In North America, this level is generally referred to as graduate school. The organization and structure of education varies in different countries. This article outlines the types of courses and of teaching and examination methods. There are two types of degrees studied for at the postgraduate level and vocational degrees. The term degree in this means the moving from one stage or level to another. University studies took six years for a degree and up to twelve additional years for a masters degree or doctorate. The first six years taught the faculty of the arts, which was the study of the seven liberal arts, geometry, music theory, logic, the main emphasis was on logic. Once a Bachelor of Arts degree had been obtained, the student could choose one of three faculties—law, medicine, or theology—in which to pursue masters or doctors degrees. Because theology was thought to be the highest of the subjects, the main significance of the higher, postgraduate degrees was that they licensed the holder to teach.
In most countries, the hierarchy of postgraduate degrees is as follows, in Scottish Universities, the Master of Philosophy degree tends to be by research or higher masters degree and the Master of Letters degree tends to be the taught or lower masters degree. In many fields such as social work, or library science in North America. Professional degrees such as the Master of Architecture degree can last to three and a years to satisfy professional requirement to be an architect. Professional degrees such as the Master of Business Administration degree can last up to two years to satisfy the requirement to become a business leader. These are often divided into academic and professional doctorates. An academic doctorate can be awarded as a Doctor of Philosophy degree or as a Doctor of Science degree, a doctorate is the terminal degree in most fields. In the United States, there is distinction between a Doctor of Philosophy degree and a Doctor of Science degree. In the second half of the 19th century, however, US universities began to follow the European model by awarding doctorates, in the UK, an equivalent formation to doctorate is the NVQ5 or QCF8.
Most universities award degrees, usually at the postgraduate level
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois. It holds top-ten positions in national and international rankings and measures. The university currently enrolls approximately 5,700 students in the College, Chicagos physics department helped develop the worlds first man-made, self-sustaining nuclear reaction beneath the viewing stands of universitys Stagg Field. The university is home to the University of Chicago Press. With an estimated date of 2020, the Barack Obama Presidential Center will be housed at the university. Both Harper and future president Robert Maynard Hutchins advocated for Chicagos curriculum to be based upon theoretical and perennial issues rather than on applied sciences, the University of Chicago has many prominent alumni. 92 Nobel laureates have been affiliated with the university as professors, faculty, or staff, similarly,34 faculty members and 16 alumni have been awarded the MacArthur “Genius Grant”. Rockefeller on land donated by Marshall Field, while the Rockefeller donation provided money for academic operations and long-term endowment, it was stipulated that such money could not be used for buildings.
The original physical campus was financed by donations from wealthy Chicagoans like Silas B, Cobb who provided the funds for the campus first building, Cobb Lecture Hall, and matched Marshall Fields pledge of $100,000. Organized as an independent institution legally, it replaced the first Baptist university of the same name, william Rainey Harper became the modern universitys first president on July 1,1891, and the university opened for classes on October 1,1892. The business school was founded thereafter in 1898, and the law school was founded in 1902, Harper died in 1906, and was replaced by a succession of three presidents whose tenures lasted until 1929. During this period, the Oriental Institute was founded to support, in 1896, the university affiliated with Shimer College in Mount Carroll, Illinois. The agreement provided that either party could terminate the affiliation on proper notice, several University of Chicago professors disliked the program, as it involved uncompensated additional labor on their part, and they believed it cheapened the academic reputation of the university.
The program passed into history by 1910, in 1929, the universitys fifth president, Robert Maynard Hutchins, took office, the university underwent many changes during his 24-year tenure. In 1933, Hutchins proposed a plan to merge the University of Chicago. During his term, the University of Chicago Hospitals finished construction, the Committee on Social Thought, an institution distinctive of the university, was created. Money that had been raised during the 1920s and financial backing from the Rockefeller Foundation helped the school to survive through the Great Depression, during World War II, the university made important contributions to the Manhattan Project. The university was the site of the first isolation of plutonium and of the creation of the first artificial, in the early 1950s, student applications declined as a result of increasing crime and poverty in the Hyde Park neighborhood
In mathematics, a proof is an inferential argument for a mathematical statement. In the argument, other previously established statements, such as theorems, in principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference. Axioms may be treated as conditions that must be met before the statement applies, Proofs are examples of exhaustive deductive reasoning or inductive reasoning and are distinguished from empirical arguments or non-exhaustive inductive reasoning. A proof must demonstrate that a statement is true, rather than enumerate many confirmatory cases. An unproved proposition that is believed to be true is known as a conjecture, Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in language instead of natural language, are considered in proof theory.
The distinction between formal and informal proofs has led to examination of current and historical mathematical practice, quasi-empiricism in mathematics. The philosophy of mathematics is concerned with the role of language and logic in proofs, the word proof comes from the Latin probare meaning to test. Related modern words are the English probe and probability, the Spanish probar, Italian provare, the early use of probity was in the presentation of legal evidence. A person of authority, such as a nobleman, was said to have probity, whereby the evidence was by his relative authority, plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. It is likely that the idea of demonstrating a conclusion first arose in connection with geometry, the development of mathematical proof is primarily the product of ancient Greek mathematics, and one of the greatest achievements thereof. Thales proved some theorems in geometry and Theaetetus formulated theorems but did not prove them.
Aristotle said definitions should describe the concept being defined in terms of other concepts already known and his book, the Elements, was read by anyone who was considered educated in the West until the middle of the 20th century. Further advances took place in medieval Islamic mathematics, while earlier Greek proofs were largely geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry. In the 10th century CE, the Iraqi mathematician Al-Hashimi provided general proofs for numbers as he considered multiplication, division and he used this method to provide a proof of the existence of irrational numbers. An inductive proof for arithmetic sequences was introduced in the Al-Fakhri by Al-Karaji, alhazen developed the method of proof by contradiction, as the first attempt at proving the Euclidean parallel postulate. Modern proof theory treats proofs as inductively defined data structures, there is no longer an assumption that axioms are true in any sense, this allows for parallel mathematical theories built on alternate sets of axioms
The Fields Medal is sometimes viewed as the highest honor a mathematician can receive. The Fields Medal and the Abel Prize have often described as the mathematicians Nobel Prize. The Fields Medal differs from the Abel in view of the age restriction mentioned above, the prize comes with a monetary award, which since 2006 has been C$15,000. The colloquial name is in honour of Canadian mathematician John Charles Fields, Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component. The medal was first awarded in 1936 to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas and its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. The Fields Medal is often described as the Nobel Prize of Mathematics, however, in contrast to the Nobel Prize, the Fields Medal is awarded only every four years. The Fields Medal has an age limit, a recipient must be under age 40 on 1 January of the year in which the medal is awarded and this is similar to restrictions applicable to the Clark Medal in economics.
The monetary award is lower than the 8,000,000 Swedish kronor given with each Nobel prize as of 2014. Other major awards in mathematics, such as the Abel Prize, in 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27. In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, léon Motchane and director of the Institut des Hautes Études Scientifiques attended and accepted Grothendiecks Fields Medal on his behalf. In 1970, Sergei Novikov, because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Nice to receive his medal. In 1978, Grigory Margulis, because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Helsinki to receive his medal. In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, the awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at the 1983 Warsaw congress. In 1990, Edward Witten became the first physicist to win this award, in 1998, at the ICM, Andrew Wiles was presented by the chair of the Fields Medal Committee, Yuri I.
Manin, with the first-ever IMU silver plaque in recognition of his proof of Fermats Last Theorem, don Zagier referred to the plaque as a quantized Fields Medal. Accounts of this award frequently make reference that at the time of the award Wiles was over the age limit for the Fields medal. Although Wiles was slightly over the age limit in 1994, he was thought to be a favorite to win the medal, however, in 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal and did not attend the congress. In 2014, Maryam Mirzakhani became the first woman as well as the first Iranian, Artur Avila the first South American and this is a list of the universities that have graduated Fields medalists
A Beautiful Mind (film)
A Beautiful Mind is a 2001 American biographical drama film based on the life of John Nash, a Nobel Laureate in Economics. The film was directed by Ron Howard, from a written by Akiva Goldsman. It was inspired by a bestselling, Pulitzer Prize-nominated 1998 book of the name by Sylvia Nasar. The film stars Russell Crowe, along with Ed Harris, Jennifer Connelly, Paul Bettany, Adam Goldberg, Judd Hirsch, Josh Lucas, Anthony Rapp, the story begins in Nashs days as a graduate student at Princeton University. Early in the film, Nash begins to develop paranoid schizophrenia and endures delusional episodes while painfully watching the loss and burden his condition brings on wife Alicia, the film opened in the United States cinemas on December 21,2001. It went on to gross over $313 million worldwide and won four Academy Awards, for Best Picture, Best Director, Best Adapted Screenplay and it was nominated for Best Actor, Best Film Editing, Best Makeup, and Best Original Score. It was well received by critics, but has criticized for its inaccurate portrayal of some aspects of Nashs life, especially his other family.
However, the filmmakers have stated that the film was not meant to be a literal representation, in 1947, John Nash arrives at Princeton University. He is co-recipient, with Martin Hansen, of the prestigious Carnegie Scholarship for mathematics, at a reception, he meets a group of other promising math and science graduate students, Richard Sol and Bender. He meets his roommate Charles Herman, a literature student, Nash is under extreme pressure to publish, but he wants to publish his own original idea. His inspiration comes when he and his graduate students discuss how to approach a group of women at a bar. Hansen quotes Adam Smith and advocates every man for himself, Nash develops a new concept of governing dynamics and publishes an article on this. On the strength of this, he is offered an appointment at MIT where Sol, some years later, Nash is invited to the Pentagon to crack encrypted enemy telecommunication. Nash can decipher the code mentally, to the astonishment of other decrypters and he is to look for patterns in magazines and newspapers in order to thwart a Soviet plot.
Nash becomes increasingly obsessive about searching for hidden patterns and believes he is followed when he delivers his results to a secret mailbox. Meanwhile, a student, Alicia Larde, asks him to dinner, on a return visit to Princeton, Nash runs into Charles and his niece, Marcee. With Charles encouragement, he proposes to Alicia and they marry, Nash begins to fear for his life after witnessing a shootout between Parcher and Soviet agents, but Parcher blackmails him into staying on his assignment. While delivering a guest lecture at Harvard University, Nash tries to flee from people he thinks are foreign Russian agents, after punching Rosen in an attempt to flee, Nash is forcibly sedated and sent to a psychiatric facility he believes is run by the Soviets
Proof is a 2000 play by the American playwright David Auburn. The play premiered Off-Broadway in May 2000, and transferred to Broadway in October 2000, the play won the 2001 Pulitzer Prize for Drama and Tony Award for Best Play. Catherine had cared for her father through a mental illness. Upon Roberts death, his ex-graduate student Hal discovers a paradigm-shifting proof about prime numbers in Roberts office, the title refers both to that proof and to the plays central question, Can Catherine prove the proofs authorship. Along with demonstrating the authenticity, the daughter finds herself in a relationship with 28-year-old Hal. Throughout, the play explores Catherines fear of following in her fathers footsteps, Act I The play opens with Catherine sitting alone in the backyard of her large, old house. Robert, her father, approaches her with a bottle of champagne to celebrate her 25th birthday, Catherine complains that she hasnt done any worthwhile work in the field of mathematics, at least not to the same level as her father, a well-known math genius.
He reassures her that she can still do work as long as she stops lying in bed till all hours. Catherine confesses shes worried about inheriting Roberts inclination towards mental instability and he begins to comfort her but alludes to a bad sign when he points out that he is, in fact, dead. Robert disappears as Catherine dozes off and she awakens when Hal, one of Roberts students, exits the house. Hes been studying the hundreds of notebooks Robert left behind after his death, Catherine assures him that the notebooks are filled with scribbles and nonsense since her father wrote them when he was at his most delusional. Hal, attempting to flirt, invites her to go see his band that night, Catherine becomes suspicious of him and demands to see whats in his backpack. She roots through it to nothing but becomes infuriated when a notebook falls out of Hals jacket. She dials the police while accusing him of trying to steal her fathers work and he admits that he was sneaking it away but only to give it back to her as a birthday present.
He opens to a page that Robert wrote during a time when he was lucid, in it, Robert writes its a good day and thanks to Catherine for taking care of him and expresses hope for the future. Hal leaves Catherine with the notebook and she begins to cry until she hears police sirens. The next day Claire, Catherines sister who just flew in from New York, is setting up a large brunch for them in the backyard, Catherine enters and Claire tries to goad her into idle chitchat as Catherine quietly seethes. Claire declares shes getting married and invites Catherine to stay with her and her fiance in New York, Catherine assures her shell come in January for the wedding, but Claire keeps pressing her to go earlier
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, quantity, space, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked.
Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, overall, science became the focus of universities in the 19th and 20th centuries.
Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
Jacob Benjamin Jake Gyllenhaal is an American actor. He subsequently appeared in indie film, The Good Girl. In 2005, Gyllenhaal portrayed Anthony Swoff Swofford in Jarhead, Gwyneth Paltrows love interest in Proof, Gyllenhaal was born in Los Angeles, the son of film producer and screenwriter Naomi Foner and film director Stephen Gyllenhaal. Actress Maggie Gyllenhaal, his sister, appeared with him in the film Donnie Darko. Gyllenhaals father, who was raised as a Swedenborgian, is of Swedish and English descent, jakes last ancestor to be born in Sweden was his great-great-grandfather, Anders Leonard Gyllenhaal. Jakes mother is Jewish, she was born in New York City, to a family from Russia, Gyllenhaal has said that he considers himself Jewish. His parents insisted that he have summer jobs to support himself and he worked as a lifeguard. Gyllenhaal said his parents encouraged artistic expression, I do have parents who supported me in certain ways. In other ways, they were lacking, its in expression and creativity where my family has always been best at.
As a child, Gyllenhaal was regularly exposed to filmmaking due to his familys ties to the industry. He made his debut as Billy Crystals son in the 1991 comedy film City Slickers. His parents did not allow him to appear in the 1992 film The Mighty Ducks because it would have required his leaving home for two months, in subsequent years, his parents allowed him to audition for roles but regularly forbade him to take them if he were chosen. He was allowed to appear in his fathers films several times, Gyllenhaal appeared in the 1993 film A Dangerous Woman, in Bop Gun, a 1994 episode of Homicide, Life on the Street, and in the 1998 comedy Homegrown. Along with their mother and Maggie appeared in two episodes of Molto Mario, an Italian cooking show on the Food Network. Prior to his year in high school, the only other film not directed by his father, in which Gyllenhaal was allowed to perform, was the 1993 film Josh. Gyllenhaal dropped out two years to concentrate on acting but has expressed intentions to eventually finish his degree.
The film earned $32 million and was described in the Sacramento News, Donnie Darko, Gyllenhaals second film, was not a box office success upon its initial 2001 release but eventually became a cult favorite. After the critical success of Donnie Darko, Gyllenhaals next role was as Pilot Kelston in 2002s Highway alongside Jared Leto and his performance was described by one critic as silly and straight to video
Mary-Louise Parker is an American actress and author. Parker is the recipient of the 2001 Tony Award for Best Actress for her performance in the Broadway play Proof and she starred in When We Rise. Parker was born in Fort Jackson, South Carolina, the youngest of four children, she is the daughter of Caroline Louise and John Morgan Parker, a judge who served in the U. S. Army. Her ancestry includes Swedish, Scottish, Scots-Irish, because of her fathers career, Parker spent parts of her childhood in Tennessee and Texas, as well as in Thailand and France. She described her childhood as unhappy, further noting that, My parents did everything they could, I had books, clothes, a home and a warm bed. She graduated from Marcos de Niza High School in Tempe, Parker majored in drama at the North Carolina School of the Arts and graduated in 1986. Parker got her start in acting with a role on the soap opera Ryans Hope, in the late 1980s, Parker moved to New York. After a few roles, she made her Broadway debut in a 1990 production of Craig Lucas Prelude to a Kiss.
She moved with the production when it transferred from its origin Off-Broadway, Parker won the Clarence Derwent Award for her performance and was nominated for a Tony Award. In addition, she appeared alongside Matthew Modine in Tim Hunters The Maker, Parkers theater career continued when she appeared in Paula Vogels 1997 critical smash How I Learned to Drive, with David Morse. In the late 1990s, she appeared in independent films, including Let the Devil Wear Black. She starred alongside Sidney Poitier in the 1999 movie The Simple Life of Noah Dearborn, on December 7,2003, HBO aired a six-and-a-half-hour adaptation of Tony Kushners acclaimed Broadway play Angels in America, directed by Mike Nichols. Parker played Harper Pitt, the Mormon Valium-addicted wife of a closeted lawyer, for her performance, Parker received Golden Globe and Emmy awards for Best Supporting Actress in a Miniseries. Parker took the role that had been Mia Farrows on screen. The production, directed by Mark Brokaw, earned Parker another nomination for a Tony Award for Best Actress in 2005, in November 2005, Parker was the subject of a career exhibition at Boston University, where memorabilia from her career were donated to the Universitys library.
In that category, she defeated the four leads of Desperate Housewives and she dedicated the award to the late John Spencer, known for his work as Leo McGarry on The West Wing. After receiving the award, Parker stated, Im really in favor of legalizing marijuana, I dont think its that controversial. In March 2007, Parker played the role in the television film The Robber Bride