21. Homepage Of Mu-Ling Chang University of WisconsinPlatteville. algebraic number theory and algebra. http://www.uwplatt.edu/~changm/

Mu-Ling Chang Position Assistant Professor Department of Mathematics University of Wisconsin-Platteville Platteville, WI 53818 Contact Information Office: 145 Gardner Hall Phone: Fax: E-mail: changm@uwplatt.edu Education Ph.D., University of Maryland, College Park M.S., Tamkang University , Taiwan, R.O.C. B.S., Tunghai University , Taiwan, R.O.C. Research Interests Algebraic number theory and Algebra Teaching Schedule and Office Hours for Spring 2004 Monday Tuesday Wednesday Thursday Friday Math 3630 Office Math 3630 Math 3630 Office Office Office Office Office Office Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Math 2840 Office Office Office For more course information please contact me directly.

22. Math 7290: Seminar In Algebra And Number Theory Advanced topics such as algebraic number theory, algebraic semigroups, quadratic forms, or algebraic Ktheory. Lecture Notes...... 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

23. Midwest Algebraic Number Theory Day Midwest algebraic number theory Day. Saturday, May 10, 2003. University of Illinois at Chicago. Midwest algebraic number theory Day Program. http://www.math.uic.edu/~jeremy/mwants03.html

Midwest Algebraic Number Theory Day Saturday, May 10, 2003 University of Illinois at Chicago Midwest Algebraic Number Theory Day Program Matthew Emerton (Northwestern)) On the p-adic interpolation of automorphic forms Payman Kassaei (MSU) p-adic modular forms over Shimura curves Mihran Papikian (Michigan) Optimal elliptic curves, discriminants and the degree conjecture over function fields. Coffee Break Jim Borger (U Chicago) Non-linear bialgebras: a structural approach to the Witt vectors. D. J. Bernstein (UIC) Sharper ABC-based bounds for congruent polynomials T.H. Yang (Wisconsin) Simplest CM abelian variety over an imaginary quadratic field. Location The meeting will take place in Lecture Center D-4 at the University of Illinois at Chicago. This is one of the small buildings in the center of the East Campus. Directions to Campus are available on the university web page here . You want EAST SIDE! Note: SEO is located in the southwestern corner of (EAST) campus, at the corner of Taylor and Morgan streets. Registration While formal registration is not required, I would appreciate it if you could

24. Basic Library List-Number Theory Compiled by the Mathematical Association of America (MAA). This site subdivides Number Theory into Introductory Texts, Expositions, Elementary Monographs, Primes and Factors, algebraic number theory, Analytic Number Theory, Modular Forms, P-adic Fields, Special Topics, Cryptography, History and Biography and Classic Works. http://www.maa.org/BLL/numtheory.htm

Number Theory Back to Table of Contents Number Theory: Introductory Texts * Andrews, George E. Number Theory. Dover Publications, 1998. ISBN 0486682528 ** Baker, Alan. A Concise Introduction to the Theory of Numbers New York, NY: Cambridge University Press, 1985. ISBN 0521286549. Burn, R.P. A Pathway Into Number Theory New York, NY: Cambridge University Press, 1996. ISBN 0521575400 Burton, David M. Elementary Number Theory, New York, McGraw-Hill Companies, 1997. Second Edition. ISBN 0070094667 * Davenport, Harold. The Higher Arithmetic: An Introduction to the Theory of Numbers, New York, NY: Cambridge University Press, 1998. ISBN 0521634466. Elements of the Theory of Numbers. San Diego, Academic Press, 1999. ISBN 0122091302 Dudley, Underwood. Elementary Number Theory, New York, NY: W.H. Freeman, 1978. ISBN 071670076X. Flath, Daniel E. Introduction to Number Theory * * * Hardy, Godfrey H. and Wright, E. M. Introduction to the Theory of Numbers. Oxford University Press, 1980. ISBN 0198531702 (Out of Print) Hua, Loo-Keng.

25. Nakagawa_Homepage Joetsu University of Education. algebraic number theory the distribution of the discriminants of algebraic number fields, class numbers of binary forms, zeta functions associated with prehomogeneous vector spaces and Igusa's local zeta functions. http://www.juen.ac.jp/math/nakagawa/jin_e.html

Welcome to Nakagawa's Homepage ( last modified on June 25, 2003 ) [Japanese Version] Jin Nakagawa (Number Theory) I am working in algebraic number theory. In particular, I am interested in the distribution of the discriminants of algebraic number fields in connection with class numbers of binary forms, zeta functions associated with prehomogeneous vector spaces and Igusa's local zeta functions. I intend to apply the results of these research to the study of unramified Galois extensions of algebraic number fields, class numbers of algebraic number fields and Iwasawa theory. Introduction to Algebraic Number Fields Publications Class numbers of pairs of symmetric matrices, Acta Arithmetica 105, 207-225 (2002) On the relations among the class numbers of binary cubic forms, Invent. math. 134, 101-138 (1998) Orders of a quaternion algebra over a number field, J. reine angew. Math. 479, 183-194 (1996) Orders of a quartic field, Memoirs Amer. Math. Soc., No. 583 (1996) Orders of quadratic extensions of number fields, Acta Arithmetica LXVII, 229-239 (1994) Binary forms and unramified A n -extensions of quadratic fields, J. reine angew. Math. 406, 167-178 (1990) (Erratum, ibid. 413, 220 (1991))

26. Title Details - Cambridge University Press Home Catalogue A Brief Guide to algebraic number theory. Related Areas A Brief Guide to algebraic number theory. HPF SwinnertonDyer. £17.99. http://titles.cambridge.org/catalogue.asp?isbn=0521004233

27. Schmitt, Susanne MaxPlanck-Institut fuer Informatik. Effective computational geometry, separation bounds; Computer algebra; algebraic number theory, elliptic curves. http://www.mpi-sb.mpg.de/~sschmitt/

Susanne Schmitt Algorithms and Complexity Group (AG1) Stuhlsatzenhausweg 85 Germany Office: Building 46.1, room 318 Phone: +49 681 9325 118 (92 118 on campus) E-mail: sschmitt@mpi-sb.mpg.de Research Interests Effective Computational Geometry, Separation bounds Computer Algebra Algebraic number theory, Elliptic curves Education April 1999: Ph. D. in (supervisor: Prof. Dr. H. G. Zimmer October 1991 - June 1995: Studies in Berechnung der Mordell-Weil Gruppe parametrisierter elliptischer Kurven (supervisor: Prof. Dr. H. G. Zimmer List of Publications S. Schmitt, Computation of the Selmer groups of certain parametrized elliptic curves, Acta Arithmetica, 78(3), pp. 241-254, 1997. Elements with bounded height in number fields, accepted from Periodica Mathematica Hungarica. Preprints S. Schmitt, A conditional algorithm for the computation of the rank of elliptic curves over quadratic number fields. M. Conrad, S. Schmitt, An object oriented concept for elliptic curves. Links Seminar on algebraic and numerical methods in computational geometry The diamond operator

28. 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. In any case, if your preferred mode of communication is the intercontinental ballistic missile , I'd love to give you precise targeting information but can't seem to find it for the present place of residence. Main pages last updated November 13, 2003 (minor updates for new place of residence). All opinions expressed here are mine and may not be those of the University of Liverpool. Pleidiol wyf i'm gwledydd

29. The Math Forum - Math Library - Algebraic Num. Th. This page contains sites relating to algebraic number theory. Browse and Search the Library Home Math Topics Number Theory Algebraic Num. Th. http://mathforum.org/library/topics/alg_nt/

Browse and Search the Library Home Math Topics Number Theory : Algebraic Num. Th. Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Algebraic Number Theory: Global Fields - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to algebraic number theory. Subcategories include rings of algebraic integers, quadratic extensions, Iwasawa theory, Galois theory, Langlands-Weil conjectures, density theorems, Adele rings and groups, class groups and Picard groups of orders, and many more. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 24 items found, showing 1 to 24 Algebraic Number Theory Archives - Boston, Grayson Preprints about algebraic number theory and arithmetic geometry are accepted in electronic form for storage until publication. There are instructions for authors who wish to submit preprints to the archives and for for joining the mailing list (members ...more>> Algebra Through Problem Solving - Hillman, Alexanderson

30. The Math Forum - Math Library - Number Theory algebraic number theory and Elliptic Curves Ghitza, Osserman; Massachusetts Institute of Technology A semester-long seminar giving a rapid introduction to http://mathforum.org/library/topics/number_theory/

Browse and Search the Library Home Math Topics : Number Theory Library Home Search Full Table of Contents Suggest a Link ... Library Help Subcategories (see also All Sites in this category Algebraic Number Theory Analytic Number Theory Sequences and Sets Fibonacci Sequence Selected Sites (see also All Sites in this category Continued Fractions: an Introduction - Adam Van Tuyl A brief introduction to the field of continued fractions, including some basic theory about the subject; the history of continued fractions, tracing some of the major developments in the field in the past 2500 years; some interactive applications that demonstrate the uses of continued fractions and let you calculate them; and the resources used in creating this site, including a bibliography and links to other sites on the Web. more>> Fermat's Last Theorem - MacTutor Math History Archives Essay describing Fermat's theorem with links to mathematicians such as Sophie Germain, Legendre, Dirichlet, Shimura and Taniyama, etc., from its inception through Andrew Wiles' proof, with another web site and 17 references (books/articles). more>> Number Theory - Dave Rusin; The Mathematical Atlas

31. Number Theory - Wikipedia, The Free Encyclopedia In algebraic number theory, the concept of number is expanded to the algebraic numbers which are roots of polynomials with rational coefficients. http://en.wikipedia.org/wiki/Number_theory

Number theory From Wikipedia, the free encyclopedia. Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers. Number theory may be subdivided into several fields according to the methods used and the questions investigated. See for example the list of number theory topics The term " arithmetic " is also used to refer to number theory. This is a somewhat older term, which is no longer as popular as it once was. Nevertheless, the term remains prevalent e.g. in the names of mathematical fields (arithmetic algebraic geometry and the arithmetic of elliptic curves and surfaces). This sense of the term arithmetic should not be confused with the branch of logic which studies arithmetic in the sense of formal systems. In elementary number theory , the integers are studied without use of techniques from other mathematical fields. Questions of

32. CRC Press Online algebraic number theory. Richard theory; Explores in detail the direct, practical application of algebraic number theory to cryptography; http://www.crcpress.com/us/product.asp?sku=3989 &dept_id=1

33. NoMaDS link to NoMaDS past programmes. North of England algebraic number theory Group. This is the home page for the North of England algebraic number theory Group. http://www.shef.ac.uk/~pm1afj/lms/

North of England Algebraic Number Theory Group This is the home page for the North of England Algebraic Number Theory Group. This group is based at Durham, Nottingham, Sheffield and UMIST, and we are grateful to the London Mathematical Society . for financially supporting the group by means of a Scheme 3 grant. This grant has been renewed for 2003-04, and pays for travel expenses for NoMaDS members, as well as other visitors (if sufficient funds are available). Although our official title is the one given above, we informally refer to ourselves as NoMaDS (an abbreviation of No ttingham, Ma nchester, D urham and S heffield, the host cities), as suggested by John Cremona. Twelfth meeting, Nottingham (1/5/2004) The twelfth meeting is on Saturday May 1st in Nottingham. The programme is as follows: TEA Shuji Saito (Nagoya) Motivic cohomology and cycle class map for semistable schemes over integer rings Alexander Stasinski (Nottingham) Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties LUNCH Caucher Birkar (Nottingham) Termination in minimal model programme Kazuya Kato (Kyoto) Ramification theory of schemes DINNER Directions to the Nottingham campus Map of the Nottingham campus Maps of the department Frazer Jarvis, April 8th, 2004.

34. Dirichlet Proved that in any arithmetic progression with first term coprime to the difference there are infinitely many primes, units in algebraic number theory, ideals, proposed the modern definition of a function. http://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Dirichlet.html

Johann Peter Gustav Lejeune Dirichlet Born: Died: Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Lejeune Dirichlet Gymnasium in Bonn in 1817, at the age of 12, he had developed a passion for mathematics and spent his pocket-money on buying mathematics books. At the Gymnasium he was a model pupil being [1]:- ... an unusually attentive and well-behaved pupil who was particularly interested in history as well as mathematics. After two years at the Gymnasium in Bonn his parents decided that they would rather have him attend the Jesuit College in Cologne and there he had the good fortune to be taught by Ohm . By the age of 16 Dirichlet had completed his school qualifications and was ready to enter university. However, the standards in German universities were not high at this time so Dirichlet decided to study in Paris. It is interesting to note that some years later the standards in German universities would become the best in the world and Dirichlet himself would play a hand in the transformation. Dirichlet set off for France carrying with him Gauss 's Disquisitiones arithmeticae Biot Fourier Francoeur Hachette ... Legendre , and Poisson Dirichlet's first paper was to bring him instant fame since it concerned the famous Fermat's Last Theorem . The theorem claimed that for n x y z such that x n y n z n . The cases n = 3 and n = 4 had been proved by Euler and Fermat , and Dirichlet attacked the theorem for

35. 11: Number Theory algebraic number theory extends the 11R algebraic number theory global fields. For complex multiplication, see 11G15. For Galois theory see also 12XX. http://www.math.niu.edu/~rusin/known-math/index/11-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11: Number theory Introduction Number theory is one of the oldest branches of pure mathematics, and one of the largest. Of course, it concerns questions about numbers, usually meaning whole numbers or rational numbers (fractions). Elementary number theory involves divisibility among integers the division "algorithm", the Euclidean algorithm (and thus the existence of greatest common divisors), elementary properties of primes (the unique factorization theorem, the infinitude of primes), congruences (and the structure of the sets Z /n Z as commutative rings), including Fermat's little theorem and Euler's theorem extending it. But the term "elementary" is usually used in this setting only to mean that no advanced tools from other areas are used not The remaining parts of number theory are more or less closely allied with other branches of mathematics, and typically use tools from those areas. For example, many questions in number theory may be posed as Diophantine equations equations to be solved in integers without much preparation. Catalan's conjecture are 8 and 9 the only consecutive powers? asks for the solution to

36. GraNTS GRAduate Number Theory Seminar algebraic number theory and Elliptic Curves. If you are looking for the web algebraic number theory http://www-math.mit.edu/~osserman/seminar/

GRAduate Number Theory Seminar: Algebraic Number Theory and Elliptic Curves If you are looking for the web page of last Spring's Kolyvagin seminar, you want here instead. Practical information Seminar description Lecture notes Lecture schedule ... References Practical Information Organizers: Alex Ghitza ( aghitza@math.mit.edu ) and Brian Osserman ( osserman@math.mit.edu When: Fall 2000, 2 hours/week, MoFr 11-12 Where: MIT, Rm 24-110 Seminar Description Format: a semester-long seminar giving a rapid introduction to algebraic number theory and elliptic curves. Hopefully, the material will end up including exactly what is needed for an elegant proof of the class number 1 problem for imaginary quadratic extensions, which we will then be able to present at the end of the semester. All participants will be expected to give lectures, and to prepare TeX lecture handouts. Topics: Dedekind domains, rings of integers, scheme-theoretic curves, finite morphisms thereof, splitting and ramification, the Tchebotarov density theorem and class field theory, selected introductory topics from elliptic curve theory, complex multiplication, modular curves, and the solution to Gauss' class number 1 problem. Prerequisites: A semester of graduate algebraic geometry, and familiarity with the commutative algebra required therein.

37. Math 254 (Number Theory) me for details. Prerequisites. Required one semester of algebraic number theory (Math 254A or equivalent). More specifically, this http://www-math.mit.edu/~kedlaya/math254b.html

Math 254B (Number Theory) This was the official course web page for Math 254B (Number Theory) at UC Berkeley, which I taught during the Spring 2002 semester. The course web page for Math 254A, which I taught in Fall 2001, is here . Math 254B took a detailed look at class field theory, the theory of abelian extensions of number fields, which extends the reciprocity laws of Gauss, Legendre, Hilbert et al. Note added 9 Nov 2003: I am planning to leave these pages "as is" for now except for updating broken links and posting errata to the course notes in case anyone points them out. (These were largely corrected verbally in the lectures but I didn't put the changes into the notes.) In particular, the contact information for me is incorrect; see my home page for updated information. Stuff to download Note added 19 Jul 2002: all PostScript files are now compressed using gzip to save space. To decompress, type "gunzip blah.ps.gz"; your browser or PostScript viewer may do the decompression automatically. Course description and syllabus Lecture notes Final papers Current announcements The final papers are being posted here. If you want me to include yours, email me a copy in any format (except Word!).

38. Algebraic Number -- From MathWorld Ferreirós, J. The Emergence of algebraic number theory. §3.3 in Labyrinth of Thought A History of Set Theory and Its Role in Modern Mathematics. http://mathworld.wolfram.com/AlgebraicNumber.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Algebra Field Theory Number Theory ... Transcendental Numbers Algebraic Number If r is a root of the polynomial equation where the s are integers and r satisfies no similar equation of degree then r is an algebraic number of degree n . If r is an algebraic number and then it is called an algebraic integer If, instead of being integers, the s in the above equation are algebraic numbers then any root of is an algebraic number. If is an algebraic number of degree n satisfying the polynomial equation then there are other algebraic numbers ... called the conjugates of Furthermore, if satisfies any other algebraic equation, then its conjugates also satisfy the same equation (Conway and Guy 1996). Any number which is not algebraic is said to be transcendental . The set of algebraic numbers is denoted Mathematica ), or sometimes

39. Algebraic Number Theory -- From MathWorld Contribute! Sign the Guestbook, MATHWORLD IN PRINT, Order book from Amazon, Number Theory algebraic number theory Math Contributors Terr. algebraic number theory. http://mathworld.wolfram.com/AlgebraicNumberTheory.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Number Theory Algebraic Number Theory Math Contributors ... Terr Algebraic Number Theory This entry contributed by David Terr Algebraic number theory is the branch of number theory that deals with algebraic numbers . Historically, algebraic number theory developed as a set of tools for solving problems in elementary number theory , namely Diophantine equations (i.e., equations whose solutions are integers or rational numbers ). Using algebraic number theory, some of these equations can be solved by " lifting " from the field of rational numbers to an algebraic extension K of More recently, algebraic number theory has developed into the abstract study of algebraic numbers and number fields themselves, as well as their properties. Algebraic Extension Algebraic Integer Algebraic Number Class Group ... search Stewart, I. and Tall, D.

40. Online Number Theory Lecture Notes algebraic number theory and commutative algebra, lecture notes by Robert Ash; Zahlentheorie (Notes by Winfried Bruns); Algebra 2 number 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 Lecture notes on elementary number theory (John Cremona) Modular forms (Igor Dolgachev) The Modular curves X (N), Lecture notes by Bas Edixhoven

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