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Topic: List of algebraic number theory topics

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List of number theory topics

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	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 (909 words)

	abigailk.com Mathematics lists
		The purpose of this list is not similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society.
		This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity of their coverage.
		One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.
	www.abigailk.com /mathematics-lists.htm (855 words)

	Graduate Study in Algebra
		Algebra is one of the oldest branches of mathematics, and the study of algebra in the Department of Mathematics has traditionally been rich and strong.
		The research strengths of the faculty are in the theory of rings (commutative and noncommutative), the theory of groups, algebraic number theory, the representation theory of groups and algebras, and algebraic geometry.
		The goal of the course is the fundamental theorem of Galois theory and the solutions to the three pearls of antiquity: the quadrature of the circle, the trisection of an angle, and the duplication of the cube.
	www.math.uiuc.edu /GraduateProgram/researchmath/gradalgebra.html (1660 words)

	Algebraic number theory - Wikipedia, the free encyclopedia
		Algebraic number theory is a branch of number theory in which the concept of a number is expanded to the algebraic numbers which are roots of polynomials with rational coefficients.
		An algebraic number field is any finite (and therefore algebraic) field extension of the rational numbers.
		This is called localization and it leads to the construction of the p-adic numbers; this field of study is called local analysis and it arises from algebraic number theory.
	en.wikipedia.org /wiki/Algebraic_number_theory (228 words)

	11: Number theory
		Number theory is one of the oldest branches of pure mathematics, and one of the largest.
		Questions in algebraic number theory often require tools of Galois theory; that material is mostly a part of 12: Field theory (particularly the subject of field extensions).
		The algebraic structure of the ring of integers is similar to that of other commutative rings such as rings of polynomials.
	www.math.niu.edu /~rusin/known-math/index/11-XX.html (2587 words)

	Transcendental number Summary
		In mathematics, a transcendental number is any complex number that is not algebraic, that is, not the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients.
		However, an algebraic function of several variables may yield an algebraic number when applied to transcendental numbers if these numbers are not algebraically independent.
		Because algebraic numbers form an algebraically closed field, this would imply that the roots of the polynomial, a and b, must be algebraic.
	www.bookrags.com /Transcendental_number (1417 words)

	Number Theory :: Math : Gourt (Site not responding. Last check: 2007-10-20)
		Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.
		Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated.
		Number Theory Foundation - Aims to collect donations from supporters of number theory and to disburse these donations to encourage research.
	science.gourt.com /Math/Number-Theory.html (883 words)

	Mathematics
		Topics to be chosen from model theory and its applications, infinitary logic and admissible sets, ordinary and generalized recursion theory, consistency and independence results in set theory, large cardinals, descriptive set theory.
		The theory of algebraic curves is a central branch of mathematics, having relations to fields as diverse as complex analysis, number theory, combinatorics, codes, topology, representation theory, and physics.
		Topics will include time-reversal invariance; definition of unitary, symplectic, and orthogonal ensembles of random matrices; unitary ensembles and orthogonal polynomials; the joint probability density function for the eigenvalues, gap probabilities, n-point correlation functions, the nearest-neighbor spacing distribution; Riemann-Hilbert problems and the Riemann-Hilbert approach to universality of distributions in random matrix theory.
	pr.caltech.edu /catalog/05_06/courses/listing/ma.html (2695 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.
		Researchers use random numbers for tackling a wide range of problems, from modeling molecular behavior and sampling opinion to solving certain equations and testing the efficiency of algorithms.
	mathforum.org /library/topics/number_theory (2144 words)

	Set theory Summary
		In naive set theory, sets are introduced and understood using what is taken to be the self-evident concept of sets as collections of objects considered as a whole.
		Naive set theory is the original set theory developed by mathematicians at the end of the 19th century.
		Axiomatic set theory is a rigorous axiomatic branch of mathematics developed in response to the discovery of serious flaws (such as Russell's paradox) in naïve set theory.
	www.bookrags.com /Set_theory (2598 words)

	Topics in Algebraic Number Theory
		Algebraic number theory has a long and distinguished history and remains one of the most significant areas of research in mathematics.
		The analysis of problems in number theory, even those of a seemingly concrete and explicit nature, may well however involve the interplay of results and techniques from may different branches of pure mathematics.
		The topics to be discussed have been chosen both because they have been of pivotal significance to recent developments and also because they illustrate well the wide variety of techniques and the nature of the problems which arise in much of the fundamental research which is being conducted today.
	www.mth.kcl.ac.uk /events/short_courses/ANT_Sep_2002.html (659 words)

	Arithmetic, Numeration, Number Theory - Numericana
		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.
		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.
	home.att.net /~numericana/answer/numbers.htm (7607 words)

	[No title]
		Differential geometry is the study of the geometry of curves and surfaces (and higher-dimensional analogues), using techniques of multivariable calculus and linear algebra.
		The list of topics includes: very ancient as well as indigenous mathematics; the contributions of ancient Greece including Euclid and Archimedes; and the birth of calculus.
		A more difficult argument shows that any theory of infinite sets has the same property: the collection of all sets described by that theory cannot be described as a set within that theory, and (more subtly) the collection of different sizes of sets cannot be a set in that set theory.
	ww2.lafayette.edu /~math/program/sptopics_list.html (1674 words)

	Number Theory Math Science
		- That the Mahler measure of an algebraic number is bounded away from 1.
		- Number Theory section of the sci.math FAQ list.
		- To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number.
	www.iaswww.com /ODP/Science/Math/Number_Theory (438 words)

	Amazon.ca: Number Theory in Function Fields: Books: Michael Rosen (Site not responding. Last check: 2007-10-20)
		Elementary number theory is concerned with arithmetic properties of the ring of integers.
		Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field.
		A variety of topics are presented, including: the ABC-conjecture, Artin¿s conjecture on primitive roots, the Brumer-Stark conjecture, Drinfeld modules, class number formulae, and average value theorems.
	www.amazon.ca /Number-Theory-Function-Fields-Michael/dp/0387953353 (552 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)

	Search Here - Science - Math - Number Theory
		Number Theory section of the sci.math FAQ list.
		To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number.
		That the Mahler measure of an algebraic number is bounded away from 1.
	www.clickheretoleave.com /Science/Math/Number_Theory (514 words)

	MIT OpenCourseWare \| Mathematics \| 18.786 Topics in Algebraic Number Theory, Spring 2006 \| Syllabus
		All course numbers in the above list should be followed by "or equivalent"; I am the sole arbiter of what constitutes an acceptable equivalent.
		I'll be particularly flexible about 18.781; if you studied number theory for an Olympiad, or in a high school summer camp, then you know what you need.
		Number theory is a popular topic, and so I expect there will be many undergraduates interested in this course; this means I need to provide a warning for such students.
	ocw.mit.edu /OcwWeb/Mathematics/18-786Spring-2006/Syllabus/index.htm (639 words)

	[No title]
		While classical DAI research was mainly concerned with distributed problem solving and task allocation in view of a common goal, MAAMAW emphasizes the problems arising when several autonomous agents, endowed with their own goals, knowledge, and abilities, share a common environment and pursue either shared or competing goals.
		This biennial event focuses on a range of topics of concern to scholars applying quantitative, combinatorial, logical, algebraic and algorithmic methods to AI areas as diverse as decision support, automatic reasoning, knowledge-based systems, machine learning, computational linguistics, computer vision, and robotics.
		Selected refereed full length theory papers will be published in a special issue of the Annals of Mathematics and Artificial Intelligence and selected application oriented papers in the journal Applied Artificial Intelligence, as a permanent record of the Symposium.
	www.cs.cmu.edu /Groups/AI/util/pubs/lists/dai-list/dailist/106.09feb93 (1644 words)

	The Number Theory Group at UCLA
		Graduate study in number theory at UCLA is based on lecture courses, faculty-led student seminars, and individual study.
		The core lecture courses include algebraic number theory, automorphic forms and L-functions, analytic number theory, arithmetic geometry, representation theory, and applied number theory.
		Kiran Kedlaya maintains a list of conferences in arithmetic geometry, and Ravi Vakil maintains a similar list of conferences in algebraic geometry.
	www.math.ucla.edu /~ntg (381 words)

	MP473 2000 (Site not responding. Last check: 2007-10-20)
		The course is an introduction to algebraic number theory, especially quadratic and cyclotomic fields.
		H.B. Mann, Introduction to Algebraic Number Theory, QA241.M31955
		MAS4002: Algebraic Number Theory, Course notes by Robin Chapman, University of Exeter
	www.numbertheory.org /courses/MP473 (290 words)

	UR Math: Algebra and Number Theory Group
		The Riemann zeta function, L functions, and the distribution of prime numbers.
		Algebraic number theory, arithmetic of quaternion algebras and its connections to modular forms, Brandt matrices, Hecke operators, and Ramanujan graphs.
		Analytic and elementary number theory; complex analysis; history of Mathematics.
	www.math.rochester.edu /research/algebra_and_number_theory (107 words)

	Math Books
		Covers all algebraic topics of algebra I and many of the topics of algebra II.
		A broad introduction to the fundamentals of number theory.
		A history of number theory culminating in the description of one of math's greatest mysteries, the Riemann Hypothesis.
	www.artofproblemsolving.com /Resources/AoPS_R_Books.php (1137 words)

	Mathematics Archives - Topics in Mathematics - Number Theory
		Elementary Number Theory, Lucas' Theorem, Pascal's triangle via cellular automata, Bernoulli numbers and polynomials, Theorems of Morley and Emma Lehmer and their generalizations, Some useful p-adic numbers
		Divisibility and primes, Euclidean algorithm, Euler's theorem, Representation of numbers, Bertrand's postulate
		Plimpton 322: a remarkable ancient Babylonian tablet on number theory
	archives.math.utk.edu /topics/numberTheory.html (675 words)

	Lectures on Topics in Algebraic Number Theory
		These are the notes of a course of ten lectures given at the Christian-Alberchts-Universität Kiel at Kiel, Germany during December 2000.
		These lectures were aimed at giving a rapid introduction to some basic aspects of Algebraic Number Theory with as few prerequisites as possible.
		There are two appendices, first containing author's older notes on Galois Theory and the second reproducing a recent article in Bona Mathematica.
	www.math.iitb.ac.in /~srg/Lecnotes/kiel_des.html (99 words)

	Topics in Algebraic Graph Theory - Cambridge University Press (Site not responding. Last check: 2007-10-20)
		The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry).
		Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book.
		To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521801974 (337 words)

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