Download or read book Elementary Number Theory Cryptography and Codes written by M. Welleda Baldoni and published by Springer Science & Business Media. This book was released on 2008-11-28 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.
Download or read book Euclid s Elements written by Euclid and published by . This book was released on 2002 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Download or read book Advanced Higher Maths written by Craig Lowther and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Euclidean Geometry written by Mark Solomonovich and published by iUniverse. This book was released on 2010 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained presentation of Euclidean Geometry, a subject that has been a core part of school curriculum for centuries. The discussion is rigorous, axiom-based, written in a traditional manner, true to the Euclidean spirit. Transformations in the Euclidean plane are included as part of the axiomatics and as a tool for solving construction problems. The textbook can be used for teaching a high school or an introductory level college course. It can be especially recommended for schools with enriched mathematical programs and for homeschoolers looking for a rigorous traditional discussion of geometry. The text is supplied with over 1200 questions and problems, ranging from simple to challenging. The solutions sections of the book contain about 200 answers and hints to solutions and over 100 detailed solutions involving proofs and constructions. More solutions and some supplements for teachers are available in the Instructor's Manual, which is issued as a separate book. Book Reviews: 'In terms of presentation, this text is more rigorous than any existing high school textbook that I know of. It is based on a system of axioms that describe incidence, postulate a notion of congruence of line segments, and assume the existence of enough rigid motions ("free mobility")... My gut reaction to the book is, wouldn't it be wonderful if American high school students could be exposed to this serious mathematical treatment of elementary geometry, instead of all the junk that is presented to them in existing textbooks. This book makes no concession to the TV-generation of students who want (or is it the publishers who want it for them?) pretty pictures, side bars, puzzles, games, historical references, cartoons, and all those colored images that clutter the pages of a typical modern textbook, while the mathematical content is diluted more and more with each successive edition.' Professor Robin Hartshorne, University of California at Berkeley. 'The textbook "Euclidean Geometry" by Mark Solomonovich fills a big gap in the plethora of mathematical textbooks - it provides an exposition of classical geometry with emphasis on logic and rigorous proofs... I would be delighted to see this textbook used in Canadian schools in the framework of an improved geometry curriculum. Until this day comes, I highly recommend "Euclidean Geometry" by Mark Solomonovich to be used in Mathematics Enrichment Programs across Canada and the USA.' Professor Yuly Billig, Carlton University.
Download or read book Cryptography written by Douglas Robert Stinson and published by CRC Press. This book was released on 2018-08-14 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through three editions, Cryptography: Theory and Practice, has been embraced by instructors and students alike. It offers a comprehensive primer for the subject’s fundamentals while presenting the most current advances in cryptography. The authors offer comprehensive, in-depth treatment of the methods and protocols that are vital to safeguarding the seemingly infinite and increasing amount of information circulating around the world. Key Features of the Fourth Edition: New chapter on the exciting, emerging new area of post-quantum cryptography (Chapter 9). New high-level, nontechnical overview of the goals and tools of cryptography (Chapter 1). New mathematical appendix that summarizes definitions and main results on number theory and algebra (Appendix A). An expanded treatment of stream ciphers, including common design techniques along with coverage of Trivium. Interesting attacks on cryptosystems, including: padding oracle attack correlation attacks and algebraic attacks on stream ciphers attack on the DUAL-EC random bit generator that makes use of a trapdoor. A treatment of the sponge construction for hash functions and its use in the new SHA-3 hash standard. Methods of key distribution in sensor networks. The basics of visual cryptography, allowing a secure method to split a secret visual message into pieces (shares) that can later be combined to reconstruct the secret. The fundamental techniques cryptocurrencies, as used in Bitcoin and blockchain. The basics of the new methods employed in messaging protocols such as Signal, including deniability and Diffie-Hellman key ratcheting.
Download or read book Disquisitiones Arithmeticae written by Carl Friedrich Gauss and published by Springer. This book was released on 2018-02-07 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
Download or read book A Readable Introduction to Real Mathematics written by Daniel Rosenthal and published by Springer. This book was released on 2014-07-03 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat's little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.
Download or read book Euclidean Shortest Paths written by Fajie Li and published by Springer Science & Business Media. This book was released on 2011-11-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical and programming exercises at the end of each chapter; presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms; discusses algorithms for calculating exact or approximate ESPs in the plane; examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves; describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems; includes lists of symbols and abbreviations, in addition to other appendices.
Download or read book Symbolic Integration I written by Manuel Bronstein and published by Springer Science & Business Media. This book was released on 2005 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: First edition received rave reviews The second edition offers a new chapter on parallel integration Includes additional exercises
Download or read book Mathematics From the Birth of Numbers written by Jan Gullberg and published by W. W. Norton & Company. This book was released on 1997-01-07 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions.
Download or read book Number Theory and Cryptography written by J. H. Loxton and published by Cambridge University Press. This book was released on 1990-04-19 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers presented by prominent contributors at a workshop on Number Theory and Cryptography, and the annual meeting of the Australian Mathematical Society.
Download or read book Mathematical Analysis of Evolution Information and Complexity written by Wolfgang Arendt and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.
Download or read book The Euclidean Algorithm written by Albert G. Fadell and published by . This book was released on 1951 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Mathematics Proof Techniques And Mathematical Structures written by Robert Clark Penner and published by World Scientific Publishing Company. This book was released on 1999-10-19 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics. No real prerequisites are needed other than a suitable level of mathematical maturity. The text is divided into two parts, the first of which constitutes the core of a one-semester course covering proofs, predicate calculus, set theory, elementary number theory, relations, and functions, and the second of which applies this material to a more advanced study of selected topics in pure mathematics, applied mathematics, and computer science, specifically cardinality, combinatorics, finite-state automata, and graphs. In both parts, deeper and more interesting material is treated in optional sections, and the text has been kept flexible by allowing many different possible courses or emphases based upon different paths through the volume.
Download or read book Mathematical Principles of the Internet Two Volume Set written by Nirdosh Bhatnagar and published by CRC Press. This book was released on 2019-03-18 with total page 1768 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, these cover only a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Download or read book Abstract Algebra written by John W. Lawrence and published by Cambridge University Press. This book was released on 2021-04-15 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Download or read book Coding Theory and Cryptography written by D.C. Hankerson and published by CRC Press. This book was released on 2000-08-04 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing data on number theory, encryption schemes, and cyclic codes, this highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an "easy-to-use" manner appropriate for students with only a basic background in mathematics offering revised and updated material on the Berlekamp-Massey decoding algorithm and convolutional codes. Introducing the mathematics as it is needed and providing exercises with solutions, this edition includes an extensive section on cryptography, designed for an introductory course on the subject.
