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Sylvan Summer Smart Workbook: Between Grades 2 & 3 (Sylvan Summer Smart Workbooks)
by Sylvan LearningStop "summer slide" and get ready to return to the classroom for 3rd grade with Sylvan's SUMMER SMART Workbooks!Research shows that kids can lose up to 2.5 months' worth of hard-earned knowledge from the previous grade over the summer vacation break. That's why we at Sylvan Learning—America's #1 tutoring brand—created the SUMMER SMART workbook series!Packed with fun exercises and teacher-created activities, this book reinforces math and reading concepts your child learned in 2nd grade, including: • Addition and subtraction• Basic fractions• Time and money• Measuring and comparing• Vowels and consonants• Compound words and contractions• Reading comprehensionInside each Summer Smart book, you'll also find:• Teacher tips for staying sharp over the summer• Special &“Vacation Challenge!&” activities and games section• Cut-out flashcard sheets and recommended reading lists• A &“Summer Smart!&” Achievement CertificateLet the experts at America's #1 tutoring brand help get your child ready for 3rd grade!***** Why Sylvan Products Work ***** Sylvan Learning Workbooks won a National Parenting Publications Awards (NAPPA) Honors Award as a top book series for children in the elementary-aged category. NAPPA is the nation&’s most comprehensive awards program for children&’s products and parenting resources and has been critically reviewing products since 1990. The Award recognizes Sylvan Learning Workbooks as some of the most innovative and useful products geared to parents. Sylvan's proven system inspires kids to learn and has helped children nationwide catch up, keep up, and get ahead in school. Sylvan has been a trusted partner for parents for thirty years, and has based their supplemental education success on programs developed through a focus on the highest educational standards and detailed research. Sylvan&’s line of educational products equips families with fun, effective, and grade-appropriate learning tools. Our workbooks and learning kits feature activities, stories, and games to reinforce the skills children need to develop and achieve their academic potential. Students will reap the rewards of improved confidence and a newfound love of learning.
Sylvan Summer Smart Workbook: Between Grades 3 & 4 (Sylvan Summer Smart Workbooks)
by Sylvan LearningStop "summer slide" and get ready to return to the classroom for 4th grade with Sylvan's SUMMER SMART Workbooks!Research shows that kids can lose up to 2.5 months' worth of hard-earned knowledge from the previous grade over the summer vacation break. That's why we at Sylvan Learning—America's #1 tutoring brand—created the SUMMER SMART workbook series!Packed with fun exercises and teacher-created activities, this book reinforces math and reading concepts your child learned in 3rd grade, including: • Addition and subtraction • Multiplication and division• Fractions, weights and measurements• Context clues and predicting what happens• Main ideas and details• Story comprehensionInside each Summer Smart book, you'll also find:• Teacher tips for staying sharp over the summer• Special &“Vacation Challenge!&” activities and games section• Cut-out flashcard sheets and recommended reading lists• A &“Summer Smart!&” Achievement CertificateLet the experts at America's #1 tutoring brand help get your child ready for 4th grade!***** Why Sylvan Products Work ***** Sylvan Learning Workbooks won a National Parenting Publications Awards (NAPPA) Honors Award as a top book series for children in the elementary-aged category. NAPPA is the nation&’s most comprehensive awards program for children&’s products and parenting resources and has been critically reviewing products since 1990. The Award recognizes Sylvan Learning Workbooks as some of the most innovative and useful products geared to parents. Sylvan's proven system inspires kids to learn and has helped children nationwide catch up, keep up, and get ahead in school. Sylvan has been a trusted partner for parents for thirty years, and has based their supplemental education success on programs developed through a focus on the highest educational standards and detailed research. Sylvan&’s line of educational products equips families with fun, effective, and grade-appropriate learning tools. Our workbooks and learning kits feature activities, stories, and games to reinforce the skills children need to develop and achieve their academic potential. Students will reap the rewards of improved confidence and a newfound love of learning.
Sylvan Summer Smart Workbook: Between Grades 4 & 5 (Sylvan Summer Smart Workbooks)
by Sylvan LearningStop "summer slide" and get ready to return to the classroom for 5th grade with Sylvan's SUMMER SMART Workbooks!Research shows that kids can lose up to 2.5 months' worth of hard-earned knowledge from the previous grade over the summer vacation break. That's why we at Sylvan Learning—America's #1 tutoring brand—created the SUMMER SMART workbook series!Packed with fun exercises and teacher-created activities, this book reinforces math and reading concepts your child learned in 4th grade, including: • Addition and subtraction • Multiplication and division• Fractions and decimals• Time and money• Facts and opinions• Comparing and contrasting• Story-planning• Reading between the linesInside each Summer Smart book, you'll also find:• Teacher tips for staying sharp over the summer• Special &“Vacation Challenge!&” activities and games section• Cut-out flashcard sheets and recommended reading lists• A &“Summer Smart!&” Achievement CertificateLet the experts at America's #1 tutoring brand help get your child ready for 5th grade!***** Why Sylvan Products Work ***** Sylvan Learning Workbooks won a National Parenting Publications Awards (NAPPA) Honors Award as a top book series for children in the elementary-aged category. NAPPA is the nation&’s most comprehensive awards program for children&’s products and parenting resources and has been critically reviewing products since 1990. The Award recognizes Sylvan Learning Workbooks as some of the most innovative and useful products geared to parents. Sylvan's proven system inspires kids to learn and has helped children nationwide catch up, keep up, and get ahead in school. Sylvan has been a trusted partner for parents for thirty years, and has based their supplemental education success on programs developed through a focus on the highest educational standards and detailed research. Sylvan&’s line of educational products equips families with fun, effective, and grade-appropriate learning tools. Our workbooks and learning kits feature activities, stories, and games to reinforce the skills children need to develop and achieve their academic potential. Students will reap the rewards of improved confidence and a newfound love of learning.
Sylvan Summer Smart Workbook: Between Grades K & 1 (Sylvan Summer Smart Workbooks)
by Sylvan LearningStop "summer slide" and get ready to return to the classroom for 1st grade with Sylvan's SUMMER SMART Workbooks!Research shows that kids can lose up to 2.5 months' worth of hard-earned knowledge from the previous grade over the summer vacation break. That's why we at Sylvan Learning—America's #1 tutoring brand—created the SUMMER SMART workbook series!Packed with fun exercises and teacher-created activities, this book reinforces math and reading concepts your child learned in kindergarten, including: • Numbers• Patterns • Shapes • Letters and sounds • Words to know• Story comprehensionInside each Summer Smart book, you'll also find:• Teacher tips for staying sharp over the summer• Special &“Vacation Challenge!&” activities and games section• Cut-out flashcard sheets and recommended reading lists• A &“Summer Smart!&” Achievement CertificateLet the experts at America's #1 tutoring brand help get your child ready for 1st grade!***** Why Sylvan Products Work ***** Sylvan Learning Workbooks won a National Parenting Publications Awards (NAPPA) Honors Award as a top book series for children in the elementary-aged category. NAPPA is the nation&’s most comprehensive awards program for children&’s products and parenting resources and has been critically reviewing products since 1990. The Award recognizes Sylvan Learning Workbooks as some of the most innovative and useful products geared to parents. Sylvan's proven system inspires kids to learn and has helped children nationwide catch up, keep up, and get ahead in school. Sylvan has been a trusted partner for parents for thirty years, and has based their supplemental education success on programs developed through a focus on the highest educational standards and detailed research. Sylvan&’s line of educational products equips families with fun, effective, and grade-appropriate learning tools. Our workbooks and learning kits feature activities, stories, and games to reinforce the skills children need to develop and achieve their academic potential. Students will reap the rewards of improved confidence and a newfound love of learning.
Sylvan Summer Smart Workbook: Between Grades Pre-K & Kindergarten (Sylvan Summer Smart Workbooks)
by Sylvan LearningStop "summer slide" and get ready to return to the classroom for kindergarten with Sylvan's SUMMER SMART Workbooks!Research shows that kids can lose up to 2.5 months' worth of hard-earned knowledge from the previous grade over the summer vacation break. That's why we at Sylvan Learning—America's #1 tutoring brand—created the SUMMER SMART workbook series!Packed with fun exercises and teacher-created activities, this book reinforces math and reading concepts your child learned in pre-k, including: • Basic numbers and counting • Upper and lowercase letters• Drawing numbers • Drawing lettersInside each Summer Smart book, you'll also find:• Teacher tips for staying sharp over the summer• Special &“Vacation Challenge!&” activities and games section• Cut-out flashcard sheets and recommended reading lists• A &“Summer Smart!&” Achievement CertificateLet the experts at America's #1 tutoring brand help get your child ready for kindergarten!***** Why Sylvan Products Work ***** Sylvan Learning Workbooks won a National Parenting Publications Awards (NAPPA) Honors Award as a top book series for children in the elementary-aged category. NAPPA is the nation&’s most comprehensive awards program for children&’s products and parenting resources and has been critically reviewing products since 1990. The Award recognizes Sylvan Learning Workbooks as some of the most innovative and useful products geared to parents. Sylvan's proven system inspires kids to learn and has helped children nationwide catch up, keep up, and get ahead in school. Sylvan has been a trusted partner for parents for thirty years, and has based their supplemental education success on programs developed through a focus on the highest educational standards and detailed research. Sylvan&’s line of educational products equips families with fun, effective, and grade-appropriate learning tools. Our workbooks and learning kits feature activities, stories, and games to reinforce the skills children need to develop and achieve their academic potential. Students will reap the rewards of improved confidence and a newfound love of learning.
Symbol and Archetype: A Study of the Meaning of Existence
by Martin LingsEvery religious tradition or metaphysical worldview involves a system of powerful symbols, most of which bear common meanings across cultures, continents, and time. This volume, complete with a 9th century Quranic manuscript, explores the significance of the most recurrent symbols and archetypes in human history and elaborates a compelling theory for why symbolism plays such an essential role in human life. The work explores certain basic aspects of symbolism in relation to the Divinity, the hierarchy of the universe, the function of human faculties and qualities, the human condition, natural objects, works of art, and the final end--all with reference to the great living religions of the world, and in particular to Christianity and Islam.
Symbol Correspondences for Spin Systems
by Pedro de M. Rios Eldar StraumeIn mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. A detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is first followed by an introduction to the Poisson algebra of the classical spin system and then by a similarly detailed examination of its SO(3)-invariant decomposition. The book next proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. The book will be a valuable guide for researchers in this field and its self-contained approach also makes it a helpful resource for graduate students in mathematics and physics.
Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 17th European Conference, ECSQARU 2023, Arras, France, September 19–22, 2023, Proceedings (Lecture Notes in Computer Science #14294)
by Zied Bouraoui Srdjan VesicThis book constitutes the refereed proceedings of the 17th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2023, held in Arras, France, in September 2023. The 35 full papers presented in this volume were carefully reviewed and selected from 46 submissions. The papers are organized in topical sections about Complexity and Database Theory; Formal Concept Analysis: Theoretical Advances; Formal Concept Analysis: Applications; Modelling and Explanation; Semantic Web and Graphs; Posters.
Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, Proceedings (Lecture Notes in Computer Science #11726)
by Gabriele Kern-Isberner Zoran OgnjanovićThis book constitutes the refereed proceedings of the 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2019, held in Belgrade, Serbia, in September 2019.The 41 full papers presented together with 3 abstracts of invited talks inn this volume were carefully reviewed and selected from 62 submissions. The papers are organized in topical sections named: Argumentation; Belief Functions; Conditional, Default and Analogical Reasoning; Learning and Decision Making; Precise and Imprecise Probabilities; and Uncertain Reasoning for Applications.
Symbolic Computation and Automated Reasoning: The CALCULEMUS-2000 Symposium
by Manfred Kerber Michael KohlhaseWhile mathematical software packages are commercially successful and widely used, the use of formal methods in hardware and software development is also becoming more and more important and necessary. This has made deduction systems indispensable because of the complexity and sheer size of the reasoning tasks involved.
The Symbolic Computation of Integrability Structures for Partial Differential Equations (Texts And Monographs In Symbolic Computation Series)
by Raffaele Vitolo Alexander Verbovetsky Joseph Krasil’shchikThis is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.
Symbolic Dynamical Systems and C*-Algebras: Continuous Orbit Equivalence of Topological Markov Shifts and Cuntz–Krieger Algebras (Mathematical Physics Studies)
by Kengo MatsumotoThis book presents the interplay between topological Markov shifts and Cuntz–Krieger algebras by providing notations, techniques, and ideas in detail. The main goal of this book is to provide a detailed proof of a classification theorem for continuous orbit equivalence of one-sided topological Markov shifts. The continuous orbit equivalence of one-sided topological Markov shifts is classified in terms of several different mathematical objects: the étale groupoids, the actions of the continuous full groups on the Markov shifts, the algebraic type of continuous full groups, the Cuntz–Krieger algebras, and the K-theory dates of the Cuntz–Krieger algebras. This classification result shows that topological Markov shifts have deep connections with not only operator algebras but also groupoid theory, infinite non-amenable groups, group actions, graph theory, linear algebras, K-theory, and so on. By using this classification result, the complete classification of flow equivalence in two-sided topological Markov shifts is described in terms of Cuntz–Krieger algebras. The author will also study the relationship between the topological conjugacy of topological Markov shifts and the gauge actions of Cuntz–Krieger algebras.
Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design
by Paul Cobb Erna Yackel Kay McClainThis volume grew out of a symposium on discourse, tools, and instructional design at Vanderbilt University in 1995 that brought together a small international group to grapple with issues of communicating, symbolizing, modeling, and mathematizing, particularly as these issues relate to learning in the classroom. The participants invited to develop chapters for this book--all internationally recognized scholars in their respective fields--were selected to represent a wide range of theoretical perspectives including mathematics education, cognitive science, sociocultural theory, and discourse theory. The work is distinguished by the caliber of the contributors, the significance of the topics addressed in the current era of reform in mathematics education, and the diversity of perspectives taken to a common set of themes and issues. The book is intended for those who are seeking to expand their understanding of the complexity of learning in order to enhance the learning experiences students have in schools, primarily researchers, instructional designers, and graduate students in mathematics education, as well as those in other fields including science education, instructional design in general, discourse theory, and semiotics.
Symmetric Discontinuous Galerkin Methods for 1-D Waves
by Aurora Marica Enrique ZuazuaThis work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid points. This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.
Symmetric Markov Processes, Time Change, and Boundary Theory (London Mathematical Society Monographs #35)
by Zhenqing Chen Masatoshi FukushimaThis book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.
Symmetric Multivariate and Related Distributions (Chapman And Hall/crc Monographs On Statistics And Applied Probability Ser. #Vol. 36)
by Kai Wang FangSince the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only.A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.
Symmetric Properties of Real Functions
by Brian thomsonThis work offers detailed coverage of every important aspect of symmetric structures in function of a single real variable, providing a historical perspective, proofs and useful methods for addressing problems. It provides assistance for real analysis problems involving symmetric derivatives, symmetric continuity and local symmetric structure of sets or functions.
Symmetrien in der Physik: Gruppen- und Darstellungstheorie mit Anwendungen
by Andreas WipfDas vorliegende Buch führt durch die Symmetrien in der Physik: Es werden wichtige Gruppen und Symmetrien aus der Molekülphysik, der Festkörperphysik und (Quanten-)Feldtheorie vorgestellt und behandelt. Das Buch richtet sich an Studierende der Physik, die entweder die Vorlesung zur Gruppen- und Darstellungstheorie hören oder sich im Rahmen einer Bachelor-, Master- oder Doktorarbeit in Gruppentheorie und Symmetrien in der Physik einlesen möchten. Behandelt werden u.a. endliche und kontinuierliche Gruppen sowie Lie-Algebren und deren Darstellungen, aber auch klassische und quantisierte Feldtheorien, Eichtheorien und konforme Feldtheorien. Der Autor verbindet in den Kapiteln die mathematischen Grundlagen mit der physikalischen Anwendung. Beispiele, Aufgaben und Zwischenfragen helfen Leserinnen und Lesern dabei, ihr Verständnis zu überprüfen..
Symmetries and Integrability of Difference Equations
by Decio Levi Raphaël Rebelo Pavel WinternitzDifference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.
Symmetries, Differential Equations and Applications: Sdea-iii, Istanbul, Turkey, January 2017 (Springer Proceedings in Mathematics & Statistics #266)
by Victor G. Kac Peter J. Olver Pavel Winternitz Teoman ÖzerBased on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.
Symmetries in Atomic Nuclei: From Isospin to Supersymmetry (Springer Tracts in Modern Physics #230)
by Alejandro Frank Jan Jolie Pieter Van IsackerThe revised edition of this established work presents an extended overview of recent applications of symmetry to the description of atomic nuclei, including a pedagogical introduction to symmetry concepts using simple examples. Following a historical overview of the applications of symmetry in nuclear physics, attention turns to more recent progress in the field. Special emphasis is placed on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei. Expanded and updated throughout, the book now features separate chapters on the nuclear shell model and the interacting boson model, the former including discussion of recent results on seniority in a single-j shell. Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed. This book focuses on nuclear structure physics, but its broad scope makes it suitable for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics.Review of the 1st Edition:"The subject of this book, symmetries in physical systems, with particular focus on atomic nuclei, is of the utmost importance in modern physical science. In contrast to most treatments, frequently characterized by fearsome formalism, this book leads the reader step-by-step, in an easily understandable way, through this fascinating field...this book is remarkably accessible to both theorists and experimentalists. Indeed, I view it as essential reading for experimental nuclear structure physicists. This is one of the finest volumes on this subject I have ever encountered." Prof. R.F. Casten, Yale University
Symmetries in Atomic Nuclei
by Pieter Van Isacker Jan Jolie Alejandro FrankSymmetries in Atomic Nuclei aims to present an overview of recent applications of symmetry to the description of atomic nuclei. Special care is given to a pedagogical introduction of symmetry concepts using simple examples. After a historical overview of the applications of symmetry in nuclear physics, progress in the field during the last decade is reviewed. Special emphasis is put on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei. Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed. Case studies show how these symmetries are displayed by real atomic nuclei which have been studied experimentally using state-of-the art spectroscopy. This book focuses on nuclear structure physics and has been written by active investigators in the field, but its scope is wider and is intended for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics.
Symmetries in Fundamental Physics (Fundamental Theories of Physics #176)
by Kurt SundermeyerOver the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N.Yang and R.Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry.The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.
Symmetries in Graphs, Maps, and Polytopes
by Jozef Širáň Robert JajcayThis volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d'enfant. Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d'Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010. This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures. iv>
Symmetries, Integrable Systems and Representations
by Sophie Morier-Genoud Kenji Iohara Bertrand RémyThis volume is the result of two international workshops; Infinite Analysis 11 - Frontier of Integrability - held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.