21. Tan Victor National University of Singapore. Automorphic forms and representations, algebraic number theory, modular forms and elliptic functions, combinatorial designs and difference sets. http://www.math.nus.edu.sg/~mattanv/

Home Page of Tan Victor Education B.Sc.(Hons), M.Sc., National University of Singapore Ph.D., University of California, Los Angeles Current interests Linear Preserver Problems Number Theory Automorphic Forms Combinatorial Designs List of publications The module I am teaching this semester Script writing for stage plays Great mathematicians Some mathematical links Tan Victor Block S14 #02-17 Department of Mathematics National University of Singapore 2 Science Drive 2, Singapore 117543 Republic of Singapore Send me an email at: mattanv@nus.edu.sg (65) 6874-7936 (office) (65) 6779-5452 (fax) Back to the home page of the Department of Mathematics

22. Algebraic Number Theory algebraic number theory, I.N. Stewart and D.O. Tall, (Second Edition), Chapman and Hall/CRC Press 1987 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

23. 11R: Algebraic Number Theory: Global Fields There are quite a few texts in algebraic number theory. Mines, Ray, algebraic number theory, a survey , The LEJ Brouwer Centenary Symposium http://www.math.niu.edu/~rusin/known-math/index/11RXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11R: Algebraic number theory: global fields Introduction History Applications and related fields For complex multiplication, See 11G15 The rings of integers in these fields are also studied in Commutative Ring Theory , where we may find discussion of Unique Factorization Domains (UFDs), Euclidean domains, etc. Subfields Algebraic numbers; rings of algebraic integers PV-numbers and generalizations; other special algebraic numbers Polynomials (irreducibility, etc.) Quadratic extensions Cubic and quartic extensions Cyclotomic extensions Other abelian and metabelian extensions Other number fields Iwasawa theory Units and factorization Class numbers, class groups, discriminants Galois theory Integral representations related to algebraic numbers; Galois module structure of rings of integers, See Also 20C10 Galois cohomology, See also 12Gxx, 16H05, 19A31 Class field theory Langlands-Weil conjectures, nonabelian class field theory, See also 11Fxx, 22E55

24. Mathematics Disclaimer Staff Web Page http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

25. Algebraic Number Theory algebraic number theory. Math 676.dvi; Math 676.ps.gz Math 676.pdf. v2.01; August 14, 1996; first version on the web; 144p. v2.10; August 31, 1998; http://www.jmilne.org/math/CourseNotes/math676.html

Algebraic Number Theory Algebraic Number Theory Math 676.dvi Math 676.ps.gz Math 676.pdf v2.01; August 14, 1996; first version on the web; 144p. v2.10; August 31, 1998; fixed many minor errors; added exercises and index; 140p. Contents Preliminaries From Commutative Algebra Rings of Integers Dedekind Domains; Factorization The Finiteness of the Class Number The Unit Theorem Cyclotomic Extensions; Fermat's Last Theorem Valuations; Local Fields Global Fields Solutions for the exercises 676sltn.dvi The final exam for the course 676exam.dvi Errata

26. Lecture Notes Taken by Sean SatherWagstaff, Utah, Spring 1999. In PS and PDF formats. http://www.math.uiuc.edu/~ssather/MATH/notes.html

Lecture Notes Notes for lectures on "Koszul cohomology and Cohen structure theorems" given at the University of Utah mini-course on "Classical Problems in Commutative Algebra", June 2004. Notes for Dick Gross' Algebraic Number Theory Course given at the University of Utah, Spring 1999: all lectures (1-18) compressed .ps or .pdf Back to Sean's homepage. Last updated 08.10.04

27. A Brief Introduction To Classical And Adelic Algebraic Number Theory A Brief Introduction To Classical And Adelic algebraic number theory. William Stein. (based on books of SwinnertonDyer and Cassels). May 2004 http://modular.fas.harvard.edu/papers/ant/

A Brief Introduction To Classical And Adelic Algebraic Number Theory William Stein (based on books of Swinnerton-Dyer and Cassels) May 2004 Download for free: Online (HTML) version PDF version DVI version (0.6MB, missing 3 diagrams) PS version Latex source files License (this is basically the license this book is released under) I wrote this book for Math 129 at Harvard during Spring 2004. I'm making it available to everyone for free under very liberal conditions. For example, please feel free to put a copy on other web sites, or to make printouts or copies available to your students (even if you have to charge the students for reproduction costs).

28. Homepage: Susanne Schmitt (Max-Planck-Institut Für Informatik) MaxPlanck-Institut f¼r Informatik. Effective computational geometry, separation bounds; Computer algebra; algebraic number theory, elliptic curves. Publications. http://www.mpi-sb.mpg.de/~sschmitt/

Department 1: Algorithms and Complexity max planck institut informatik Homepage Susanne Schmitt Department 1: Algorithms and Complexity Building 46.1 , Room 318 Stuhlsatzenhausweg 85 Germany Email: Get my email address via email Phone: Fax: Research Interests Real algebraic numbers, Root isolation, Separation bounds Effective Computational Geometry Computer Algebra Algebraic number theory, Elliptic curves Publications Publications of Dr. Susanne Schmitt Teaching Summer term 2005: Seminar Geometrische Algorithmen, Dr. Susanne Schmitt, Dr. Nicola Wolpert Earlier terms Winter term 2004/2005: Seminar Geometric Rounding, Dr. Lutz Kettner, Dr. Susanne Schmitt Winter term 2004/2005: Lecture Dr. Lutz Kettner, Dr. Susanne Schmitt, Dr. Nicola Wolpert Summer term 2004: Seminar Theorie und Praxis geometrischer Algorithmen, Dr. Susanne Schmitt, Dr. Nicola Wolpert Winter term 2003/2004: Lecture Effective Computational Geometry for Curves and Surfaces, Dr. Lutz Kettner, Dr. Susanne Schmitt, Dr. Nicola Wolpert

29. Online Number Theory Lecture Notes algebraic number theory and commutative algebra, lecture notes by Robert Ash Lecture notes on algebraic number theory (Jerome Hoffman) http://www.numbertheory.org/ntw/lecture_notes.html

Online number theory lecture notes Selected from N4.html Lecture notes in Greek (Jannis Antoniadis) Number theory in the 17th and 18th centuries (ps 1281K) Elliptic curves (Mordell's theorem) (ps 1021K) L-series (ps 1953K) Lecture notes on p-adic numbers and introductory number theory (Andrew Baker) Algebraic Number Theory and commutative algebra , lecture notes by Robert Ash Zahlentheorie (Notes by Winfried Bruns) Algebra 2 - number theory for teacher education , Michal Bulant (in Czech) MAS4002: Algebraic Number Theory , Course notes by Robin Chapman, University of Exeter Algebraic Number Theory and Automorphic L-functions , lecture notes by Ching-Li Chai Lectures on irregularities of point distribution , (notes by William Chen) Elementary and Analytic Number Theory , Lecture notes by William Chen Computational class field theory , A course given at the Middle East Technical University, Ankara, 1997 by Henri Cohen (dvi 255K) Draft chapters of elliptic curve handbook ECH1 Modular forms (Igor Dolgachev) The Modular curves X (N), Lecture notes by Bas Edixhoven

30. Algebra And Number Theory KANT stands for Computational algebraic number theory with a slight hint to its German origin (Immanuel Kant). The KANT functions are accessible through a http://www.math.tu-berlin.de/~kant/

Algebra and Number Theory The KANT Group The KANT Group: [members] [publications] [database] ... KANT/KASH - computer algebra system KANT is a computer algebra system for sophisticated computations in algebraic number fields. It has been developed under the project leadership of Prof. Dr. M. Pohst at the Technische Universität Berlin. KANT stands for Computational Algebraic Number Theory with a slight hint to its German origin ( Immanuel Kant The KANT functions are accessible through a user-friendly shell named KASH (KAnt SHell) which is freely available. You can pick up the current release of KASH using ftp or from our downlad page Most of the functionality of KASH is also available through a web interface ( webkash QaoS - Querying Algebraic Objects System  new  QaoS is a database interface implemented under the aspect to establish a common gateway via web-browsers and computer algebra systems. QaoS is designed to fulfil modern demands for accessing large amounts of pre-computed algebraic data, both comfortably and fast. ANTS VII The 7th Algorithmic Number Theory Symposium will take place from July 23 to July 28, 2006 at Technische Universität Berlin.

31. Useful Websites University of WisconsinPlatteville. algebraic number theory and algebra. http://www.uwplatt.edu/~changm/

Mu-Ling Chang Position Contact Information Research Assistant Professor Office: 145 Gardner Hall Algebraic Number Theory and Algebra Department of Mathematics Phone: (608) 342-1945 University of Wisconsin-Platteville E-mail: changm@uwplatt.edu Education Platteville, WI 53818 Fax: (608) 342-1767 Ph.D., University of Maryland at College Park Teaching Schedule and Office Hours for Fall 2005 Monday Tuesday Wednesday Thursday Friday Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Office Office Office Office Math 3630 Math 3630 Math 3630 Office Office Office Office Office Office

32. Math 129: Introduction To Algebraic Number Theory Introduction to algebraic number theory. The Spring 2005 Math 129 Web Site. By William Stein Student Projects Course Textbook http://modular.fas.harvard.edu/edu/Spring2004/129/

Mathematics 129 Introduction to Algebraic Number Theory The Spring 2005 Math 129 Web Site By William Stein Student Projects Course Textbook Virtual Office Hours Spring 2004 Harvard University Department of Mathematics

33. Jürgen Klüners Universit¤t Kassel. algebraic number theory, computational class field theory, Galois rheory, computer algebra. KANT software, tables of extensions of the rationals which contains polynomials for all Galois groups up to degree 15. http://www.mathematik.uni-kassel.de/~klueners/

der Heinrich-Plett-Str. 40 34132 Kassel Germany E-Mail: klueners@mathematik.uni-kassel.de Telefon: +49 561/804-4192 Telefax: +49 561/804-4646 Fields of mathematical interest: Algebraic Number Theory, Computational Class Field Theory, Galois Theory, Computer Algebra I have developed and implemented algorithms for algebraic number fields. All algorithms are implemented in the computer algebra system KANT . Have a look at the homepage of our research group Computational Mathematics . I have created a database for field extensions of the rationals which contains polynomials for all Galois groups up to degree 15. Research Publications Lehre (in German) Private stuff (Chess,...) (in German) ... webmaster Last modified: Mon Apr 11 13:22:49 CEST 2005

34. UR Department Of Mathematics - Naomi Jochnowitz University of Rochester. algebraic number theory, modular forms, padic modular forms. http://www.math.rochester.edu/people/faculty/what/

Naomi Jochnowitz Department of Mathematics University of Rochester Rochester, NY 14627 Office: Hylan 1003 Fax: (716) 244-6631 E-mail: what@math.rochester.edu Research Interests Algebraic number theory, modular forms, p-adic modular forms.

35. Math 7290: Seminar In Algebra And Number Theory Advanced topics such as algebraic number theory, algebraic semigroups, quadratic forms, or algebraic Ktheory.......Course http://www.math.lsu.edu/~hoffman/7290algnmbrtheory.html

Math 7290: Seminar in Algebra and Number Theory Spring 2000 Course Information Professor: Jerome W. Hoffman Time and Place: 2:40-3:30 MWF, 111 Lockett Course Description: Advanced topics such as algebraic number theory, algebraic semigroups, quadratic forms, or algebraic K-theory. Lecture Notes To view these files, you may need the following free software: Adobe Acrobat Reader (pdf) IBM techexplorer HyperMedia Browser (tex) MiKTeX (dvi) Lecture 1 tex dvi Lecture 2 tex dvi Lecture 3 tex dvi Lecture 4 tex dvi Lecture 5 tex dvi Lecture 6 tex dvi Lecture 7 tex dvi Lecture 8 tex dvi Lecture 9 tex dvi Lecture 10 ( tex dvi Lecture 11 tex dvi Lecture 12 tex dvi Lecture 13 tex dvi Lecture 14 tex dvi Lecture 15 tex dvi Lecture 16 tex dvi Lecture 17 tex dvi Lecture 18 tex dvi Lecture 19 tex dvi Lecture 20 tex dvi Lecture 21 tex dvi Lecture 22 ( tex dvi Lecture 23 tex dvi Lecture 24 tex dvi Lecture 25 tex dvi Lecture 26 tex dvi Lecture 27 tex dvi Lecture 28 tex dvi Lecture 29 tex dvi Lecture 30 tex dvi Lecture 31 tex dvi Lecture 32 tex dvi Lecture 33 tex dvi Lecture 34 tex dvi Lecture 35 tex dvi Lecture 36 tex dvi Lecture 37 tex dvi Lecture 38 tex dvi Lecture 39 tex dvi Lecture 40 tex dvi Lecture 41 tex dvi Lecture 42 tex dvi Lecture 43 tex dvi Lecture 44 tex dvi Department of Mathematics Louisiana State University 374 Lockett Baton Rouge, LA, 70803

36. Adam's Home Page University of Liverpool. algebraic number theory and elliptic curves; the BrauerManin obstruction to rational points on surfaces; Iwasawa theory. http://www.liv.ac.uk/~adaml/

Adam Logan's Very Basic Home Page Welcome to Adam's WWW page. May I direct you to my professional page or to my personal page If you need to get in touch with me from here: my e-mail address (generally preferred) is adaml@liv.ac.uk . My office telephone number is 44 (0)151 794 4042, and my office is Mathematics and Oceanography 512. If you want to contact me in some other way, sending e-mail first is probably a good idea. If your preferred mode of communication is the intercontinental ballistic missile Main pages last updated April 27, 2005 (plans for next year added to professional page). Any opinions expressed here are mine and not those of the University of Liverpool. Pleidiol wyf i'm gwledydd

37. PlanetMath: Algebraic Number Theory algebraic number theory is the study of algebraic numbers, 11R99 (Number theory algebraic number theory global fields Miscellaneous) http://planetmath.org/encyclopedia/AlgebraicNumberTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About algebraic number theory (Topic) Algebraic Number Theory This entry is a collection of links to entries on algebraic number theory in Planetmath (therefore bound to be always under construction ). It is the hope of the author(s) that someday this can be used as a ``graduate text'' to learn the subject by reading the individual entries listed here. Each section contains a brief description of the concepts, which is expanded in the entries. Some of the concepts might be missing in Planetmath as of today (please consider writing an entry on them!). In order to organize the entry in sections , we followed the main reference [ Mar Introduction The entry number theory contains a nice introduction to the broad subject. From very early on, mathematicians have tried to understand the

38. PlanetMath: Number Theory class field theory constituted the bulk of algebraic number theory research. In the latter half, algebraic number theory has been subsumed under http://planetmath.org/encyclopedia/NumberTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About number theory (Topic) Number theory is the branch of math concerned with the study of the integers , and of the objects and structures that naturally arise from their study. It is one of the oldest parts of mathematics, alongside geometry , and has been studied at least since the ancient Mesopotamians. Perhaps because of its purely mathematical nature (at least until the development of cryptography in the twentieth century, number theory was devoid of practical applications), number theory has often been considered as a central and particularly beautiful part of mathematics. Carl Friedrich Gauss , arguably the greatest number theorist of all time, has called mathematics the ``Queen of science'' and he referred to Number Theory as the ``Queen of Mathematics''. Number theory has attracted many of the most outstanding mathematicians in history: Euclid, Diophantus, Fermat, Legendre, Euler Number theory is also remarkable because small, easy-to-understand

39. Henri Darmon - Home Page - Math McGill McGill University. algebraic number theory, with a special emphasis on elliptic curves, modular forms, and their associated Lfunctions. http://www.math.mcgill.ca/~darmon/

Graduate Student Theses Number Theory Software ... Seminar Henri Darmon James McGill Professor, Department of Mathematics. Office: Burnside Hall, Room 1111 Office Hours: By appointement. Office Phone: Office Fax: Previous Trips and Conferences May 25-27, 2005. Workshop on p-adic methods in automorphic forms. Columbia University, New York. June 4-6, 2005. Symposium on L-functions and algebraic curves, Waterloo. June 13-17, 2005. Open questions and recent developments in Iwasawa Theory. In honor of Ralph Greenberg's 60th birthday. Boston, Massachusetts. Upcoming Trips and Conferences August 1-10, 2005. Number theory conference, Morningside Center, Beijing, China. 2005-06 Academic year. (With David and Granville) Special year in Analysis and Number Theory at the CRM in Montreal. Sept 12-16, 2005. (With Iovita) Workshop on p-adic representations at the CRM in Montreal. Nov 12, 2005. Fields Institute Scientific Advisory Panel meeting (Toronto). Dec 12-16, 2005. (With Goren) Workshop on intersection of arithmetic cycles and automorphic forms at the CRM in Montreal. February 4-8, 2006. NSERC GSC meeting, Ottawa.

40. Algebraic Number Theory The book `algebraic number theory and Fermat s last theorem by Stewart and Tall and several books entitled `algebraic number theory , such as those by E. http://www.math.leidenuniv.nl/~reinier/ant.shtml

Algebraic Number Theory, 2004 Organization Instructors: Peter Stevenhagen , office 225, Mathematisch Instituut, Leiden, e-mail: psh@math.leidenuniv.nl , office 250, Mathematisch Instituut, Leiden, e-mail: reinier@math.leidenuniv.nl The lectures will be given on Thursday morning from 10:15 until 13:00 in room P.016 of the Euclides building (Plantage Muidergracht 24) of the University of Amsterdam. The final hour (12:15-13:00) will be devoted to homework problems. The lectures start on September 9th and continue until December 16th; there won't be any lecture on October 14th. Attending this course will be rewarded with 8 EC points. Prerequisites Undergraduate algebra, i.e., the basic properties of groups, rings and fields. This material is covered in first and second year algebra courses in the bachelor program of most universities. The course notes used in Leiden-Delft can be found here Literature AddAll Description Introduction to algebraic numbers and number rings. Ideal factorization, finiteness results on class groups and units, explicit computation of these invariants. Special topics: binary quadratic forms, the number field sieve. Valuations and completions, local fields, introduction to class field theory. Special topics: reciprocity laws, representation of primes by quadratic forms, density theorems. Examination The final grade is exclusively based on the results obtained for the weekly homework assignments. The final homework assignment will be slightly more substantial.

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