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# Topic: Field (mathematics)

 Field (mathematics) - Wikipedia, the free encyclopedia In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. For a given field F, the set F(X) of rational functions in the variable X with coefficients in F is a field; this is defined as the set of quotients of polynomials with coefficients in F. Differential field, a field equipped with a derivation. en.wikipedia.org /wiki/Field_(mathematics)   (1374 words)

 Field theory (mathematics) - Wikipedia, the free encyclopedia Field theory is a branch of mathematics which studies the properties of fields. Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex numbers. For instance, the field of algebraic numbers is the algebraic closure of the field of rational numbers and the field of complex numbers is the algebraic closure of the field of real numbers. en.wikipedia.org /wiki/Field_theory_(mathematics)   (615 words)

 Field (mathematics) In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication, and division (except division by zero) may be performed and the associative, commutative, and distributive rules hold, which are familiar from the arithmetic of ordinary number s. Fields are important objects of study in algebra since they provide the proper generalization of number domains, such as the sets of rational numbers, real numbers, or complex number s. The concept of a field is of use, for example, in defining vector s and matrices, two structures in linear algebra whose components can be elements of an arbitrary field. www.nebulasearch.com /encyclopedia/article/Field_(mathematics).html   (1243 words)

 Encyclopedia :: encyclopedia : Field (mathematics)   (Site not responding. Last check: 2007-10-22) A structure which satisfies all the properties of a field except for commutativity, is today called a division ring or sometimes a skew field, but also non-commutative field is still widely used. An algebraic number field is a finite field extension of the rational numbers Q, that is, a field containing Q which has finite dimension as a vector space over Q. The surreal numbers form a Field containing the reals, and would be a field except for the fact that they are a proper class, not a set. www.hallencyclopedia.com /Field_(mathematics)   (1584 words)

 Mathematics...Artilifes.com Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers". Mathematics is widely acknowledged as probably the only perfect science, in the sense that the solutions it gives (from proven theorems) are absolute and stand the test of time. Mathematics might accordingly be seen as an extension of spoken and written natural languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. www.artilifes.com /mathematics.html   (1110 words)

 Field (mathematics) - Search Results - MSN Encarta   (Site not responding. Last check: 2007-10-22) Field (mathematics), set of elements that can be operated on according to rules that satisfy certain properties. Mathematics, a way of describing relationships between numbers and other measurable quantities. This international prize for achievement in the field of mathematics is awarded every four years by the International Mathematical Union at the... encarta.msn.com /Field_(mathematics).html   (146 words)

 Field - Wikipedia, the free encyclopedia Field (mathematics), one of a class of objects studied in abstract algebra, in which one can add, subtract, multiply, and divide. Field (geography), with a definition similar to that of physics but in a different context and using unique models and methods Visual field or field of view, the area visible from a point of view (it can be a camera or an eye) en.wikipedia.org /wiki/Field   (479 words)

 Mathematics 9-12   (Site not responding. Last check: 2007-10-22) Field experiences are coordinated so that each candidate demonstrates experience and competence in a wide range of high school settings serving diverse student populations and learning needs. The program is based on the premise that the most effective facilitator of learning in the high school mathematics classroom is one who has an understanding of the student, of mathematics, and of mathematics pedagogy. In field experiences and student teaching, evidence of pedagogical and content knowledge, including the use of technology and the ability to assess student learning and develop appropriate instruction, is documented in evaluations of candidates by public school teachers and administrators as well as university supervisors. www.wingate.edu /SACS/NCDPI/mathematics_912.htm   (2955 words)

 Marlboro College : Academics One finds that a mathematical form that represents competition in an ecology course stands a good chance of being the same one that represents a chemical reaction or a knight's move on a chess board. Mathematics is a field that (by its own structure) uses forms to investigate itself. Indeed, learning mathematics at Marlboro is learning to spot the reflections of one course in another and to see that there is a great unity and beauty to the subject. www.marlboro.edu /academics/study/mathematics   (468 words)

 Department of Mathematics and Statistics The Department of Mathematics and Statistics provides an environment that is conducive to and promotes the understanding of mathematics and statistics by all students, encourages community and institutional service, and encourages and supports continued faculty development and scholarship. MTH 031D Developmental Mathematics I. This course deals with fundamental operations involving whole numbers, fractions, decimals and percents, ratio and proportion, interpretation of graphs, geometry, and introductory algebra including axioms and properties of the real number system, fundamental operations involving algebraic expressions, fi rst and second degree equations and inequalities in one unknown. MTH 476 Topics in Applied Mathematics I. This course, in conjunction with MTH 376, is intended to develop a basic competence in areas of mathematics that are used in solving problems from the physical sciences. www.shsu.edu /catalog/mth.html   (2383 words)

 UIC Graduate College -- Programs: Mathematics   (Site not responding. Last check: 2007-10-22) Study and research is available in the general areas of pure mathematics, applied mathematics, probability and statistics, mathematical computer science, the teaching of mathematics, and an integrated interdisciplinary curriculum combining mathematics, computer science, project management and communication skills. If a candidate is not certified to teach mathematics at the secondary level in Illinois, up to 8 elective hours may be selected from courses in psychology or education, if taken at the graduate level. Mathematics courses must be chosen so that the areas of computer science, differential equations, geometry, logic, and probability and statistics are all represented. www.uic.edu /depts/grad/programs/math.shtml   (1501 words)

 Department of Mathematics: Welcome Page A major in mathematics features applications of mathematics in the physical sciences and computer science, providing knowledge and skills required for entry level positions in business, industry or secondary education. Mathematics can be coupled with Psychology to pursue the graduate level Psychometry degree and work with statistical data in psychological research. Mathematics is also vital in supplementing the medical school preparatory program. www.sterling.edu /academics/math   (224 words)

 Mathematicians In fact, because mathematics is the foundation on which so many other academic disciplines are built, the number of workers using mathematical techniques is much greater than the number formally designated as mathematicians. In early 2005, the average annual salary for mathematicians employed by the Federal Government in supervisory, nonsupervisory, and managerial positions was \$88,194; that for mathematical statisticians was \$91,446; and for cryptanalysts the average was \$70,774. A strong background in mathematics also facilitates employment as teachers—postsecondary; teachers—preschool, kindergarten, elementary, middle, and secondary; engineers; economists; market and survey researchers; financial analysts and personal financial advisors; and physicists and astronomers. www.bls.gov /oco/ocos043.htm   (1727 words)

 Department of Mathematics and Statistics The required field examination is a comprehensive oral examination given near the end of coursework. The general aim of the program leading to the Ph.D. in mathematics is to prepare students to become productive research scholars capable of communicating their knowledge to students and to the mathematical community. The program is planned to develop in the student a fundamental understanding of certain basic fields of mathematics, a deep understanding of the major field of interest, the ability to formulate and recognize significant research problems, and the ability to analyze problems and reach solutions and to transmit ideas to others. www.albany.edu /grad/department_mathematics_statistics.html   (1159 words)

 Field (mathematics) The concept of a field is of use, for example, in defining vectorss and matrices, two structures in linear algebra whose components can be elements of an arbitrary field. It has important uses in computer science, especially in cryptography and coding theory. If F is a field, and p(X) is an irreducible polynomial in the polynomial ring F[X], then the quotient F[X]/ www.brainyencyclopedia.com /encyclopedia/f/fi/field__mathematics_.html   (1281 words)

 PCC :: Mathematics Education Major Our knowledge of God's absolute mathematical laws may be incomplete or at times in error, but that is a human frailty and thus does not indicate relativity in mathematical laws. A student whose high school mathematics background includes a precalculus course may begin his mathematics sequence with MA 221 Calculus I. He would take two upper-level mathematics courses in lieu of MA 122 College Algebra II and MA 131 College Trigonometry. EG 241 may be taken as a mathematics elective (minimum grade of “C”) for those who need or want to take it. www.pcci.edu /Academics/Majors/Education/Mathematics.html   (254 words)

 MIT OpenCourseWare | Mathematics | 18.238 Geometry and Quantum Field Theory, Fall 2002 | Syllabus The development of quantum field theory and string theory in the last two decades led to an unprecedented level of interaction between physics and mathematics, incorporating into physics such "pure" areas of mathematics as algebraic topology, algebraic geometry, and even number theory. In particular, even the basic setting of quantum field theory, necessary for understanding its more advanced (and mathematically exciting) parts, is already largely unknown to mathematicians. Nevertheless, many of the basic ideas of quantum field theory can in fact be presented in a completely rigorous and mathematical way. ocw.mit.edu /OcwWeb/Mathematics/18-238Fall2002/Syllabus/index.htm   (311 words)

 Department of Mathematics There are many good reasons to study mathematics: preparation for a career, use in another field, or the beauty of the subject itself. Students at Colgate who concentrate in mathematics go on to careers in medicine, law, or business administration as well as areas of industry and education having an orientation in science. Non-concentrators often require mathematical skills to carry on work in other disciplines, and all students can use the study of mathematics to assist them in forming habits of precise expression, in developing their ability to reason logically, and in learning how to deal with abstract concepts. www.colgate.edu /DesktopDefault1.aspx?tabid=2324&pgID=3434   (130 words)

 Fields Institute - Mathematics Education Forum   (Site not responding. Last check: 2007-10-22) The Fields Institute Mathematics Education Forum promotes discussion of issues in mathematics education at all levels, with special emphasis on education in the Province of Ontario. It is the goal of the Forum to consider objectively new ideas and diverse views in mathematics education, to facilitate consensus and to promote the enhancement of mathematics education in Ontario and Canada. To subscribe to the Fields Institute electronic maillist to receive announcements about activities in the field of mathematics education please subcribe here. www.fields.utoronto.ca /programs/mathed/meforum/index.html   (249 words)

 Cornell College - Mathematics Department - Field of Study Observing that the three in "the three bears" is the same as the three in "a three-day weekend" is a first step towards the idea of counting. Seeing that the basic rules of logic, set theory and computer circuits are essentially the same leads to understanding in philosophy and computer science as well as in mathematics. Students in many fields must be comfortable with the skills and ideas of calculus. www.cornellcollege.edu /mathematics/mathatcornell.shtml   (118 words)

 Agnes Scott College | Graduate and Post-Baccalaureate Programs | M.A.T. Secondary Mathematics Curriculum   (Site not responding. Last check: 2007-10-22) A three-semester sequence in which mathematical ideas are developed from a teacher’s perspective, enhanced by two undergraduate courses to fill gaps in the student’s background. The program is designed to link coursework that strengthens the disciplinary content in the teaching field (mathematics), coursework in areas of application, and professional education courses, including field experiences and a 12-week student teaching experience in the spring. Reflection on both human interactions and mathematics encountered during student teaching, filling disciplinary gaps, deepening understanding of the nature and history of mathematics and its importance to individuals as citizens. www.agnesscott.edu /graduateandpost-bacc/p_matmathematicscurriculum.asp   (825 words)

 Geertsema Mathematics and Christianity has only recently developed sufficient constituency to actively organize and publish a journal. The Association of Christians in the Mathematical Sciences (ACMS) formally organized in 1985. Journal of the Association of Christians in the Mathematical Sciences, December 2004. www.asa3.org /ASA/topics/Mathematics/index.html   (290 words)

 Field (mathematics) - Search Results - MSN Encarta Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes,... Algebra, branch of mathematics in which symbols represent relationships. Classical algebra grew out of methods of solving equations; it represents... uk.encarta.msn.com /Field_(mathematics).html   (136 words)

 Open Directory - Science: Math: History   (Site not responding. Last check: 2007-10-22) History and Overview - Front for the Mathematics Arxiv of eprints section HO: biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics. Mathematics in Latvia throughout the Centuries - Covers the early mathematical development in the country, such as the use of geometrical symbols. Renaissance Mathematics - Discusses the technological, commercial and political reasons for the increase in mathematical development during this period. dmoz.org /Science/Math/History   (1074 words)

 CSU, SAN MARCOS - Special Field in Mathematics   (Site not responding. Last check: 2007-10-22) The Mathematics Special Field builds on the mathematics required for the Liberal Studies lower-division core to provide depth in exposure to the power, beauty, and utility of mathematical thought. In studying mathematics, students develop the ability to explore, to conjecture, and to reason logically, as well as the ability to use effectively a variety of mathematical methods to solve problems. As a result, students are better prepared to teach according to the new standards called for at the elementary and middle school level, or to enter careers in government or private industry. www.csusm.edu /Math/mathSpecField.html   (266 words)

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