Discrete Mathematics Foundations And Applications
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Discrete Mathematics Foundations And Applications
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Author : Dr. Mohd Shadab Alam
language : en
Publisher: Crown Publishing
Release Date : 2025-02-16
Discrete Mathematics Foundations And Applications written by Dr. Mohd Shadab Alam and has been published by Crown Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-16 with Mathematics categories.
Discrete Mathematics is a systematically structured academic textbook that provides a rigorous exploration of fundamental mathematical concepts essential for various disciplines, particularly computer science and engineering. The book comprehensively covers key topics, including set theory, relations, propositional calculus, functions, Boolean algebra, recurrence relations, graph theory, trees, planar graphs, combinatorial counting principles, algebraic systems, and matrix algebra. The text is designed to facilitate a progressive understanding of discrete mathematical structures, beginning with foundational principles and advancing toward more complex theoretical frameworks. Each chapter presents clearly defined concepts, supplemented with illustrative examples, well-structured exercises, and relevant diagrams to reinforce comprehension and analytical reasoning. A distinguishing feature of this book is its emphasis on the practical applicability of discrete mathematics in computational and algorithmic problem-solving. Topics such as graph theory, Boolean algebra, and recurrence relations play a pivotal role in the design and analysis of algorithms, data structures, and digital logic circuits. Furthermore, the integration of combinatorial techniques and algebraic structures enhances students’ ability to model and solve real-world mathematical problems. With its academic rigor and structured pedagogical approach, this book is well-suited for undergraduate students, educators, and researchers seeking a deeper insight into discrete mathematical principles. The accessible yet comprehensive presentation ensures that learners with diverse mathematical backgrounds can engage effectively with the material. Discrete Mathematics serves as a valuable resource for fostering logical reasoning, problem-solving skills, and mathematical abstraction, making it indispensable for academic and professional growth.
Combinatorics
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Author : Nicholas Loehr
language : en
Publisher: CRC Press
Release Date : 2017-08-10
Combinatorics written by Nicholas Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-10 with Mathematics categories.
Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
Introduction To Combinatorics
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Author : Walter D. Wallis
language : en
Publisher: CRC Press
Release Date : 2016-12-12
Introduction To Combinatorics written by Walter D. Wallis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-12 with Mathematics categories.
What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM
Graphs Algorithms And Optimization Second Edition
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Author : William Kocay
language : en
Publisher: CRC Press
Release Date : 2016-11-03
Graphs Algorithms And Optimization Second Edition written by William Kocay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-03 with Mathematics categories.
The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs. ?
Handbook Of Enumerative Combinatorics
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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2015-03-24
Handbook Of Enumerative Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Mathematics categories.
Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he
Graph Polynomials
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Author : Yongtang Shi
language : en
Publisher: CRC Press
Release Date : 2016-11-25
Graph Polynomials written by Yongtang Shi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.
This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.
Introduction To Enumerative And Analytic Combinatorics
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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2015-09-18
Introduction To Enumerative And Analytic Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Computers categories.
Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumerat
Representation Theory Of Symmetric Groups
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Author : Pierre-Loic Meliot
language : en
Publisher: CRC Press
Release Date : 2017-05-12
Representation Theory Of Symmetric Groups written by Pierre-Loic Meliot and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-12 with Mathematics categories.
Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.
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Author :
language : en
Publisher: EduGorilla Community Pvt. Ltd.
Release Date :
written by and has been published by EduGorilla Community Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Crossing Numbers Of Graphs
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Author : Marcus Schaefer
language : en
Publisher: CRC Press
Release Date : 2018-01-02
Crossing Numbers Of Graphs written by Marcus Schaefer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Mathematics categories.
Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory. Aimed at graduate students and professionals in both mathematics and computer science The first book of its kind devoted to the topic Authored by a noted authority in crossing numbers