Number-theory - Factbites

Number-theory - Factbites
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Topic: Number-theory

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	Number theory - Wikipedia, the free encyclopedia
		In algebraic number theory, the concept of a number is expanded to the algebraic numbers which are roots of polynomials with rational coefficients.
		Number theory was a favorite study among the Ancient Greeks, who were aware of the Diophantine equation concept in numerous special cases.
		Originally, number theory is the branch of pure mathematics concerned with the properties of integers.
	en.wikipedia.org /wiki/Number_theory (1464 words)

	number theory on Encyclopedia.com
		NUMBER THEORY [number theory] branch of mathematics concerned with the properties of the integers (the numbers 0, 1, -1, 2, -2, 3, -3, …).
		Analytic number theory has given a further refinement of Euclid's theorem by determining a function that measures how densely the primes are distributed among all integers.
		An important area in number theory is the analysis of prime numbers.
	www.encyclopedia.com /html/n1/numberth.asp (1144 words)

	Number Theory
		In multiplicative number theory the connection between squarefree values of polynomials and the abc-conjecture has been studied in [6], while some estimates for pseudo-squares have been given in [11].
		In algebraic number theory exponential congruences have been studied in [5], [12] and [18], while a certain problem of I. Korec concerning algebraic integers has been solved in [9].
		In elementary number theory a problem (proposed by T. Cochrane and G. Meyerson) concerning covering systems of congruences has been solved in [10] and another one (proposed by W. Narkiewicz) concerning arithmetical functions in [14].
	www.impan.gov.pl /About/numberth.html (509 words)

	Number Theory
		This number theory seminar also enjoys the active participation of some of the leading figures who come to Montreal on a regular basis and give short courses suitable for graduate students.
		Students specializing in number theory are expected to fulfil first the basic requirements in algebra and analysis.
		The number theory group teaches on a regular basis fundamental courses in number theory, algebra and algebraic geometry.
	www.math.mcgill.ca /department/numtheory.php (445 words)

	Number Theory Glossary
		A Carmichael Number is a composite number which passes the Fermat pseudoprime test for all bases.
		A prime number is a number which has no factors other than 1 (called non-trivial factors).
		A Galois Field is a field with finite number of elements.
	www.math.umbc.edu /~campbell/NumbThy/Class/Glossary.html (827 words)

	Number Theory
		Number Theory at the Mathematics Dept. of the University of Texas
		Jeffrey Vaaler (vaaler@math.utexas.edu): Analytic number theory, Diophantine approximation and the geometry of numbers in local and global fields, Diophantine inequalities, polynomials, effective measures of irrationality and transcendence, applications of Fourier analysis in number theory, inequalities and extremal problems.
		John Tate (tate@math.utexas.edu): Algebraic Number Theory (local and global fields), Class Field Theory, Galois cohomology, Galois representations, L-functions and their special values, modular forms, elliptic curves and abelian varieties.
	www.ma.utexas.edu /users/voloch/numberthy.html (199 words)

	Number Theory at the University of Natural Resources (Vienna)
		Proceedings of the Number Theory Conference held at Graz in September 1998, eds.
		His research concentrates on the theory of lattice points in large regions and on the asymptotic theory of arithmetic functions.
		In fact, since the early 1960's the mathematics chair was held by Karl Prachar whose contributions to the theory of primes (in particular his monograph Primzahlverteilung) obtained the highest esteem by mathematicians all over the world.
	www.boku.ac.at /math/nth.html (807 words)

	Research in Number Theory & Combinatorics
		Both number theory and combinatorics are part of what is called discrete mathematics, which has important applications in computer science and information technology, as well as an intrinsic elegance and fascination for mathematicians, professionals and amateurs alike.
		Number theory originated as the study of the structure and properties of the ordinary integers, but nowadays has expanded into the study of analogous properties of other (possibly non-commutative) rings.
		The following member of staff are involved in research in Number Theory and Combinatorics:
	www.maths.gla.ac.uk /research/groups/ntc/ntc.html (256 words)

	Number Theory - Numericana
		Since the number 9N divides the number which consists of P nines followed by a certain number J of zeroes, N divides the number consisting of P ones followed by J zeroes, and also the integer composed of P sevens followed by J zeroes.
		The next two numbers in the list, the 13th and 14th Mersenne primes, are much larger (corresponding to n=521 and n=607) and were both discovered the same day (January 30, 1952, around 22:00 PST and shortly before midnight) by Raphael Mitchel Robinson (1911-1995), at the dawn of the computer age.
		Recall that a number is divisible by 3 or 9 iff (if and only if) the sum of its digits is. It is divisible by 11 iff the difference between the sum of its odd digits (units, hundreds, etc.) and the sum of its even digits (tens, thousands, etc.) is so divisible.
	home.att.net /~numericana/answer/numbers.htm (7454 words)

	The Math Forum - Math Library - Number Theory
		Papers from a Mathematics graduate from The University Of Sussex at Brighton: Number Theory: GCD and Prime Factorisation; Molien's Theorem, Invariant Theory and Gregor Kemper; A History of Equality.
		In number theory, straightforward, reasonable questions are remarkably easy to ask, yet many of these questions are surprisingly difficult or even impossible to answer.
		Andrew Granville researches number theory, combinatorics, and arithmetic geometry.
	mathforum.org /library/topics/number_theory (2144 words)

	number theory -- Encyclopædia Britannica
		the number of atoms, ions, or molecules that a central atom or ion holds as its nearest neighbours in a complex or coordination compound or in a crystal.
		This theory states that matter is made up of small particles called atoms, that each chemical element has its own kind of atoms (in contrast to earlier ideas that...
		The next milestone was the atomic theory, advanced in 1805 by an English schoolteacher, John Dalton.
	www.britannica.com /eb/article-9109430 (867 words)

	Number theory - Wikipedia, the free encyclopedia
		Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers.
		In algebraic number theory, the concept of number is expanded to the algebraic numbers which are roots of polynomials with rational coefficients.
		Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated.
	en.wikipedia.org /wiki/Number_theory (1354 words)

	Computational number theory
		Most results have been obtained in unpublished studies: a survey paper which documents these developments will appear in the Proceedings of the Conference in Number Theory in Honour of Professor H.C. Williams, (to be) held in Banff, Alberta, Canada, May 24-30, 2003.
		The number and the size of known amicable number pairs has grown explosively in recent years: from 1108 amicable pairs in 1972 (the largest pair consisting of two 25-digit numbers), to more than five million amicable pairs in May 2003 (the largest pair consisting of two 5577-digit numbers).
		The six largest numbers factored so far with NFS have 174 (factored on December 3, 2003), 160 (factored on April 1, 2003), 158 (factored on January 19, 2002), 155, 140, and 130 decimal digits.
	db.cwi.nl /projecten/project.php4?prjnr=84 (1003 words)

	Math 254 (Number Theory)
		The Berkeley Number Theory Seminar meets Wednesdays from 3:10 to 4:00 PM in 891 Evans, and sometimes on Friday at the same time and place.
		This was the official course web page for Math 254B (Number Theory) at UC Berkeley, which I taught during the Spring 2002 semester.
		Prospective students in number theory are encouraged to attend.
	www-math.mit.edu /~kedlaya/math254b.html (400 words)

	Number Theory - Mathematics and the Liberal Arts
		This book is somewhere between simple arithmetic and elementary number theory, but develops the subjects quite differently than we do today.
		Schroeder, Manfred R. Number theory and the real world.
		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/NumberTheory.html (1152 words)

	Explicit algebraic number theory
		The title Explicit algebraic number theory is borrowed from the series of Oberwolfach meetings on Explicit methods in number theory.
		The advanced techniques from algebraic number theory that apply to these problems include class field theory, infinite Galois theory, and the theory of quadratic forms.
		Prerequisites: basic algebra, number theory, and point set topology, including Galois theory, algebraic number theory and a knowledge of p-adic numbers.
	www.math.leidenuniv.nl /~psh/EANT (334 words)

	Basic Library List-Number Theory
		Manin, Yuri and Panchishkin, A. Number Theory: Introduction to Number Theory.
		An Introduction to the Analytic Theory of Numbers.
		Cassels, J.W. An Introduction to the Geometry of Numbers.
	www.maa.org /BLL/numtheory.htm (793 words)

	MathPages: Number Theory
		Numbers Expressible As (a^2 - 1)(b^2 - 1)
	www.mathpages.com /home/inumber.htm (109 words)

	Math - Number Theory
		Aims to collect donations from supporters of number theory and to disburse these donations to encourage research.
		That the Mahler measure of an algebraic number is bounded away from 1.
		To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number.
	www.canadiancontent.net /dir/Top/Science/Math/Number_Theory (481 words)

	Number Theory
		Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal c...
		Two classic essays by great German mathematician: on the theory of irrational numbers; and on transfinite numbers and properties of natural numbers.
		Superb, high-level study of landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude" traces developments in mathematical theory that it inspired.
	store.doverpublications.com /0486682528.html (383 words)

	Number theory - Wikipedia, the free encyclopedia
		Number theory may be subdivided into several fields according to the methods used and the questions investigated.
		Number Theory and Its History, Oystein Ore, Dover Publications, Inc., 1948,1976.
		In elementary number theory, the integers are studied without use of techniques from other mathematical fields.
	en.wikipedia.org /wiki/Number_theory (383 words)

	Theory
		Statistical theory The theory of statistics includes a number of topics: Statistical models of the sources of data and t...
		Cox-Forbes theory The Cox-Forbes theory is a theory on the evolution of Duncan Forbes.
		Dempster-Shafer theory The Dempster-Shafer theory is a mathematical theory of Glenn Shafer.
	www.brainyencyclopedia.com /topics/theory.html (383 words)

	PlanetMath: algebraic number theory
		Algebraic number theory is the study of algebraic numbers, their properties and their applications.
		As an introduction, the reader should be comfortable with the basic theory of rational and irrational numbers, and its complementary entry, the basic theory of algebraic and transcendental numbers.
		The main object of study in algebraic number theory is the number field.
	planetmath.org /encyclopedia/AlgebraicNumberTheory.html (383 words)

	INTEGERS: The Electronic Journal of Combinatorial Number Theory
		We welcome original research articles in combinatorics and number theory, with a preference for those that have a connection to both fields.
		INTEGERS is a refereed electronic journal devoted to research in the area of combinatorial number theory.
		Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory.
	www.integers-ejcnt.org (173 words)

	Fields Institute - Conference in Number Theory - 2003
		The conference is open to all areas of Number Theory, with emphasis on Computational Number Theory and applications to Cryptography.
		Conference in Number Theory in Honour of Professor H.C. Williams
		Researchers in these fields of study are welcomed to participate, as we honour Canada's foremost computational number theorist, whose contributions include results on integer factorization, primality testing, diophantine equations, linear recurrences, the infrastructure of quadratic number fields and function fields, and their applications to Cryptography.
	www.fields.utoronto.ca /programs/scientific/02-03/numtheory (409 words)

	Algebraic Number Theory Archive
		This archive is for research in algebraic number theory and arithmetic geometry.
		math.NT/0304377: 24 Apr 2003, Theory of Generalized Bernoulli-Hurwitz Numbers for the Algebraic Functions of Cyclotomic Type, by Yoshihiro Ônishi.
		ANT-0267: 27 Nov 2000, On an analogue for number fields of a conjecture of de Jong on F_q[[t]]-analytic extensions of function fields, by Gebhard Boeckle.
	front.math.ucdavis.edu /ANT (12251 words)

	Number Theory
		Algebraic number theory: rational, algebraic and transcendental numbers, approximation of irrationals by rationals, continued fractions, Liouville’s transcendental numbers, e and pi are irrational.
		Unsolved problems in number theory: including the twin primes conjecture, Goldbach’s conjecture, and the Riemann hypothesis.
		An Introduction to the Theory of Numbers, Niven and Zuckerman (Wiley 1972)
	www.math.waikato.ac.nz /~kab/math314.html (1159 words)

	Earliest Uses of Symbols of Number Theory
		I think the first Bourbaki volume published was the results summary on set theory, in 1939, and it does not contain any symbol for the complex numbers.
		The symbol φ(m) for the number of integers less than m that are relatively prime to m was introduced by Carl Friedrich Gauss (1777-1855) in 1801 in his Disquisitiones arithmeticae articles 38, 39 (p.
		Q for the set of rational numbers and Z for the set of integers are apparently due to N. Bourbaki.
	members.aol.com /jeff570/nth.html (1263 words)

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Topic: Number-theory

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