An Illustrated Theory Of Numbers

Author: Martin H. Weissman
Publisher: American Mathematical Soc.
ISBN: 9781470434939
File Size: 68,27 MB
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Seeing arithmetic -- Foundations -- The Euclidean algorithm -- Prime factorization -- Rational and constructible numbers -- Gaussian and Eisenstein integers -- Modular arithmetic -- The modular worlds -- Modular dynamics -- Assembling the modular worlds -- Quadratic residues -- Quadratic forms -- The topograph -- Definite forms -- Indefinite forms

Elements Of Number Theory

Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 0387217355
File Size: 31,69 MB
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Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.

Number Theory And Its History

Author: Oystein Ore
Publisher: Courier Corporation
ISBN: 0486136434
File Size: 10,94 MB
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Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

Mathematics

Author: Tom Jackson
Publisher: Ponderables
ISBN: 9781627950954
File Size: 26,26 MB
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"Includes foldout timeline with over 1,000 milestone facts" -- Cover.

Theory Of Algebraic Integers

Author: Richard Dedekind
Publisher: Cambridge University Press
ISBN: 9780521565189
File Size: 65,66 MB
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A translation of a classic work by one of the truly great figures of mathematics.

Not Always Buried Deep

Author: Paul Pollack
Publisher: American Mathematical Soc.
ISBN: 0821848801
File Size: 42,48 MB
Format: PDF
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Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. Not Always Buried Deep is designed to be read and enjoyed by those who wish to explore elementary methods in modern number theory. The heart of the book is a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. Rather than trying to present a comprehensive treatise, Pollack focuses on topics that are particularly attractive and accessible. Other topics covered include Gauss's theory of cyclotomy and its applications to rational reciprocity laws, Hilbert's solution to Waring's problem, and modern work on perfect numbers. The nature of the material means that little is required in terms of prerequisites: The reader is expected to have prior familiarity with number theory at the level of an undergraduate course and a first course in modern algebra (covering groups, rings, and fields). The exposition is complemented by over 200 exercises and 400 references.

Fundamentals Of Number Theory

Author: William J. LeVeque
Publisher: Courier Corporation
ISBN: 0486141500
File Size: 66,15 MB
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DIVBasic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition. /div

Theories For Everything

Author: John Langone
Publisher: National Geographic Books
ISBN: 9780792239123
File Size: 51,14 MB
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Discusses current theories about the natural and physical world and shows how they developed as mankind explored the world around them.

Number Theory Fermat S Dream

Author: Kazuya Kato
Publisher: American Mathematical Soc.
ISBN: 9780821808634
File Size: 64,12 MB
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This is the English translation of the original Japanese book. In this volume, ``Fermat's Dream'', core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.

An Illustrated Introduction To Topology And Homotopy

Author: Sasho Kalajdzievski
Publisher: CRC Press
ISBN: 1482220814
File Size: 78,18 MB
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An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs. The first part of the text covers basic topology, ranging from metric spaces and the axioms of topology through subspaces, product spaces, connectedness, compactness, and separation axioms to Urysohn’s lemma, Tietze’s theorems, and Stone-Čech compactification. Focusing on homotopy, the second part starts with the notions of ambient isotopy, homotopy, and the fundamental group. The book then covers basic combinatorial group theory, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The last three chapters discuss the theory of covering spaces, the Borsuk-Ulam theorem, and applications in group theory, including various subgroup theorems. Requiring only some familiarity with group theory, the text includes a large number of figures as well as various examples that show how the theory can be applied. Each section starts with brief historical notes that trace the growth of the subject and ends with a set of exercises.