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CPSC 490 Number Theory GCD and the extended Euclidean algorithm Number TheoryNumber Theory is a branch of mathematics that explores the properties of integers most of the timeonly the natural numbers Most problems in Elementary Number Theory are easy to state andunderstand because they just extensions of grade school mathematics At the same time theresolutions to these problems are not simple usua...

**Author:**none**Size:**22975 KB**Created:**2015-01-30 04:06:21

Hypergeometric sums and combinatorial Number Theory A hypergeometric sum is a nite or in nite sum of the formckkwhere the ratio of successive terms ck 1 is a rational function of k Such sums have beenckstudied extensively for centuries and comprise a class of special functions with tremendousimportance in mathematics They frequently emerge in the study of Number-theoretic prob-lems of combinatoria...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

MATH4300 DIRECTED READING IN Number Theory WINTER 2013InstructorYouness LamzouriO ce N515 Ross BuildingEmail Lamzouri mathstat yorku caWebsite www math yorku ca lamzouriWeekly Meetings Tuesdays 2 30-4 00 pm in N501 RossCourse DescriptionThis course is an advanced introduction to Elementary and analytic Number the-ory We will cover material ranging from basic concepts such as modular arithmeticquad...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Number Theory and Elementary arithmetic Jeremy AvigadJune 12 2002AbstractElementary arithmetic also known as Elementary function arith-metic is a fragment of rst-order arithmetic so weak that it cannotprove the totality of an iterated exponential function Surprisingly how-ever the Theory turns out to be remarkably robust I will discuss formalresults that show that many theorems of Number Theory an...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

18 784 Additive Number Theory Section 6 2 Notes 1 Chebyshev s TheoremToday we prove some asymptotic results about the distribution of prime numbers Specif-ically we derive estimates for the prime-counting functionsx ln pp xx ln ppk xx 1p xNote that we will always use p to denote a primeLacking the tools of complex analysis it is di cult to nd the exact asymptoticformulas however our Elementary met...

**Author:**none**Size:**12069 KB**Created:**2013-10-24 04:02:48

ALGEBRAIC Number Theory - COURSE NOTES STEVE DONNELLYHousekeeping1 There ll be a nal exam 3 hours or so on the whole semesterrepresentation Theory and algebraic Number Theory weightedtowards algebraic Number theory2 There ll be homework assignments each week due on Tuesdaysby lunchtime3 The assignments will consist of core problems and more chal-lenging problems for discussion we ll schedule a cou...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Algorithmic Number Theory S Arun-KumarDecember 1 20022ContentsI Lectures 91 Lecture-wise break up 112 Divisibility and the Euclidean Algorithm 133 Fibonacci Numbers 154 Continued Fractions 195 Simple In nite Continued Fraction 236 Rational Approximation of Irrationals 297 Quadratic Irrational Periodic Continued Fraction 338 Primes and ther In nitude 379 Tchebychev s Theorem 459 1 Primes and their ...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Number Theory EMT3605 MZUZU UNIVERSITYFACULTY OF EDUCATIONDEPARTMENT OF MATHEMATICSSYLLABUS1 Programme Bachelor of Science Education2 Subject Mathematics3 Course Title Number Theory4 Course Code EMT 36055 Prerequisites EMT 35026 Level of Study Three7 Duration 14 weeks8 Lecture Hours per week Four9 Tutorials Seminars per week One every two weeks10 Assessment Continuous 50Examination 5011 Aim s of t...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Applications of Number Theory to Fermat s Last TheoremCameron ByerleyMay 14 20062Abstract This paper is in the form of the fth and sixth chapters of lecturenotes designed for an introductory Number Theory class It uses a Number ofbasic Number Theory concepts to prove three cases of Fermat s Last TheoremFermat s Last Theorem states there are no integral solutions to the equationxn y n z n for n 2 W...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Microsoft Word - Ionescu - Remarks on Physics as Number Theory.doc 232 Ionescu Remarks on Physics as Number Theory Vol 9Remarks on Physics as Number TheoryLucian M IonescuIllinois State University Mathematics Department Campus Box 4520 Normal IL 61790e-mail LMIones ilstu eduThere are numerous indications that Physics at its foundations is algebraic Number Theory startingwith solid state physics ev...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Elementary Coding Theory MATH 280 Discrete Mathematical Structures Elementary Coding Theory 1Information TransmissionEncode Code word Transmission Received DecodeMessage special n tuple n tuple Decoded messagewith noiseThe message is a binary string m-tupleThe code word is also a binary string n-tupleMATH 280 Discrete Mathematical Structures Elementary Coding Theory 2ErrorsError - change in some o...

**Author:**none**Size:**28206 KB**Created:**2014-02-07 20:07:24

Recursion Theory Notes Fall 2011 Lecturer Lou van den Dries0 1 IntroductionRecursion Theory or Theory of computability is a branch of mathematical logicstudying the notion of computability from a rather theoretical point of viewThis includes giving a lot of attention to what is not computable or what iscomputable relative to any given not necessarily computable function Thesubject is interesting o...

**Author:**none**Size:**496 KB**Created:**2015-02-01 03:34:55

Notes on Number Theory and Discrete Mathematics Vol 19 2013 No 2 69 76Generalization of a few results in integer partitionsManosij Ghosh Dastidar1 and Sourav Sen Gupta21Ramakrishna Mission Vidyamandira Belur West Bengal Indiae-mail gdmanosij gmail com2Indian Statistical Institute Kolkata Indiaemail sg sourav gmail comCorresponding authorAbstract In this paper we generalize a few important results ...

**Author:**none**Size:**20106 KB**Created:**2015-04-23 20:11:38

Alberta Number Theory Days Amir Akbary University of LethbridgeBrandon Fodden University of LethbridgeJune 17 June 19 20111 OverviewThe fourth installment of the Alberta Number Theory Days was held in BIRS on the weekend of June 17 to 1929 people participated in this event including 12 faculty members 13 graduate students and 4 postdoctoralfellows A total of nine 45-minutes lectures were given Thr...

**Author:**none**Size:**15674 KB**Created:**2013-02-07 19:32:41

Introduction to Number Theory M328K INTRODUCTION TO Number Theory FALL 2005GERGELY HARCOSPrinciple of Induction Some equivalent and frequently used formulations1 If a given statement holds for the Number 1 and the validity of the statementis inherited from any positive integer to its successor then the statementholds for all positive integers2 If the validity of a given statement for any given pos...

**Author:**none**Size:**24176 KB**Created:**2013-08-06 15:18:01

Turkish Journal of Analysis and Number Theory 2014 Vol 2 No 2 47-52 Available online at http pubs sciepub com tjant 2 2 4Science and Education PublishingDOI 10 12691 tjant-2-2-4Modified SSOR Modelling for Linear ComplementarityProblemsM T Yahyapour S A EdalatpanahDepartment of Mathematics Ramsar Branch Islamic Azad University Ramsar IranCorresponding author saedalatpanah gmail comReceived March 27...

**Author:**none**Size:**26201 KB**Created:**2013-08-13 03:34:44

Algebraic Number Theory Algebraic Number TheoryJ S MilneVersion 3 01September 28 2008An algebraic Number eld is a nite extension of Q an algebraic Number is an elementof an algebraic Number eld Algebraic Number Theory studies the arithmetic of algebraicnumber elds the ring of integers in the Number eld the ideals and units in the ring ofintegers the extent to which unique factorization holds and s...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

6.042J Course Notes, Number Theory Chapter 14Number TheoryNumber Theory is the study of the integers Why anyone would want to study theintegers is not immediately obvious First of all what s to know There s 0 there s1 2 3 and so on and oh yeah -1 -2 Which one don t you understand Second what practical value is there in it The mathematician G H Hardy expressedpleasure in its impracticality when he ...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Theory of Numbers Spring Semester 2014Course MATH 416 Section 1 MWF 9 00 9 50am RB 450Instructor Dr Hanspeter FischerContact O ce RB 426Phone 285-8680E-mail h scher bsu edu please use MATH 416 as subject linehttp www cs bsu edu fischer math416O ce Hours Mon 10 00 10 50am Tue 9 00 9 50am Wed 10 00 10 50amThu 9 00 9 50am Fri 10 00 10 50am and by appointmentPrerequisites MATH 215Text Elementary Numbe...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

The role of complex conjugation in transcendental Number Theory The role of complex conjugation in transcendentalnumber theoryMichel WaldschmidtTo cite this versionMichel Waldschmidt The role of complex conjugation in transcendental Number Theory NSaradha International Conference on Diophantine Equations DION 2005 Dec 2005 Mum-bai India Narosa Publishing House New Delhi pp 297-308 TIFR Mumbai hal-...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Proceedings of the Sixth International Conference on Number Theory and Smarandache Notions RESEARCH ON Number Theory ANDSMARANDACHE NOTIONSPROCEEDINGS OF THE SIXTH INTERNATIONALCONFERENCE ON Number Theory ANDSMARANDACHE NOTIONSEdited byZHANG WENPENGDepartment of MathematicsNorthwest UniversityXi an P R ChinaHexis2010iThis book can be ordered in a paper bound reprint fromBooks on DemandProQuest Inf...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Number Theory Number TheoryPURE A N D APPLIED M A T H E AT ICSMA Series of Monographs and TextbooksEdited byA and EILENBERGPAUL SMITH SAMUELColumbia University N e w York1 ARNOLD SOMMERFELD Differential Equations in Physics 1949 LecturesPartialon Theoretical Physics Volume V I2 REINHOLD BAER Linear Algebra and Projective Geometry 19523 HERBERT BUSEMANN D PAULAN KELLY Projective Geometry and Projec...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Download Digital Signal Processing Algorithms: Number Theory, Convolution, Fast Fourier Transforms, and Applications (Computer Science & Engineering).pdf Free Digital Signal Processing Algorithms Number Theory ConvolutionFast Fourier Transforms and Applications Computer ScienceEngineeringBy Garg Hari KrishnaSyllabus for the Phd - Thapar University3 Department of Computer Science Engineering Am...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

MATH 361 Number Theory FIFTH LECTURE 1 The Sun Ze TheoremThe Sun Ze Theorem is often called the Chinese Remainder Theorem Here isan example to motivate it Suppose that we want to solve the equation13x 23 mod 2310Note that 2310 2 3 5 7 11 Since gcd 13 2310 1 we can solve thecongruence using the extended Euclidean algorithm but we want to think about itin a di erent way now The idea is that13x 23 mo...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Introductory Number Theory Introductory Number Theory - Problem Set 1Spring 2006Michael StollDue Monday February 13 12 00 noon in Prof Stoll s o ce1 Prove the following basic facts from the de nitionsa If a b and a c then a b cb If a b and b a then a bc gcd ac bc c gcd a bd gcd a b gcd a ka b2 Use the Euclidean algorithm to nd gcd 451 3693 Find a solution in integers to the equation 23 x 30 y 3 or...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Theoretical Foundations - Introduction to Computational Number Theory - Part 4 Theoretical FoundationsIntroduction to Computational Number Theory - Part 4Jean-S bastien CoroneUniversit du LuxembourgeOctober 10 2009Jean-S bastien Corone Theoretical FoundationsSummaryC programmingFunctionsAlgorithmic Number theoryModular arithmeticSolving linear congruence equationsChinese remainder theoremJean-S ba...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Elementary Number Theory FINAL1 Complete the following de nitions for integers a b d p we say thata b a if a bc for some c Zb a is a unit if a 1c p is irreducible if p is a nonunit and if p ab implies that a or b is aunitd p is prime if p is a nonunit and if p ab implies that p a or p be d gcd a b if d a and d b and if e a and e b implies e d2 Solve the following problemsa What is 40 mod 41By Wils...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

REPRESENTATION Theory AND Number Theory Contents1 Tuesday September 20 21 1 The local Langlands conjectures 21 2 Some examples 31 3 Unrami ed representations parameters 31 4 Other examples 41 5 Wildly rami ed representations of SU3 E k 52 Tuesday September 27 62 1 Review of algebraic Number Theory global Theory 62 2 Galois Theory 72 3 Artin s Theory 82 4 Review of algebraic Number Theory local the...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

FLINT 1 5 2 Fast Library for Number Theory William B Hart and David HarveyApril 8 2010Contents1 Introduction 12 Building and using FLINT 13 Test code 24 Reporting bugs 25 Example programs 26 FLINT macros 37 The fmpz poly module 37 1 Simple example 37 2 De nition of the fmpz poly t polynomial type 47 3 Initialisation and memory management 47 4 Setting retrieving coe cients 57 5 String conversions a...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015

Course notes on Number Theory In Number Theory we make the decision to work entirely with whole num-bers There are many reasons for this besides just mathematical interestnot the least of which is that computers can only work with whole numbersprecisely everything else is just an approximation So if all that we areallowed to work with are whole numbers what can we do Can we add twowhole numbers Ye...

**Author:**none**Size:**100 KB**Created:**Tue Jun 26 08:58:39 2015