A Readable Introduction To Real Mathematics

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A Readable Introduction To Real Mathematics

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Author : Daniel Rosenthal
language : en
Publisher: Springer
Release Date : 2019-04-02

A Readable Introduction To Real Mathematics written by Daniel Rosenthal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-02 with Mathematics categories.

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

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Author : SINGH, KHUMANTHEM MANGLEM
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2025-02-01

Applied Cryptography written by SINGH, KHUMANTHEM MANGLEM and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-01 with Computers categories.

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

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Author : Simon Deakin
language : en
Publisher: Bloomsbury Publishing
Release Date : 2020-11-26

Is Law Computable written by Simon Deakin and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Law categories.

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.

Introduction To Proof In Abstract Mathematics

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Author : Andrew Wohlgemuth
language : en
Publisher: Courier Corporation
Release Date : 2011-02-17

Introduction To Proof In Abstract Mathematics written by Andrew Wohlgemuth and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-17 with Mathematics categories.

Originally published: Philadelphia: Saunders College Pub., c1990.

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

Real Mathematical Analysis

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Author : Charles C. Pugh
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-14

Real Mathematical Analysis written by Charles C. Pugh 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 2003-11-14 with Mathematics categories.

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Basic Analysis I

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Author : Jiri Lebl
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-05-08

Basic Analysis I written by Jiri Lebl and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-08 with categories.

Version 5.0. A first course in rigorous mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. Originally developed to teach Math 444 at University of Illinois at Urbana-Champaign and later enhanced for Math 521 at University of Wisconsin-Madison and Math 4143 at Oklahoma State University. The first volume is either a stand-alone one-semester course or the first semester of a year-long course together with the second volume. It can be used anywhere from a semester early introduction to analysis for undergraduates (especially chapters 1-5) to a year-long course for advanced undergraduates and masters-level students. See http://www.jirka.org/ra/ Table of Contents (of this volume I): Introduction 1. Real Numbers 2. Sequences and Series 3. Continuous Functions 4. The Derivative 5. The Riemann Integral 6. Sequences of Functions 7. Metric Spaces This first volume contains what used to be the entire book "Basic Analysis" before edition 5, that is chapters 1-7. Second volume contains chapters on multidimensional differential and integral calculus and further topics on approximation of functions.

An Introduction To Mathematics

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Author : Alfred North Whitehead
language : en
Publisher: Courier Dover Publications
Release Date : 2017-05-17

An Introduction To Mathematics written by Alfred North Whitehead and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with Mathematics categories.

Originally published: New York: Henry Holt & Company, 1911.

Spaces

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Author : Tom Lindstrøm
language : en
Publisher:
Release Date : 2017

Spaces written by Tom Lindstrøm and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with MATHEMATICS categories.

Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years

How To Prove It

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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16

How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.