Geometry.Net - Pure_And_Applied_Math: Algebraic Number Theory

AMCA: Frobenius Groups: It's All Algebraic Number Theory Presented By Ron Brown
Abstracts Conference Homepage. Frobenius groups it's all algebraicnumber theory by Ron Brown University of Hawaii Frobenius groups
http://at.yorku.ca/cgi-bin/amca/cacv-07

Extractions: University of Hawaii Frobenius groups play a prominent role in the general theory of finite groups. After reviewing definitions we show that the problem of finding all Frobenius groups with abelian Frobenius kernel is a problem in algebraic number theory. We illustrate this with a very elementary construction of all Frobenius groups whose Frobenius complement is either the quaternion group or the special linear group SL(2,Z/5Z) and with some combinatorial results (e.g., a count of the metabelian Frobenius groups of order at most one million). The key idea is that Frobenius groups with abelian kernel correspond precisely to finite modules over certain well-behaved classical maximal orders, and the indecomposable modules correspond to powers of maximal ideals of the associated Dedekind domain. Connections with Amitsur's calculation of the finite groups which are subgroups of division rings will be mentionned.
Math 525: Algebraic Number Theory. Information Page
Math 525 algebraic number theory. Supplemental material on algebraic numberfields will be drawn from algebraic number theory by Stewart and Tall.
http://www.math.binghamton.edu/dikran/525/

Extractions: This is the information page for Math 525, Fall 2002. Text: A Classical Introduction to Modern Number Theory, 2nd edition, by K. Ireland and M. Rosen. Supplemental material on algebraic number fields will be drawn from "Algebraic Number Theory" by Stewart and Tall. I do not expect to cover the complete text in a single semester. Instead I plan to discuss Chapters 5-12, with supplemental material on algebraic number fields as time permits. Many of the standard results in algebraic number theory can also be regarded as results in algebraic K-theory, so algebraic topologists may be interested in this course. Assignment Chapter Problems Date Due September 10 September 19 September 26 Thursday, October 10 Thursday, October 17 2, 3, 4, 5, 6 [(a) only], 7 [-7-3w only], 8 [143 only], 13, 14 Tuesday, October 29 Thursday, November 7 handout (8 problems) Tuesday, November 26 handout (7 problems) Thursday, December 12 Test Material Location Date and Time Chapters 5-7 LN 2205 October 2, 7-9 PM
International Conference On Number Theory
Topics elementary, analytical and algebraic number theory and its applications. Ostravice, 38 September 2001.
http://www.osu.cz/prf/katedry/matematiky/cz_announcement.html

Extractions: September 3. - 8., 2001 Organized by the Department of Mathematics of the Faculty of Sciences of the University of Ostrava Department of Mathematics, Institute of Chemical Technology, Prague Department of Mathematics, Masaryks University of Brno Department of Mathematical Analysis, Charles University, Prague Mathematical institute of Slovak Academy of Scientes, Bratislava PARTICIPANTS The following mathematicians confirmed the participation INVITED SPEAKERS Takashi Agoh, Japan
Algebraic Number Theory
algebraic number theory. The lectures for MATH0053, Algebraic NumberTheory, FebruaryMay 2001, have now finished. Fairly complete
http://www.bath.ac.uk/~masgks/MATH0053/

Extractions: The lectures for MATH0053, Algebraic Number Theory, February-May 2001, have now finished. Fairly complete notes on the course are available as Postscript. There are copies of them and of the solutions to the examples sheets in the pigeonholes in 1 West Level 3. Examples sheets The reading list for the course, available from the library catalogue , lists some relevant books which are available in the University of Bath Library . For number theory, Stewart and Tall is a useful source. For pure commutative ring theory, there are three standard books, all called Commutative Algebra . All are excellent, but all are hard to read as a first introduction. They are by Zariski and Samuel, by Atiyah and Macdonald, and by Matsumura. The first two are in the library; the last is not, but I have a copy I am willing to lend if anybody is interested. Examples sheet 1 (also as a dvi file). Examples sheet 2 (also as a dvi file). Examples sheet 3 (also as a dvi file). Examples sheet 4 (also as a dvi file).
E. Pohst Computational Algebraic Number Theory
Translate this page E. Pohst Computational algebraic number theory. Michael E. Pohst Computationalalgebraic number theory, DMV Seminar, Bd. 21, Birkhäuser
http://www.uni-karlsruhe.de/~CAIS/CAR/CAR14/node26.html
H. Cohen A Course In Computational Algebraic Number Theory
Translate this page H. Cohen A Course in Computational algebraic number theory. H. Cohen A Coursein Computational algebraic number theory, 1993, ISBN 3-540-55640-0, Grad.
http://www.uni-karlsruhe.de/~CAIS/CAR/CAR14/node21.html

Extractions: Den Anwendungen gelten die letzten drei Kapitel, und zwar Kapitel 8 der Faktorisierung von Zahlen und den Primzahltests in ''the dark ages'' (Pocklington-Lehmerscher (N-1)-Test, Pollard's rho-Methode, Verfahren von Shanks und die (p-1)-Methode), Kapitel 9 den Primzahltests (mittels Jacobisummen oder elliptischer Kuven, Goldwasser-Kilian-Atkin) und Kapitel 10 der Faktorisierung (Kettenbruchmethode, Klassengruppenverfahren, Methode der elliptischen Kurven nach Lenstra, quadratisches Sieb, zahlentheoretisches Sieb) jeweils in ''modern times''.
Topics In Algebraic Number Theory
Topics in algebraic number theory (EPSRC/LMS Short Course). Schedule. Suggestedreading list. TOPICS IN algebraic number theory. LMS/EPSRC Short Course.
http://www.mth.kcl.ac.uk/events/short_courses/ANT_Sep_2002.html

Extractions: (EPSRC/LMS Short Course) Organiser: David Burns Algebraic number theory has a long and distinguished history and remains one of the most significant areas of research in mathematics. The subject has in particular enjoyed spectacular advances in recent years, with Wiles' proof of Fermat's last theorem standing as one of the undisputed milestones of twentieth century 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. In conjunction with the increasing pace of current developments this means that it is all too easy to feel relatively isolated from the fundamental advances which are being achieved today. With this problem in mind, the lectures at this short course aim to provide students with a grounding in some of the areas which are of central importance in both algebraic number theory and arithmetic algebraic geometry. 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. The lecturers and course titles are:
London Postgraduate Study Group In Algebraic Number Theory
London postgraduate study group in algebraic number theory, Study groupon padic Galois Representations. This term (Spring 2002) there
http://www.mth.kcl.ac.uk/events/psgant2.html

Extractions: London postgraduate study group in algebraic Number theory This term (Spring 2002) there will be a study group on Wednesday afternoons in Imperial College, revolving around the paper: "Construction des representations p-adiques semi-stables" - Colmez, Fontaine Inventiones 140 (2000) 143 In fact the main aim of the study group will be to learn the general theory of p-adic Galois representations that would enable one to read Colmez-Fontaine.... this general theory (due mainly to Fontaine) appears all over the place in modern arithmetic geometry. The first organisational meeting will take place on Wednesday 9th Jan at 2:30pm in the usual room (658). Ill also give an overview of the syllabus. I think there are very few prerequisites: Basically it would be helpful to know something about profinite groups and the basics about finite extensions of the p-adics. But if you don't then don't worry too much. cheers, - jon dee Return to list of seminar series KCL Maths Dept Home page UCL Maths Dept Home page ... IC Maths Dept Home page Department of Mathematics - King's College London document.write("This document was last modified by G.M.T. Watts on " + document.lastModified)
Introduction To Algebraic Number Theory
Introduction to algebraic number theory. 34 hours of lectures perweek. Lecturer Steffen D. Bentzen. Content Aims and objectives
http://www.imf.au.dk/Mathematics/education/courses2/node20.html

Extractions: Aims and objectives: Keywords: Course description: An algebraic number is a root of a rational polynomial, and an algebraic number field is a field obtained from Q by adjoining an algebraic number. In this course we study the basic theory of such fields. An essential property of the ordinary integers is the unique factorization theorem. This theorem is no longer valid for a general number field. A major theme in the course will be to "repair" this defect. The students are required to participate actively in the course, in the form of either seminars or exercises (depending on the number of participants). Prerequisites: 1. del plus a general algebraic interest.
Introduction To Algebraic Number Theory
Introduction to algebraic number theory. 34 hours of lectures perweek. Lecturer Steffen Bentzen Content Aims and objectives
http://www.imf.au.dk/Mathematics/education/F99/courses2/node18.html

Extractions: Next: Linear algebraic groups Up: C courses - introductory Previous: Harmonic analysis [] 3-4 hours of lectures per week. [ Lecturer: Steffen Bentzen Content: ] Aims and objectives: Keywords: Course description: An algebraic number is a root of a rational polynomial, and an algebraic number field is a field obtained from Q by adjoining an algebraic number. In this course we study the basic theory of such fields. An essential property of the ordinary integers is the unique factorization theorem. This theorem is no longer valid for a general number field. A major theme in the course will be to "repair" this defect. The students are required to participate actively in the course, in the form of either seminars or exercises (depending on the number of participants). Prerequisites ] 1. del plus a general algebraic interest. [
Algebraic Number Theory
algebraic number theory. This leads to understanding that number theoryand algebraic geometry is in fact one and the same domain.
http://www.mccme.ru/mathinmoscow/courses/number.htm

Extractions: We present the basics of number theory emphasizing the striking similarity between the properties of usual integers and those of polynomials over a finite field. This leads to understanding that number theory and algebraic geometry is in fact one and the same domain. The core of number theory being an elementary problem, we stick to concrete examples. What is a number theory problem? Rings of residues, finite fields Integers and polynomials Quadratic fields Global fields Prime decomposition and class group Sign and units Zeta-functions Arithmetic of curves Books: K. Ireland and M. Rosen, A classical introduction to modern number theory. Springer, 1982. Math in Moscow Home Page List of courses
Algorithmic Number Theory
9.5. ERHbased methods. 9.6. Primality testing using algebraic number theory.9.7. Generation of random primes. 9.8. Prime number sieves. 9.9.
http://www.math.uwaterloo.ca/~shallit/antdesc.html

Extractions: From the Preface: This is the first volume of a projected two-volume set on algorithmic number theory, the design and analysis of algorithms for problems from the theory of numbers. This volume focuses primarily on those problems from number theory that admit relatively efficient solutions. The second volume will largely focus on problems for which efficient algorithms are not known, and applications thereof. We hope that the material in this book will be useful for readers at many levels, from the beginning graduate student to experts in the area. The early chapters assume that the reader is familiar with the topics in an undergraduate algebra course: groups, rings, and fields. Later chapters assume some familiarity with Galois theory. As stated above, this book discusses the current state of the art in algorithmic number theory. This book is not The book contains a large bibliography with references to more than 1800 papers and books. The BibTeX files for the bibliography of the book are available for your use without charge.
Algebraic Number Theory
Click to enlage algebraic number theory Edwin Weiss. Our Price, $12.95. AvailabilityIn Stock. (Usually ships in 24 to 48 hours). Format Book. ISBN 0486401898.
http://store.doverpublications.com/0486401898.html

Extractions: American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Astronomy Biology and Medicine Bridge and Other Card Game...... Chemistry Chess Children Consumer Catalogs Cookbooks, Nutrition Crafts Detective Stories, Science...... Dover Phoenix Editions Earth Science Engineering Ethnic Interest Features Science Gift Certificates Gift Ideas Giftpack History, Political Science...... Holidays Humor Languages And Linguistics Literature Magic, Legerdemain Mathematics Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy And Religion Photography Physics Psychology Puzzles, Amusement, Recrea...... Reference Specialty Stores Sports, Out-of-door Activi...... Science and Mathematics Stationery, Gift Sets Summer Fun Shop Travel and Adventure Women's Studies (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Careful organization and clear, detailed proofs make this book ideal either for classroom use or as a stimulating series of exercises for mathematically minded individuals. Modern abstract techniques focus on introducing elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
Workshop Information Explicit Algebraic Number Theory NWO-OTKA
Workshop Information Explicit algebraic number theory NWOOTKAworkshop from 27 Sep 2002 through 2 Oct 2002,
http://www.lc.leidenuniv.nl/lc/web/2002/20020927/info.php3?wsid=67
Workshop Participants List B Explicit Algebraic Number Theory
Translate this page Workshop participants list Explicit algebraic number theory NWO-OTKA workshop,
http://www.lc.leidenuniv.nl/lc/web/2002/20020927/participants.php3?wsid=67
Colin D. Walter - Algebraic Number Theory Publications
Colin D. Walter algebraic number theory Publications. From the goodold days before Fermat's Last Theorem had been proved, here
http://www.co.umist.ac.uk/~cdw/algebraic-number-theory.html

Extractions: Colin D. Walter - Algebraic Number Theory Publications From the good old days before Fermat's Last Theorem had been proved, here are some of my contributions to the subject: ( Some over bars etc may not be clear in the post script files, and some symbols may not print properly - particularly symbols for the rational integers and rational field - contact me for the sources if you wish. [6] C. D. Walter, Pure fields of degree 9 with class number prime to 3 , Annales de l'Institut Fourier, Grenoble (1980), pp. 1-16. [5] C. D. Walter, The ambiguous class group and the genus group of certain non-normal extensions , Mathematika (1979), pp. 113-124. [4] C. D. Walter, Kuroda's class number relation , Acta Arithmetica (1979), pp. 41-51. [3] C. D. Walter, Brauer's class number relation , Acta Arithmetica (1979), pp. 33-40. [2] C. D. Walter, A class number relation in Frobenius extensions of number fields , Mathematika (1977), pp. 216-225. The class number of pure fields of prime degree , Mathematika (1976), pp. 220-226.
Number Theory - Wikipedia
In algebraic number theory, the concept of number is expanded to the algebraicnumbers which are roots of polynomials with rational coefficients.
http://www.wikipedia.org/wiki/Number_theory

Extractions: Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Other languages: Esperanto Nederlands Polski From Wikipedia, the free encyclopedia. Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers . More generally, it has come to be concerned with a wider class of problems that are "easily understood by laymen" - this expansion has occurred as the techniques are used to attack wider varieties of problems. Number theory may be subdivided into several fields according to the methods used and the questions investigated. In elementary number theory , the integers are studied without use of techniques from other mathematical fields. Questions of divisibility, the Euclidean algorithm to compute greatest common divisors , factorization of integers into prime numbers , investigation of perfect numbers and congruences belong here. Typical statements are
Oberwolfach-Seminars 2002
Explicit algebraic number theory November 10 16, 2002. The spirit of the presentseminar is similar, within the smaller compass of algebraic number theory.
http://www.mfo.de/Seminars/Seminars_2002.html

Extractions: Mathematisches Forschungsinstitut Oberwolfach / Oberwolfach-Seminars These seminars are a continuation of the DMV-Seminars initiated by Deutsche Mathematiker Vereinigung. They address postdocs and Ph.D. students from all over Europe. The aim is to introduce the participants to a particular hot development. The seminars take place at Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 25. Applications including a short summary of previous work and interest should be sent to: Prof. Dr. Gert-Martin Greuel Deadline for Application: April 15, 2002 Organizers: Jim Fill (Baltimore) Laurent Saloff-Coste (Ithaca) Subjects: The aim of these lectures is to present some modern aspects of the theory of finite ergodic Markov chains. One focus will be on bounds on the time needed to reach approximate equilibrium; another will be on perfect simulation. Techniques to be presented include both (1) analytic methods based on eigenvalues, functional inequalities, and comparison, and (2) probabilistic methods such as coupling, strong stationary times and duality, coupling from the past, and the Randomness Recycler.
Number Theory - Cambridge University Press
A Brief Guide to algebraic number theory HPF SwinnertonDyer Price£16.95. Broad graduate-level account of algebraic number theory
http://publishing.cambridge.org/stm/mathematics/number/
Algebra And Number Theory At PSU
Algebra and number theory group. Members, seminars, preprints, links.Category Science Math Number Theory Research Groups Colloquium F2000 . Links to some interesting sites Number Theory WebHave fun! algebraic number theory Archives Preprints appear here!
http://www.math.psu.edu/vstein/alg/antheory/numtheory.html

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