61. Number Theory Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral http://store.doverpublications.com/0486682528.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Bridge and Other Card Game...... Business and Economics Chess Children Clip Art and Design on CD-...... Coloring Books Cookbooks, Nutrition Crafts Detective, Ghost , Superna...... Dover Patriot Shop Ethnic Interest Features Gift Certificates Gift Ideas History, Political Science...... Holidays Humor Languages and Linguistics Literature Magic, Legerdemain Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy and Religion Photography Posters Psychology, Education Puzzles, Amusement, Recrea...... Science and Mathematics Shakespeare Shop Sociology, Anthropology, M...... Sports, Out-of-Door Activi...... Stationery, Gift Sets Stationery, Seasonal Books...... Summer Fun Shop Summer Reading Shop Teacher's Store Travel and Adventure Women's Studies Clearance Center By Subject Science and Mathematics Mathematics Number Theory Number Theory George E. Andrews Our Price Availability: In Stock Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Multiplicativity-divisibility, quadratic congruences, additivity, more.

62. Hisao TAYA -Math. Lab. GSIS Tohoku Univ.- English Tohoku University. algebraic number theory, Iwasawa theory. http://www.math.is.tohoku.ac.jp/~taya/index-e.html

Division of Mathematics, Graduate School of Information Sciences, Tohoku University English Japanese Welcome to HISAO TAYA's Home Page !! Research Interest List of Papers My Vita Home Page of Div. of Math., GSIS, Tohoku University ... Home Page of Mathematical Institute, Tohoku University Graduate School of Information Sciences, Tohoku University, Aramaki-Aza-Aoba 09, Aoba-ku, Sendai 980-8579, JAPAN TEL:+081-22-795-4638, FAX:+081-22-795-4654 Hisao TAYA

63. The Theory Of Algebraic Numbers An excellent introduction to the basics of algebraic number theory, this concise, wellwritten volume examines Gaussian primes; polynomials over a field; http://store.doverpublications.com/0486404544.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Bridge and Other Card Game...... Business and Economics Chess Children Clip Art and Design on CD-...... Coloring Books Cookbooks, Nutrition Crafts Detective, Ghost , Superna...... Dover Patriot Shop Ethnic Interest Features Gift Certificates Gift Ideas History, Political Science...... Holidays Humor Languages and Linguistics Literature Magic, Legerdemain Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy and Religion Photography Posters Psychology, Education Puzzles, Amusement, Recrea...... Science and Mathematics Shakespeare Shop Sociology, Anthropology, M...... Sports, Out-of-Door Activi...... Stationery, Gift Sets Stationery, Seasonal Books...... Summer Fun Shop Summer Reading Shop Teacher's Store Travel and Adventure Women's Studies Clearance Center By Subject Science and Mathematics Mathematics Number Theory The Theory of Algebraic Numbers Harry Pollard Harold G. Diamond Our Price (Table of Contents) Availability: In Stock Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

64. Ronald Van Luijk University of California Berkeley. Algebraic geometry, algebraic number theory, arithmetic geometry and related topics. Catalogue of algebraic surfaces. http://math.berkeley.edu/~rmluijk/

Graduate Students Mathematics UC Berkeley University of California Ronald van Luijk 853 Evans Hall Office Hours: Department Fax: E-Mail: rmluijk@math.berkeley.edu Department of Mathematics 3840 853 Evans Hall University of California Berkeley, CA 94720-3840 USA Application Material I am applying for postdoc positions. My application material can be found here Thesis My graduate thesis can be found here Research I did my undergraduate at the University of Utrecht. I graduated in 2000 under the supervision of Frits Beukers and Ben Moonen . My thesis was about Perfect Cuboids I am currently a PhD student at UC Berkeley in my final year, interested in Algebraic Geometry, Algebraic Number Theory, Arithmetic Geometry and related topics. I expect to graduate in May 2005. My thesis will be titled "Rational points on K3 surfaces." Papers and Presentations Preprints of articles based on my thesis work and slides from presentations can be found here Catalogue of Surfaces I intend to start a catalogue of algebraic surfaces , that are of interest to number theorists because of their rational points. The catalogue will include references, so that if "new" surfaces pop up, they can be compared with other surfaces, that have already been analysed. As for now, the catalogue doesn't contain many surfaces yet. Please e-mail me about any surfaces you've encountered and/or worked on, that might be of interest. Teaching Math 1B (Calculus), spring 2001

65. IMSAS Staff - Dr Chris Woodcock, University Of Kent University of Kent at Canterbury. Commutative algebra, algebraic geometry and algebraic number theory; padic analogues of classical functions and their applications in number theory. http://www.kent.ac.uk/ims/people/cfw/index.htm

Skip search Search: all of kent.ac.uk IMSAS only text only University of Kent Dr Chris Woodcock You are here: Kent home ims people cfw Senior Lecturer in Pure Mathematics Pure Mathematics Group Publications Room Telephone internal 3803 external +44 1227 823803 Email C.F.Woodcock@kent.ac.uk Interests: Commutative algebra, algebraic geometry and algebraic number theory; p-adic analogues of classical functions and their applications in number theory. contact us at ims_secs@kent.ac.uk Skip browse form Browse: Main website sections About the University Maps and directions Courses and studying at Kent Research Services for business Schools and colleges Arts, leisure and public events Conference, functions and holidays Departments and people Alumni, families and friends Student and staff intranet News, press releases and job vacancies

66. NoMaDS North of England algebraic number theory Group, meeting termly, based at Durham, Nottingham, Sheffield and Manchester. Fifteenth meeting Nottingham 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 Manchester, 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 2004-05, 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. Fifteenth meeting, Nottingham (29/4/2005) The fifteenth meeting will take place on Friday April 29th in Nottingham. Here is the programme: Anand Pillay (UIUC) Nonstandard objects in model theory and geometry Abstract Angus MacIntyre (QMW) Model theory of d/dp for prime p Abstract : Tate's da/dp=(a^p-Frob(a))/p involves the Frobenius operator on the Witt vectors over the algebraic closure of the field of p elements. In joint work with Belair and Scanlon, I analyze this structure from model theory point of view. In particular, I will present details on a Hensel's lemma for the above operator, and discuss the model theory of letting

67. Algebra & Number Theory In The Department Of Mathematics & Statistics @ McMaster algebraic number theory concerns the special case when the equations have rational or integral coefficients, and Algebraic Geometry involves a powerful http://www.math.mcmaster.ca/research/area.php?area_id=1

68. Algebraic Number Theory 3) J. Neukirch, algebraic number theory (Chapters 1 2). 4) JWS Cassels, A. Fršhlich, eds., algebraic number theory (Chapters IIII) http://www.math.mcmaster.ca/~sharifi/syllabus.html

Algebraic Number Theory Math 705 Prof. Romyar Sharifi W 12:30-2:30, Th 12:30-1:30 in HH-312 We will assume knowledge on the level of a first year graduate sequence in algebra (e.g., Math 701-702) and some basic point-set topology: Field and Galois theory characteristic, finite fields field extensions (finite, normal, separable, Galois, abelian, cyclic, infinite, algebraic, transcendental) splitting field of a polynomial, Galois closure, degree automorphisms, embeddings primitive element, conjugate elements algebraic and separable closure, maximal abelian extension restriction, invariant subfields vector spaces, duals Commutative Ring Theory domains, UFDs, PIDs, Euclidean domains prime ideals, maximal ideals, unit groups polynomial rings, quotient fields Noetherian rings modules, generators, rank homomorphisms of rings and modules NakayamaÕs Lemma modules over PIDs Noncommutative rings group rings, division algebras, matrix rings Homological algebra kernel, image, cokernel of module homomorphisms inverse/direct limits exact sequences, left/right exactness

69. Www.lsoft.com/scripts/wl.exe?SL1=ALGEBRAIC-NUMBER- algebraic number field Information From Answers.comalgebraic number field In mathematics , an algebraic number field (or simply number KroneckerWeber theorem List of algebraic number theory topics http://www.lsoft.com/scripts/wl.exe?SL1=ALGEBRAIC-NUMBER-THEORY&H=LISTSERV.UIUC.

70. Dr V Abrashkin University of Durham. algebraic number theory. Publications and links. http://maths.dur.ac.uk/pure/temphome/va.html

71. Andrew Granville -- Publications In Algebraic Number Theory Andrew Granville s publications in algebraic number theory Journal of Number Theory, vol. 42 (1992) pages 297312. Article and AMS Review http://www.dms.umontreal.ca/~andrew/Algebraic.html

Publications by year: Preprints Andrew Granville 's publications in algebraic number theory By subject: Analytic Algebraic Algorithmic , and Combinatorial number theory, other research , and expository writing. Topics: Applications of Faltings' Theorem, Generalized Fermat equations, Class number of cyclotomic fields, the abc-conjecture, Finite fields, Elliptic Curves, and Fermat's Last Theorem. Applications of Faltings' Theorem with Enrico Bombieri and Janos Pintz Article and AMS Review Squares in arithmetic progressions Duke Mathematical Journal, vol. (1992) pages 165-204 with Henri Darmon Article and AMS Review On the equations z m =F(x,y) and Ax p +By q =Cz r Bulletin on the London Mathematical Society, (1995) pages 515-543 Article and AMS Review The set of exponents, for which Fermat's Last Theorem is true, has density one , vol (1985) pages 55-60 Generalized Fermat equations with Henri Darmon Article and AMS Review On the equations z m =F(x,y) and Ax

72. Math 254 (Number Theory) Home page for Math 254 (algebraic number theory) Required one semester of algebraic number theory (Math 254A or equivalent). 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!).

73. John Jones Home Page Arizona State University. algebraic number theory Iwasawa theory, the arithmetic of elliptic curves, Galois theory; questions in computational number theory. Tables of number fields of small degree. Discovering number theory course material. http://math.la.asu.edu/~jj/

John Jones Links Misc. Fun Pedagogy ... Home Outside Links ASU Main ASU site Department of Mathematics and Statistics The Department of Mathematics and Statistics main site Contact Information Office: PSA 729 E-mail: Phone: Fax: Office hours: Monday 11:00-12:00, Wednesday 10:30-12:30, and by appointment. My history: a.k.a.

74. Topics In Algebraic Number Theory Topics in algebraic number theory (EPSRC/LMS Short Course) algebraic number theory has a long and distinguished history and remains one of the most http://www.mth.kcl.ac.uk/events/short_courses/ANT_Sep_2002.html

King's Maths Home What's new Search ... Mathsoc Mathematics Department Topics in Algebraic Number Theory (EPSRC/LMS Short Course) Schedule Suggested reading list TOPICS IN ALGEBRAIC NUMBER THEORY LMS/EPSRC Short Course King's College London, 2-6 September 2002 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:

75. Lemmermeyer, Franz Bilkent University. algebraic number theory, elliptic curves. Papers, lecture notes, texts. http://www.fen.bilkent.edu.tr/~franz/

Franz Lemmermeyer Visiting associate professor Department of Mathematics Office: FEN 116 Telephone 1265 Fall 2005 Linear Algebra Algebraic Number Theory Cryptography and Coding Theory Here's some material for students doing their senior project or thesis with me. Past Fall 1996 - Spring 2005 Publications Stolen Books My mathematical ancestors Links A Collection of Lecture Notes My Elliptic Curves page HD-home

76. PARI/GP Development Headquarter PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves. http://pari.math.u-bordeaux.fr/

Main: PARI/GP? Download Search Support: FAQ Documentation Mailing Lists Links Development: CVS Last Changes Buildlogs Bugs ... WWW Stats PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations. Originally developed by Henri Cohen and his co-workers (Université Bordeaux I, France), PARI is now under the GPL and maintained by Karim Belabas with the help of many volunteer contributors. PARI is a C library, allowing fast computations. gp is an easy-to-use interactive shell giving access to the PARI functions. GP is the name of gp's scripting language. , the GP-to-C compiler, combines the best of both worlds by compiling GP scripts to the C language and transparently loading the resulting functions into gp. (gp2c-compiled scripts will typically run 3 or 4 times faster.) gp2c currently only understands a subset of the GP language. PARI/GP Development Last Modified: 2005-09-05 16:03:22 the PARI group

77. Algebraic Number Theory Course Title Topics in Number Theory, algebraic number theory. Unique Number M390C (58965). Time and place TTh 9301100 RLM 9.166 http://www.ma.utexas.edu/users/voloch/algnoth.html

Fall Semester, 2004 Course Title: Topics in Number Theory, Algebraic Number Theory Unique Number: M390C (58965) Time and place: TTh 9:30-11:00 RLM 9.166 Instructor: Felipe Voloch Brief description: This course will cover the basic theory of Algebraic Number Fields and Function Fields, their rings of integers and the basic theorems of unique factorization into prime ideals, finiteness of class number and Dirichlet's unit theorem. We will take the approach of Artin and Whaples and give an axiomatic characterization of Number Fields and Function Fields. Here is their original paper Prerequisite: Graduate Algebra Textbook: None. But here is a long list of lecture notes on number theory, some of which are relevant. Course notes: Each student will be required to take notes for a week and TeX them. Here is the whole course available as one file. First week Second week Third week Fourth week ... Thirteenth week

78. David R. Dorman's Home Page Middlebury College. algebraic number theory and Arithmetical Algebraic Geometry. Contact information. http://community.middlebury.edu/~dorman/

David R. Dorman I graduated from the Department of Mathematics at Brown University. My main areas of interest are Algebraic Number Theory and Arithmetical Algebraic Geometry I am currently a professor at Middlebury College. Some Favorite Links Yahoo the super big WWW directory dorman@panther.middlebury.edu

79. Number Theory John Tate (tate@math.utexas.edu) algebraic number theory (local and global fields), Class Field Theory, Galois cohomology, Galois representations, http://www.ma.utexas.edu/users/voloch/numberthy.html

Number Theory at the Mathematics Dept. of the University of Texas Permanent faculty in Number Theory, and their fields of interest. Frank Gerth gerth@math.utexas.edu ): Algebraic number theory, including class numbers, class groups, discriminants, class field theory, density theorems, Iwasawa theory. 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. 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. villegas@math.utexas.edu ): Special values of L-functions (Birch-Swinnerton-Dyer and Bloch-Beilinson conjectures), arithmetic of elliptic curves, modular forms, Mahler measure of polynomials. Felipe Voloch ): Arithmetic of function fields. Diophantine geometry over function fields. Geometry of algebraic curves. Algebraic varieties over finite fields. Modular forms, elliptic curves and abelian varieties. Finite fields and applications to coding theory and cryptography.

80. Paul Garrett's Lecture Notes, Exercises, Course Material With exercises and course material. Topics include algebraic number theory; Automorphic (Modular) Forms, Representations, Lfunctions. http://www.math.umn.edu/~garrett/m/

Lecture Notes and Exercises home Buildings book ] (PostScript) ... [ HTML Bibilography Automorphic (Modular) Forms, Representations, L-functions, Number Theory Functional Analysis Abstract Algebra ... Calculus [this page is http://www.math.umn.edu/~garrett/m/ The University of Minnesota explicitly requires that I state that "The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota."

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