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17 Lectures on Fermat Numbers: From Number Theory to Geometry
ISBN: 9780387953328 / Angielski / Twarda / 257 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth, providing readers with an overview of the many properties of Fermat numbers and demonstrating their applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers.
The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written i...
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401,99 zł |
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Number Theory in Function Fields
ISBN: 9780387953359 / Angielski / Twarda / 358 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of...
Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. ...
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306,26 zł |
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Computational Excursions in Analysis and Number Theory
ISBN: 9780387954448 / Angielski / Twarda / 220 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This book is designed for a topics course in computational number theory. It is based around a number of difficult old problems that live at the interface of analysis and number theory. Some of these problems are the following: The Integer Chebyshev Problem. Find a nonzero polynomial of degree n with integer eoeffieients that has smallest possible supremum norm on the unit interval. Littlewood's Problem. Find a polynomial of degree n with eoeffieients in the set { + 1, -I} that has smallest possible supremum norm on the unit disko The Prouhet-Tarry-Escott Problem. Find a polynomial with...
This book is designed for a topics course in computational number theory. It is based around a number of difficult old problems that live at the inter...
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cena:
382,84 zł |
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Elements of Number Theory
ISBN: 9780387955872 / Angielski / Twarda / 256 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem...
This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it ...
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172,11 zł |
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P-Adic Numbers, P-Adic Analysis, and Zeta-Functions
ISBN: 9780387960173 / Angielski / Twarda / 153 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu. I. Manin's "Course in Mathematical Logic" (GTM 53). He taught at Harvard from 1975 to 1979, and since 1979 has been at the University of Washington in Seattle. He has published papers in number theory, algebraic geometry, and p-adic analysis, and he is the author of "p-adic Analysis: A Short Course on Recent Work" (Cambridge University Press and...
Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and t...
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cena:
287,12 zł |
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Ramanujan's Notebooks: Part I
ISBN: 9780387961101 / Angielski / Twarda / 357 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Srinivasa Ramanujan is, arguably, the greatest mathematician that India has produced. His story is quite unusual: although he had no formal education inmathematics, he taught himself, and managed to produce many important new results. With the support of the English number theorist G. H. Hardy, Ramanujan received a scholarship to go to England and study mathematics. He died very young, at the age of 32, leaving behind three notebooks containing almost 3000 theorems, virtually all without proof. G. H. Hardy and others strongly urged that notebooks be edited and published, and the result is...
Srinivasa Ramanujan is, arguably, the greatest mathematician that India has produced. His story is quite unusual: although he had no formal education ...
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cena:
765,72 zł |
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Cyclotomic Fields I-II
ISBN: 9780387966717 / Angielski / Twarda / 436 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummer's work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek Po], Artin-Hasse A-H] and Vandiver Va]. In the mid 1950's, the theory of cyclotomic fields was...
Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi...
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cena:
325,42 zł |
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Introduction to Arakelov Theory
ISBN: 9780387967936 / Angielski / Twarda / 187 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Riemann-Roch theorem. The book is intended for second year graduate students and researchers in the field who want a systematic introduction to the subject. The residue theorem, which forms the basis for the adjunction...
Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfac...
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421,13 zł |
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Ramanujan's Notebooks: Part II
ISBN: 9780387967943 / Angielski / Twarda / 360 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the second of four volumes devoted to the editing of Ramanujan's Notebooks. Part I, published in 1985, contains an...
During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his result...
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cena:
612,57 zł |
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Factorization and Primality Testing
ISBN: 9780387970400 / Angielski / Twarda / 240 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. "About binomial theorems I'm teeming with a lot of news, With many cheerful facts about the square on the hypotenuse. " - William S. Gilbert (The Pirates of Penzance, Act I) The question of divisibility is arguably the oldest problem in mathematics. Ancient peoples observed the cycles of nature: the day, the lunar month, and the year, and assumed that each divided evenly into the next. Civilizations as separate as the Egyptians of ten thousand years ago and the Central American Mayans adopted a month of thirty days and a year of twelve months. Even when the inaccuracy of a 360-day year became...
"About binomial theorems I'm teeming with a lot of news, With many cheerful facts about the square on the hypotenuse. " - William S. Gilbert (The Pira...
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198,91 zł |
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Modular Functions and Dirichlet Series in Number Theory
ISBN: 9780387971278 / Angielski / Twarda / 207 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. The second volume presupposes a background in number theory com- parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences...
This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology duri...
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cena:
325,42 zł |
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Numbers
ISBN: 9780387974972 / Angielski / Miękka / 398 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi cult to develop broad perspective about their subject....
A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by...
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287,12 zł |
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Ramanujan's Notebooks: Part III
ISBN: 9780387975030 / Angielski / Twarda / 510 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was...
During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathemat...
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cena:
957,17 zł |
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Numbers and Geometry
ISBN: 9780387982892 / Angielski / Twarda / 343 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history...
A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provi...
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187,43 zł |
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Analytic Number Theory
ISBN: 9780387983080 / Angielski / Twarda / 80 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion. It covers an amazing amount of material, despite the leisurely pace and emphasis on readability. The author's heartfelt enthusiasm enables readers to see what is magical about the subject. Topics included are: The Partition Function; The Erdos-Fuchs Theorem; Sequences without Arithmetic Professions; The Waring Problem; A "Natural" Proof of the Non-vanishing of L-Series, and a Simple Analytic Proof of the Prime Number Theorem - all presented in a surprisingly elegant and...
Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion. It covers an amazing amount of mat...
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cena:
248,84 zł |
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Fourier Analysis on Number Fields
ISBN: 9780387984360 / Angielski / Twarda / 354 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This book grew out of notes from several courses that the first author has taught over the past nine years at the California Institute of Technology, and earlier at the Johns Hopkins University, Cornell University, the University of Chicago, and the University of Crete. Our general aim is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. Our more particular goal is to cover Jolm Tate's visionary thesis, giving virtually all of the necessary analytic details and topological...
This book grew out of notes from several courses that the first author has taught over the past nine years at the California Institute of Technology, ...
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cena:
382,84 zł |
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Fermat's Last Theorem for Amateurs
ISBN: 9780387985084 / Angielski / Twarda / 407 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. ItisnowwellknownthatFermat slasttheoremhasbeenproved. For more than three and a half centuries, mathematicians from the greatnamestothecleveramateurs triedtoproveFermat sfamous statement. The approach was new and involved very sophisticated theories. Finallythelong-soughtproofwasachieved. Thearithmetic theory of elliptic curves, modular forms, Galois representations, and their deformations, developed by many mathematicians, were the tools required to complete the di?cult proof. Linked with this great mathematical feat are the names of TANI- YAMA, SHIMURA, FREY, SERRE, RIBET, WILES, TAYLOR....
ItisnowwellknownthatFermat slasttheoremhasbeenproved. For more than three and a half centuries, mathematicians from the greatnamestothecleveramateurs ...
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cena:
306,26 zł |
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Sphere Packings, Lattices and Groups
ISBN: 9780387985855 / Angielski / Twarda / 706 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional...
The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal...
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cena:
325,42 zł |
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Advanced Topics in Computational Number Theory
ISBN: 9780387987279 / Angielski / Twarda / 581 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations. The practical com- pletion of this task (sometimes known as the Dedekind program) has been one of the major achievements of computational number theory in the past ten years, thanks to the efforts of many people. Even though some practical problems still exist, one can consider the subject as solved in a satisfactory...
The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit gro...
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cena:
344,56 zł |
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Math Talks for Undergraduates
ISBN: 9780387987491 / Angielski / Twarda / 121 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. For many years Serge Lang has given talks to undergraduates on selected items in mathematics which could be extracted at a level understandable by students who have had calculus. Written in a conversational tone, Lang now presents a collection of those talks as a book. The talks could be given by faculty, but even better, they may be given by students in seminars run by the students themselves. Undergraduates, and even some high school students, will enjoy the talks which cover prime numbers, the abc conjecture, approximation theorems of analysis, Bruhat-Tits spaces, harmonic and symmetric...
For many years Serge Lang has given talks to undergraduates on selected items in mathematics which could be extracted at a level understandable by stu...
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cena:
382,84 zł |
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