101. Number Theory Pascal's Triangle . Pascal's triangle was first introduced by the Chinese mathematician Yang Hui, but it got it's name from Blaise Pascal who 500 years later rediscovered it http://www.math.wichita.edu/history/Topics/notheory.html

Topics in Number Theory Topic Tree Home Following are some topics in number theory. Contents of this Page Pascal's Triangle Perfect Numbers Fermat's Last Theorem Magic Squares ... Moessner's Magic Pascal's Triangle Pascal's triangle was first introduced by the Chinese mathematician Yang Hui, but it got it's name from Blaise Pascal who 500 years later rediscovered it along with Omar Khayyam. The triangle is used to look for the probability of any particular event to occur. There are many other things that can be found in the triangle. Listed below are a few of them and how to achieve them. PASCAL'S TRIANGLE How to make Pascal's Triangle. Row is the first row, it will have a 1. Row 1 is actually the second row it will have 1 and 1, but not to be confused with 11. The next row is the numbers 1 and 2 and 1. Now how did we get these numbers? 1 is ALWAYS going to be the first number in the row, but in order to make the triangle grow you add the two numbers above. Example: 1 + 2 = 3 and 2 + 1 = 3, so for the next line we will have 1 (always on the outside) and 3 and 3 and then 1 again. The next line gets even bigger, 1 (outside again) 1 + 3 = 4, and 3 + 3 = 6, and 3 + 1 = 4, and then that 1 again. This can go on as long as anyone wants it to go.

102. A Friendly Introduction To Number Theory J.H. Silverman. Contents, preface, errata, further material. http://www.math.brown.edu/~jhs/frint.html

A Friendly Introduction to Number Theory Joseph H. Silverman Available from Amazon A Friendly Introduction to Number Theory is an introductory undergraduate text designed to entice non-math majors into learning some mathematics, while at the same time teaching them how to think mathematically. The exposition is informal, with a wealth of numerical examples that are analyzed for patterns and used to make conjectures. Only then are theorems proved, with the emphasis on methods of proof rather than on specific results. Starting with nothing more than basic high school algebra, the reader is gradually led to the point of producing their own conjectures and proofs, as well as getting some glimpses at the frontiers of current mathematical research. Instructors : To receive an evaluation copy of A Friendly Introduction to Number Theory , send an email request to: Kendra Bassi, Marketing Manager, Prentice-Hall. Please include your title and full mailing address. Click on the links for the following material. Table of Contents, Preface, and Introduction

103. A Computational Introduction To Number Theory And Algebra By Victor Shoup (Cambridge University Press, 2005). Full text free in PDF, list of errata, supplementary exercises. http://www.shoup.net/ntb/

A Computational Introduction to Number Theory and Algebra A book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background. The book (now in its second edition ) is published by Cambridge University Press . It can be purchased directly from Cambridge University Press , or from online book retailers . However, the book will continue to be freely available online in PDF format under a Creative Commons license. DOWNLOADS Version 2 [ pdf ] (6/16/2008, corresponds to the second print editon) List of errata [ pdf Version 1 [ pdf ] (1/15/2005, corresponds to the first print edition) List of errata [ pdf Supplementary material [ pdf many additional exercises and examples some alternative proofs and stronger theorems LINKS Review in Math. Comp. Review in Computing Reviews - also available here Review in SIGACT News Vol 37, No 1 Back to Victor Shoup's Home Page

104. Number Theory Authors/titles "new.NT" Submissions received from Wed 6 Oct 10 to Thu 7 Oct 10, announced Fri, 8 Oct 10 http://arxiv.org/list/math.NT/new

arXiv.org math math.NT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Number Theory New submissions Submissions received from Wed 27 Oct 10 to Thu 28 Oct 10, announced Fri, 29 Oct 10 New submissions Cross-lists Replacements [ total of 8 entries: [ showing up to 2000 entries per page: fewer more New submissions for Fri, 29 Oct 10 arXiv:1010.5805 pdf ps other Title: Constellations in P^d Authors: Brian Cook Akos Magyar Comments: 14 pages Subjects: Number Theory (math.NT) ; Classical Analysis and ODEs (math.CA) Let A be a subset of positive relative upper density of P^d, the d-tuples of primes. We prove that A contains an affine copy of any finite set of lattice points E, as long as E is in general position in the sense that it has at most one point on every coordinate hyperplane. arXiv:1010.6009 pdf ps other Title: Computing local p-adic height pairings on hyperelliptic curves Authors: Jennifer S. Balakrishnan Amnon Besser Subjects: Number Theory (math.NT) ; Algebraic Geometry (math.AG) We describe an algorithm to compute the local component at p of the Coleman-Gross p-adic height pairing on divisors on hyperelliptic curves. As the height pairing is given in terms of a Coleman integral, we also provide new techniques to evaluate Coleman integrals of meromorphic differentials and present our algorithms as implemented in Sage.

105. Fundamental Number Theory With Applications Richard A. Mollin. Contents. http://www.math.ucalgary.ca/~ramollin/fnt2.html

FUNDAMENTAL NUMBER THEORY WITH APPLICATIONS Richard A. Mollin ISBN#: 0-8493-3987-1 Order el ectronically: TABLE OF CONTENTS: Review: A textbook for an undergraduate c ourse at lower-level without and at upper-level with optional sections on applications. Assumes no background in computer science and no mathematics past solid high- school level. Combines elementary number theory with algebraic number theory and applications such as those in cryptology. Begins with the arithmetic of the rational integers and proceeds through quadratic orders to an introduction of algebraic number theory. Also briefly traces the history of number theory from the earliest inscriptions. Book News, Inc.B., Portland, OR BRIEF OVERVIEW: If you want to give an introductory number theory course at any level, then this text is for you. The applications to computer science, especially cryptography, are rich and extensive, ranging from computer arithmetic to an elementary presentation of the elliptic curve factoring method. There are also optional applications to algebraic number theory. A human touch is given by the more than 70 biographies of mathematicians, which are woven through the text as footnotes. The text is exercise-rich, with over 740 problems, ranging from the routine to the more difficult star problems, and all odd numbered exercises are solved in detail at the end of the text. To aid the instructor who adopts the text for a course, a solutions manual for the even numbered exercises is available free of charge.

106. Number Theory Definition Of Number Theory In The Free Online Encyclopedia. number theory, branch of mathematics concerned with the properties of the integers (the numbers 0, 1, −1, 2, −2, 3, −3, …). An important area in number theory is the http://encyclopedia2.thefreedictionary.com/number theory

107. Discovering Number Theory A textbook by John Jones and Jeff Holt. http://math.la.asu.edu/~jj/dnt/

Discovering Number Theory is a textbook by John Jones and Jeff Holt published by W. H. Freeman and Company Requests for examination copies of the materials should go directly to the publisher. Visit this W.H. Freeman page and you should find a link which you can use to request a copy of the book. W.H. Freeman is starting a web page with materials for the book . It is in the process of being updated. Development of these course materials was supported by the NSF under grant Revitalizing Undergraduate Number Theory Course Basics The basic operation of the course is as follows. (This is also explained in the first day handout below.) Each chapter starts with the pre-lab sheet. It contains background, exercises to be worked by hand, and may mention the larger questions which will be taken up in the computer lab. Each student turns in their individual answers to pre-lab questions the following class, which is . . . The next 2-3 classes are held in the lab. Students work through the lab notebooks in teams of two. Each notebook contains "Research questions" and "Exercises". Exercises are intended to be straightforward while research questions are not. Typically, the research questions will require experimentation, forming of conjectures, and proofs. We expect students to make varying degrees of progress on these questions. Then, there is 1 or 2 classes where teams of 2 pair up to make teams of 4. These groups compare notes and improve their results to produce a single report. The report should include conjectures formed with any progress on their resolution (counter-examples, partial proofs, complete proofs).

108. Number Theory — FactMonster.com Encyclopedia number theory. number theory, branch of mathematics concerned with the properties of the integers (the numbers 0, 1, 1, 2, -2, 3, -3, …). http://www.factmonster.com/ce6/sci/A0836174.html

Home U.S. People Word Wise ... Homework Center Fact Monster Favorites Halloween Math Flashcards Geography Guide Seven New Wonders of the World ... The Fifty States Reference Desk Atlas Almanacs Dictionary Encyclopedia ... Encyclopedia number theory number theory, p p a is a product ( a p p p p n Euler , C. F. Gauss , and Pierre de Fermat . It remains a major area of mathematical research, to which the most sophisticated mathematical tools have been applied. See O. Ore, Number Theory and Its History (1988); R. P. Burn, A Pathway into Number Theory (2d ed. 1996); J. H. Silverman, A Friendly Introduction to Number Theory (1996); M. A. Herkommer, Number Theory: A Programmer's Guide (1998); R. A. Mollin, Algebraic Number Theory The Columbia Electronic Encyclopedia, Cite Print More on number theory from Fact Monster: prime number - prime number: prime number: see number theory. integer - integer: integer: see number; number theory. symbolic logic: Analysis of the Foundations of Mathematics - Analysis of the Foundations of Mathematics Symbolic logic has been extended to a description and ... Srinivasa Ramanujan Leopold Kronecker See more Encyclopedia articles on: Mathematics Help Site Map Atlas ... Encyclopedia Click Here!

109. Elliptic Curves: Number Theory And Cryptography, 2nd Edition By Larry Washington (Chapman+Hall/CRC, 2003). Contents, errata. http://www.math.umd.edu/~lcw/ec.html

Elliptic Curves: Number Theory and Cryptography, 2nd edition By Lawrence C. Washington The Table of Contents for the book can be viewed here The web page for the first edition of the book. Contact Information: Larry Washington Department of Mathematics University of Maryland College Park, MD 20742 lcw "at" math.umd.edu. Errata A list of corrections is being compiled and periodically updated here Please send comments and corrections to lcw "at" math.umd.edu.

110. Python For Number Theory The Python programming language has basic commands which implement integer arithmetic. More involved number theory will require us to write short programs and modules in Python http://www.umbc.edu/~rcampbel/Computers/Python/numbthy.html

Number Theory with Python Contents Integer Operations Number Theory Operations Gaussian Integer Operations Polynomial Operations ... Next The Python programming language has basic commands which implement integer arithmetic. More involved number theory will require us to write short programs and modules in Python. (Given the option, the best way to do number theory in Python is to use SAGE , a Python-based symbolic algebra system.) A general introduction to Python use and where it can be found/installed at UMBC can be found in a separate document A particular strength of Python for number theory is its native support for arbitrary sized integers. These numbers are entered by writing the number followed by the letter "L" (for example 1234512L). Starting with Python 2.x there is an automatic conversion from regular integers to long integers when the size of the number is large enough. Integer Operations The basic arithmetic operations, , are available from the keyboard. Note that when used with integers, the division operator returns the greatest integer less than the exact result. (Note that this is done consistently, even for negative values - this differs from many programming languages.) The modular reduction operator is represented by the operator (eg returns 1. Again, this differs from many languages in that, if the modulus is positive the result is always positive.) Exponentiation is represented with the

111. Algorithmic Number Theory Eric Bach and Jeffrey Shallit. Errata, bibliography in BibTeX format. http://www.cs.uwaterloo.ca/~shallit/ant.html

Algorithmic Number Theory Eric Bach and Jeffrey Shallit Algorithmic Number Theory, Volume I: Efficient Algorithms Published by MIT Press , August 1996 xvi + 512 pages US $55.00 ISBN 0-262-02405-5 (v.1) Library of Congress Call Number QA 241.B1085 1996 Description and Table of Contents What Some Readers and Reviewers Have Said Bibliography Errata and Addenda ... When will Volume 2 be published? E-mail:

112. ONLINE THESES IN NUMBER THEORY Links to over 100 dissertations in various languages maintained by Keith Matthews. http://www.numbertheory.org/ntw/N5.html

Online Theses in Number Theory On Euclidean Ideal Classes , PhD thesis, Hester K. Graves, U. Michigan 2009 Applications of Sieve Methods in Analytic Number Theory , PhD thesis, Youness Lamzouri, University of Montreal, 2009 Theoretical and algorithmic aspects of congruences between modular Galois representations Some aspects of analytic number theory: parity, transcendence, and multiplicative functions , Ph.D. Thesis, Michael Coons, Simon Fraser University, 2009 On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms The canonical fractional Galois ideal at s=0 , PhD thesis, Paul Buckingham, Universtiy of Sheffield, 2008 , PhD thesis, Maria Carrizosa, Paris VI, 2008 Algorithms for p-adic cohomology and p-adic heights , PhD thesis, David Harvey, Harvard University 2008 Constructing Abelian Varieties for Pairing-Based Cryptography , PhD Thesis, David Mandell Freeman, University of California, Berkeley, 2008 Number theoretic algorithms for elliptic curves , PhD thesis, Juliana Belding, University of Maryland, College Park, 2008 Integral transforms of the Minkowski question mark function , PhD thesis, Giedrius Alkauskas, University of Nottingham, 2008 Prime polynomials over finite fields , PhD thesis, Paul Pollack, Dartmouth College, 2008 Honours Thesis and slidetalk on Descent on Elliptic Curves , Martin Leslie Asymptotically counting points of bounded height Congruence properties of Fourier coefficients of modular forms , PhD thesis, Timothy Kilbourn, University of Illinois at Urbana-Champaign, 2007

113. Number Theory (mathematics) -- Britannica Online Encyclopedia number theory (mathematics), branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the http://www.britannica.com/EBchecked/topic/422325/number-theory

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. number-theory My Britannica CREATE MY number theor... NEW ARTICLE ... SAVE number theory Table of Contents: number theory Article Article From prehistory through Classical Greece From prehistory through Classical Greece - Pythagoras Pythagoras - Euclid Euclid - Diophantus Diophantus Number theory in the East Number theory in the East Modern number theory Modern number theory - Pierre de Fermat Pierre de Fermat - Number theory in the 18th century Number theory in the 18th century - Number theory in the 19th century Number theory in the 19th century - - Disquisitiones Arithmeticae Disquisitiones Arithmeticae - - From classical to analytic number t...

114. Mathematics Of Computation Areas covered include numerical analysis, computational number theory and algebra, and related fields. Table of contents. Articles available to subscribers. http://www.ams.org/mcom/

115. Number Theory | Arizona Mathematics The research of the number theory group encompasses classical and algebraic number theory, computational number theory, and especially the modern subject of arithmetic geometry. http://math.arizona.edu/research/numbertheory.html

UA Calendars UA Phonebook Site Index Locate Math Building on Campus Map ... Computer Support You are here: Home Research Faculty Areas of Interest Algebra / Geometry: Number Theory Number Theory The research of the number theory group encompasses classical and algebraic number theory, computational number theory, and especially the modern subject of arithmetic geometry. Two of the Millenium Prize Problems in mathematics, offered by the Clay Mathematics Institute, are in the area of number theory and one more is closely related to number theory. Related websites: Southwest Center for Arithmetic Geometry (SWC) Members Ana M Castravet Kirti N Joshi Daniel Madden William G Mccallum David L Savitt Romyar T Sharifi Dinesh S Thakur William Y Velez Groups: Research Research Centers and Institutes Affiliated Interdisciplinary Programs Faculty Areas of Interest Algebra / Geometry: Group Theory Number Theory Topology and Geometry Analysis: Analysis and its Applications Dynamical Systems Geometric Analysis Mathematical Physics Applied Mathematics: Computational Science and Numerical Analysis Fluids and Mechanics Mathematical Biology Nonlinear Waves ... Optical Science Education: Mathematics Education Research, Teacher Preparation, and Outreach

116. Smarandache Notions Journal Containing several number theory articles primarily about Smarandache s work. http://www.gallup.unm.edu/~smarandache/

Economics Linguistics Mathematics Philosophy ... Globe Trekker This is an electronic and hard copy journal in many languages about Smarandache type functions, sequences, primes, transcendental numbers, generalized palindromes, constants, continued fractions, numeration bases, algorithms, criteria of primality and simultaneously primality, criteria of coprimality, functional iterations, infinite products, k-factorials, relationships, series, solved and unsolved problems, conjectures, theorems, algebraic structures, Non-Euclidean geometries, manifolds, recreational sciences, paradoxes, tautologies, psychological tests and law on sensations and stimuli, unmatter and unparticle, physics hypothesis that there is no speed barrier in the universe, SC-potential, neutrosophy as a new branch of philosophy, neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, Poly-Emporium Theory, Dezert-Smarandache Theory of plausible and paradoxical reasoning in information fusion, etc.

117. INTEGERS: The Electronic Journal Of Combinatorial Number Theory Free refereed electronic journal. http://www.integers-ejcnt.org/

Editorial board Author index Subscribe News The proceedings of the Integers Conference 2007 have be published by deGruyter as "Combinatorial Number Theory," and are now available online at Volume 9 Supplement The in Prague have been published as part of Volume 9. Current and Recent Volumes Volume Volume 9 Supplement Proceedings of the Integers 2007 Conference Volume All Volumes Instructions for Authors Download statistics Beginning with Volume 9 (2009), Integers is being published both at this website and also in print by deGruyter. Visit deGruyter's website for more information on the hardcopy version of Integers. INTEGERS is a refereed electronic journal devoted to research in the area of combinatorial number theory. It is published with the help of the University of West Georgia, Charles University, and DIMATIA. Subscriptions to INTEGERS are free. We welcome original research articles in combinatorics and number theory, with a preference for those that have a connection to both fields. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. The principal subject areas, according to the American Mathematical Society subject classification scheme are 05A, 05C55, 05C65, 05D, 11A, 11B, 11K, 11N, 11P, 11Y, and 91A46. INTEGERS also houses a combinatorial games section. ISSN 1553-1732

118. BUBL LINK: Number Theory s Computational Complexity; Fermat's Last Theorem; Journal of Number Theory; Mathematics of Computation; Number Theory; Number Theory Web......Titles http://bubl.ac.uk/link/n/numbertheory.htm

BUBL LINK Catalogue of Internet Resources Home Search Subject Menus Countries ... Z Number theory Titles Descriptions Computational Complexity Fermat's Last Theorem Journal of Number Theory Mathematics of Computation ... Work of Robert Langlands Comments: bubl@bubl.ac.uk Computational Complexity Journal which presents research at the interface between mathematics and theoretical computer science, with a clear mathematical profile and strictly mathematical format. Specific areas of concentration include structure of complexity classes, algebraic complexity, cryptography, interactive proofs, complexity issues in: computational geometry, robotics, and motion planning, learning theory, number theory, logic, combinatorial optimisation and approximate solutions, and distributed computing. Author: Springer Subjects: combinatorics, complex systems, computational mathematics, cryptography, number theory, optimisation DeweyClass: Resource type: journal Fermat's Last Theorem Explanation of the famous theorem of Pierre de Fermat who died in 1665, and a summary of its proof by Andrew Wiles in 1993. Author: St Andrews University Subjects: mathematicians, number theory

119. ScienceDirect - Journal Of Number Theory, Volume 131, Issue 2 In Progress (Febru Publisher s site. http://www.sciencedirect.com/science/journal/0022314X

Hub ScienceDirect Scopus Register ... Go to SciVal Suite Username: Password: Remember me Not Registered? Forgotten your username or password? Go to Athens / Institution login Home ... Help All fields Author Advanced search Journal/Book title Volume Issue Page Search tips Journal of Number Theory Sample Issue Online About this Journal Submit your Article Shortcut link to this Title ... New Article Feed Signed up for new Volumes / Issues [ remove Alert me about new Volumes / Issues Your selection(s) could not be saved due to an internal error. Please try again. Added to Favorites [ remove Add to Favorites Font Size: Add to my Quick Links Volume 131, Issue 2 In Progress Volume / Issue In Progress A Volume/Issue that is "In Progress" contains final, fully citable articles that are published online, but the volume/issue itself is awaiting more articles before it can be considered "final". Individual article details such as volume, issue and page numbers will not change. (February 2011) = Full-text available = Abstract only Articles in Press Volume 131 (2011) Volume 131, Issue 2

120. Journal Of Number Theory | Department Of Mathematics Editorial contact information. http://www.math.ohio-state.edu/JNT/

@import "/misc/drupal.css"; @import "/modules/acidfree/acidfree.css"; @import "/themes/osumath/style.css"; @import "/modules/codefilter/codefilter.css"; @import "/modules/event/event.css"; @import "/modules/img_assist/img_assist.css"; @import "/modules/quote/quote.css"; @import "/modules/rsvp/rsvp.css"; @import "/modules/tables/tables.css"; @import "/modules/devel/devel.css"; @import "/modules/tinymce/upload_image/upload_image.css"; @import "/themes/osumath/navbar.css"; Begin OSU masthead and toolbar The Ohio State University www.osu.edu OSU Help Campus map ... Home Journal of Number Theory The Journal of Number Theory was founded at The Ohio State University in 1969 by Professors R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus. Editor-in-Chief: David Goss For more information, including a list of editorial board members and author instructions, please see Elsevier To submit to JNT, please go to http://ees.elsevier.com/jnt/ Office Susan Hunter Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, Ohio 43210-1174

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