereotypes in the Media. Available: http://www.edubook.com/stereotypes-in-the-modern-media/9200/. Last accessed 2nd May 2011. Long, P & Wall, T (2009). Media Studies- Texts, production and context. Italy: Pearson Education Limited 2009. p82-85. Wilson, K. (2010 - 2011). Gender and Media representation. Available: http://www.mediaknowall.com/as_alevel/alevkeyconcepts/alevelkeycon.php?pageID=gender. Last accessed 1st May 2011. Wright, M. (2005). Stereotypes of women are widespread in media and society. Available: http://www.quchronicle.com/2005/02/stereotypes-of-women-are-widespread-in-media-and-society/. Last accessed 4th May 2011.

Athenian Artistic Performances Were They a Form of Propaganda Essay

The â€Å"glory that was Greece† reached its height in 5th century BCE in Athens, under the leadership of Pericles. He opened Athenian democracy to the ordinary citizen, was responsible for the construction of magnificent temples and statues on the Acropolis and he, in effect created the Athenian empire. The definition of propaganda is â€Å"the planned use of any form of public or mass-produced communication designed to affect the minds of a given group for a specific purpose, whether military, economic or political† (Linearger, p. 39, 1954). This has connotations of dishonesty and while people assume it is a modern phenomenon, its roots go back much further. The question is however, was propaganda rife in 5th century BCE Athens and if so, was it the driving force whether explicitly or not behind many of the public displays? A funeral oration or epitaphios logos is an official speech delivered at a funeral. The epitaphios is regarded as a virtually unique Athenian concept, although early elements of such speeches exist in the Epic poetry of Homer and in Lyric poetry of Pindar; in addition modern parallels have been drawn between Lincoln’s Gettysburg address and Pericles. When Pericles gave the epitaphios for Athenian soldiers who had been killed in the first year of the Peloponnesian War. He took the opportunity to not only praise the deceased, but Athens itself, in an oration which has been both praised as enshrining the archetypal democratic system and condemned as barefaced propaganda. In Thucydides’ book History of the Peloponnesian War, Pericles’ Funeral Oration is a powerful rhetorical piece. In addition it is important evidence for the study of the Athenian sense of identity and the way they represented themselves and others. It eloquently discusses the ancient democratic model and the picture it portrays serves as a prototype for democratic states today (Abbott, 1970). Thucydides specified a man would be chosen to make an ‘appropriate speech’ i. e. it matched formulaic prescriptions of the epitaphios, which according to Edinger, â€Å"consisted of a number of recognised topics: praise of the dead, praise of the ancestors, praise of the city, consolation of the families of the dead.