Geometry.Net - Pure_And_Applied_Math: Algebraic Number Theory

Algebraic Number Theory -- From MathWorld
algebraic number theory, Number Theory. Stewart, I. and Tall, D. Algebraic NumberTheory and Fermat's Last Theorem, 3rd ed. Natick, MA A. K. Peters, 2000.
http://mathworld.wolfram.com/AlgebraicNumberTheory.html
Algebraic Number -- From MathWorld
Ferreirós, J. The Emergence of algebraic number theory. §3.3 in Labyrinthof Thought A History of Set Theory and Its Role in Modern Mathematics.
http://mathworld.wolfram.com/AlgebraicNumber.html

Extractions: 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 the s in (0) are algebraic numbers, then any root of this equation is also 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 (Nesterenko 1999), and is implemented in Mathematica as Algebraics . A number x can then be tested to see if it is algebraic using the command Element[ x , Algebraics] Algebraic Integer Euclidean Number Hermite-Lindemann Theorem Radical Integer ... Transcendental Number
GraNTS
A semesterlong seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes Category Science Math Elliptic Curves and Modular FormsGRAduate Number Theory Seminar algebraic number theory and EllipticCurves. If you are looking for the web algebraic number theory
http://www-math.mit.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.
A Brief Guide To Algebraic Number Theory - Cambridge University Press
Broad graduatelevel account of algebraic number theory, including exercises,by a world-renowned author. A Brief Guide to algebraic number theory.
http://books.cambridge.org/0521004233.htm

Extractions: Pure Mathematics Hardback In stock This is an account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. It is written primarily for beginning graduate students in pure mathematics, and encompasses everything that most such students are likely to need; others who need the material will also find it accessible. It assumes no prior knowledge of the subject, but a firm basis in the theory of field extensions at an undergraduate level is required, and an appendix covers other prerequisites. The book covers the two basic methods of approaching Algebraic Number Theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to Fermats Last Theorem, as well as a comprehensive account of class field theory. Many exercises and an annotated reading list are also included. masterfully written. It has to be recommended to number theorists and more general to working algebraists.J. Schoissengeier, Monatshefte für Mathematik
KLUWER Academic Publishers | Algebraic Number Theory, Field Theory And Polynomia
Home » Browse by Subject » Mathematics » Algebra and Number Theory» algebraic number theory, Field Theory and Polynomials. Sort
http://www.wkap.nl/home/topics/J/8/4/
KLUWER Academic Publishers | An Introduction To Algebraic Number Theory
Books » An Introduction to algebraic number theory. An Introductionto algebraic number theory. Add to cart. by Takashi Ono Johns
http://www.wkap.nl/prod/b/0-306-43436-9
Algebra And Number Theory
Algebra and Number Theory the KANT group. Members, software (KANT/KASH), publications.Category Science Math Number Theory Research Groups Universität Berlin. KANT stands for Computational algebraic number theorywith a slight hint to its German origin (Immanuel Kant). The
http://www.math.tu-berlin.de/algebra/
Kash
KANT is a software package for sophisticated computations in number fields and in global function Category Science Math Number Theory SoftwareKANT / KASH. Computational algebraic number theory / KAnt SHell. KANT is a softwarepackage for mathematicians interested in algebraic number theory.
http://www.math.tu-berlin.de/~kant/kash.html

Extractions: KANT / KASH Computational Algebraic Number Theory / KAnt SHell The KANT Group: [members] [publications] [database] ... main features ] [doc] [acknowledgement] [examples] [download] ... [ftp] Visit our stand at the CeBIT 2003 (hall 11, stand D37) KANT is a software package for mathematicians interested in algebraic number theory. For those KANT is a tool for sophisticated computations in number fields and in global function fields. With KASH you are able to use the powerful KANT V4 functions within a shell and you do not need to know anything at all about programming in C. KASH is freely available. You can pick up the current release of KASH using ftp . You can download the documentation for KASH separately. Many of the algorithms, which are implemented in KASH/KANT, are described in the publications of the KANT Group . Take a look at a KASH sample-session (taken from the ICM 98 Mathematical Software Session).
Midwest Algebraic Number Theory Day
University of Illinois at Chicago; 18 April 1998.Category Science Math Number Theory Events Past EventsMidwest algebraic number theory Day. Saturday, April 18, 1998. University ofIllinois at Chicago. Midwest algebraic number theory Day Program.
http://raphael.math.uic.edu/~jeremy/mwants.html
Citations: A Course In Computational Algebraic Number Theory - Cohen (ResearchIn
H. Cohen. A Course in Computational algebraic number theory, volume 138 of GraduateTexts in Mathematics. A Course in Computational algebraic number theory.
http://citeseer.nj.nec.com/context/14978/0

Extractions: The Hardness of Hensel Lifting: The Case of RSA and.. - Catalano, Nguyen, Stern (Correct) ....p and then performing a so called Hensel lifting, which iteratively transforms solutions modulo p into solutions modulo arbitrary powers of p. This is for instance the case with factorization of univariate integer polynomials, and with integer root finding of univariate integer polynomials (see ) The lifting process has been dubbed Hensel lifting because of the pioneering work of the German mathematician Hensel on p adic numbers at the end of the 19th century. The p adic numbers are beyond the scope of this paper, and we refer the interested reader to [8] for more information: Let us ....
Algebraic Number Theory
algebraic number theory algebraic number theory. Math 676.dvi; Math 676.ps.gzMath 676.pdf v2.01; August 14, 1996; first version on the web; 144p.
http://www.jmilne.org/math/CourseNotes/math676.html

Extractions: v2.10; August 31, 1998; fixed many minor errors; added exercises and index; 140p. 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
Algebraic Number Theory Resources
algebraic number theory resources. Recommended References. see indexfor total category for your convenience Best Retirement
http://futuresedge.org/mathematics/Algebraic_Number_Theory.html
Suggested Readings In Algorithmic Number Theory
Provided by the organizers of the MSRI Fall 2000 research program.Category Science Math Number Theory Computational computer science SerNo 1423 Status HERE Editor Cassels, JWS (John William Scott)ed. / Frölich, Albrecht ed. Title algebraic number theory; proceedings of
http://www.msri.org/local/library/reading_lists/0001-ant.html
Department Of Mathematics: University Of Michigan Department Of Mathematics: Num
Graduate Program in Number Theory. Staff, research interests, courses, seminars.Category Science Math Number Theory Research Groups algebraic number theory and class field theory (Math 676/776). Oneadditional advanced number theory course is offered each term.
http://www.math.lsa.umich.edu/research/number_theory/

Extractions: VIGRE The department has long maintained a vigorous graduate program in number theory. Permanent: (tenured and tenure-track) D.J. Lewis (currently on retirement furlough), H.L. Montgomery, C. Skinner (starts Fall 2000) T. Wooley Junior: M. Emerton, A. Toth. Faculty in related areas include: I. Dolgachev (algebraic geometry), W. Fulton (algebraic geometry), T. Hales (representation theory; Langlands program), R. Lazarsfeld (algebraic geometry), A. Moy (representation theory), G. Prasad (arithmetic of algebraic groups). Each year the department offers an undergraduate course in number theory, Math 475, and an introductory graduate course, Math 575. The following full-year courses are offered in alternating years One additional advanced number theory course is offered each term. Recent courses include:
Algebraic Number Theory Archives
algebraic number theory Archives. http//www.math.uiuc.edu/AlgebraicNumber-Theory/.Features Web Journal , , - This is a prereprint
http://www.aldea.com/guides/ag/a618ud.html

Extractions: Features: Web Journal , , . This is a prereprint archive for papers in algebraic number theory and arithmetic geometry hosted by University of Illinois at Urbana Champaign. Faculty: Quality ; Quantity ; Ease ; Up-to-date Graduates: Quality ; Quantity ; Ease ; Up-to-date Undergraduates: Quality ; Quantity ; Ease ; Up-to-date Other: Quality ; Quantity ; Ease ; Up-to-date Back to Mathematical sciences Community Commentary Back to UniGuide Academic Guide Site developed and designed by AldeaCommunications
Algebraic Number Theory Archives
return button, algebraic number theory Archives. http//www.math.uiuc.edu/AlgebraicNumber-Theory/,
http://www.aldea.com/guides/ag/a618.html

Extractions: http://www.math.uiuc.edu/Algebraic-Number-Theory/ This is a prereprint archive for papers in algebraic number theory and arithmetic geometry hosted by University of Illinois at Urbana Champaign. For explanation of categories see Commentary form. Quality Quantity Ease Up-to-date Faculty Grad Students Undergrads Others Community Commentary Back to UniGuide Academic Guide Help with icons Site developed and designed by AldeaCommunications
Algebraic Number Theory
next up previous Next About this document Up References PreviousAnalytic Number Theory algebraic number theory. (G = Global
http://math.dartmouth.edu/graduate-students/syllabi/graduate-syllabi/number-theo
Algebraic Number Theory:
next up previous Next Global Theory Up Number Theory Previous Analytic NumberTheory algebraic number theory Global Theory Local Theory root 199812-03.
http://math.dartmouth.edu/graduate-students/syllabi/graduate-syllabi/number-theo
1.8.1 Algebraic Number Theory -- Prof D Segal -- 16 HT
1.8.1 algebraic number theory Prof D Segal 16 HT. 1.8.1.3 Reading. I.Stewart and DA Tall, algebraic number theory, Chapman and Hall (1987).
http://www.maths.ox.ac.uk/teaching/synopses/2002/sect-c-02/node37.html

Extractions: Subsections Prerequisites : a3 algebra is sufficient. Necessary facts concerning Galois theory and quadratic residues will be mentioned as and when they are needed. A little knowledge of elementary number theory may enhance enjoyment. To get a deeper understanding of the ordinary integers, it is useful to ' the solutions of equations, and be free to operate with numbers in this larger domain (just as one does when moving from the real numbers to the complex numbers). Algebraic number theory determines to what extent arithmetic in rings like is the same as ordinary arithmetic, and in what ways it differs. Having established some basic principles one can apply these to problems in number theory such as finding integer solutions to polynomial equations. Algebraic number fields. Algebraic integers; existence and properties of an integral basis; examples, including quadratic and cyclotomic fields. Ideals, fractional ideals, unique factorisation of ideals. Splitting of rational primes in field extensions. The ideal class group and the group of units. Applications to Diophantine equations
6.2.2 ALGEBRAIC NUMBER THEORY--Prof D Segal--16 Lectures HT
6.2.2 algebraic number theoryProf D Segal16 lectures HT. 6.2.2.1 Aims. IStewart and DA Tall, algebraic number theory Chapman and Hall (1987).
http://www.maths.ox.ac.uk/teaching/synopses/2002/mfoc-02/node21.html

Extractions: Subsections To get a deeper understanding of the ordinary integers, it is useful to 'adjoin' the solutions of equations, and be free to operate with numbers in this larger domain (just as one does when moving from the real numbers to the complex numbers). Algebraic number theory determines to what extent arithmetic in rings like is the same as ordinary arithmetic, and in what ways it differs. Having established some basic principles one can apply these to problems in number theory such as finding integer solutions to polynomial equations. Algebraic number fields. Algebraic integers; existence and properties of an integral basis; examples, including quadratic and cyclotomic fieds. Ideals, fractional ideals, unique factorisation of ideals. Splitting of rational primes in field extensions. The ideal class group and the group of units. Applications to Diophantine equations. 6.2.2.3 Reading

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