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Paul Chester Kainen
Paul Chester Kainen is an American mathematician, an adjunct associate professor of mathematics and director of the Lab for Visual Mathematics at Georgetown University. Kainen is the author of a popular book on the four color theorem, and is also known for his work on book embeddings of graphs. Biography Kainen received his Bachelor of Arts degree from George Washington University in 1966 and was awarded the Ruggles Prize for Excellence in Mathematics. He went on to get his Ph.D. from Cornell University in 1970 with Peter Hilton Peter John Hilton (7 April 1923Peter Hilton, "On all Sorts of Automorphisms", '' The American Mathematical Monthly'', 92(9), November 1985, p. 6506 November 2010) was a British mathematician, noted for his contributions to homotopy theory and ... as his thesis advisor. Kainen's father was the American artist Jacob Kainen. Selected publications *. 2nd ed., Dover, 1986, , . *. References External linksHome pageat GeorgetownPaul Kainen's Page on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georgetown University
Georgetown University is a private university, private research university in the Georgetown (Washington, D.C.), Georgetown neighborhood of Washington, D.C. Founded by Bishop John Carroll (archbishop of Baltimore), John Carroll in 1789 as Georgetown College (Georgetown University), Georgetown College, the university has grown to comprise eleven Undergraduate education, undergraduate and Postgraduate education, graduate schools, including the School of Foreign Service, Walsh School of Foreign Service, McDonough School of Business, Georgetown University School of Medicine, Medical School, Georgetown University Law Center, Law School, and a Georgetown University in Qatar, campus in Qatar. The school's main campus, on a hill above the Potomac River, is identifiable by its flagship Healy Hall, a National Historic Landmark. The school was founded by and is affiliated with the Society of Jesus, and is the oldest Catholic institution of higher education in the United States, though the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four Color Theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubters remain. The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map). To dispel any remaining doubts about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Book Embedding
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings into a ''book'', a collection of half-planes all having the same line as their boundary. Usually, the vertices of the graph are required to lie on this boundary line, called the ''spine'', and the edges are required to stay within a single half-plane. The book thickness of a graph is the smallest possible number of half-planes for any book embedding of the graph. Book thickness is also called pagenumber, stacknumber or fixed outerthickness. Book embeddings have also been used to define several other graph invariants including the pagewidth and book crossing number. Every graph with vertices has book thickness at most \lceil n/2\rceil, and this formula gives the exact book thickness for complete graphs. The graphs with book thickness one are the outerplanar graphs. The graphs with book thickness at most two are the subhamiltonian graphs, which are always planar; more generally, ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruggles Prize
William Ruggles (September 5, 1797 – September 10, 1877) was a professor at George Washington University. Biography William Ruggles was born in Rochester, Massachusetts, about fifty miles south of present-day Boston, on Tuesday September 5, 1797. He was the son of Elisha Ruggles and Mary Clap who also parented six other children: Nathaniel, Micah, Henry, Charles, James, and Lucy. William was the second youngest child in his family. Not much is known about his childhood growing up in Massachusetts until he enrolled in Brown University; where he later graduated from, at the age of twenty-three, in the class of 1820. Two years after graduating from Brown University, Ruggles became a tutor at Columbian College. On February 9, 1821 Congress chartered Columbian College, a nonsectarian school but with Baptist sponsorship that would not become the George Washington University until January 23, 1904. In 1824, two years after he became a tutor, Ruggles became a Professor of Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Hilton
Peter John Hilton (7 April 1923Peter Hilton, "On all Sorts of Automorphisms", '' The American Mathematical Monthly'', 92(9), November 1985, p. 6506 November 2010) was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during World War II. Early life He was born in Brondesbury, London, the son Mortimer Jacob Hilton, a Jewish physician who was in general practice in Peckham, and his wife Elizabeth Amelia Freedman, and was brought up in Kilburn. The physiologist Sidney Montague Hilton (1921–2011) of the University of Birmingham Medical School was his elder brother. Hilton was educated at St Paul's School, London."About the speaker"announcement of a lecture given by Peter Hilton at Bletchley Park on 12 July 2006. Retrieved 18 January 2007. He went to The Queen's College, Oxford in 1940 to read mathematics, on an open scholarship, where the mathematics tutor was Ughtred Haslam-Jones. Bletchley Park A wartime undergraduate in wartime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Kainen
Jacob Kainen (December 7, 1909 – March 19, 2001) was an American painter and printmaker. He is also known as an art historian, writing books on John Baptist Jackson (US Government Printing Office, Washington, DC, 1962) and the etchings of Canaletto (Smithsonian Press, Washington, DC, 1967). In addition, Kainen was a collector of German Expressionist art, and he and his second wife, Ruth, donated a collection of this work to the National Gallery of Art in 1985. Biography Jacob Kainen was born in Waterbury, Connecticut, in 1909. As the second of three sons born to Russian immigrants, Kainen grew up in a family that appreciated culture and talent. His father's artistry as an inventor and his mother's love for music and literature undoubtedly fostered in Kainen an insatiable interest in art. Even at age ten, Kainen was eager to study master works, including clippings of art reproductions from ''The Jewish Daily Forward'' in his scrapbooks. In 1918 the family moved to New York ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Combinatorial Theory
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. An electronic, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman empero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theorists
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discrete mathematics * Graph of a function *Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing * Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software This is a list of software to create any kind of information graphics: * either includes the ability t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbian College Of Arts And Sciences Alumni
Columbian is the adjective form of Columbia. It may refer to: Buildings * The Columbian Theatre, a music hall in northeastern Kansas * The Columbian (Chicago), a building in Illinois Published works * ''The Columbian'', a daily newspaper published in Vancouver, Washington, U.S. * '' Olympia Pioneer and Democrat'', the first newspaper published in what is now the state of Washington, was known in its first two years (1852-53) as ''The Columbian''. * '' The Columbian Orator'', a collection of political essays, poems, and dialogues first published in 1797 * ''Columbian Magazine'', a monthly magazine published from 1786 to 1792 Transportation * ''Columbian'' (B&O train), a passenger train operated by Baltimore and Ohio Railroad until 1971 * ''Columbian'' (MILW train), a passenger train which operated from 1911 to 1955 * Sternwheeler ''Columbian'' disaster, a sternwheeler lost in the worst accident in the Yukon River's history in 1906 Other uses * Columbian (typography), a nam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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