A Gateway To Number Theory
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A Gateway To Number Theory Applying The Power Of Algebraic Curves
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Author : Keith Kendig
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-23
A Gateway To Number Theory Applying The Power Of Algebraic Curves written by Keith Kendig 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 2021-04-23 with Education categories.
Challenge: Can you find all the integers a, b, c satisfying 2a2+3b2=5c2? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of a, b, c will usually be large. So the challenge remains … Find all integers a a, b, c satisfying 2a2+3b2=5c2 A major advance in number theory means this book can give an easy answer to this and countless similar questions. The idea behind the approach is transforming a degree-two equation in integer variables a, b, c into a plane curve defined by a polynomial. Working with the curve makes obtaining solutions far easier, and the geometric solutions then get translated back into integers. This method morphs hard problems into routine ones and typically requires no more than high school math. (The complete solution to 2a2+3b2=5c2 is included in the book.) In addition to equations of degree two, the book addresses degree-three equations—a branch of number theory that is today something of a cottage industry, and these problems translate into “elliptic curves”. This important part of the book includes many pictures along with the exposition, making the material meaningful and easy to grasp. This book will fit nicely into an introductory course on number theory. In addition, the many solved examples, illustrations, and exercises make self-studying the book an option for students, thus becoming a natural candidate for a capstone course.
Number Theory In Mathematics Education
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Author : Rina Zazkis
language : en
Publisher: Routledge
Release Date : 2012-10-12
Number Theory In Mathematics Education written by Rina Zazkis and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-12 with Education categories.
This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education. Topics variously engaged include: *understanding particular concepts related to numerical structure and number theory; *elaborating on the historical and psychological relevance of number theory in concept development; *attaining a smooth transition and extension from pattern recognition to formative principles; *appreciating the aesthetics of number structure; *exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; *reexamining previously constructed knowledge from a novel angle; *investigating connections between technique and theory; *utilizing computers and calculators as pedagogical tools; and *generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs. Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.
Problems In Algebraic Number Theory
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Author : M. Ram Murty
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Problems In Algebraic Number Theory written by M. Ram Murty 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 2005 with Mathematics categories.
The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
A Gateway To Number Theory
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Author : Keith Kendig
language : en
Publisher: MAA Press
Release Date : 2021
A Gateway To Number Theory written by Keith Kendig and has been published by MAA Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Curves, Algebraic categories.
"Challenge: Can you find all the integers a, b, c satisfying 2a2+3b2=5c2? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of a, b, c will usually be large. So the challenge remains...Find all integers a, b, c satisfying 2a2+3b2=5c2. A major advance in number theory means this book can give an easy answer to this and countless similar questions. The idea behind the approach is transforming a degree-two equation in integer variables a, b, c into a plane curve defined by a polynomial. Working with the curve makes obtaining solutions far easier, and the geometric solutions then get translated back into integers. This method morphs hard problems into routine ones and typically requires no more than high school math. (The complete solution to 2a2+3b2=5c2 is included in the book.) In addition to equations of degree two, the book addresses degree-three equations--a branch of number theory that is today something of a cottage industry, and these problems translate into "elliptic curves". This important part of the book includes many pictures along with the exposition, making the material meaningful and easy to grasp. This book will fit nicely into an introductory course on number theory. In addition, the many solved examples, illustrations, and exercises make self-studying the book an option for students, thus becoming a natural candidate for a capstone course."--
Number Theory
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Author : Prof. Jyothi M. J.
language : en
Publisher: RK Publication
Release Date : 2024-09-13
Number Theory written by Prof. Jyothi M. J. and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-13 with Mathematics categories.
Number Theory is a comprehensive exploration of the foundational concepts, theorems, and applications in number theory. Prime numbers, congruences, and Diophantine equations, offering both classical insights and modern perspectives. It caters to a broad audience, from students to advanced mathematicians, with a focus on problem-solving, proofs, and historical context. Rich with examples, exercises, and applications, Number Theory illuminates the subject's intrinsic beauty and its significance in fields like cryptography, computer science, and mathematical research.
Number Fields
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Author : Daniel A. Marcus
language : en
Publisher: Springer
Release Date : 2018-07-05
Number Fields written by Daniel A. Marcus and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Mathematics categories.
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
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.
45 Essential Number Theory Concepts Explored In 7 Minutes Each
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Author : Nietsnie Trebla
language : en
Publisher: Shelf Indulgence
Release Date :
45 Essential Number Theory Concepts Explored In 7 Minutes Each written by Nietsnie Trebla and has been published by Shelf Indulgence this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
45 Essential Number Theory Concepts Explored in 7 Minutes Each Unlock the mysteries of numbers in this concise and engaging guide, 45 Essential Number Theory Concepts Explored in 7 Minutes Each. Perfect for students, educators, and number enthusiasts alike, this book breaks down complex concepts into digestible segments that can be understood in just a few minutes. The journey begins with an Introduction to Number Theory, laying the foundation for deeper exploration of the subject. From Prime Numbers and Composite Numbers to the intricacies of the Euclidean Algorithm and Modular Arithmetic, each chapter unveils essential theories and methodologies that have influenced mathematics for centuries. Understand the importance of Fermat's Little Theorem, Euler's Theorem, and discover the Chinese Remainder Theorem, along with fascinating concepts like Perfect Numbers and Amicable Numbers. Explore Number Patterns and Sequences and delve into advanced topics like Diophantine Equations and Pythagorean Triples. Learn how the Sieve of Eratosthenes revolutionized prime number discovery and appreciate the foundations of Cryptography in the digital age with insights into the RSA Algorithm and Public Key Cryptography. Discover the applications of number theory in computer science, including Hash Functions and Algorithm Complexity. The book culminates with explorations of ongoing mathematical mysteries such as the Goldbach Conjecture and the Twin Prime Conjecture, while summarizing the future potential of this vibrant field. Each chapter is designed to be quick yet profound, allowing readers to grasp essential number theory concepts efficiently. Ideal for anyone looking to strengthen their mathematical foundation or simply satiate their curiosity about the numbers that shape our world. Whether you're a novice or a seasoned mathematician, 45 Essential Number Theory Concepts Explored in 7 Minutes Each is your essential companion for a fast-paced journey through the fascinating landscape of number theory.
Elementary Number Theory
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Author : Edmund Landau
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-22
Elementary Number Theory written by Edmund Landau and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-22 with Mathematics categories.
This three-volume classic work is reprinted here as a single volume.
General Financial Awareness Vol 2 Topicwise Notes For All Banking Related Exams A Complete Preparation Book For All Your Banking Exams With Solved Mcqs Ibps Clerk Ibps Po Sbi Po Sbi Clerk Rbi And Other Banking Exams
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Author : EduGorilla Prep Experts
language : en
Publisher: EduGorilla Community Pvt. Ltd.
Release Date : 2023-04-29
General Financial Awareness Vol 2 Topicwise Notes For All Banking Related Exams A Complete Preparation Book For All Your Banking Exams With Solved Mcqs Ibps Clerk Ibps Po Sbi Po Sbi Clerk Rbi And Other Banking Exams written by EduGorilla Prep Experts and has been published by EduGorilla Community Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Education categories.
EduGorilla's General/Financial Awareness (Vol 2) Study Notes are the best-selling notes for General/Financial Awareness in the English edition. Their content for banking exams is well-researched and covers all topics related to General/Financial Awareness. The notes are designed to help students prepare thoroughly for their exams, with topic-wise notes that are comprehensive and easy to understand. The notes also include solved multiple-choice questions (MCQs) for self-evaluation, allowing students to gauge their progress and identify areas that require further improvement. These study notes are tailored to the latest syllabus of all banking-related exams, making them a valuable resource for exam preparation.