Information: - The colonial colleges are nine institutions of higher education chartered in the American Colonies before the United States of America became a sovereign 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 member of the Ivy League, Cornell University, was founded in 1865.) - In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" (also called "nodes" or "points") and each of the related pairs of vertices is called an "edge" (also called an "arc" or "line"). Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. - In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects. In many such problems, exhaustive search is not feasible. It operates on the domain of those optimization problems, in which the set of feasible solutions is discrete or can be reduced to discrete, and in which the goal is to find the best solution. Some common problems involving combinatorial optimization are the travelling salesman problem ("TSP") and the minimum spanning tree problem ("MST"). - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets "S" indexed by the natural numbers, enumerative combinatorics seeks to describe a "counting function" which counts the number of objects in "S" for each "n". Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description. The twelvefold way provides a unified framework for counting permutations, combinations and partitions. - Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects (numbers, graphs, vectors, sets, etc.) can be, if it has to satisfy certain restrictions. - Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics). - In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions. - Algebra (from Arabic ""al-jabr"" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. - Herbert Saul Wilf ( June 13 , 1931 -- January 7 , 2012 ) was a mathematician , specializing in combinatorics and graph theory . He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania . He wrote numerous books and research papers . Together with Neil Calkin he founded The Electronic Journal of Combinatorics in 1994 and was its editor - in - chief until 2001 . - The Association of American Universities (AAU) is an international organization of leading research universities devoted to maintaining a strong system of academic research and education. It consists of 60 universities in the United States (both public and private) and two universities in Canada. - 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", "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. - Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. - Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of "balance" and/or "symmetry". These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in Sudoku grids. - A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br> It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. - 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. - Pennsylvania (Pennsylvania German: "Pennsylvaani"), officially the Commonwealth of Pennsylvania, is a state located in the northeastern and Mid-Atlantic regions of the United States. The Appalachian Mountains run through its middle. The commonwealth borders Delaware to the southeast, Maryland to the south, West Virginia to the southwest, Ohio to the west, Lake Erie and the Canadian province of Ontario to the northwest, New York to the north, and New Jersey to the east. - 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 academic excellence, selectivity in admissions, and social elitism. What is the relationship between 'herbert wilf' and 'philadelphia'?
place of birth