Field extension

In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q that includes every real solution to the equation x² = 2.

Definitions

Let L be a field. A subfield of L is a subset K of L that is closed under the field operations of L and under taking inverses in L. In other words, K is a field with respect to the field operations inherited from L. The larger field L is then said to be an extension field of K. To simplify notation and terminology, one says that L / K (read as "L over K") is a field extension to signify that L is an extension field of K.

If L is an extension of F which is in turn an extension of K, then F is said to be an intermediate field (or intermediate extension or subextension) of the field extension L / K.

Academic degree

An academic degree is the state of recognized completion of studies at a school or university. A diploma is generally issued in recognition of having satisfactorily completed the prescribed course of study. The two most common degrees awarded today are associate and bachelor's.

Higher education institutions commonly offer master’s, doctoral, academic certificates, and professional degrees.

Overview

The modern academic system of academic degrees evolved and expanded in the medieval university, spreading everywhere across the globe as the institution did:

Emergence of the doctor’s and master’s degrees and the licentiate

The doctorate (Latin: doceo “I teach”) appeared in medieval Europe as a license to teach (Latin: licentia docendi) at a medieval university. Its roots can be traced to the early church when the term "doctor" referred to the Apostles, church fathers and other Christian authorities who taught and interpreted the Bible. The right to grant a licentia docendi was originally reserved to the church which required the applicant to pass a test, to take oath of allegiance and pay a fee. The Third Council of the Lateran of 1179 guaranteed the access – now largely free of charge – of all able applicants, who were, however, still tested for aptitude by the ecclesiastic scholastic. This right remained a bone of contention between the church authorities and the slowly emancipating universities, but was granted by the Pope to the University of Paris in 1231 where it became a universal license to teach (licentia ubique docendi). However, while the licentia continued to hold a higher prestige than the bachelor's degree (Baccalaureus), it was ultimately reduced to an intermediate step to the Magister and doctorate, both of which now became the exclusive qualification for teaching.

Vision (festival)

Vision is the annual national-level technical symposium of Department of Electronics and Communication Engineering, Anna University, Chennai. It was started in 1997 to promote technology and entrepreneurship in India. Vision 2013 was held April 10–12, 2013.

References

Vision statement

A vision statement is a declaration of an organization's objectives, ideally based on economic foresight, intended to guide its internal decision-making.

Definition and structure

A vision statement is a company's road map, indicating both what the company wants to become and guiding transformational initiatives by setting a defined direction for the company's growth. Vision statements undergo minimal revisions during the life of a business, unlike operational goals which may be updated from year-to-year. Vision statements can range in length from short sentences to multiple pages. Vision statements are also formally written and referenced in company documents rather than, for example, general principles informally articulated by senior management. A vision statement is not limited to business organizations and may also be used by non-profit or governmental entities.

A consensus does not exist on the characteristics of a "good" or "bad" vision statement. Commonly cited traits include:

Vision (Marvel Comics)

The Vision is the name of multiple fictional superheroes appearing in American comic books published by Marvel Comics. The first Vision was an alien created by Joe Simon and Jack Kirby that first appeared in Marvel Mystery Comics # 13 (November 1940). The second Vision is an android and a member of the Avengers that first appeared in The Avengers #57 (October 1968) by Roy Thomas, Stan Lee and John Buscema. The third Vision was the time traveler previously known as Iron Lad, who was fused with the operating system of the second Vision. The second Vision was portrayed by Paul Bettany in the 2015 film Avengers: Age of Ultron; he will reprise the role in the 2016 film Captain America: Civil War.

Publication history

The first Vision was created by the writer-artist team of Joe Simon and Jack Kirby in Marvel Mystery Comics #13 (Nov. 1940), published by Marvel predecessor Timely Comics during the 1930s and 1940s, a period which fans and historians call the Golden Age of Comic Books.