3 The language of proof In Section 3 we examine the language used to express mathematical statements and proofs, and discuss various techniques for proving that a mathematical statement is true. These techniques include direct proof, proof by mathematical induction, proof by contradiction and proof by contraposition. We also illustrate the use of counter-examples to show that a statement is false. Click the link below to open Section 3 (17 pages, 374KB).
4.2 An introduction to the Board of Trade photographs It is important to bear in mind that these shots show the bridge remains in the state they were in just after the accident, and are almost exactly what the investigators would have seen when they inspected the bridge (see Input 8, linked below). Click 'View document' below to open Input 8 London DataStore DataBlog Dealing With Controversial Issues Pill bug curled up on back Westward Expansion Farewell2iCube Kobe schools Chinese on the court Stiglitz: Enemy of the Free Market People, Power, and Profits: Progressive Capitalism for an Age of Discontent. By Joseph E. Stiglitz. Norton, 2019. Xxvii + 371 pages. Joseph Stiglitz is an eminent economist, but it is evident from People, Power, and Profits that he is a moralist as well, and one of a peculiar sort. Early in the book, he says this: “to answer such questions [about what to do] I have to explain the true source of wealth, distinguishing wealth creation from wealth extraction. The 18.315 Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics (M What Is Broadcast Journalism? Menu costs at work : restaurant prices and the introduction of the Euro IAS Plus 1.9.6 On the right lines: summing up Timetables and distance-time graphs are different representations of scheduled train movements. They are both models which can be used to predict when trains will run, to analyse and compare different schedules when problems occur, and to design new operating schedules to meet new demands. Both models provide information which allows the company to operate safely and flexibly. The information is used by different groups of people: Microsoft Campus Tours - The Connector With thousands of employees coming to the Microsoft Redmond campus every day, getting around can be a challenge. The Microsoft Connector team manage a large fleet of buses, vans and on-demand cars to get people to and from their meetings, their offices and back home again. Season 3 – Lesson 27 – Coffee Break Spanish This week we return to a topic we covered previously – in response to listeners’ requests. It’s time to look at your tricks and tips for language learning. Mark and Alba talk about the suggestion of one of our listeners which involves printing out internet texts and cutting out the words. Listen to the episode for more information and further suggestions! Language topics this week include the alternative forms of the possessive adjectives including mÃo, 1.5 Vitamin K Like vitamin E, vitamin K is fat-soluble and composed of a series of related compounds. Vitamin K is widely distributed in the diet (see Table 1) and it is absorbed from the small intestine with the assistance of bile acids. Vitamin K is also manufactured by the bacteria that inhabit the human large intestine and appears to be absorbed there too. The main role of vitamin K is in blood clotting. This process requires the presence of a number of different chemicals, called clotting factors, in 4.6 Gender and power in the workplace If you are, or have been, employed in a health and social care service, think about the ways in which gendered power ‘works’ in that setting. If y Researcher attacking Zika virus by stirring up mosquitoes’ taste buds
The London DataStore is maintained by the Greater London Authority. It seeks to provide free open access to government statistical datasets relating to London. These include materials relating to business and the economy; political transparency and the work of the Greater London Assembly and Mayor of London (including expenses of the mayor and London Assembly members); crime; the population and demography of London; employment, health, housing and crime rates in London. The site includes statist
The Guardian's DataBlog contains links to a range of data via their datastore ( a directory of all the statistics that they post and publish pertaining to current affairs) which can be downloaded in various formats incl. MS Excel. This site (which compliments the Guardina's 'free-our-data' campaign) has links to Environmental data, US data, in addition to a range of -easy-to-use visualisation and sharing Web 2.0 tools and APIs. The Blog also acts as a discussion forum for data in the public doma
This program examines how social studies teachers in any grade level can encourage open and informed discussions with their students while dealing with controversial issues. Topics range from stereotypes and gender–based discrimination to the conflict in the Middle East. Through clearly identifying issues, listening to multiple perspectives, and formulating personal positions, teachers can explore a variety of
strategies that can be used to teach challenging issues such as these in thei
Many pill bugs curl up in a ball to protect themselves. Pill bugs use their antennae to feel around their environment. They use their eyes to see where they are going. They use their legs to walk or crawl around.
By the mid-nineteenth century, the American economy that had been based on local commerce and small-scale farming was maturing into a dynamic, wide-reaching capitalist marketplace. As the industrial revolution in the northeast altered the economy and intensified the process of urbanization, an agricultural empire began to emerge in the west, and westward expansion began. In this video you will learn about westward expansion and it's trials and tribulations. (Video is of high q
Announcing the end of iCube. Thanks to all of our listeners throughout the 9 years of our podcast series. Visit our new series, Psychological Science, at: https://itunes.apple.com/us/podcast/psychological-science/id1016929637.
NBA All-Star Kobe Bryant delights fans in Shanghai on the start of his summer tour in China. Nathan Frandino reports.
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Reuters tells the world's stories like no one else. As the largest international multimedia news provider, Reuters provides coverage around the globe and across topics including business, financial, national, and international news. For over 160 years, Reuters has main
This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.
Broadcast journalism used to be restricted to TV and radio
only, but now the Internet plays an integral role in the field of
broadcasting the news through blogs, videos and station Web sites.
A former TV news anchors explains the the definition of broadcast journalism with insider information in this clip. Words shown on bottom of screen as we see the head shot of the CEO speaking. (1:13)
This paper on menu costs by Bart Hobijn, Federico Ravenna and Andrea Tambalotti was originally published in the Quarterly Journal of Economics, Volume 121, August 2006. "Restaurant prices in the euro area increased dramatically after the introduction of the euro. We argue that this increase can be explained by a common model of menu cost pricing, extended to include the state-dependent decision of firms on when to adopt the new currency. Two mechanisms drive this result. First, firms concentrate
'The International Accounting Standards Board (IASB), formerly International Accounting Standards Committee (IASC), sets standards for business financial statements. This website, maintained by Deloitte Touche Tohmatsu, provides free comprehensive information about international financial reporting. ' It is presented in blog-style format, with the latest standards news, plus giving many useful links to more information or other finance websites. for example, there is information on major bodies
Coming up in this lesson:
Activity 16
Summer is here, and the United States is bracing for the mosquito-transmitted Zika virus. A Vanderbilt researcher is working on one way to stop the spread of the disease – by revving up the mosquito’s taste buds.
