A Guide to Hollywood Film Practitioners - Michael Mann essays

A Guide to Hollywood Film Practitioners - Michael Mann essays Michael Manns life is not as open and public as many of his colleagues and rivals in Hollywood, but over the last few years he has been brought into the forefront through his increasingly impressive work, which will hit a peak this year with the release of his latest offering, Ali. Mann was born in Chicago on 5th February, 1943. After High School, he attended the University of Wisconsin, from there he moved to London, and the London International Film School. All in all, Mann spent 7 years in London, attending Film school, and also directing commercials and documentaries. Mann moved back to USA after his time in England, and in the 70s began writing for American television, working on shows such as Starsky and Hutch. In 1979, Mann directed his first TV movie, The Jericho Mile, which won him an award for Outstanding Directorial Achievement in Specials, and acted as a springboard for his move away from television, and towards Hollywood. Manns first foray into film directing was Thief (1981). Even though this was a critical success, the relatively unknown director, caused Thief to be a box-office failure. One of the main things that Thief did was introduce many tropes that run throughout Manns work to this day. Mann, in many ways, is an old-fashioned director. He likes to create the right atmosphere for all his films, and scenes within, and there is more than one example of this in Thief. Attempting to recreate rush hour at 2am, complete with rain, Mother Nature failed to provide this, so he ordered a 60,000 gallon water truck to keep both the streets and actors soaked, for 12 hours. This among other examples in Thief, such as the scene where Caan blows up his characters house, a real house was used and the immediate neighbours were moved to a hotel for the three days of shooting, which showed that Mann was and still is a Alt...

Set Theory and How It Is Used

Set Theory and How It Is Used Set theory is a fundamental concept throughout all of mathematics.  This branch of mathematics forms a foundation for other topics.   Intuitively a set is a collection of objects, which are called elements. Although this seems like a simple idea, it has some far-reaching consequences.   Elements The elements of a set can really be anything – numbers, states, cars, people or even other sets are all possibilities for elements. Just about anything that can be collected together may be used to form a set, though there are some things we need to be careful about. Equal Sets Elements of a set are either in a set or not in a set. We may describe a set by a defining property, or we may list the elements in the set. The order that they are listed is not important. So the sets {1, 2, 3} and {1, 3, 2} are equal sets, because they both contain the same elements. Two Special Sets Two sets deserve special mention. The first is the universal set, typically denoted U. This set is all of the elements that we may choose from. This set may be different from one setting to the next. For example, one universal set may be the set of real numbers whereas for another problem the universal set may be the whole numbers {0, 1, 2,...}.   The other set that requires some attention is called the empty set. The empty set is the unique set is the set with no elements. We can write this as { } and denote this set by the symbol ∅. Subsets and the Power Set A collection of some of the elements of a set A is called a subset of A. We say that A is a subset of B if and only if every element of A is also an element of B. If there are a finite number n of elements in a set, then there are a total of 2n subsets of A. This collection of all of the subsets of A is a set that is called the power set of A. Set Operations Just as we can perform operations such as addition - on two numbers to obtain a new number, set theory operations are used to form a set from two other sets. There are a number of operations, but nearly all are composed from the following three operations: Union – A union signifies a bringing together. The union of the sets A and B consists of the elements that are in either A or B.Intersection - An intersection is where two things meet. The intersection of the sets A and B consists of the elements that in both A and B.Complement - The complement of the set A consists of all of the elements in the universal set that are not elements of A. Venn Diagrams One tool that is helpful in depicting the relationship between different sets is called a Venn diagram.  A rectangle represents the universal set for our problem.  Each set is represented with a circle.  If the circles overlap with one another, then this illustrates the intersection of our two sets.   Applications of Set Theory Set theory is used throughout mathematics. It is used as a foundation for many subfields of mathematics. In the areas pertaining to statistics, it is particularly used in probability. Much of the concepts in probability are derived from the consequences of set theory. Indeed, one way to state the axioms of probability involves set theory.