First Steps In Number Theory
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First Steps In Number Theory
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Author : S. Shirali
language : en
Publisher: Universities Press
Release Date : 2001-07
First Steps In Number Theory written by S. Shirali and has been published by Universities Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07 with Number theory categories.
Number Theory
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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-07-21
Number Theory written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-21 with Mathematics categories.
EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.
A Conversational Introduction To Algebraic Number Theory
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Author : Paul Pollack
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-01
A Conversational Introduction To Algebraic Number Theory written by Paul Pollack and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-01 with Mathematics categories.
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Number Theory
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Author : Peter D. Schumer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-08-18
Number Theory written by Peter D. Schumer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-18 with Mathematics categories.
This is a book for an undergraduate number theory course, senior thesis work, graduate level study, or for those wishing to learn about applications of number theory to data encryption and security. With no abstract algebra background required, it covers congruences, the Euclidean algorithm, linear Diophantine equations, the Chinese Remainder Theorem, Mobius inversion formula, Pythagorean triplets, perfect numbers and amicable pairs, Law of Quadratic Reciprocity, theorems on sums of squares, Farey fractions, periodic continued fractions, best rational approximations, and Pell’s equation. Results are applied to factoring and primality testing including those for Mersenne and Fermat primes, probabilistic primality tests, Pollard’s rho and p-1 factorization algorithms, and others. Also an introduction to cryptology with a full discussion of the RSA algorithm, discrete logarithms, and digital signatures. Chapters on analytic number theory including the Riemann zeta function, average orders of the lattice and divisor functions, Chebyshev’s theorems, and Bertrand’s Postulate. A chapter introduces additive number theory with discussion of Waring’s Problem, the pentagonal number theorem for partitions, and Schnirelmann density.
Commutative Algebra Constructive Methods
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Author : Henri Lombardi
language : en
Publisher: Springer
Release Date : 2015-07-22
Commutative Algebra Constructive Methods written by Henri Lombardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.
Proof Theory
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Author : Vincent F. Hendricks
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Proof Theory written by Vincent F. Hendricks and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.
Lectures On Number Theory
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Author : Peter Gustav Lejeune Dirichlet
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Lectures On Number Theory written by Peter Gustav Lejeune Dirichlet and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.
Great Moments In Mathematics Before 1650
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Author : Howard Whitley Eves
language : en
Publisher: MAA
Release Date : 1983
Great Moments In Mathematics Before 1650 written by Howard Whitley Eves and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with History categories.
[V.2] This is a companion to Great moments in mathematics before 1650. It can be appreciated by anyone with a working knowledge of beginning deferential and integral calculus. Includes: the birth of mathematical probability, the invention of the differential calculus, the discovery of non-Euclidean geometry, the discovery of noncommutative algebra, and the resolution of the four-color problem.
Number Theory
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Author : Tristin Cleveland
language : en
Publisher: Scientific e-Resources
Release Date : 2018-04-11
Number Theory written by Tristin Cleveland and has been published by Scientific e-Resources this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-11 with categories.
In spite of the fact that arithmetic majors are generally familiar with number hypothesis when they have finished a course in conceptual polynomial math, different students, particularly those in training and the human sciences, regularly require a more essential prologue to the theme. In this book the writer takes care of the issue of keeping up the enthusiasm of understudies at the two levels by offering a combinatorial way to deal with basic number hypothesis. In concentrate number hypothesis from such a point of view, arithmetic majors are saved reiteration and furnished with new bits of knowledge, while different understudies advantage from the subsequent effortlessness of the verifications for some hypotheses. Of specific significance in this content is the creator's accentuation on the estimation of numerical cases in number hypothesis and the part of PCs in getting such illustrations. The point of this book is to acquaint the reader with essential subjects in number hypothesis: hypothesis of distinctness, arithmetrical capacities, prime numbers, geometry of numbers, added substance number hypothesis, probabilistic number hypothesis, hypothesis of Diophantine approximations and logarithmic number hypothesis.
Python Arithmetic
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Author : Vincenzo Manca
language : en
Publisher: Springer Nature
Release Date : 2024-11-05
Python Arithmetic written by Vincenzo Manca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Computers categories.
The book is a gentle introduction to Python using arithmetic, and vice versa, with a historical perspective encompassing programming languages within the wider process of development of mathematical notation. The revisitation of typical algorithms that are the core of elementary mathematical knowledge helps to grasp their essence and to clarify some assumptions that are often taken for granted but are very profound and of a very general nature. The first mathematician to define a systematic system for generating numbers was Archimedes of Syracuse in the third century B.C. The Archimedean system, which was defined in a book with the Latin title Arenarius, was not intended to define all numbers, but only very large numbers [13, 22, 23]. However, it can be considered the first system with the three main characteristics of a counting system that have the most important properties for complete arithmetic adequacy: creativity, infinity, and recursion. Creativity means that each numeral is new for numerals that precede it; infinity means that after any numeral there is always another numeral; recursion means that after an initial sequence of numerals coinciding with the digits of the system, digits repeat regularly in all subsequent numerals. Since the numerals are finite expressions of digits, their lengths increase along their generation. In the next chapter, Python is briefly introduced by linking this language to standard mathematical notation, which took its current form throughout a long process that extends from the introduction of decimal numerals to the eighteenth century, particularly within Euler’s notational and conceptual framework. The third chapter is devoted to counting algorithms, showing that something that is usually taken for granted has intriguing aspects that deserve a very subtle analysis: the authors will show that the Python representation of counting algorithms is very informative and demonstrates the informational nature of numbers.