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Algebraic Number Theory: more books (102)

Algebraic K Theory and Algebraic Number Theory: Proceedings of a Seminar Held January 12-16, 1987 With Support from the National Science Foundation (Contemporary Mathematics) by Seminar on Algebraic K-Theory and Algebraic Number Theory, Michael R. Stein, et all 1989-01
Algebraic Number Theory (Pure and Applied Mathematics) by R. Long, 1977-09-01
Algebraic Number Theory and Algebraic Geometry: Papers Dedicated to A.N. Parshin on the Occasion of His Sixtieth Birthday (Contemporary Mathematics)
Algebraic Theory of Numbers by Hermann Weyl, 1998-04-20
The Theory of Algebraic Number Fields by David Hilbert, 2010-11-02
Lectures on the Theory of Algebraic Numbers (Graduate Texts in Mathematics) by E. T. Hecke, 2010-11-02
Algebraic theory of numbers by Pierre Samuel, 1970
The Elements Of The Theory Of Algebraic Numbers by Legh Wilber Reid, 2010-09-10
Selected Papers on Number Theory and Algebraic Geometry (American Mathematical Society Translations Series 2)
Select Topics in Algebra: and Its Interrelations with Logic, Number Theory and Algebraic Geometry (Mathematics and its Applications) by I. Bucur, 1984-09-30
Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry (American Mathematical Society Translations Series 2)
Foundations of the theory of algebraic numbers by Harris Hancock, 1964
P-Adic Methods in Number Theory and Algebraic Geometry (Contemporary Mathematics) by Steven Sperber, Alan Adolphson, 1992-07
The theory of algebraic numbers (Carus mathematical monographs series;no.9) by Harry Pollard, 1950

lists with details

A Brief Introduction To Classical And Adelic Algebraic Number Theory
By William Stein. Text in HTML/DVI/LaTeX/PDF/PS.
http://modular.fas.harvard.edu/papers/ant/
Math 784 Algebraic NUMBER THEORY
File Format PDF/Adobe Acrobat
http://www.math.sc.edu/~filaseta/gradcourses/TheMath784Notes.pdf
Algebraic Number Theory
Course notes by Robin Chapman, University of Exeter, May 2000.
http://www.secamlocal.ex.ac.uk/~rjc/courses/ant99/ant99.html

Extractions: This is the home page for the Algebraic Number Theory course. At present it is still under construction. Eventually it will contain copies of course handouts, commentaries on some of my more challenging problems, and useful links. Most files are in dvi format. The course will be closely based on the following book: Ian Stewart and David Tall, Algebraic Number Theory , Chapman and Hall. Alas the paperback is out of print (and the hardback is overpriced) but the following alternative is very cheap (but a bit old-fashioned): Harry Pollard and Harold G. Diamond, The Theory of Algebraic Numbers , Dover. Robin Chapman
ALGEBRAIC NUMBER THEORY AND QUADRATIC RECIPROCITY 1. Introduction
File Format PDF/Adobe Acrobat Quick View
http://research.microsoft.com/en-us/um/people/cohn/Papers/algnumb.pdf
Algebraic Number Theory - Cambridge University Press
Algebraic Number Theory Series Cambridge Studies in Advanced Mathematics (No. 27) A. Fr hlich University of London M. J. Taylor University of Manchester Institute of Science
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521438349
Jan Nekovar's Web Page
Universit Pierre et Marie Curie (Paris VI). Algebraic number theory, arithmetic algebraic geometry.
http://www.math.jussieu.fr/~nekovar/
ALGEBRAIC NUMBER THEORY 1. Algebraic Integers Let A Be A Subring
File Format PDF/Adobe Acrobat Quick View
http://www.fen.bilkent.edu.tr/~franz/ant-st.pdf
Proofs Of Quadratic Reciprocity - Wikipedia, The Free Encyclopedia
We are finished because the left hand side is just an alternative expression for (q / p. Proof using algebraic number theory. The proof presented here is by no means the simplest known
http://en.wikipedia.org/wiki/Proofs_of_quadratic_reciprocity

Extractions: From Wikipedia, the free encyclopedia Jump to: navigation search In the mathematical field of number theory , the law of quadratic reciprocity , like the Pythagorean theorem , has lent itself to an unusual number of proofs . Several hundred proofs of the law of quadratic reciprocity have been found. Proof using algebraic number theory ... Of relatively elementary, combinatorial proofs, there are two which apply types of double counting . One by Ferdinand Eisenstein counts lattice points . Another applies Zolotarev's lemma to Z pqZ expressed by the Chinese remainder theorem as Z pZ Z qZ , and calculates the signature of a permutation Eisenstein 's proof of quadratic reciprocity is a simplification of Gauss's third proof. It is more geometrically intuitive and requires less technical manipulation. The point of departure is "Eisenstein's lemma", which states that for distinct odd primes p q where denotes the floor function (the largest integer less than or equal to x ), and where the sum is taken over the
Nagaraj, D.S.
Institute of Mathematical Sciences, C.I.T., Chennai. Algebraic number theory, algebraic geometry.
http://www.imsc.res.in/~dsn/
Algebraic Number Theory
Schedule Mo 1340 1530, SAZ 02 We 1540 - 1730, SAZ 02 Motivation A standard course in algebraic number theory discusses the proofs of the main results on integral bases
http://www.fen.bilkent.edu.tr/~franz/ant06.html

Extractions: Mo 13:40 - 15:30, SAZ 02 We 15:40 - 17:30, SAZ 02 A standard course in algebraic number theory discusses the proofs of the main results on integral bases, discriminants, Dedekind rings, class groups, Dirichlet's unit theorem, etc. In this semester, I will instead concentrate on quadratic extensions of the rationals and of the rational function fields and introduce elliptic curves. This will allow us to do a lot of explicit calculations that cannot be done (by hand) for extensions of higher degree. I. Quadratic Number Fields. Here we will discuss failure of unique factorization, ideal arithmetic, class number computation, and units. Applications: Bachet-Mordell equations y = x +k, some simple 3-descents on elliptic curves like x +y = Az , possibly the cubic reciprocity law. II. Quadratic Function Fields. These are quadratic extensions of the rational function fields F p [X]; their arithmetic has a lot in common with quadratic number fields. III. Arithmetic of Elliptic and Hyperelliptic Curves. These can essentially be identified with quadratic extensions of function fields.
Brown University Mathematics Department
Brown University. Algebraic number theory and topology. Pictures, research papers, notes, transparencies.
http://www.math.brown.edu/faculty/abramovich.html

Extractions: @import url("http://www.brown.edu/Templates/common/academic/3col-default.css"); @import url("http://www.brown.edu/Templates/common/print/3col-print.css"); @import url("http://www.brown.edu/Templates/common/academic/2-column.css"); @import url("http://www.brown.edu/Templates/common/print/2col-print.css"); @import url("http://www.math.brown.edu/css/math.css"); skip navigation This page is designed for modern browsers. You will have a better experience with a better browser.
GraNTS
GRAduate Number Theory Seminar Algebraic Number Theory and Elliptic Curves Ramblings on how elementary number theory motivates algebraic number theory,
http://www.math.ucdavis.edu/~osserman/seminar/

Extractions: Where: MIT, Rm 24-110 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.
Algebraic Number Theory
Calculus I page. Day Time Monday and Wednesday 210am — 325am. Location Goldsmith 0226
http://people.brandeis.edu/~jbellaic/numbertheory/numbertheory.html

Extractions: Location: Goldsmith 0226 Instructor: Joel Bellaiche Contents : Dedekind domains: definition, stability by integral closure, unique factorization of ideals, modules over Dedekind Domain; Extensions of Dedekind domain : discriminant, behaviour of primes; Ring of algebraic numbers of a number field; Finiteness of the class number; Dirichlet units Theorem; Cyclotomic Extensions; Local Fields; Adeles and Ideles, Grossencharacter; Class field theory; Cebotarev Density Theorem; Galois representations Tentative program: PART I : Global Theory (Algebraic methods) : General theory of Dedekind domains and application to algebraic numbers (2 weeks) (Geometric methods) : Bounds on discriminants and finiteness results (Class groups, Dirichlet's Unit Theorem) (2 weeks) (Analytic methods) : Zeta and L-functions and applications (Class Number Formula, Dirichlet's prime number theorem, Cebotarev) (2 weeks) PART II : Local Theory Complete fields, $p$-adic fields, completions of number fields (1 week) Adeles and Ideles (1 week) PART III : Class Field Theory Class Field Theory : adelic formulation and consequences (1 week and half) Class Field theory : proofs or skecths of the proofs (1 week) PART IV : Introduction to the theory of Galois representations Grossenchracters and algebraic grossenchracters (1 week) Higher dimensional Galois representations (depending on time) Bibliography : We will not follow one specific book. Good references on algebraic number theory abound. Here are some:
Mathematics Staff Homepage
Manchester. Algebraic number theory, Galois module structure.
http://www.maths.manchester.ac.uk/~mjt/

Extractions: Report: 'The Scientific Century: securing our future prosperity.' Professor in Pure Mathematics Honorary D.Sc. University of Bordeaux 2009 Honorary D.Sc. , University of Leicester 2006 Royal Society Wolfson Research Fellow Qualifications: M.A. (Oxford), Ph.D (London). Room No. 2.106 Administrative duties: Research: Galois, Hermitian and quadratic structure for arithmetic varieties. Publications List CV Flyfishing, Hill walking. Postal Address: Professor M J Taylor FRS The University of Manchester School of Mathematics Alan Turing Building Oxford Road Manchester, M13 9PL UK Tel: use + 44 161 306 3640 from overseas Fax: Email: Martin.Taylor@manchester.ac.uk
PmWiki - Main - MAA PREP -- Algebraic Number Theory
Jul 1, 2010 This is the website for the 2010 MAA PREP course in Algebraic Number Theory. The MAA PREP is funded by the National Science Foundation (NSF
http://math.bard.edu/cullinan/prep/
Math 248B - Algebraic Number Theory - Winter 2004
We conclude by discussing automorphic forms in general and their role in solving fundamental questions in algebraic number theory. It will be sweet.
http://math.stanford.edu/~brubaker/math248b.html

Extractions: Content We will review the basics of class field theory in the first week through the lens of reciprocity. Then we'll head to Davenport, covering the first 8 chapters, essential and classical analytic number theory from which all else follows. We'll break and do several weeks on the zeta function. Classical stuff again, but often shoved under the rug. We'll end with a potpourri of topics, including Siegel's theorem and proofs of algebraic facts using analytic information. We conclude by discussing automorphic forms in general and their role in solving fundamental questions in algebraic number theory. It will be sweet. Prerequisites There are essentially no prerequisites for this course. If you took Rubin's 248A in the fall, or know the equivalent information, you'll have a better view from which to understand the arc of the course, but its not at all necessary in understanding the day to day material.
Algebraic Number Theory
Algebraic Number Theory From its history as an elegant but abstract area of mathematics algebraic number theory now takes i.
http://www.ramex.com/cr/cr-3696.html
HOME PAGE OF DAVID J. WRIGHT
Oklahoma State University. Algebraic number theory and algebraic groups, with methods from functional analysis and analytic number theory.
http://www.math.okstate.edu/~wrightd/

Extractions: I am a mathematician on the faculty of Oklahoma State University. My home page is divided up into the following areas of information: Current Teaching Schedule My resume and other personal information Some facts about my education, career and family are given here. Guide to my published works. MSRI MathGraphics info: notes and info about lectures Number Theory and PARI This a web supplement I created to the textbook Elementary Number Theory and its Applications by Ken Rosen. It contains among other things: The Indra's Pearls Web Site Information on a book about kleinian groups which I co-authored and which is now published by Cambridge University Press. MATH 6490: Indra's Pearls Course Materials The course ran in the spring of 2004. Introduction to Dynamical Systems and Fractals These are the materials I prepared for a course given in the spring of 1996, including a 170-page book processed in latex2html. Symmetry Web This is a World Wide Web machine for experimenting with symmetry groups of simple geometric figures.
Notes For Dick Gross' Algebraic Number Theory Course
May 25, 1999 As many of you know, I have been typing up the notes for the Number Theory Course being taught by Dick Gross who is visiting from Harvard
http://www.math.utah.edu/~sather/notes.html

Extractions: As many of you know, I have been typing up the notes for the Number Theory Course being taught by Dick Gross who is visiting from Harvard during the Spring Semester of 1999. I am posting the notes only in .ps and .pdf format since some of the files contain .eps figures. If you need a hard copy or something, email me Before I post anything, I get it approved by Professor Gross, but if you find any mistakes, email me . Cheers. Sean Lectures 1-4 .ps or .pdf : material from 14 January to 26 January Lectures 5-8 .ps or .pdf : material from 28 January to 9 February Lectures 9-12 .ps or .pdf : material from 2 February to 25 February Lectures 13-16 .ps or .pdf : material from 2 March to 11 March Lectures 17-18 .ps or .pdf : material from 23 March to 25 March Lectures 1-18 .ps or .pdf : material from 14 January to 25 March Lectures 1-18 compressed .ps.gz or .pdf.gz : material from 14 January to 25 March Last updated 5.25.99
Marcus Wagner
Technische Universit t Berlin. Algebraic number theory.
http://www.math.tu-berlin.de/~wagner/

Extractions: This table contains 21 Humbert forms which are listed with their minimal vectors, eutactic coefficients and the dimension of perfection. 18 Humbert forms are extreme. Here is a little course on correspondences which introduces to the theory of correspondences between algebraic function fields. This course is under construction, but you can make first steps with elliptic correspondences in MAGMA.

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