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# Topic: Group (mathematics)

###### In the News (Wed 17 Apr 19)

 Group (mathematics) Groups underlie the other algebraic structures such as fieldss and vector spaces and are also important tools for studying symmetry in all its forms. A group that we are introduced to in elementary school is the integers under addition. Given a group G and a normal subgroup N, the quotient group is the set of cosets of G/N together with the operation (gN)(hN)=ghN. www.teachersparadise.com /ency/en/wikipedia/g/gr/group__mathematics_.html   (1656 words)

 TU Delft - Dr. Johannes Bruining Geostatistical modeling of fractal fields: Outcome: Improved spectral model to compute fractal fields and multiscale and multiresolution stochastic modelling of subsurface heterogeneity by tree-indexed Markov chains (TU-working group+ post-doc) Focus: mathematical aspects of improved models involving analysis of shocks, bifurcations, finite condensation rates and mixing mechanisms (one Ph-D student in Brazil) Enhanced mass transfer of CO into water and oil by density-driven natural convection www.tudelft.nl /live/pagina.jsp?id=f5c42462-96ff-4326-afc9-e1ea042a7158&lang=nl   (382 words)

 Group theory Summary Group theory is one of a number of branches of mathematics that have proven useful to chemists and physicists in their work. Group theory is that branch of mathematics concerned with the study of groups. Groups are used throughout mathematics, often to capture the internal symmetry of other structures, in the form of automorphism groups. www.bookrags.com /Group_theory   (3252 words)

 Group (mathematics) - Wikipedia, the free encyclopedia Previous to this work, groups were mainly studied concretely, in the form of permutations; some aspects of abelian group theory were known in the theory of quadratic forms. A group that we are introduced to in elementary school is the integers under addition. You can perform division in groups; that is, given elements a and b of the group G, there is exactly one solution x in G to the equation x * a = b and exactly one solution y in G to the equation a * y = b. en.wikipedia.org /wiki/Group_(mathematics)   (1972 words)

 AllRefer.com - group (Mathematics) - Encyclopedia The real numbers (see number) form a commutative group both under addition, with 0 as identity element and -a as inverse, and, excluding 0, under multiplication, with 1 as identity element and 1/a as inverse. The elements of a group need not be numbers; they may often be transformations, or mappings, of one set of objects into another. Group theory has wide applications in mathematics, including number theory, geometry, and statistics, and is also important in other branches of science, e.g., elementary particle theory and crystallography. reference.allrefer.com /encyclopedia/G/group.html   (298 words)

 Encyclopedia: Group (mathematics)   (Site not responding. Last check: ) Group theory is that branch of mathematics concerned with the study of groups. Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. The mathematical concept of a group is one of the fundamental notions of modern algebra. www.nationmaster.com /encyclopedia/Group-(mathematics)   (1051 words)

 Group - Wikipedia, the free encyclopedia Group (mathematics), a set together with a binary operation satisfying certain algebraic conditions in group theory Group (sociology), a sub-set of a culture or of a society Functional group, a functional entity consisting of certain atoms whose presence provides a certain property to a molecule. en.wikipedia.org /wiki/Group   (216 words)

 Group (mathematics)   (Site not responding. Last check: ) Previous to this work, groups were mainly studied concretely, in the form of permutations; some aspects of abelian group theory were known in the theory of quadratic forms. A group that we are introduced to in elementary school is the integers under addition. You can perform division in groups; that is, given elements a and b of the group G, there is exactly one solution x in G to the equation x * a = b and exactly one solution y in G to the equation a * y = b. www.guideofpills.com /Group_%28mathematics%29.html   (2060 words)

 Combining Individual and Group Evaluations Mathematics classes are small, with a maximum of 20 students in calculus sections and even fewer students in upper level courses. Seven of ten problems on one discrete mathematics group test asked students to determine whether a statement is true or false and to provide either a proof or counterexample with a full explanation; one such statement was: The square of an integer has the form 4k or 4k + 1 for some integer k. The group assignments, which vary with each course, comprise challenging problems that are submitted and graded Students in all the courses have time to become acclimated to the course before the individual work counts heavily, and no students have withdrawn from my Calculus I classes in recent years. www.maa.org /saum/maanotes49/134.html   (2269 words)

 Group (mathematics) Info - Encyclopedia WikiWhat.com   (Site not responding. Last check: ) A great many of the objects investigated in mathematics turn out to be groups, including familiar number systems, such as the integers, rational, real, and complex numbers under addition, non-zero rational, real, and complex numbers under multiplication, non-singular matricies under multiplication, invertable functions under composition, and so on. Groups underlie the other algebraic structures such as fieldss and vector spaces and are also important tools for studying symmetry in all its forms. A group (G,*) is defined as a set G together with a binary operation *: G × G → G. www.wikiwhat.com /encyclopedia/g/gr/group__mathematics_.html   (1657 words)

 Group (mathematics)   (Site not responding. Last check: ) Groups underlie many other algebraic structures such as fields and vector spaces and are also important tools for studying symmetry in all its forms. For these reasons, group theory is considered to be an important area in modern mathematics, and it has many applications to mathematical physics (for example, in particle theory). A group (G, *) is a nonempty set G together with a binary operation * ;: G × G → G, satisfying the group axioms. www.alloffinance.com /Group_%28mathematics%29.html   (2482 words)

 !GROUP THEORY! Along with the set of the group, thereis a binary operation such that when one element operates on another thenthe result is still an element in the set. Given a finite group (G,*)-where G isthe set of the group and the * is the binary operation; and give a andb being elements of the set G; then a*b=b*a. Whena free group is given a number of operations then the most general groupthat can be built from them using the powers of these elements and theinverses of the powers. www.geocities.com /CapeCanaveral/Hangar/9302/group.html   (3637 words)

 Department of Mathematics at MIT | Undergraduate Study: Degree Options Applied Mathematics and Theoretical Mathematics) lead to the degree Bachelor of Science in Mathematics, and the fourth (Mathematics with Computer Science) to the degree Bachelor of Science in Mathematics with Computer Science. Applied mathematics is the mathematical study of general scientific concepts, principles, and phenomena that, because of their widespread occurrence and application, relate or unify various disciplines. Theoretical mathematics (or "pure" mathematics) is the study of the basic concepts and structures that underlie the mathematical tools used in science and engineering. math.mit.edu /undergraduate/degree-options.html   (896 words)

 Groups of Transformations in Music Mathematics has been called the science of quantity, primarily because its fundamental objects are numbers, (numbers which measure quantity, amount,...) and groups appear automatically in various kinds of numbers. To see this group as a group of translations is easy, it is a group of discrete translations of the set of integers it self. The table on the left is an abstraction for the multiplicative group of {1, -1, i, -i}, where i is the square root of (-1). graham.main.nc.us /~bhammel/MUSIC/group.html   (1521 words)

 ADEA: Working Group on Mathematics and Science Education The Working Group on Mathematics and Science Education (WGMSE) was created in November 2004 to contribute to the improvement of Africa's mathematics and science education (MSE) programs and their greater adaptation to the challenges of the 21st century. Every year, the working group will train a number of trainers in MSE from selected countries to strengthen institutional capacities in MSE, muster broader participation of experienced and interested participants and widen the circulation and the dissemination of the knowledge and skills in the area of mathematics and science education. The working group seeks to upgrade the capacity of practitioners and responsible educators to improve their ability to conduct participatory evaluation and action research based on their own experience, and to be able to communicate results more widely. www.adeanet.org /workgroups/en_wgmse.html   (959 words)

 Guide to the Mathematics Subject Classification Scheme One way to divide the mathematics literature is to decide which books and articles are designed to reveal the structure of mathematics itself, and which are intended to apply mathematics to closely allied areas. Algebra is principally concerned with symmetry, patterns, discrete sets, and the rules for manipulating arithmetic operations; one might think of this as the outgrowth of arithmetic and algebra classes in primary and secondary school. The second broad part of the mathematics literature includes those areas which could be considered either independent disciplines or central parts of mathematics, as well as those areas which clearly use mathematics but are interested in non-mathematical ideas too. www.math.niu.edu /~rusin/known-math/index/beginners.html   (5525 words)

 Group Theory at the Library of Math (Free Online Mathematics)   (Site not responding. Last check: ) One of the main unifying themes in mathematics, group theory originated from concrete examplesinvolving the study of polynomials in the earlypart of the 1800's. In this topic, many examples are given to explain the importance of permutation groups when the underlying set is a finite set of counting numbers; and the matrix form and cycle notation of such permutations are detailed so as to fully explore the groups of permutations of finite sets of counting numbers (called symmetric groups). Basically, the center of a group is the collection of elements in the group that commute with all elements in the group and the centralizer of a given element in the group is the collection of all elements in the group that commute with that given element. libraryofmath.com /Group_Theory.html   (1788 words)

 Math Forum: Learning and Mathematics: Small group interactions - Yackel, Cobb, & Wood Children were grouped in pairs and spent half of each math period working together to solve math problems. Work was not graded, nor was there a set amount of work to be completed; rather, the teacher gave report card grades based on her knowledge of the children, and the students were allowed to spend as much time as they needed to discuss each problem and arrive at a solution. Thus the authors believe that social situations are crucial in mathematics instruction, especially with regard to allowing the child to construct and modify his or her own mathematical knowledge. mathforum.org /~sarah/Discussion.Sessions/Yackel.html   (998 words)

 Open Directory - Science: Math: Algebra: Group Theory Computational Tools for Group Theory - Describes work to create a program that could be used to generate, identify, and analyze finite groups presented in the form of a Cayley Table as well as visualize the groups that are generated. Group Action Forum - Association for the study of the theory of transformation groups and related topics. Group Theory is a branch of algebra, but has strong connections with almost all parts of mathematics. dmoz.org /Science/Math/Algebra/Group_Theory   (626 words)

 group - Search Results - MSN Encarta Group (mathematics), a basic structure of modern algebra, consisting of a set of elements and an operation. Map of Group of Eight (map of member countries) Map of Group of 77 (map of member countries) encarta.msn.com /encnet/refpages/search.aspx?q=group   (195 words)

 Study Group Mathematics with Industry 2005 The 52nd European Study Group Mathematics with Industry (ESGI52), also known as Studiegroup Wiskunde met de Industrie (SWI2005), was held from 31st January until 4th February 2005 at the Department of Mathematics of the Vrije Universiteit in Amsterdam. The next study group in the Netherlands, will be held in Eindhoven from January 30 to February 3, 2006: SWI2006 website. In a week of brainstorming and mathematical modelling there is usually enough time to generate and reject many ideas for solving the problem, and usually some of the ideas are checked in more detail. www.few.vu.nl /~swi2005   (710 words)

 The Math Forum - Math Library - Group Theory Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this way. Group theory takes an abstract approach, dealing with many mathematical systems at once and requiring only that a mathematical system obey a few simple rules, seeking then to find properties common to all systems that obey these few rules. A mathematics professor at Ben Gurion University of the Negev in Israel. mathforum.org /library/topics/group_theory   (2240 words)

 Department of Mathematics Applied mathematics is a research area of increasing importance in the Department of Mathematics. The Applied Mathematics Group has interests in wave scattering and imaging, nonlinear dynamics, mechanics and geometry, and the work spans the areas of theoretical modelling, computational modelling and applications, including industrial applications as well as the theoretical development of the mathematical framework of large classes of models. The Applied Mathematics Group has a strong international reputation that is built on significant interactions with other mathematicians, scientists and engineers, in Australia and internationally, and is demonstrated by its work with scientific and industrial organisations, such as the DSTO and the CSIRO, and their overseas counterparts. www.maths.mq.edu.au /research/groups.html   (668 words)

 Applied Mathematics   (Site not responding. Last check: ) The language, tools and theorems of mathematics are applied in a vast range of disciplines within engineering and computer science, the physical sciences, the biomedical sciences, management and economics, psychology, etc. As a field of study and research applied mathematics lies at the borderline between mathematics and its applications. While not easily defined with any great precision applied mathematics involves the application of interesting mathematical tools to significant applied problems or to the development of novel mathematics adapted to particular applications. Nilima Nigam): Computational mathematical sciences are now having a huge impact on the biological sciences, from models of disease-spread to gene transcription to the study of cellular processes and dynamics. www.math.mcgill.ca /department/appliedmath.php   (826 words)

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