A Brief Journey In Discrete Mathematics

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A Brief Journey in Discrete Mathematics

Randolph Nelson
A Brief Journey in Discrete Mathematics Book PDF

Author : Randolph Nelson
Publisher : Unknown
Page : 185 pages
File Size : 40,9 Mb
Release : 2020
Category : Discrete mathematics
ISBN : 3030378624

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A Brief Journey in Discrete Mathematics by Randolph Nelson Pdf

The goal of this book is to showcase the beauty of mathematics as revealed in nine topics of discrete mathematics. In each chapter, properties are explored through a series of straightforward questions that terminate with results that lie at the doorstep of a field of study. Each step along the way is elementary and requires only algebraic manipulation. This frames the wonder of mathematics and highlights the complex world that lies behind a series of simple, mathematical, deductions. Topics addressed include combinatorics, unifying properties of symmetric functions, the Golden ratio as it leads to k-bonacci numbers, non-intuitive and surprising results found in a simple coin tossing game, the playful, trick question aspect of modular systems, exploration of basic properties of prime numbers and derivations of bewildering results that arise from approximating irrational numbers as continued fraction expansions. The Appendix contains the basic tools of mathematics that are used in the text along with a numerous list of identities that are derived in the body of the book. The mathematics in the book is derived from first principles. On only one occasion does it rely on a result not derived within the text. Since the book does not require calculus or advanced techniques, it should be accessible to advanced high school students and undergraduates in math or computer science. Senior mathematicians might be unfamiliar with some of the topics addressed in its pages or find interest in the book's unified approach to discrete math.

A Brief Journey in Discrete Mathematics

Randolph Nelson
A Brief Journey in Discrete Mathematics Book PDF

Author : Randolph Nelson
Publisher : Springer Nature
Page : 191 pages
File Size : 51,9 Mb
Release : 2020-02-11
Category : Mathematics
ISBN : 9783030378615

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A Brief Journey in Discrete Mathematics by Randolph Nelson Pdf

The goal of this book is to showcase the beauty of mathematics as revealed in nine topics of discrete mathematics. In each chapter, properties are explored through a series of straightforward questions that terminate with results that lie at the doorstep of a field of study. Each step along the way is elementary and requires only algebraic manipulation. This frames the wonder of mathematics and highlights the complex world that lies behind a series of simple, mathematical, deductions. Topics addressed include combinatorics, unifying properties of symmetric functions, the Golden ratio as it leads to k-bonacci numbers, non-intuitive and surprising results found in a simple coin tossing game, the playful, trick question aspect of modular systems, exploration of basic properties of prime numbers and derivations of bewildering results that arise from approximating irrational numbers as continued fraction expansions. The Appendix contains the basic tools of mathematics that are used in the text along with a numerous list of identities that are derived in the body of the book. The mathematics in the book is derived from first principles. On only one occasion does it rely on a result not derived within the text. Since the book does not require calculus or advanced techniques, it should be accessible to advanced high school students and undergraduates in math or computer science. Senior mathematicians might be unfamiliar with some of the topics addressed in its pages or find interest in the book's unified approach to discrete math.

Journey into Discrete Mathematics

Owen D. Byer,Deirdre L. Smeltzer,Kenneth L. Wantz
Journey into Discrete Mathematics Book PDF

Author : Owen D. Byer,Deirdre L. Smeltzer,Kenneth L. Wantz
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 41,9 Mb
Release : 2018-11-13
Category : Combinatorial analysis
ISBN : 9781470446963

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Journey into Discrete Mathematics by Owen D. Byer,Deirdre L. Smeltzer,Kenneth L. Wantz Pdf

Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject.

Tale Of Discrete Mathematics, A: A Journey Through Logic, Reasoning, Structures And Graph Theory

Joseph Khoury
Tale Of Discrete Mathematics A A Journey Through Logic Reasoning Structures And Graph Theory Book PDF

Author : Joseph Khoury
Publisher : World Scientific
Page : 820 pages
File Size : 51,9 Mb
Release : 2024-03-19
Category : Mathematics
ISBN : 9789811285806

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Tale Of Discrete Mathematics, A: A Journey Through Logic, Reasoning, Structures And Graph Theory by Joseph Khoury Pdf

Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory.An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills.All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers.As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book.

A Journey Through Discrete Mathematics

Martin Loebl,Jaroslav Nešetřil,Robin Thomas
A Journey Through Discrete Mathematics Book PDF

Author : Martin Loebl,Jaroslav Nešetřil,Robin Thomas
Publisher : Springer
Page : 810 pages
File Size : 46,8 Mb
Release : 2017-10-11
Category : Computers
ISBN : 9783319444796

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A Journey Through Discrete Mathematics by Martin Loebl,Jaroslav Nešetřil,Robin Thomas Pdf

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Discrete Mathematics

Martin Aigner
Discrete Mathematics Book PDF

Author : Martin Aigner
Publisher : American Mathematical Society
Page : 402 pages
File Size : 43,9 Mb
Release : 2023-01-24
Category : Mathematics
ISBN : 9781470470630

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Discrete Mathematics by Martin Aigner Pdf

The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints and solutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition… This book is a well-written introduction to discrete mathematics and is highly recommended to every student of mathematics and computer science as well as to teachers of these topics. —Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of the MAA for expository writing, and his book Proofs from the BOOK with Günter M. Ziegler has been an international success with translations into 12 languages.

Discrete Mathematics

Oscar Levin
Discrete Mathematics Book PDF

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 55,6 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)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.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.

A Beginner's Guide to Discrete Mathematics

W.D. Wallis
A Beginner s Guide to Discrete Mathematics Book PDF

Author : W.D. Wallis
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 54,6 Mb
Release : 2011-10-07
Category : Mathematics
ISBN : 9780817682866

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A Beginner's Guide to Discrete Mathematics by W.D. Wallis Pdf

Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students. —Choice reviews (Review of the First Edition) Very appropriately entitled as a 'beginner's guide', this textbook presents itself as the first exposure to discrete mathematics and rigorous proof for the mathematics or computer science student. —Zentralblatt Math (Review of the First Edition) This second edition of A Beginner’s Guide to Discrete Mathematics presents a detailed guide to discrete mathematics and its relationship to other mathematical subjects including set theory, probability, cryptography, graph theory, and number theory. This textbook has a distinctly applied orientation and explores a variety of applications. Key Features of the second edition: * Includes a new chapter on the theory of voting as well as numerous new examples and exercises throughout the book * Introduces functions, vectors, matrices, number systems, scientific notations, and the representation of numbers in computers * Provides examples which then lead into easy practice problems throughout the text and full exercise at the end of each chapter * Full solutions for practice problems are provided at the end of the book This text is intended for undergraduates in mathematics and computer science, however, featured special topics and applications may also interest graduate students.

A Journey Through The Realm of Numbers

Menny Aka,Manfred Einsiedler,Thomas Ward
A Journey Through The Realm of Numbers Book PDF

Author : Menny Aka,Manfred Einsiedler,Thomas Ward
Publisher : Springer Nature
Page : 344 pages
File Size : 44,9 Mb
Release : 2020-10-03
Category : Mathematics
ISBN : 9783030552336

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A Journey Through The Realm of Numbers by Menny Aka,Manfred Einsiedler,Thomas Ward Pdf

This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

Markov's Theorem and 100 Years of the Uniqueness Conjecture

Martin Aigner
Markov s Theorem and 100 Years of the Uniqueness Conjecture Book PDF

Author : Martin Aigner
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 55,8 Mb
Release : 2013-07-18
Category : Mathematics
ISBN : 9783319008882

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Markov's Theorem and 100 Years of the Uniqueness Conjecture by Martin Aigner Pdf

This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.

Discrete Mathematics

Amanda Chetwynd,Peter Diggle
Discrete Mathematics Book PDF

Author : Amanda Chetwynd,Peter Diggle
Publisher : Elsevier
Page : 224 pages
File Size : 49,8 Mb
Release : 1995-09-17
Category : Mathematics
ISBN : 9780080928609

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Discrete Mathematics by Amanda Chetwynd,Peter Diggle Pdf

As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students. Assuming very little prior knowledge, and with the minimum of technical complication, it gives an account of the foundations of modern mathematics: logic; sets; relations and functions. It then develops these ideas in the context of three particular topics: combinatorics (the mathematics of counting); probability (the mathematics of chance) and graph theory (the mathematics of connections in networks). Worked examples and graded exercises are used throughout to develop ideas and concepts. The format of this book is such that it can be easily used as the basis for a complete modular course in discrete mathematics.

Discrete Mathematics and Combinatorics

T. Sengadir
Discrete Mathematics and Combinatorics Book PDF

Author : T. Sengadir
Publisher : Pearson Education India
Page : 572 pages
File Size : 51,6 Mb
Release : 2009-09
Category : Applied mathematics
ISBN : 8131714055

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Discrete Mathematics and Combinatorics by T. Sengadir Pdf

Discrete Mathematics and Combinatorics provides a concise and practical introduction to the core components of discrete mathematics, featuring a balanced mix of basic theories and applications. The book covers both fundamental concepts such as sets and logic, as well as advanced topics such as graph theory and Turing machines. The example-driven approach will help readers in understanding and applying the concepts. Other pedagogical tools - illustrations, practice questions, and suggested reading - facilitate learning and mastering the subject."--Cover

In Code

Sarah Flannery
In Code Book PDF

Author : Sarah Flannery
Publisher : Unknown
Page : 271 pages
File Size : 40,8 Mb
Release : 2000
Category : Coding theory
ISBN : OCLC:1256253469

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In Code by Sarah Flannery Pdf

At the age of 16, Sarah won the 1999 Irish Young Scientist of the Year award with her "Cayley-Purser algorithm", an innovative, speedy and secure system of encoding data on the Internet. This book, co-written with her father David, tells the story of her life, mathematics and making codes.

A Journey Into Partial Differential Equations

William O. Bray
A Journey Into Partial Differential Equations Book PDF

Author : William O. Bray
Publisher : Jones & Bartlett Publishers
Page : 334 pages
File Size : 42,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780763772567

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A Journey Into Partial Differential Equations by William O. Bray Pdf

Part of the International Series in Mathematics Ideal for the 1-term course, A Journey into Partial Differential Equations provides a solid introduction to PDEs for the undergraduate math, engineering, or physics student. Discussing underlying physics, concepts and methodologies, the text focuses on the classical trinity of equations: the wave equation, heat/diffusion equation, and Laplace's equation. Bray provides careful treatment of the separation of variables and the Fourier method, motivated by the geometrical notion of symmetries and places emphasis on both the qualitative and quantitative methods, as well as geometrical perspectives. With hundred of exercises and a wealth of figures, A Journey into Partial Differential Equations proves to be the model book for the PDE course.

Fundamental Approach To Discrete Mathematics

D.P. Acharjya
Fundamental Approach To Discrete Mathematics Book PDF

Author : D.P. Acharjya
Publisher : New Age International
Page : 18 pages
File Size : 52,8 Mb
Release : 2005
Category : Computer science
ISBN : 9788122416923

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Fundamental Approach To Discrete Mathematics by D.P. Acharjya Pdf

Salient Features * Mathematical Logic, Fundamental Concepts, Proofs And Mathematical Induction (Chapter 1) * Set Theory, Fundamental Concepts, Theorems, Proofs, Venn Diagrams, Product Of Sets, Application Of Set Theory And Fundamental Products (Chapter 2) * An Introduction To Binary Relations And Concepts, Graphs, Arrow Diagrams, Relation Matrix, Composition Of Relations, Types Of Relation, Partial Order Relations, Total Order Relation, Closure Of Relations, Poset, Equivalence Classes And Partitions. (Chapter 3) * An Introduction To Functions And Basic Concepts, Graphs, Composition Of Functions, Floor And Ceiling Function, Characteristic Function, Remainder Function, Signum Function And Introduction To Hash Function. (Chapter 4) * The Algebraic Structure Includes Group Theory And Ring Theory. Group Theory Includes Group, Subgroups, Cyclic Group, Cosets, Homomorphism, Introduction To Codes And Group Codes And Error Correction For Block Code. The Ring Theory Includes General Definition, Fundamental Concepts, Integral Domain, Division Ring, Subring, Homomorphism, An Isomorphism And Pigeonhole Principle (Chapters 5, 6 And 7) * A Treatment Of Boolean Algebras That Emphasizes The Relation Of Boolean Algebras To Combinatorial Circuits. (Chapter 8) * An Introduction To Lattices And Basic Concepts (Chapter 9) * A Brief Introduction To Graph Theory Is Discussed. Elements Of Graph Theory Are Indispensable In Almost All Computer Science Areas. Examples Are Given Of Its Use In Such Areas As Minimum Spanning Tree, Shortest Path Problems (Dijkastra'S Algorithm And Floyd-Warshall Algorithm) And Traveling Salesman Problem. The Computer Representation And Manipulation Of Graphs Are Also Discussed So That Certain Important Algorithms Can Be Included(Chapters 10 And 11) * A Strong Emphasis Is Given On Understanding The Theorems And Its Applications * Numbers Of Illustrations Are Used Throughout The Book For Explaining The Concepts And Its Applications. * Figures And Tables Are Used To Illustrate Concepts, To Elucidate Proofs And To Motivate The Material. The Captions Of These Figures Provide Additional Explanation. Besides This, A Number Of Exercises Are Given For Practice