Counting And Configurations
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Counting And Configurations
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Author : Jiri Herman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Counting And Configurations written by Jiri Herman 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 2013-03-14 with Mathematics categories.
This book can be seen as a continuation of Equations and Inequalities: El ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series. How ever, it can be independently read or used as a textbook in its own right. This book is intended as a text for a problem-solving course at the first or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with combinatorics, graph theory, number theory, or geometry, or for any of the discrete mathematics courses that are offered at most American and Canadian universities. The underlying "philosophy" of this book is the same as that of Equations and Inequalities. The following paragraphs are therefore taken from the preface of that book.
Principles Of Combinatorics
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Author : Berge
language : en
Publisher: Academic Press
Release Date : 1971-04-20
Principles Of Combinatorics written by Berge and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-04-20 with Computers categories.
Berge's Principles of Combinatorics is now an acknowledged classic work of the field. Complementary to his previous books, Berge's introduction deals largely with enumeration. The choice of topics is balanced, the presentation elegant, and the text can be followed by anyone with an interest in the subject with only a little algebra required as a background. Some topics were here described for the first time, including Robinston-Shensted theorum, the Eden-Schutzenberger theorum, and facts connecting Young diagrams, trees, and the symmetric group.
Techniques Of Counting
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Author : Richard Johnson
language : en
Publisher: HiTeX Press
Release Date : 2025-06-20
Techniques Of Counting written by Richard Johnson and has been published by HiTeX Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-20 with Computers categories.
"Techniques of Counting" "Techniques of Counting" is a comprehensive and authoritative guide that delves deeply into the art and science of enumeration, a cornerstone of combinatorics and discrete mathematics. The book commences with a meticulous treatment of fundamental counting principles—such as the sum and product rules, permutations, combinations, and critical axioms like the pigeonhole principle and inclusion-exclusion. Through crisp exposition and illustrative examples, the early chapters lay a robust groundwork, equipping readers with the essential tools needed for both elementary and intricate counting scenarios, all while seamlessly connecting to the broader framework of set theory and combinatorial identities. Building on this foundation, the text skillfully navigates advanced topics including generating functions, recurrence relations, and a rich array of combinatorial structures such as multinomials, Stirling and Bell numbers, Catalan numbers, and Ferrers diagrams. It ventures further into specialized domains, providing thorough coverage of graph enumeration, group-theoretic methods, and analytic tools like asymptotics and singularity analysis. Readers are introduced to elegant algebraic techniques, probabilistic methods, and the challenges of counting within complexity theory, with dedicated chapters on the computational hardness of counting problems, approximate algorithms, and the subtleties of constraint-based enumeration. The final chapters broaden the book’s relevance by surveying real-world applications across diverse fields. These range from error-correcting codes and cryptographic protocols to statistical mechanics, bioinformatics, and machine learning, illustrating the versatility and profound utility of combinatorial enumeration in both theory and practice. Whether for students eager to master foundational techniques or researchers seeking advanced insights, "Techniques of Counting" stands as an indispensable reference—a lucid and exhaustive resource for anyone fascinated by the universe of counting.
Oxford Handbook Of Numerical Cognition
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Author : Roi Cohen Kadosh
language : en
Publisher: Oxford University Press
Release Date : 2015-07-30
Oxford Handbook Of Numerical Cognition written by Roi Cohen Kadosh and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Psychology categories.
How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.
Concepts Frames And Cascades In Semantics Cognition And Ontology
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Author : Sebastian Löbner
language : en
Publisher: Springer Nature
Release Date : 2021-05-28
Concepts Frames And Cascades In Semantics Cognition And Ontology written by Sebastian Löbner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-28 with Language Arts & Disciplines categories.
This open access book presents novel theoretical, empirical and experimental work exploring the nature of mental representations that support natural language production and understanding, and other manifestations of cognition. One fundamental question raised in the text is whether requisite knowledge structures can be adequately modeled by means of a uniform representational format, and if so, what exactly is its nature. Frames are a key topic covered which have had a strong impact on the exploration of knowledge representations in artificial intelligence, psychology and linguistics; cascades are a novel development in frame theory. Other key subject areas explored are: concepts and categorization, the experimental investigation of mental representation, as well as cognitive analysis in semantics. This book is of interest to students, researchers, and professionals working on cognition in the fields of linguistics, philosophy, and psychology.
Probability An Introduction
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Author : David A. Santos
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2010-04-30
Probability An Introduction written by David A. Santos and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-30 with Mathematics categories.
Probability: An Introduction provides the fundamentals, requiring minimal algebraic skills from the student. It begins with an introduction to sets and set operations, progresses to counting techniques, and then presents probability in an axiomatic way, never losing sight of elucidating the subject through concrete examples. The book contains numerous examples and solved exercises taken from various fields, and includes computer explorations using Maple.
Eureka Math Grade K Study Guide
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Author : Great Minds
language : en
Publisher: John Wiley & Sons
Release Date : 2015-09-18
Eureka Math Grade K Study Guide written by Great Minds and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Education categories.
Eureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade K provides an overview of all of the Kindergarten modules, including Numbers to 10; Two-Dimensional and Three-Dimensional Shapes; Comparison of Length, Weight, Capacity, and Numbers to 10; Number Pairs, Addition and Subtraction to 10; Numbers 10–20 and Counting to 10; and Analyzing Comparing and Composing Shapes.
Probability
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Author : David Santos
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2011-08-24
Probability written by David Santos and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with Mathematics categories.
Probability: An Introduction provides the fundamentals, requiring minimal algebraic skills from the student. It begins with an introduction to sets and set operations, progresses to counting techniques, and then presents probability in an axiomatic way, never losing sight of elucidating the subject through concrete examples. The book contains numerous examples and solved exercises taken from various fields, and includes computer explorations using Maple.
Farewell To Entropy A Statistical Thermodynamics Based On Information
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Author : Arieh Ben-naim
language : en
Publisher: World Scientific
Release Date : 2008-01-18
Farewell To Entropy A Statistical Thermodynamics Based On Information written by Arieh Ben-naim and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-18 with Science categories.
The principal message of this book is that thermodynamics and statistical mechanics will benefit from replacing the unfortunate, misleading and mysterious term “entropy” with a more familiar, meaningful and appropriate term such as information, missing information or uncertainty. This replacement would facilitate the interpretation of the “driving force” of many processes in terms of informational changes and dispel the mystery that has always enshrouded entropy.It has been 140 years since Clausius coined the term “entropy”; almost 50 years since Shannon developed the mathematical theory of “information” — subsequently renamed “entropy”. In this book, the author advocates replacing “entropy” by “information”, a term that has become widely used in many branches of science.The author also takes a new and bold approach to thermodynamics and statistical mechanics. Information is used not only as a tool for predicting distributions but as the fundamental cornerstone concept of thermodynamics, held until now by the term “entropy”.The topics covered include the fundamentals of probability and information theory; the general concept of information as well as the particular concept of information as applied in thermodynamics; the re-derivation of the Sackur-Tetrode equation for the entropy of an ideal gas from purely informational arguments; the fundamental formalism of statistical mechanics; and many examples of simple processes the “driving force” for which is analyzed in terms of information.
Symmetry And Combinatorial Enumeration In Chemistry
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Author : Shinsaku Fujita
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetry And Combinatorial Enumeration In Chemistry written by Shinsaku Fujita 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 2012-12-06 with Science categories.
This book is written to introduce a new approach to stereochemical problems and to combinatorial enumerations in chemistry. This approach is based on group the ory, but different from conventional ways adopted by most textbooks on chemical group theory. The difference sterns from their starting points: conjugate subgroups and conjugacy classes. The conventional textbooks deal with linear representations and character ta bles of point groups. This fact implies that they lay stress on conjugacy classesj in fact, such group characters are determined for the respective conjugacy classes. This approach is versatile, since conjugacy classes can be easily obtained by ex amining every element of a group. It is unnecessary to know the group-subgroup relationship of the group, which is not always easy to obtain. The same situa tion is true for chemical enumerations, though these are founded on permutation groups. Thus, the P6lya-Redfield theorem (1935 and 1927) uses a cycle index that is composed of terms associated with conjugacy classes.