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Projective Set (game)
Projective Set (sometimes shortened to ProSet) is a real-time card game derived from the older game ''Set''. The deck contains cards consisting of colored dots; some cards are laid out on the table and players attempt to find "Sets" among them. The word ''projective'' comes from the game's relation to projective spaces over the finite field with two elements. Projective Set has been studied mathematically as well as played recreationally. It has been a popular game at Canada/USA Mathcamp. Rules A Projective Set card has six binary attributes, or bits, generally represented by colored dots. For each color of dot, each card either has that dot or does not. There is one card for each possible combination of dots except the combination of no dots at all, making 2^6 - 1 = 63 cards total. Three cards are said to form a "set" if the total number of dots of each color is either 0 or 2. Similarly, four or more cards form a "set" if the number of dots of each color is an even numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turns, Rounds And Time-keeping Systems In Games
Timekeeping is relevant to many types of games, including video games, tabletop role-playing games, board games, and sports. The passage of time must be handled in a way that players find fair and easy to understand. In many games, this is done using real-time and/or turn-based timekeeping. In real-time games, time within the game passes continuously. However, in turn-based games, player turns represent a fixed duration within the game, regardless of how much time passes in the real world. Some games use combinations of real-time and turn-based timekeeping systems. Players debate the merits and flaws of these systems. There are also additional timekeeping methods, such as timelines and progress clocks. Real-time In real-time games, time progresses continuously. This may occur at the same or different rates from the passage of time in the real world. For example, in '' Terraria'', one day-night cycle of 24 hours in the game is equal to 24 minutes in the real world. In a mult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Card Game
A card game is any game that uses playing cards as the primary device with which the game is played, whether the cards are of a traditional design or specifically created for the game (proprietary). Countless card games exist, including families of related games (such as poker). A small number of card games played with traditional decks have formally standardized rules with international tournaments being held, but most are folk games whose rules may vary by region, culture, location or from circle (cards), circle to circle. Traditional card games are played with a ''deck'' or ''pack'' of playing cards which are identical in size and shape. Each card has two sides, the ''face'' and the ''back''. Normally the backs of the cards are indistinguishable. The faces of the cards may all be unique, or there can be duplicates. The composition of a deck is known to each player. In some cases several decks are Shuffling, shuffled together to form a single ''pack'' or ''shoe''. Modern car ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (game)
''Set'' (stylized as SET or SET!) is a real-time card game designed by Marsha Falco in 1974 and published by Set Enterprises in 1991. The deck consists of 81 unique cards that vary in four features across three possibilities for each kind of feature: number of shapes (one, two, or three), shape (diamond, squiggle, oval), shading (solid, striped, or open), and color (red, green, or purple). Each possible combination of features (e.g. a card with three striped green diamonds) appears as a card precisely ''once'' in the deck. Gameplay In the game, certain combinations of three cards are said to make up a "set". For each one of the four categories of features—color, number, shape, and shading—the three cards must display that feature as either a) all the same, or b) all different. Put another way: For each feature the three cards must ''avoid'' having two cards showing one version of the feature and the remaining card showing a different version. For example, 3 solid red di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GF(2)
(also denoted \mathbb F_2, or \mathbb Z/2\mathbb Z) is the finite field with two elements. is the Field (mathematics), field with the smallest possible number of elements, and is unique if the additive identity and the multiplicative identity are denoted respectively and , as usual. The elements of may be identified with the two possible values of a bit and to the Boolean domain, Boolean values ''true'' and ''false''. It follows that is fundamental and ubiquitous in computer science and its mathematical logic, logical foundations. Definition GF(2) is the unique field with two elements with its additive identity, additive and multiplicative identity, multiplicative identities respectively denoted and . Its addition is defined as the usual addition of integers but modulo 2 and corresponds to the table below: If the elements of GF(2) are seen as Boolean values, then the addition is the same as that of the logical XOR operation. Since each element equals its opposite (m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canada/USA Mathcamp
Canada/USA Mathcamp is a five-week academic summer program for middle and high school students in mathematics. Mathcamp was founded in 1993 by Dr. George Thomas, who believed that students interested in mathematics frequently lacked the resources and camaraderie to pursue their interest. Mira Bernstein became the director when Thomas left in 2002 to found MathPath, a program for younger students. Mathcamp is held each year at a college campus in the United States or Canada. Past locations have included the University of Toronto, the University of Washington, Colorado College, Reed College, University of Puget Sound, Colby College, the University of British Columbia, Mount Holyoke College, and the Colorado School of Mines. Mathcamp enrolls about 120 students yearly, 55 returning and 65 new. The application process for new students includes an entrance exam (the "Qualifying Quiz"), personal essay, but no grade reports or letters of recommendation (although a reference, who may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector (mathematics And Physics)
In mathematics and physics, vector is a term that refers to physical quantity, quantities that cannot be expressed by a single number (a scalar (physics), scalar), or to elements of some vector spaces. Historically, vectors were introduced in geometry and physics (typically in mechanics) for quantities that have both a magnitude and a direction, such as displacement (geometry), displacements, forces and velocity. Such quantities are represented by geometric vectors in the same way as distances, masses and time are represented by real numbers. The term ''vector'' is also used, in some contexts, for tuples, which are finite sequences (of numbers or other objects) of a fixed length. Both geometric vectors and tuples can be added and scaled, and these vector operations led to the concept of a vector space, which is a set (mathematics), set equipped with a vector addition and a scalar multiplication that satisfy some axioms generalizing the main properties of operations on the abov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Examples Of Vector Spaces
This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension (vector space), dimension, basis (linear algebra), basis. ''Notation''. Let ''F'' denote an arbitrary Field (mathematics), field such as the real numbers R or the complex numbers C. Trivial or zero vector space The simplest example of a vector space is the trivial one: , which contains only the zero vector (see the third axiom in the Vector space article). Both vector addition and scalar multiplication are trivial. A Basis (linear algebra), basis for this vector space is the empty set, so that is the 0-Dimension (vector space), dimensional vector space over ''F''. Every vector space over ''F'' contains a Linear subspace, subspace isomorphic to this one. The zero vector space is conceptually different from the null space of a linear operator ''L'', which is the Kernel (linear algebra), kernel of ''L''. (Incidentally, the null space of ''L'' is a z ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diane Maclagan
Diane Margaret Maclagan (born 1974) is a professor of mathematics at the University of Warwick. She is a researcher in combinatorial and computational commutative algebra and algebraic geometry, with an emphasis on toric varieties, Hilbert schemes, and tropical geometry. Education and career As a student at Burnside High School in Christchurch, New Zealand, Maclagan competed in the International Mathematical Olympiad in 1990 and 1991, earning a bronze medal in 1991. As an undergraduate, she studied at the University of Canterbury, graduating in 1995. She did her PhD at the University of California, Berkeley, graduating in 2000. Her dissertation, ''Structures on Sets of Monomial Ideals'', was supervised by Bernd Sturmfels. After postdoctoral research at the Institute for Advanced Study, Maclagan was a Szegő Assistant Professor at Stanford University from 2001 to 2004, an assistant professor at Rutgers University from 2004 to 2007, then an associate professor there from 2007 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
