A Pythagorean Introduction To Number Theory
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A Pythagorean Introduction To Number Theory
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Author : Ramin Takloo-Bighash
language : en
Publisher: Springer
Release Date : 2018-11-26
A Pythagorean Introduction To Number Theory written by Ramin Takloo-Bighash and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-26 with Mathematics categories.
Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.
Numbers And Figures
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Author : Giancarlo Travaglini
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-31
Numbers And Figures written by Giancarlo Travaglini 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 2023-05-31 with Mathematics categories.
One of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their connections to geometry, calculus, and real-life problems such as COVID-19 vaccines or fiscal frauds. Each conversation is in two parts—an introductory essay which provides a gentle introduction to the topic and a second section that delves deeper and requires study by the reader. The topics themselves are extremely appealing and include, for example, Pick's theorem, Simpson's paradox, Farey sequences, the Frobenius problem, and Benford's Law. Numbers and Figures will be a useful resource for college faculty teaching Elementary Number Theory or Calculus. The chapters are largely independent and could make for nice course-ending projects or even lead-ins to high school or undergraduate research projects. The whole book would make for an enjoyable semester-long independent reading course. Faculty will find it entertaining bedtime reading and, last but not least, readers more generally will be interested in this book if they miss the accuracy and imagination found in their high school and college math courses.
Introduction To Analytic Number Theory
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Author : Tom M. Apostol
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Introduction To Analytic Number Theory written by Tom M. Apostol 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 2013-06-29 with Mathematics categories.
"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS
Introduction To Number Theory
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Author : Mark Hunacek
language : en
Publisher: CRC Press
Release Date : 2023-03-24
Introduction To Number Theory written by Mark Hunacek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-24 with Mathematics categories.
Introduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics. Aligning with the trend toward smaller, essential texts in mathematics, the author strives for clarity of exposition. Proof techniques and proofs are presented slowly and clearly. The book employs a versatile approach to the use of algebraic ideas. Instructors who wish to put this material into a broader context may do so, though the author introduces these concepts in a non-essential way. A final chapter discusses algebraic systems (like the Gaussian integers) presuming no previous exposure to abstract algebra. Studying general systems helps students to realize unique factorization into primes is a more subtle idea than may at first appear; students will find this chapter interesting, fun and quite accessible. Applications of number theory include several sections on cryptography and other applications to further interest instructors and students alike.
Geometry Of Submanifolds And Applications
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Author : Bang-Yen Chen
language : en
Publisher: Springer Nature
Release Date : 2024-03-26
Geometry Of Submanifolds And Applications written by Bang-Yen Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-26 with Mathematics categories.
This book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications. The book covers a wide range of topics such as Chen–Ricci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal η-Ricci–Yamabe solitons, submersion on statistical metallic structure, solitons in f(R, T)-gravity, metric-affine geometry, generalized Wintgen inequalities, tangent bundles, and Lagrangian submanifolds. Moreover, the book showcases the latest findings on Pythagorean submanifolds and submanifolds of four-dimensional f-manifolds. The chapters in this book delve into numerous problems and conjectures on submanifolds, providing valuable insights for scientists, educators, and graduate students looking to stay updated with the latest developments in the field. With its comprehensive coverage and detailed explanations, this book is an essential resource for anyone interested in submanifold theory.
A Friendly Introduction To Number Theory
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Author : Joseph H. Silverman
language : en
Publisher:
Release Date : 1997
A Friendly Introduction To Number Theory written by Joseph H. Silverman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This brief text is for an easy introduction to number theory for more than just the math major. Written by a well known mathematician, it is the first undergraduate text to cover elliptic curves (needed for solving Fermat's last theorem).
An Introduction To Number Theory With Cryptography
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Author : James Kraft
language : en
Publisher: CRC Press
Release Date : 2018-01-29
An Introduction To Number Theory With Cryptography written by James Kraft and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-29 with Computers categories.
Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.
Geometry Creation And Import With Comsol Multiphysics
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Author : Layla S. Mayboudi
language : en
Publisher: Mercury Learning and Information
Release Date : 2019-09-20
Geometry Creation And Import With Comsol Multiphysics written by Layla S. Mayboudi and has been published by Mercury Learning and Information this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-20 with Technology & Engineering categories.
This book focuses on the geometry creation techniques for use in finite element analysis. Examples are provided as a sequence of fin designs with progressively increasing complexity. A fin was selected as it is a feature widely employed for thermal management. As the content progresses, the reader learns to create or import a geometry into a FEM tool using COMSOL Multiphysics®. The fundamentals may also be applied to other commercial packages such as ANSYS® or AbaqusTM. The content can be utilized in a variety of engineering disciplines including mechanical, aerospace, biomedical, chemical, civil, and electrical. The book provides an overview of the tools available to create and interact with the geometry. It also takes a broader look on the world of geometry, showing how geometry is a fundamental part of nature and how it is interconnected with the world around us. Features: Includes example models that enable the reader to implement conceptual material in practical scenarios with broad industrial applications Provides geometry modeling examples created with built in features of COMSOL Multiphysics® v. 5.4 or imported from other dedicated CAD tools Presents meshing examples and provides practical advice on mesh generation Includes companion files with models and custom applications created with COMSOL Multiphysics® Application Builder.
Popular Science
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Author :
language : en
Publisher:
Release Date : 2008-06
Popular Science written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06 with categories.
Popular Science gives our readers the information and tools to improve their technology and their world. The core belief that Popular Science and our readers share: The future is going to be better, and science and technology are the driving forces that will help make it better.
An Introduction To Number Theory
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Author : G. Everest
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-21
An Introduction To Number Theory written by G. Everest 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 2007-05-21 with Mathematics categories.
Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight