A Readable Introduction To Real Mathematics
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A Readable Introduction to Real Mathematics
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 teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. 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 * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book. From the reviews of the first edition: “It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences.” (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) “The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an ‘appreciation of mathematics’ course, among other possibilities.” (G.A. Heuer, Mathematical Reviews, February, 2015) “Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers.” (D.V. Feldman, Choice, Vol. 52 (6), February, 2015)
APPLIED CRYPTOGRAPHY
Author: SINGH, KHUMANTHEM MANGLEM
language: en
Publisher: PHI Learning Pvt. Ltd.
Release Date: 2025-02-01
Cryptography is often perceived as a highly mathematical subject, making it challenging for many learners to grasp. Recognizing this, the book has been written with a focus on accessibility, requiring minimal prerequisites in number theory or algebra. The book, aims to explain cryptographic principles and how to apply and develop cryptographic algorithms and systems. The book comprehensively covers symmetric and asymmetric ciphers, hashes, digital signatures, random number generators, authentication schemes, secret sharing schemes, key distribution, elliptic curves, and their practical applications. To simplify the subject, the book begins with an introduction to the essential concepts of number theory, tailored for students with little to no prior exposure. The content is presented with an algorithmic approach and includes numerous illustrative examples, making it ideal for beginners as well as those seeking a refresher. Overall, the book serves as a practical and approachable guide to mastering the subject. KEY FEATURE • Includes recent applications of elliptic curves with extensive algorithms and corresponding examples and exercises with detailed solutions. • Primality testing algorithms such as Miller-Rabin, Solovay-Strassen and Lucas-Lehmer for Mersenne integers are described for selecting strong primes. • Factoring algorithms such as Pollard r – 1, Pollard Rho, Dixon's, Quadratic sieve, Elliptic curve factoring algorithms are discussed. • Paillier cryptosystem and Paillier publicly verifiable secret sharing scheme are described. • Signcryption scheme that provides both confidentiality and authentication is explained for traditional and elliptic curve-based approaches. TARGET AUDIENCE • B.Tech. Computer Science and Engineering. • B.Tech Electronics and Communication Engineering.
Is Law Computable?
Author: Simon Deakin
language: en
Publisher: Bloomsbury Publishing
Release Date: 2020-11-26
What does computable law mean for the autonomy, authority, and legitimacy of the legal system? Are we witnessing a shift from Rule of Law to a new Rule of Technology? Should we even build these things in the first place? This unique volume collects original papers by a group of leading international scholars to address some of the fascinating questions raised by the encroachment of Artificial Intelligence (AI) into more aspects of legal process, administration, and culture. Weighing near-term benefits against the longer-term, and potentially path-dependent, implications of replacing human legal authority with computational systems, this volume pushes back against the more uncritical accounts of AI in law and the eagerness of scholars, governments, and LegalTech developers, to overlook the more fundamental - and perhaps 'bigger picture' - ramifications of computable law. With contributions by Simon Deakin, Christopher Markou, Mireille Hildebrandt, Roger Brownsword, Sylvie Delacroix, Lyria Bennet Moses, Ryan Abbott, Jennifer Cobbe, Lily Hands, John Morison, Alex Sarch, and Dilan Thampapillai, as well as a foreword from Frank Pasquale.