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Topic: Reciprocity (mathematics)

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	Reciprocity - Wikipedia, the free encyclopedia
		Reciprocity (international relations), a principle that favours, benefits, or penalties that are granted by one state to the citizens or legal entities of another, should be returned in kind.
		Reciprocity (Canadian politics), 19th Century concept of free trade with the United States of America.
		Reciprocity (photography), the relationship between the intensity of the light and duration of the exposure that result in identical exposure.
	en.wikipedia.org /wiki/Reciprocity (292 words)

	Reciprocity (social psychology) - Wikipedia, the free encyclopedia
		Positive reciprocal actions differ from altruistic actions as they only follow from other positive actions and they differ from social gift giving in that they are not actions taken with the hope or expectation of future positive responses.
		Reciprocal actions are important to social psychology as they can help explain the maintenance of social norms.
		In public good experiments, behavioral economists have demonstrated that the potential for reciprocal actions by players increases the rate of contribution to the public good, providing evidence for the importance of reciprocity in social situations (Fehr and Gatcher, 2003).
	en.wikipedia.org /wiki/Reciprocity_(social_psychology) (289 words)

	Reciprocity Theorem - Search Results - MSN Encarta
		Reciprocity, in international relations, the policy, usually formalized by two or more countries signing a treaty, of granting equally advantageous...
		Theorem, proposition or formula in mathematics or logic that is provable from a set of postulates and basic assumptions.
		Postulate (mathematics), statement that has not been proven but is assumed to be true.
	encarta.msn.com /encnet/refpages/search.aspx?q=Reciprocity+Theorem (138 words)

	History overview
		The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC.
		Further mathematical discoveries were driven by the astronomy, for example the study of trigonometry.
		Copernicus and Galileo revolutionised the applications of mathematics to the study of the universe.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/History_overview.html (1886 words)

	Untitled
		MATH112 is not open to Mathematics and Mathematics Education majors except by permission of the chairperson.
		This seminar has featured such topics as the study of the history of mathematics, the impact and potential effects of computers upon society, and the study of mathematics as it occurs with society in the forms of puzzles, games, and other types of recreation.
		Mathematical logic, set theory, relevant topological and algebraic properties together with proof techniques are heavily utilized throughout the course.
	www.lhup.edu /academic/acad_affairs/MATHEMATICS.htm (1870 words)

	Photo Tips
		Reciprocity failure is a term bandied about by photographers every once in a while.
		In math class, we all learned that the reciprocal fraction for 2/3 is 3/2 (remember from the third grade?).
		In photography, ther is a reciprocal relationship between aperture and shutter speed in exposures.
	www.parkwestcameraclub.org /tips/reciprocity.html (707 words)

	[No title]
		Mathematics is classified with both the humanities and the sciences.
		Departments in a variety of fields which use mathematics, including some in the social and biological sciences as well as in engineering and the physical sciences, are interested in attracting math majors into their graduate programs.
		Students with only minimum and intermediate mathematical competence are strongly advised to remove this deficiency by independent study through the UW-Extension or by enrolling for the summer session preceding the freshman year.
	www.wisc.edu /pubs/ug/10lettsci/depts/math.html (5050 words)

	Computing Papers on Reciprocity (Site not responding. Last check: 2007-11-03)
		We propose a system of national organ insurance based on a social contract of reciprocal obligation under which aggregated present consent to donate guarantees future availability of organs for those who need them, at least to the level that prevents death while awaiting an organ.
		reciprocity is an ancient and important social practice that evolved in very small-scale societies.
		reciprocity is important for limbic regulation, since each station is a duplicate, awareness flows in both directions in a continual feedback loop.
	computing.breinestorm.net /reciprocity (3008 words)

	Read This: Briefly Noted
		The first part of the book is all business: each of the (multiple choice) examinations is included, followed by a list of answers which includes the distribution of responses on the exam and some brief comments on "the distractors," that is, the wrong answers in the multiple choice questions.
		Right at the beginning, he makes the point that even the quadratic reciprocity law should be understood in terms of algebraic number theory, and from then on he leads us on a wild ride through some very deep mathematics indeed as he surveys the attempts to understand and to extend the reciprocity law.
		Reciprocity Laws : From Euler to Eisenstein, by Franz Lemmermeyer.
	www.maa.org /reviews/brief_jun00.html (1139 words)

	math lessons - Number theory (Site not responding. Last check: 2007-11-03)
		Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers.
		Proofs of the transcendence of mathematical constants, such as π or e, are also classified as analytical number theory.
		Mathematics is the queen of the sciences and number theory is the queen of mathematics.
	www.mathdaily.com /lessons/Number_theory (1302 words)

	MATHEMATICS
		The major in mathematics includes options in pure and applied mathematics and teaching mathematics in elementary and secondary schools.
		Students may satisfy a mathematics major by completing the Mathematics Core, together with one of the following options or, upon consultation with a mathematics adviser, by developing programs to suit their special needs, subject to the written approval of the Mathematics Department.
		Students are encouraged to consider combining a major in mathematics with a major in a related area, such as computer science, engineering, behavioral science, a physical science, business, or economics.
	oldweb.uwp.edu /academic/mathematics/allcourses.htm (1588 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		The automorphic representations of GL(2) and its metaplectic cover are compared in two different ways: one way is by means of a "relative trace formula"; the relative trace formula presented her is actually a generalization of the work of Iwaniec.
		The purpose of the note is to draw attention to the connection between this theorem and Ramanujan sums, and to the question of what happens for non-congruence subgroups..
		Deligne's generalization of the Hadamard–Vallée Poussin method in classical number theory is formulated as the representability of certain states of the character ring of a compact group, and the determination of all the representable states is carried out.
	www.ias.ac.in /mathsci/specialissue/absdec1987.html (1855 words)

	Master's Degree Programs in Mathematics-Graduate Catalogue 2003-2004 (Site not responding. Last check: 2007-11-03)
		To ensure that the mathematical prerequisites have been met, any student not enrolled in the mathematics degree program or the Master of Education in secondary education mathematics track must obtain permission from the Department of Mathematical Sciences to register for any graduate course offered by the department.
		The bachelor’s/master’s degree program is designed to provide a student in mathematics a means to complete the requirements for both degrees in a period of five years.
		Completed a minimum of seventy-five (75) and a maximum of ninety-eight (98) credit hours in their undergraduate programs in mathematics, including credits earned from advanced placement if they started at UNCW or are transfer students and have completed a minimum of two semesters as a full-time student at UNCW, a minimum of 24 hours.
	www.uncwil.edu /grad_cat/math.htm (2958 words)

	Eisner's reciprocity paradox and its resolution: part I
		The principle of reciprocity says that when a vertical source (a vibrator) and a vertical receiver (a geophone) are interchanged, the same seismogram will be recorded in each case.
		In a field study, Fenati and Rocca [1984] found that the reciprocal principle also applies surprisingly well even when the required conditions are technically violated, such as when an isotropic source (dynamite) is used with a vertical receiver (again a geophone).
		Dahlen and R. Odom in their reply [1984] to Eisner's original short note analytically calculate the amplitude at the focus for each case and show that they are the same.
	sepwww.stanford.edu /oldsep/joe/oldArticles/Eisner/README.html (1255 words)

	Career Services Center: Major Resource Kits - Mathematics
		Mathematics is both a scientific profession and a tool essential to many other scientific disciplines and careers.
		The Mathematical Sciences Department at the University offers both the bachelor of arts and bachelor of sciences degrees in mathematical sciences, and the bachelor of arts in mathematics education.
		The mathematics education degree prepares the student to be a high school math teacher.
	www.udel.edu /CSC/math.html (510 words)

	Quadratic Reciprocity (Site not responding. Last check: 2007-11-03)
		Mathematics Archives - Topics in Mathematics - Number Theory...
		UCSB Mathematics Student Seminar, directed by Akira Kurosawa...
		Gauß, Eisenstein, and the ``third'' proof of the Quadratic Reciprocity Theorem:...
	www.scienceoxygen.com /math/311.html (87 words)

	MATHEMATICS - Math
		Prerequisite(s): Permission of instructor; no formal mathematical prerequisite, but one year of college calculus would be helpful.
		A survey of a number of actively-growing areas of mathematics, according to the interests of the students and the instructor.
		Lectures will be supplemented by informal talks by guest speakers from industry about examples and their experience of using mathematics in the real world.
	www.upenn.edu /registrar/register/math.html (5131 words)

	Eisenstein
		This stimulated Eisenstein to research in mathematics and on his return to Germany he enrolled at the University of Berlin.
		Soon he was to spend most of his time in bed although his amazing output of mathematics did not diminish as he published one treatise after another on quadratic partition of prime numbers and reciprocity laws.
		Biographies of mathematicians are from the History of Mathematics archive at the University of St. Andrews, and are used with permission.
	library.wolfram.com /examples/quintic/people/Eisenstein.html (318 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Anytime the series sum seems to occur naturally in mathematics with the parallel sum nowhere in sight, it is an illusion.
		MacMahon Chain-Yoke Reciprocity Theorem The theorem amounts to the observation that the reciprocity map interchanges the two sums while preserving multiplication and unity.
		In addition to precise mathematical procedure for dualizing equations, it is also possible to establish the duality at a conceptual level so that verbal statements of an equation can be immediately dualized into the verbal statement for the dual equation.
	www.ellerman.org /Davids-Stuff/Maths/sp_math.doc (4901 words)

	Teaching with Original Historical Sources in Mathematics (Site not responding. Last check: 2007-11-03)
		The benefits for instructors and students alike are a deepened appreciation for the origins and nature of modern mathematics, as well as the lively and stimulating class discussions engendered by the interpretation of original sources.
		A graduate course on the role of history in teaching mathematics describes the course and its origins.
		Our long-term dream is that the entire mathematics curriculum should be historically based, with original sources playing a role throughout, and we ourselves are endeavoring to incorporate both history and original sources into all the courses we teach.
	www.math.nmsu.edu /~history (2430 words)

	article (Site not responding. Last check: 2007-11-03)
		Kronecker's Views on the Foundations of Mathematics, in: "The History of Modern Mathematics," D. Rowe and J. McCleary, eds.
		Kronecker on the Foundations of Mathematics, in: "From Dedekind to Goedel," Jaako Hintikka, ed.
		Kummer and Kronecker, in: "Mathematics in Berlin," H. Begehr et al, eds.
	www.math.nyu.edu /faculty/edwardsh/articles.htm (301 words)

	Doug's Expositions (Site not responding. Last check: 2007-11-03)
		This is an outline for a course which gives real mathematics about the 4th dimension, from linear equations to the Hopf fibration, to gifted high school students.
		Quadratic reciprocity is a startling result in elementary number theory.
		Although such a course starts with trivial-seeming results (such as negativenegative=positive), within a couple of months one reaches striking, completely nonobvious results, and quadratic reciprocity* is one of the milestones.
	www.math.columbia.edu /~zare/expositions.html (1039 words)

	Theory of Reciprocity - Enigma of Existence
		For every measure of distance point 'A' is separated from point 'B', point 'B' is an equal and opposite distance from point 'A'.
		And it's not just coincidence that mathematics - the language of science - encodes logic into a device called an equation which requires its elements to be equivalent on opposite sides of the argument.
		From simple addition to quantum mechanics, reciprocal balance is a prevailing dynamic which even the rules of cause and effect must obey.
	www.theory-of-reciprocity.com (720 words)

	The Unity of Mathematics
		A conference to honor the 90th birthday (Sept. 2) of Israel Gelfand is currently underway in Cambridge, Massachusetts.
		Forster famously advised his readers, "Only connect." "Reciprocity" would be Michael Kruger's succinct philosophy, with all that the word implies.
		The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.
	log24.com /log03/0902.htm (1986 words)

	UniMelb UGHB96 : 618-312 Number Theory
		Prerequisite: One of Mathematics 618-111, 618-121, 618-142, 618-200, 618-211; or Mathematics 101 (1995 Handbook).
		the extent and uses of elementary number theory; its applicability in other parts of mathematics; its potential for application outside of mathematics.
		Maintained by: Dept. of Mathematics, Faculty of Science.
	www.unimelb.edu.au /HB/1996/Sci/618/618-312.html (329 words)

	Search Results for Artin
		Similarly, Artin's Reciprocity Law opens the way to new applications and progress.The most striking application was given by Furtwangler's proof of the principal ideal theorem of class field theory, given one year after the publication of Artin's Reciprocity Law.
		In 1949 Brauer was awarded the Cole Prize from the American Mathematical Society for his paper On Artin's L-series with general group characters which he published in the Annals of Mathematics in 1947.
		This was nothing to do with his mathematical ability which everyone accepted as outstanding, but rather some mathematicians such as Artin felt that they could not have Nash as a colleague due to his aggressive personality.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Artin&CONTEXT=1 (2714 words)

	Course Descriptions
		Prerequisites: Mathematics 105 or 107, and Mathematics 121 or 122
		Mathematics courses numbered in the 500+s and listed below are introductory graduate courses and may be taken by qualified undergraduate students in their senior year with the permission of the Department Chair.
		Offered on occasionThe purpose of this course is to define the strengths of the individual student and to sharpen analytical, communication and presentation skills.
	www.liu.edu /brookund/page121.htm (596 words)

	What's New on the Mathematics Archives
		This site is intended for educators who teach mathematics and are interested in integrating common technologies into their daily instruction.
		While much of this site focuses on mathematics, there are a number of lessons and activities that are intended to blend mathematics with writing and make use of mathematical reasoning in other content areas such as social studies.
		The School Science and Mathematics Association is dedicated to improving instruction at all levels in and between science and mathematics by providing leadership in the field.
	archives.math.utk.edu /whatsnew/mar99.html (1047 words)

	Imaginary and Complex Numbers - Mathematics and the Liberal Arts
		The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses.
		When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation.
		The author discusses parameterization of Pythagorean triangles, the law of quadratic reciprocity, representation of numbers in a fixed finite number of sums of squares numbers, quadratic forms, and connections with the complex numbers, quaternions, and Cayley numbers.
	math.truman.edu /~thammond/history/ComplexNumbers.html (287 words)

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