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Number Theory:     more books (100)

Transcendental Number Theory (Cambridge Mathematical Library) by Alan Baker, 1990-09-28 Making Transcendence Transparent: An intuitive approach to classical transcendental number theory by Edward B. Burger, Robert Tubbs, 2010-11-02 Elementary Number Theory by Charles Vanden Eynden, 2001-01-12 Introduction to Number Theory by Mathew Crawford, 2008-06-30 Contributions to the founding of the theory of transfinite numbers by Georg Cantor, Philip E. B. 1879-1919 Jourdain, 2010-08-29 Additive Number Theory The Classical Bases (Graduate Texts in Mathematics) by Melvyn B. Nathanson, 2010-11-02 Elementary Methods in Number Theory by Melvyn B. Nathanson, 1999-12-21 Introduction to Number Theory With Computing by R. B. J. T. Allenby, E. J. Redfern, 1989-09 Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences) by Yu. I. Manin, Alexei A. Panchishkin, 2010-11-30 Number Theory 1: Fermat's Dream (Translations of Mathematical Monographs) (Vol 1) by Kazuya Kato, Nobushige Kurokawa, et all 2000-01-01 Introduction to Number Theory by James E Shockley, 1967-01-01 Number Story: From Counting to Cryptography by Peter Michael Higgins, 2008-02-25 Algebraic Number Theory by Edwin Weiss, 1998-01-29 The Higher Arithmetic: An Introduction to the Theory of Numbers by H. Davenport, 2008-11-17

lists with details

81. Home Page J. S. Milne.
    Includes preprints and course notes on Group Theory, Fields and Galois Theory, Algebraic Geometry, Algebraic number theory,Modular Functions and Modular Forms, Elliptic Curves, Abelian Varieties, Etale Cohomology, and Class Field Theory.  
    http://www.jmilne.org/math/

82. Number Theory And Physics Archive
    This website is an attempt to document in detail the rapidly emerging connections between physics and number theory. number theory and physics archive.  
    http://www.maths.ex.ac.uk/~mwatkins/zeta/physics.htm

83. Jlpe's Number Recreations Page
    Features original number recreations by the author, such as generalized perfect numbers, digital diversions, diophantine equations, didactic numbers, and number theory.  
    http://www.geocities.com/windmill96/numrecreations.html
    
    Extractions: jlpe's number recreations page The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures. Joseph Marie de Maistre I have hardly ever known a mathematician who was capable of reasoning. Plato On a Generalization of Perfect Numbers Ana's Golden Fractal The 3x + 1 Fractal The Picture-Perfect Numbers ... The Justice of Numbers : The author will not be responsible for any frustration or sleepless nights suffered by the would-be solver. Number of Visits: J. L. Pe Last update: 16 February 2003. var PUpage="76001088"; var PUprop="geocities";

84. The USC Number Theory Home Page
    s in number theory. I also have interests in the application of these results to gap problems in number theory. Graduate Course  
    http://www.math.sc.edu/~filaseta/numthry.html
    
    Extractions: Information: Sergei Konyagin of Moscow State University will be visiting for the month of January, 2004. He is world renowned for his work in Number Theory, Approximation Theory, and Harmonic Analysis. In particular, he was recognized for his work in Harmonic Analysis as a recipient of the Salem Prize in 1990.

85. Number Theory Website Home Page
    Welcome To number theory Web site. NextCard Internet Visa.  
    http://numbertheory.freeservers.com/
    
    Extractions: Free Web site hosting - Freeservers.com Web Hosting - GlobalServers.com Choose an ISP NetZero High Speed Internet ... Dial up $14.95 or NetZero Internet Service $9.95 Site owner: Li Ke Xiong Email: likexiong@126.com The Correction Of Part F Of "Primary Proof" For The FLT A New Interesting Way in Mathematics -"Relative congruence" From the basic facts: integer a,b,s. prime the solution always exists and unique (except ). We can use the fractions to express congruence value, directly (2) Never can p be denomination divisor in any finite expression, otherwise meaningless. 3. Thus the basic operation can be used on the both sides of without any doubt, it is easy to be proved. 4. Furthermore, we extend the above concept to real number, based on and controlled by power expansion series, that is to say we have discovered the concept of Relative Congruence. 5. Thus we get the necessary condition mod p

86. 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
    
    Extractions: 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

87. Math 780 Material
    Math 780 Elementary number theory. A postcript version of the course description can be obtained below. Class notes (55 pages) can  
    http://www.math.sc.edu/~filaseta/gradcourses/Math780.html

88. Wiley::Primality And Cryptography
    Evangelos Kranakis. A comprehensive account of recent algorithms developed in computational number theory and primality testing.  
    http://www.wiley.com/cda/product/0,,0471909343,00.html

89. By J. Orlin Grabbe
    The ability of digital cash systems to give some measure of security and privacy has more to do with number theory than banking regulations.  
    http://www.aci.net/kalliste/cryptnum.htm
    
    Extractions: Cryptography and Number Theory for Digital Cash by J. Orlin Grabbe Note: In order to read the following text properly, your web browser must be able to handle subscripts and superscripts; i.e. the html commands “sub” and “sup”. These commands are used sparingly, but they are used. The ability to attack or misuse a digital cash system depends a lot on the cryptography and cryptographic protocols involved. A good cash system uses good cryptography. Good cryptography requires strong algorithms, keys of adequate length, and secure key management. Without these, there can be little privacy. A good cash system uses good protocols. The digital cash system of Stefan Brands, for example, is largely based on digital signaturesthe Schnorr signature scheme, in particular. The system, properly implemented, is thus only as secure as the underlying signature system. If there are flaws in the latter, the attractive features of anonymous digital cash disappear alsofeatures like untraceability, unlinkability, and security for all parties. If we are looking for privacy and security in banking, we can't ignore cryptography and we can't ignore mathematics. The ability of digital cash systems to give some measure of security and privacy has more to do with number theory than banking regulations.

90. VersionUS
    Conference in honour of Michel Raynaud. Orsay, 1822 June 2001.  
    http://www.math.u-psud.fr/~mr2001/confraynaudus.htm
    
    Extractions: Invited speakers Ahmed Abbes, John Coates, Gerd Faltings, David Harbater, Yasutaka Ihara, Johan de Jong, Nicholas M. Katz, Barry Mazur, Vikram. B. Mehta, Laurent Moret-Bailly, Frans Oort, Michael Rapoport, Kenneth A. Ribet, Jean-Pierre Serre, Christopher Skinner, Tetsuji Shioda, Akio Tamagawa, John Tate.

91. ANTS VI
    ANTS VI. Algorithmic number theory Symposium. University of Vermont. 13 18 June 2004. Since their inception in Cornell in 1994, the  
    http://web.ew.usna.edu/~ants/
    
    Extractions: General Schedule Participants Proceedings ... Registration Algorithmic Number Theory Symposium University of Vermont 13 - 18 June 2004 NEW Information for Participants NEW Since their inception in Cornell in 1994, the biennial ANTS meetings have become the premier international forums for the presentation of new research in computational number theory. The sixth Algorithmic Number Theory Symposium (ANTS VI) will be held Sunday 13 June to Friday 18 June 2004 on the campus of the University of Vermont in Burlington, Vermont, USA. Important Dates Friday 18 June 2004 - last day of talks for ANTS VI conference 20-25 June 2004 - CNTA-8 (Canadian Number Theory Association meeting, Toronto, Canada) Location ANTS VI will be held on the campus of the University of Vermont in Burlington, Vermont. Burlington, the largest city in Vermont, is located on the east coast of the United States, approximately 220 miles (355 kilometers) northwest of Boston, 285 miles (460 kilometers) north of New York City and 100 miles (160 kilometers) southeast of Montreal.

92. Five College Number Theory Seminar
    Five College number theory Seminar 20032004. Where and When, March 2. David Cox (Amherst College). Geometry and number theory on Clovers. March 9.  
    http://www.math.umass.edu/~siman/seminar.html
    
    Extractions: Where and When Five College Number Theory Seminar talks are generally held at Amherst College in the Seeley Mudd building , which houses Amherst College's Department of Mathematics and Computer Science. Unless noted otherwise, all talks take place at 4:00 p.m. in room Seeley-Mudd 207 . Refreshments are served at 3:30 p.m. in Seeley-Mudd 208. Driving Direction to Amherst College Campus map of Amherst College Map of Lord Jeffrey Inn Parking Directions To find the parking lot in back of Seeley Mudd, drive east on College Street (Route 9) past the Amherst town common on your left. Two blocks after the common, turn right onto the College campus (just before you go under a railroad overpass). Take your second right and follow it until the road ends at the Seeley Mudd parking lot. From the parking lot, take the stairs in the Life Sciences building, just to the right of Seeley Mudd, up one flight, exit and turn left toward Seeley Mudd. Campus maps for Hampshire, Mt. Holyoke, Smith, and UMass

93. Number Theory At The University Of Georgia
    number theory and Arithmetic Geometry Group. Members, seminars.  
    http://www.math.uga.edu/~lorenz/Number_Theory_Group.html
    
    Extractions: Number Theory and Arithmetic Geometry Group William Alford Associate Professor, Ph.D. Tulane, 1963. Factoring and other number theory problems by computer. Matthew Baker Assistant Professor, Ph.D. U.C. Berkeley, 1999. Galois actions on torsion points. Modular curves and their Jacobians. Discreteness problems for arithmetic heights. Linear series and vector bundles in characteristic p. Arithmetic of curves and their Jacobians. Sybilla Beckmann Associate Professor, Ph.D. U. Penn., 1986. Galois theory. The inverse galois problem, that is, to determine whether every finite group is the galois group of some extension of the rational numbers. Arithmetic information on branched coverings, such as fields of definition. Tilings of the plane. Mathematics education. Andrew Granville Barrow Professor, Ph.D. Queens,1987. Distribution of primes. Sieving intervals. Distribution of `smooth' numbers. Properties of binomial coefficients. Cyclotomic fields. Carmichael numbers. Exponential sums. Integer solutions to Diophantine equations. Binary quadratic forms and the elementary theory of elliptic curves. Questions related to factoring and primality testing. Symbolic computation and `computing by homomorphisms'. Computational complexity, particularly lower bounds. Power series and the combinatorics of coefficients. Counting lattice points.

94. The Math Forum - Math Library - Number Theory
    mathematics. This page contains sites relating to number theory. Browse and Search the Library Home Math Topics number theory.  
    http://mathforum.org/library/topics/number_theory/
    
    Extractions: 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

95. Home Page Of Robert B. Ash
    University of Illinois. Downloadable texts in Abstract Algebra, Algebraic number theory, Commutative Algebra (PDF).  
    http://www.math.uiuc.edu/~r-ash/

96. Pi à La Mode: Science News Online, Sept. 1, 2001
    An article describing a potential link between two disparate mathematical fieldsnumber theory and chaotic dynamics-that could lead to a proof that every digit of pi occurs with the same frequency.  
    http://www.sciencenews.org/20010901/bob9.asp
    
    Extractions: Week of Sept. 1, 2001; Vol. 160, No. 9 , p. 136 Ivars Peterson Memorizing the digits of pi—the ratio of a circle's circumference to its diameter—presents a hefty challenge to anyone undertaking that quixotic exercise. Starting with 3.14159265, the decimal digits of pi run on forever, and there is no discernible pattern to ease the task. This irregular landscape represents the form that emerges when a computer plots the first 1 million decimal digits of pi as a random walk. D.V. Chudnovsky and G.V. Chudnovsky The apparent randomness of pi's digits has long intrigued mathematician David H. Bailey of the Lawrence Berkeley (Calif.) National Laboratory. In the 1970s, when Bailey was a graduate student at Stanford University, he memorized the value of pi to more than 300 decimal places. It served "as a diversion during classroom lectures," Bailey confesses. In 1986, after joining NASA's Ames Research Center in Mountain View, Calif., he tested a new supercomputer by having it compute pi to nearly 30 million digits (SN: 2/8/86, p. 91). Any errors would reflect problems in the computer. "The program actually did disclose hardware bugs," Bailey says.

97. Courses
    Introduction to number theory ps file (495K); Introduction to number theory - pdf file (242K) This is a first course in number theory.  
    http://www.maths.nott.ac.uk/personal/ibf/courses.html
    
    Extractions: Introduction to number theory - ps file (495K) Introduction to number theory - pdf file (242K) This is a first course in number theory. It includes p-adic numbers. Commutative algebra - ps file (381K) Commutative algebra - pdf file (202K) This course is an introduction to categories, modules over rings, Noetherian modules, unique factorization domains and polynomial rings over them, modules over principal ideal domains, localization. Introduction to algebraic number theory - ps file (432K) Introduction to algebraic number theory - pdf file (193K) This course (36 hours) is a relatively elementary course which requires minimal prerequisites from Commutative Algebra (see above) for its understanding. Integrality over rings, algebraic extensions of fields, field isomorphisms, norms and traces are discussed in the second part. Dedekind rings, factorization in Dedekind rings, norms of ideals, splitting of prime ideals in field extensions, finiteness of the ideal class group and Dirichlet's theorem on units are treated in the second part. Homological algebra - ps file (479K) Homological algebra - pdf file (228K) This is a very short introduction to homological algebra This course (25 hours) presents categories, functors, chain complexes, homologies, free, projective and injective obejcts in the category of modules over a ring, projective and injective resolutions, derived functors, Tor and Ext, cohomologies of modules over a finite group, restriction and corestriction.

98. Thabit
    Gives information on background and contributions to noneuclidean geometry, spherical trigonometry, number theory and the field of statics. Was an important translator of Greek materials, including Euclid's Elements, during the Middle Ages.  
    http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Thabit.html
    
    Extractions: Thabit ibn Qurra was a native of Harran and a member of the Sabian sect. The Sabian religious sect were star worshippers from Harran often confused with the Mandaeans (as they are in [1]). Of course being worshipers of the stars meant that there was strong motivation for the study of astronomy and the sect produced many quality astronomers and mathematicians. The sect, with strong Greek connections, had in earlier times adopted Greek culture, and it was common for members to speak Greek although after the conquest of the Sabians by Islam, they became Arabic speakers. There was another language spoken in southeastern Turkey, namely Syriac, which was based on the East Aramaic dialect of Edessa. This language was Thabit ibn Qurra's native language, but he was fluent in both Greek and Arabic. Some accounts say that Thabit was a money changer as a young man. This is quite possible but some historians do not agree. Certainly he inherited a large family fortune and must have come from a family of high standing in the community.

99. G13NUM: NUMBER THEORY
    G13NUM number theory. Module aims To provide an an introduction to number theory, including elementary theory and some advanced topics and applications.  
    http://www.maths.nott.ac.uk/personal/jec/courses/G13NUM/
    
    Extractions: Information Lecture log Handouts Coursework ... Links Credits Duration : 33 lectures, three lectures a week in Autumn Semester, starting Monday 29/9/2003 Lecturer : Prof J. E. Cremona Lecture times Office hours : Monday 11-12, Tuesday 9-10, Wednesday 9-10 (C100). Brief content description: This is a first module in number theory, the study of problems concerning integers, including such topics as solutions of equations in integers, functions of an integer variable, and the distribution of special types of integers. The module includes topics such as unique factorization , linear congruences , quadratic congruences, the quadratic reciprocity law Gaussian integers Diophantine equations p -adic integers. Prerequisites: Module aims: To provide an an introduction to number theory, including elementary theory and some advanced topics and applications. Module objectives: By the end of the module, students should:

100. Rsabook
     S.C. Coutinho. An introduction to number theory and its applications to cryptography. A revised and updated translation from original in Portuguese.  
     http://www.dcc.ufrj.br/~collier/rsabook.htm
     
     Extractions: About the book This is an introduction to number theory and its applications to cryptography. The aim of the book is to explain in detail how the public key cryptosystem known as RSA works. The system was invented in 1977 by Rivest, Shamir and Adlemanhence RSAand it is one of the most successful of the public key cryptosystem now in use in commercial applications. Althouth this is the aim of the book, we do not follow a straight path to this end. Instead we stroll about the landscape, never forgetting our aim, but stopping to explore whatever reachs are available on the way. Thus the book includes a chapter on group theory, and it is pepered with historical notes that range from biographical facts on famous mathematicians to little anecdotes. The mathematics behind most of the books subject is, naturally enough, number theory. Most of the traditional topics of a beginners course on number theory are to be found here. Thus there are chapters on the Euclidean algorithm, factorization of integers, primes, modular arithmetic, Fermat's little theorem, the Chinese remainder theorem and Mersenne and fermat numbers. However we follow na algorithmic approach, so that the proofs the theorems are, whenever possible, of a constructive nature. Back to the top

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