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Author: Stefano Capparelli
Publisher: Società Editrice Esculapio
ISBN: 8835362547
Category : Mathematics
Languages : en
Pages : 260
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Book Description
These are notes of my Discrete Mathematics lectures held for students in Communication and Electric Engineering at Sapienza, the University of Roma. Roughly, the course is composed of the following parts: 1. Elements of Number Theory 2. elements of modern algebra 3. elements of combinatorics 4. elements of graph theory My objective was to illustrate several topics in dierent areas of modern mathematics into which Discrete Mathematics can be subdivided. Moreover, I wanted to give an \experimental" approach to the study of the material by repeatedly inviting students, whenever possible or feasible, to use a computer and a computer algebra system to carry out experimentation. Given the great variety of possible topics it was dicult to select a single book containing everything I wanted to show and only that. I therefore consulted many dierent sources that are acknowledged in the bibliography and I recommend them for further study. Some sections written in smaller fonts can be skipped or skimmed in a rst reading as they do not properly belong to a traditional course on Discrete Mathematics, but that I felt important enough to include here with the aim of stimulating the curiosity of inquiring young minds.
Author: Stefano Capparelli
Publisher: Società Editrice Esculapio
ISBN: 8835362547
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
These are notes of my Discrete Mathematics lectures held for students in Communication and Electric Engineering at Sapienza, the University of Roma. Roughly, the course is composed of the following parts: 1. Elements of Number Theory 2. elements of modern algebra 3. elements of combinatorics 4. elements of graph theory My objective was to illustrate several topics in dierent areas of modern mathematics into which Discrete Mathematics can be subdivided. Moreover, I wanted to give an \experimental" approach to the study of the material by repeatedly inviting students, whenever possible or feasible, to use a computer and a computer algebra system to carry out experimentation. Given the great variety of possible topics it was dicult to select a single book containing everything I wanted to show and only that. I therefore consulted many dierent sources that are acknowledged in the bibliography and I recommend them for further study. Some sections written in smaller fonts can be skipped or skimmed in a rst reading as they do not properly belong to a traditional course on Discrete Mathematics, but that I felt important enough to include here with the aim of stimulating the curiosity of inquiring young minds.
Author: Oscar Levin
Publisher: Createspace Independent Publishing Platform
ISBN: 9781534970748
Category :
Languages : en
Pages : 342
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Book Description
This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.
Author: M. Welleda Baldoni
Publisher: Springer Science & Business Media
ISBN: 3540692002
Category : Mathematics
Languages : en
Pages : 530
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Book Description
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.
Author: Bernard Kolman
Publisher: Prentice Hall
ISBN:
Category : Mathematics
Languages : en
Pages : 488
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Book Description
This text has been designed as a complete introduction to discrete mathematics, primarily for computer science majors in either a one or two semester course. The topics addressed are of genuine use in computer science, and are presented in a logically coherent fashion. The material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. For example, relations and directed graphs are treated as two aspects of the same mathematical idea. Whenever possible each new idea uses previously encountered material, and then developed in such a way that it simplifies the more complex ideas that follow.
Author: Sara Brunetti
Publisher: Springer Nature
ISBN: 3031577930
Category :
Languages : en
Pages : 462
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Book Description
Author: César Beltrán-Castañón
Publisher: Springer
ISBN: 3319522779
Category : Computers
Languages : en
Pages : 560
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Book Description
This book constitutes the refereed post-conference proceedings of the 21st Iberoamerican Congress on Pattern Recognition, CIARP 2016, held in Lima, Peru, in November 2016. The 69 papers presented were carefully reviewed and selected from 131 submissions. The papers feature research results in the areas of pattern recognition, biometrics, image processing, computer vision, speech recognition, and remote sensing. They constitute theoretical as well as applied contributions in many fields related to the main topics of the conference.
Author: Alvaro Rocha
Publisher: Springer Nature
ISBN: 3031456459
Category :
Languages : en
Pages : 700
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Book Description
Author: Ralph P. Grimaldi
Publisher: Pearson College Division
ISBN: 9780321200334
Category : Education
Languages : en
Pages : 260
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Book Description
Author: László Lovász
Publisher: Springer Science & Business Media
ISBN: 0387217770
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.
Author: Ernesto Salinelli
Publisher: Springer
ISBN: 3319022911
Category : Mathematics
Languages : en
Pages : 398
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Book Description
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations. The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty; in the last chapter the detailed solution is given for most of them.
