Libros a Descargar Gratis

Problem Solving in Automata, Languages, and Complexity

Autor: Ding-zhu Du , Ker-i Ko

Número de Páginas: 405

Automata and natural language theory are topics lying at the heart of computer science. Both are linked to computational complexity and together, these disciplines help define the parameters of what constitutes a computer, the structure of programs, which problems are solvable by computers, and a range of other crucial aspects of the practice of computer science. In this important volume, two respected authors/editors in the field offer accessible, practice-oriented coverage of these issues with an emphasis on refining core problem solving skills.

Maths Tle S Spécifique & spécialité

Autor: Fabrice Barache , Sophie Barache , Raphaël Bauer , Sophie Bauer

Número de Páginas: 546

• Vous êtes en terminale S spécialité maths et vous souhaitez vous entraîner intensivement en maths. • Sur chaque thème du nouveau programme, 100 % exos Maths Tle S Spécifique & spécialité met à votre disposition : – les rappels de cours et de méthode indispensables, – une batterie d’exercices progressifs et minutés, – des sujets de type bac pour se mettre dans les conditions de l’examen , – des exercices d’approfondissement, – les corrigés, avec des explications pas à pas. Toutes ces ressources vous permettent d’aborder en confiance l’épreuve du bac et – au-delà – l’entrée en classe préparatoire scientifique si vous avez choisi cette orientation. • Notez qu’avec cet ouvrage, vous pouvez également bénéficier, pendant un an, d’un accès gratuit à toutes les ressources du site http://www.annabac.com en maths Tle S : fiches de cours, quiz audio, tests interactifs, sujets d’annales corrigés...

Fast Software Encryption

Autor: Lars Knudsen

Número de Páginas: 325

This book constitutes the thoroughly refereed post-workshop proceedings of the 6th International Workshop on Fast Software Encryption, FSE'99, held in Rome, Italy, in March 1999. The 22 revised full papers presented were carefully selected from a total of 51 submissions during two rounds of reviewing and revision. The volume is divided into sections on advanced encryption standard (AES), remotely keyed encryptions, analysis of block ciphers, miscellaneous, modes of operation, and stream ciphers.

New Comprehensive Mathematics for 'O' Level

Autor: Alec Greer , Alex Greer

Número de Páginas: 502

Based on part of the material from the author's best-selling book 'A Complete O-level Mathematics', this book provides the most effective examination revision guide for the modern 'O' level, GCSE.

Transformational analysis in practice: Music-analytical studies on composers and musicians from around the world

Autor: Bozhidar Chapkanov

Número de Páginas: 368

'Transformational analysis in practice' is a Must-Have for everyone working in the field or aspiring to develop their music-analytical and theoretical skills in transformational theory. This co-authored book puts together a plethora of analytical studies, diverse both in the repertoires covered and the methodologies employed. It is a much-needed anthology in this sub-field of music analysis, which has been developing and growing in recent years, reaching ever wider outlets in English-speaking countries and beyond, from dedicated conference panels to YouTube videos. The book is divided into four parts based on the repertoires under discussion. Part I encompasses four analytical studies on familiar composers from the European Romanticism of the nineteenth century. Part II analyzes the music of less familiar composers from Brazil and Turkey. Part III offers four contrasting ways to adapt the analytical capabilities of neo-Riemannian theory to the post-tonal music of the twentieth century. Catering to the interests of jazz performers and researchers, as well as those into popular music production, Part IV offers transformational analytical approaches to both notated and improvised...

Number Theory Revealed: A Masterclass

Autor: Andrew Granville

Número de Páginas: 617

Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew...

Number Theory Revealed: An Introduction

Autor: Andrew Granville

Número de Páginas: 290

Number Theory Revealed: An Introduction acquaints undergraduates with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p p and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an “elective appendix” with additional reading, projects, and references. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach to these core topics and adds additional material in further chapters and appendices, allowing instructors to create an individualized course tailored to their own (and their students') interests.

Toutes les maths – Algèbres et Probabilités en 62 fiches

Autor: François Cottet-emard

Número de Páginas: 625

Ce livre regroupe l'ensemble de l'algèbre linéaire et générale, de la théorie des graphes et des probabilités couramment enseignés en L1-L2 et au sein des CPGE. Véritable outil pratique, ses 62 fiches mettent en valeur toutes les notions importantes que les étudiants doivent maîtriser. Dans le livre : l'ensemble des énoncés de cours certaines démonstrations essentielles une parties des exemples et des exercices corrigés En fiches téléchargeables facilement accessibles : la majorité des démonstrations une partie des exemples et des exercices corrigés l'ensemble des problèmes récapitulatifs Ce livre est aussi une excellente base pour s'entraîner à la préparation aux concours de l'enseignement.

Polynomial Diophantine Equations

Autor: Bogdan Grechuk

Número de Páginas: 824

This book proposes a novel approach to the study of Diophantine equations: define an appropriate version of the equation’s size, order all polynomial Diophantine equations by size, and then solve the equations in order. Natural questions about the solution set of Diophantine equations are studied in this book using this approach. Is the set empty? Is it finite or infinite? Can all integer solutions be parametrized? By ordering equations by size, the book attempts to answer these questions in a systematic manner. When the size grows, the difficulty of finding solutions increases and the methods required to determine solutions become more advanced. Along the way, the reader will learn dozens of methods for solving Diophantine equations, each of which is illustrated by worked examples and exercises. The book ends with solutions to exercises and a large collection of open problems, often simple to write down yet still unsolved. The original approach pursued in this book makes it widely accessible. Many equations require only high school mathematics and creativity to be solved, so a large part of the book is accessible to high school students, especially those interested in...

Mathematical Expeditions

Autor: Reinhard Laubenbacher , David Pengelley

Número de Páginas: 288

This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective...

Number Theory and its Applications

Autor: Satyabrota Kundu , Supriyo Mazumder

Número de Páginas: 307

Number Theory and its Applications is a textbook for students pursuing mathematics as major in undergraduate and postgraduate courses. Please note: Taylor & Francis does not sell or distribute the print book in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

Number Theory and Geometry: An Introduction to Arithmetic Geometry

Autor: Álvaro Lozano-robledo

Número de Páginas: 506

Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic ...

DISCRETE MATHEMATICS

Autor: Dr. Vinay Kumar

Número de Páginas: 492

Description:This book is intended to be a textbook for the student pursuing B.E.B.Tech in Computer Science or MCAM Tech and NIELIT - B & C Level or equivalent courses. Topics included are self contained. Sequence is maintained in such a way that no prerequisite is necessary. This book contains topics ranging from set, relation, recurrence relation, generating function, posets, lattice, methods of proofs, Quine McKluskey Method, Floyd Warshall's algorithm, finite automata, bipartite graph etc. Only necessary theorems have been included, and wherever required, theirs applicability has been demonstrated using appropriate examples. Whenever required, a diagram is used to make the concept easily understood to the reader. It contains good number of solved examples and exercises for hands on practice.Table of Contents:Chapter 1 : Seti Chapter 2 : Relationi Chapter 3 : Number Theoryi Chapter 4 : Functioni Chapter 5 : Predicate Calculusi Chapter 6 : Poseti Chapter 7 : Latticei Chapter 8 : Finite Boolean Algebrai Chapter 9 : Recursive Equationsi Chapter 10 : Generating Functioni Chapter 11 : Method Of Proofsi Chapter 12 : Permutationsi Chapter 13 : Combinationsi Chapter 14 : Groupi Chapter...

Mathematical Principles of the Internet, Volume 2

Autor: Nirdosh Bhatnagar

Número de Páginas: 698

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, they cover 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,...

Selected Exercises in Algebra

Autor: Rocco Chirivì , Ilaria Del Corso , Roberto Dvornicich

Número de Páginas: 252

This book, the first of two volumes, contains over 250 selected exercises in Algebra which have featured as exam questions for the Arithmetic course taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking in order to be solved. The themes covered in this volume are: mathematical induction, combinatorics, modular arithmetic, Abelian groups, commutative rings, polynomials, field extensions, finite fields. The book includes a detailed section recalling relevant theory which can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at first year students in Mathematics and Computer Science.

Number Theory for Computing

Autor: Song Y. Yan

Número de Páginas: 454

Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping Ralph Merkle receive the credit he deserves. Diffie, Rivest, Shamir, Adleman and I had the good luck to get expedited review of our papers, so that they appeared before Merkle's seminal contribu tion. Your noting his early submission date and referring to what has come to be called "Diffie-Hellman key exchange" as it should, "Diffie-Hellman-Merkle key exchange", is greatly appreciated. It has been gratifying to see how cryptography and number theory have helped each other over the last twenty-five years. :'-Jumber theory has been the source of numerous clever ideas for implementing...

A Textbook of B.Sc. Mathematics Abstract Algebra

Autor: V. Venkateswara Rao, N. Krishnamurthy & B.v.s.s. Sharma S. Anjaneya Sastry

Número de Páginas: 258

This Textbook of B.Sc. Mathematics for the students studying second year in all universities of Andhra Pradesh was first published in the year 1988 and has undergone several editions and many reprints. The revised syllabus is being adopted by all the universities in Andhra Pradesh, following Common Core model curriculum from the academic year 2015 - 2016 based on CBCS (Choice Based Credit System). This book strictly covers the new curriculum for Semester III (2nd year, 1st semester).

Algèbre générale et graphes

Autor: François Cottet-emard

Número de Páginas: 258

15 fiches détaillées et 90 exercices corrigés pour comprendre et maîtriser les notions d'algèbre, de la structure et la théorie des graphes. Cet ouvrage de la nouvelle collection Sup en poche (L1/L2) rédigé sous forme de fiches constituées de résumés de cours, énoncés d'exercices et les corrigés détaillés, donne les bases essentielles d'algèbre que l'étudiant doit maitriser pour réussir son examen. Chaque fiche propose les grands concepts et leurs utilisations. -L’essentiel à savoir, notions théoriques fondamentales illustrées d'exemples -Des conseils méthodo. -Des mises en pratique, avec exercices et corrigés.

Concrete Approach to Abstract Algebra

Autor: W. W. Sawyer

Número de Páginas: 241

Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.

The Mathematics of Various Entertaining Subjects

Autor: Jennifer Beineke , Jason Rosenhouse

Número de Páginas: 290

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics. Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much ...

Mathématiques d'excellence - Cours pour lycéens très motivés - Niveau Terminale

Autor: Francisco Del Rey , Éric Dubon

Número de Páginas: 500

Ce livre – le dernier volume d’une série de trois – a été conçu au départ pour des personnes soucieuses d’avoir des bases solides en mathématiques. Il pourrait tout à fait servir, également, de manuel de mathématiques offrant un cours exigeant pour des élèves de niveau terminale qui veulent aborder des études supérieures en ayant un raisonnement rigoureux et de qualité. En évitant autant que possible les deux écueils principaux – le manque de rigueur et le manque d’applications – les auteurs proposent un cours susceptible d’intéresser les enseignants souhaitant compléter leur cours comme les étudiants préparant le capes de mathématiques. Grâce à des exercices variés et corrigés pour la plupart, il pourra servir également aux élèves préparant le Concours Général des Lycées. Le contenu se veut le plus exhaustif possible en présentant tous les thèmes nécessaires à la bonne compréhension des mathématiques et c’est pour cette raison que tous les résultats importants sont démontrés. Le lecteur va ici – au prix d’un effort certain – se familiariser avec les mathématiques du lycée, mais avec une approche bien différente ! ...

Quadratic Number Fields

Autor: Franz Lemmermeyer

Número de Páginas: 348

This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.

Modern Computer Algebra

Autor: Joachim Von Zur Gathen , Jürgen Gerhard

Número de Páginas: 804

Computer algebra systems are gaining importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority also make it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. For the new edition, errors have been corrected, the text has been smoothed and updated, and new sections on greatest common divisors and symbolic integration have been added.

Problem Solving Through Recreational Mathematics

Autor: Bonnie Averbach , Orin Chein

Número de Páginas: 482

Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website.

Mathématiques d'excellence - Niveau Terminale

Autor: Francisco Del Rey , Éric Dubon

Número de Páginas: 578

Ce livre est une réédition d'une série de trois volumes. Il a été conçu au départ pour des personnes soucieuses d’avoir des bases solides en mathématiques. Il pourrait tout à fait servir, également, de manuel de mathématiques offrant un cours exigeant pour des élèves de niveau terminale qui veulent aborder des études supérieures en ayant un raisonnement rigoureux et de qualité. En évitant autant que possible les deux écueils principaux – le manque de rigueur et le manque d’applications – les auteurs proposent un cours susceptible d’intéresser les enseignants souhaitant compléter leur cours comme les étudiants préparant le CAPES de mathématiques. Grâce à des exercices variés et corrigés, il pourra servir également aux élèves préparant le Concours Général des Lycées. Le contenu se veut le plus exhaustif possible en présentant tous les thèmes nécessaires à la bonne compréhension des mathématiques et c’est pour cette raison que tous les résultats importants sont démontrés. Le lecteur va ici – au prix d’un effort certain – se familiariser avec les mathématiques du lycée, mais avec une approche bien différente ! Le cours,...

The Whole Truth About Whole Numbers

Autor: Sylvia Forman , Agnes M. Rash

Número de Páginas: 296

The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students’ mastery of the material.

Combinatorial Methods with Computer Applications

Autor: Jonathan L. Gross

Número de Páginas: 664

This combinatorics text provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. It presents the computer and software algorithms in pseudo-code and incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition. Numerous problems, solutions, and hints reinforce basic skills and assist with creative problem solving. The author also offers a website with extensive graph theory informational resources as well as a computational engine to help with calculations for some of the exercises.

Discovering Higher Mathematics

Autor: Alan Levine , Alan L. Levine

Número de Páginas: 196

Funded by a National Science Foundation grant, Discovering Higher Mathematics emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses. * Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization * Guidelines for effective mathematical thinking, covering a variety of interrelated topics * Numerous problems and exercises designed to reinforce the key themes

Fibonacci and Lucas Numbers with Applications, Volume 1

Autor: Thomas Koshy

Número de Páginas: 708

Praise for the First Edition “ ...beautiful and well worth the reading ... with many exercises and a good bibliography, this book will fascinate both students and teachers.” Mathematics Teacher Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: • A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices,...

Cybercryptography: Applicable Cryptography for Cyberspace Security

Autor: Song Y. Yan

Número de Páginas: 443

This book provides the basic theory, techniques, and algorithms of modern cryptography that are applicable to network and cyberspace security. It consists of the following nine main chapters: Chapter 1 provides the basic concepts and ideas of cyberspace and cyberspace security, Chapters 2 and 3 provide an introduction to mathematical and computational preliminaries, respectively. Chapters 4 discusses the basic ideas and system of secret-key cryptography, whereas Chapters 5, 6, and 7 discuss the basic ideas and systems of public-key cryptography based on integer factorization, discrete logarithms, and elliptic curves, respectively. Quantum-safe cryptography is presented in Chapter 8 and offensive cryptography, particularly cryptovirology, is covered in Chapter 9. This book can be used as a secondary text for final-year undergraduate students and first-year postgraduate students for courses in Computer, Network, and Cyberspace Security. Researchers and practitioners working in cyberspace security and network security will also find this book useful as a reference.

Experimental Mathematics with Maple

Autor: Franco Vivaldi

Número de Páginas: 236

As discrete mathematics rapidly becomes a required element of undergraduate mathematics programs, algebraic software systems replace compiled languages and are now most often the computational tool of choice. Newcomers to university level mathematics, therefore, must not only grasp the fundamentals of discrete mathematics, they must also learn to use an algebraic manipulator and develop skills in abstract reasoning. Experimental Mathematics with MAPLE uniquely responds to these needs. Following an emerging trend in research, it places abstraction and axiomatization at the end of a learning process that begins with computer experimentation. It introduces the foundations of discrete mathematics and, assuming no previous knowledge of computing, gradually develops basic computational skills using the latest version of the powerful MAPLE® software. The author's approach is to expose readers to a large number of concrete computational examples and encourage them to isolate the general from the particular, to synthesize computational results, formulate conjectures, and attempt rigorous proofs. Using this approach, Experimental Mathematics with MAPLE enables readers to build a foundation ...

The Universal Book of Mathematics

Autor: David Darling

Número de Páginas: 692

Praise for David Darling The Universal Book of Astronomy "A first-rate resource for readers and students of popular astronomy and general science. . . . Highly recommended." -Library Journal "A comprehensive survey and . . . a rare treat." -Focus The Complete Book of Spaceflight "Darling's content and presentation will have any reader moving from entry to entry." -The Observatory magazine Life Everywhere "This remarkable book exemplifies the best of today's popular science writing: it is lucid, informative, and thoroughly enjoyable." -Science Books & Films "An enthralling introduction to the new science of astrobiology." -Lynn Margulis Equations of Eternity "One of the clearest and most eloquent expositions of the quantum conundrum and its philosophical and metaphysical implications that I have read recently." -The New York Times Deep Time "A wonderful book. The perfect overview of the universe." -Larry Niven

Algebra & Trigonometry

Autor: A. R. Vasishtha

Número de Páginas: 469

Mathématiques expertes - Terminale

Autor: Nicolas Nguyen , Stéphane Daniel , Mathieu Fontes

Número de Páginas: 288

Cet ouvrage est destiné aux élèves de Terminale qui ont choisi l’option Mathématiques expertes, c’est-à-dire ceux qui souhaitent acquérir un très bon niveau dans l'optique d'aborder dans les meilleures conditions les études supérieures dans une formation ayant une composante mathématique importante. Tout en suivant strictement le programme de l’option Mathématiques expertes proposée aux élèves à la rentrée 2020, cet ouvrage l'appréhende différemment, en particulier, il aide à comprendre les méthodes de raisonnement et de résolution qui sont la clé de la réussite dans les études supérieures scientifiques. Dans chaque chapitre, vous trouverez : Le résumé de cours. Il vous permettra d'accéder à une connaissance synthétique des notions.Les démonstrations. Elles vous initieront au raisonnement mathématique et développeront votre esprit logique.Les méthodes. Elles vous inculqueront les techniques usuelles qu'il faut savoir mettre en place.Le vrai/faux. Il testera votre compréhension du cours et vous évitera de tomber dans les erreurs classiques.Les exercices, avec indications. Ils vous entraîneront tout au long de l'année pour aborder les...

Fermat’s Last Theorem for Amateurs

Autor: Paulo Ribenboim

Número de Páginas: 418

In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.

An Introduction to the Theory of Numbers

Autor: Ivan Niven , Herbert S. Zuckerman , Hugh L. Montgomery

Número de Páginas: 548

The Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility. New features include expanded treatment of the binomial theorem, techniques of numerical calculation and a section on public key cryptography. Contains an outstanding set of problems.

Pell and Pell–Lucas Numbers with Applications

Autor: Thomas Koshy

Número de Páginas: 444

Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences. A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book. Finally, Pell and Pell–Lucas Numbers provides enjoyment and...

Number Theory and Cryptography

Autor: Mr. Rohit Manglik

Número de Páginas: 226

EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.

Performance Analysis and Modeling of Digital Transmission Systems

Autor: William Turin

Número de Páginas: 451

This book is an expanded third edition of the book Performance Analysis of Digital Transmission Systems, originally published in 1990. Second edition of the book titled Digital Transmission Systems: Performance Analysis and Modeling was published in 1998. The book is intended for those who design communication systems and networks. A computer network designer is interested in selecting communication channels, error protection schemes, and link control protocols. To do this efficiently, one needs a mathematical model that accurately predicts system behavior. Two basic problems arise in mathematical modeling: the problem of identifying a system and the problem of applying a model to the system analysis. System identification consists of selecting a class of mathematical objects to describe fundamental properties of the system behavior. We use a specific class of hidden Markov models (HMMs) to model communication systems. This model was introduced by C. E. Shannon more than 50 years ago as a Noisy Discrete Channel with a finite number of states. The model is described by a finite number of matrices whose elements are estimated on the basis of experimental data. We develop several...

The Power of q

Autor: Michael D. Hirschhorn

Número de Páginas: 422

This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across...