occupation john robert kline
Athanasios Papoulis ( 1921  April 25 , 2002 ) was a Greek - American ___MASK25___ and applied ___MASK70___ . Robert Lee Moore ( November 14 , 1882  October 4 , 1974 ) was an American ___MASK70___ , known for his work in general topology and the Moore method of teaching university mathematics . The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States . The conference name is also commonly used to refer to those eight schools as a group beyond the sports context . The eight institutions are Brown University , Columbia University , Cornell University , Dartmouth College , Harvard University , the University of Pennsylvania , Princeton University , and Yale University . The term " Ivy League " has connotations of ___MASK99___ excellence , selectivity in admissions , and social elitism . Engineers design materials , structures , and systems while considering the limitations imposed by practicality , regulation , safety , and cost . The word " ___MASK25___ (" from the Latin " ingeniator "")" is derived from the Latin words " ingeniare " (" to contrive , devise ") and " ingenium " (" cleverness "). The foundation education of an ___MASK25___ is typically a 4 - year bachelor ' s degree or in some countries , a ___MASK34___ ' s degree in an engineering discipline plus 4  6 years ___MASK53___ - reviewed professional practice culminating in a project report or thesis . Engineers who seek a professional ___MASK25___ license in N . America will be required to take further exams in ethics , law and professional practice . The Moore method is a deductive manner of instruction used in advanced mathematics courses . It is named after Robert Lee Moore , a famous ___MASK62___ who first used a stronger version of the method at the University of Pennsylvania when he began teaching there in 1911 . In mathematics graph theory is the study of " graphs ", which are mathematical structures used to ___MASK12___ pairwise relations between objects . A graph in this context is made up of " vertices ", " nodes ", or " points " which are connected by " edges ", " arcs ", or " lines ". A graph may be " undirected ", meaning that there is no distinction between the two vertices associated with each edge , or its edges may be " directed " from one vertex to another ; see Graph ( discrete mathematics ) for more detailed definitions and for other variations in the types of graph that are commonly considered . Graphs are one of the prime objects of study in discrete mathematics . The colonial colleges are nine institutions of higher education chartered in the American Colonies before the ___MASK79___ became a ___MASK50___ nation after the American Revolution . These nine have long been considered together , notably in the survey of their origins in the 1907 " The Cambridge History of English and American Literature ". Seven of the nine colonial colleges are part of the Ivy League athletic conference : Harvard , Yale , Penn , Princeton , Columbia , Brown , and Dartmouth . ( The eighth ___MASK93___ of the Ivy League , Cornell University , was founded in 1865 .) The Association of American Universities ( AAU ) is an international organization of leading ___MASK41___ universities devoted to maintaining a strong system of academic ___MASK41___ and education . It consists of 60 universities in the United States ( both public and private ) and two universities in ___MASK78___ . Tibor Gallai ( born Tibor Grünwald , 15 July 1912  2 January 1992 ) was a Hungarian ___MASK70___ . He worked in combinatorics , especially in graph theory , and was a lifelong friend and collaborator of Paul Erds . He was a student of Dénes Knig and an advisor of László Lovász . He was a corresponding member of the Hungarian Academy of Sciences ( 1991 ). In mathematics , ___MASK35___ topology is the branch of topology that deals with the basic set - theoretic definitions and constructions used in topology . It is the foundation of most other branches of topology , including differential topology , geometric topology , and algebraic topology . Another name for ___MASK35___ topology is point - set topology . The University of Pennsylvania ( commonly known as Penn or UPenn ) is a private , Ivy League university located in Philadelphia , Pennsylvania , United States . Incorporated as " The Trustees of the University of Pennsylvania ", Penn is one of 14 founding members of the Association of American Universities and one of the nine original colonial colleges . Arthur Norton Milgram ( 3 June 1912 , in Philadelphia  30 January 1961 ) was an American ___MASK70___ . He made contributions in functional analysis , combinatorics , differential geometry , topology , partial differential equations , and Galois theory . Perhaps one of his more famous contributions is the Lax  Milgram theorem  a theorem in functional analysis that is particularly applicable in the study of partial differential equations . In the third chapter of Emil Artin ' s book " Galois Theory ", Milgram also discussed some applications of Galois theory . Milgram also contributed to graph theory , by co - authoring the article " Verallgemeinerung eines graphentheoretischen Satzes von Rédei " with Tibor Gallai in 1960 . A ___MASK70___ is someone who uses an extensive knowledge of mathematics in his / her work , typically to solve mathematical problems . Emil Artin ( March 3 , 1898  December 20 , 1962 ) was an Austrian ___MASK70___ . Artin was one of the leading mathematicians of the twentieth century . He is best known for his work on algebraic number theory , contributing largely to class field theory and a new construction of L - functions . He also contributed to the pure theories of rings , groups and fields . John Robert Kline ( 1891 -- 1955 ) was a US - American Professor of Mathematics at the University of Pennsylvania from 1920 to 1955 . A Ph . D . ___MASK55___ of Robert Lee Moore , he was a Guggenheim Fellow in 1925 , later Chairman of the Department of Mathematics from 1933 to 1954 and Thomas A . Scott Professor of Mathematics from 1941 to 1955 . His doctoral students include Lida Barrett , Arthur Milgram , Athanasios Papoulis , Dudley Weldon Woodard , and Leo Zippin .