{"title":"Groups and group theory Books","description":"","products":[{"product_id":"insurgent-terrorism-intergroup-relationships-and-the-killing-of-civilians-causes-and-consequences-of-terrorism-9780197607060","title":"Insurgent Terrorism Intergroup Relationships and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book uses Big Allied and Dangerous (BAAD) as the dataset for a modern and comprehensive exploration of why insurgent groups attack civilians, even though their existence depends on public support. The book examines this phenomenon in specific contexts, including schools, news media, and nonmilitary\/nongovernment spaces designed for the general public.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eIn this compelling book, Asal, Phillips, and Rethemeyer provide a much-needed investigation into why armed militant organizations target civilians during conflicts. The authors use both original quantitative data and numerous case references to construct a comprehensive picture of militant group targeting behavior that considers group relations with civilians, state counter-insurgency strategy, inter-group competition, group criminal activity, group ideology and ethnic ties and a host of other factors. The end result is a book that will inform both scholarly and policy audiences alike. A must-read for anyone interested in insurgent group behavior. * James Piazza, Liberal Arts Professor of Political Science, The Pennsylvania State University *\u003cbr\u003eBy honing in on relational explanations, this book makes a major contribution to our understanding of why insurgent organizations sometimes kill civilians and other times not. The concept of insurgent embeddedness provides a compelling and novel theoretical lens to explain this variation. Combined with a rich qualitative and quantitative empirical material, it generates profound insights that will inform and inspire students of insurgent violence in years to come. * Hanne Fjelde, Associate Professor, Uppsala University *\u003cbr\u003eInsurgent Terrorism is a thought-provoking, provocative investigation by three leading scholars on why insurgent groups may target civilians in pursuit of political goals. This is an important question of increasing relevance for sub-Saharan Africa and the Middle East and North Africa. The book supports its theses with data-driven, careful empirical analysis based on insurgent attacks, goals, and inter-organization linkages. * Todd Sandler, Emeritus Chair, University of Texas at Dallas *\u003cbr\u003eThis book provides a fresh look at organizations' choices to engage in terrorist attacks against civilians. Advancing a theory of embeddedness, the authors examine complex relationships between insurgent organizations, the state, other insurgents, and the civilian population. They find a diverse set of factors impact different types of terrorism, advancing our understanding of this phenomena. * Kathleen Gallagher Cunningham, Cunningham, Professor, University of Maryland *\u003cbr\u003eInsurgent Terrorism is an important book that presents detailed cross-national data and analyses of civilian targeting by insurgent groups in civil conflict. Asal, Phillips, and Rethemeyer persuasively argue that the embeddedness of insurgent groups - that is, their relations with the state, the public, and each other - explains variation in civilian victimization. This relational account produces novel and intriguing findings, such as that both alignment and rivalry with other groups lead to more frequent civilian targeting. Marked by empirical richness, the book advances knowledge on the behavior of insurgent groups, civilian victimization, and civil conflict. * Ursula Daxecker, Associate Professor, University of Amsterdam *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eSECTION I. Introduction, Theory, and Initial Testing Chapter 1. Introduction                   Chapter 2. The Embeddedness Theory of Civilian Targeting by Insurgent Groups            Chapter 3. Describing the BAAD2 Insurgency Data and Other Data Sources           Chapter 4. Testing Primary Hypotheses                 SECTION II. Empirical Extensions: Types of Civilian Targeting Chapter 5. Why Do Some Insurgent Groups Attack Schools?             Chapter 6. Why Do Some Insurgent Groups Attack Journalists?                      Chapter 7. Why Do Some Insurgent Groups Mostly Attack the General Public?            SECTION III. Further Analysis of Inter-Group Relationships Chapter 8. Longitudinal Modelling of Insurgent Alliances              Chapter 9. Understanding Insurgent Rivalry                Chapter 10. Conclusion","brand":"Oxford University Press Inc","offers":[{"title":"Default Title","offer_id":48732657123671,"sku":"9780197607060","price":35.14,"currency_code":"GBP","in_stock":true}]},{"product_id":"symmetry-9780199651986","title":"Symmetry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature.It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction ; 1. What is symmetry? ; 2. Origins of symmetry ; 3. Types of symmetry ; 4. Structure of groups ; 5. Groups and games ; 6. Nature's patterns ; 7. Nature's laws ; 8. Atoms of symmetry ; Further reading ; References","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732876112215,"sku":"9780199651986","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199651986.jpg?v=1791378743"},{"product_id":"the-psychology-of-belonging-9780367347529","title":"The Psychology of Belonging","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eCan a sense of belonging increase life satisfaction? Why do we sometimes feel lonely? How can we sustain lasting human connections?\u003c\/p\u003e\u003ci\u003e\u003c\/i\u003e\u003cp\u003eThe Psychology of Belonging explores why feeling like we belong is so important throughout our lives, from childhood to old age, irrespective of culture, race or geography. With its virtues and shortcomings, belonging to groups such as families, social groups, schools, workplaces and communities is fundamental to our identity and wellbeing, even in a time when technology has changed the way we connect with each other.\u003c\/p\u003e\u003cp\u003eIn a world where loneliness and social isolation is on the rise, \u003ci\u003eThe Psychology of Belonging\u003c\/i\u003e shows how meaningful connections can build a sense of belonging for all of us.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. The beginnings of belonging 2. Belonging begins at birth 3. Belonging in adulthood 4. Rejection 5. Belonging in an age of technology 6. Belonging bad 7. Building belonging References\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":48733710352727,"sku":"9780367347529","price":16.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780367347529.jpg?v=1791378797"},{"product_id":"the-psychology-of-prejudice-9780367534639","title":"The Psychology of Prejudice","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eWhy do we develop extreme attitudes to others? Can our personality contribute to our prejudices? How do we reduce prejudice and discrimination?\u003c\/p\u003e\u003ci\u003e\u003c\/i\u003e\u003cp\u003eThe Psychology of Prejudice explores different forms of prejudice and discrimination, from racial jokes to genocide. It looks at what might cause our prejudiced attitudes, including our personalities, social influences, group identity, and evolutionary factors, and how prejudice can be reduced through education, campaigning, and consciousness raising.\u003c\/p\u003e\u003cp\u003eOffering insights into a topic of great public concern and debate, \u003ci\u003eThe Psychology of Prejudice\u003c\/i\u003e shows us how we can confront our prejudiced attitudes and contribute to greater tolerance and understanding.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. What do we mean by ‘Prejudice’? 2. Prejudice within Biology, Psychology and Psychiatry 3. Prejudice and Personality 4. The Impact of Environmental Factors on Prejudice and Discrimination 5. The Influence of Group Membership 6. Reducing Prejudice and Discrimination\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":48733711139159,"sku":"9780367534639","price":16.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780367534639.jpg?v=1720001344"},{"product_id":"berkeley-problems-in-mathematics-9780387008929","title":"Berkeley Problems in Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews of the third edition:\u003c\/p\u003e \u003cp\u003e\"This new edition has been updated with the most recent exams … . There are numerous new problems and solutions which were not included in previous editions. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph. D program. … this book will develop problem-solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. … Tags with the exact exam year provide the opportunity to rehearse complete examinations. … This new edition has been updated with the most recent exams … .\" \u003cem\u003e(Zentralblatt für Didaktik der Mathematik, November 2004)\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"The Mathematics department of the University of California, Berkeley, has set a written preliminary examination to determine whether first year Ph.D. students have mastered enough basic mathematics to succeed in the doctoral program. Berkeley Problems in Mathematics is a compilation of all the … questions, together with worked solutions … . All the solutions I looked at are complete … . Some of the solutions are very elegant. … This is an impressive piece of work and a welcome addition to any mathematician’s bookshelf.\" \u003cem\u003e(Chris Good, The Mathematical Gazette, 90:518, 2006)\u003c\/em\u003e \u003c\/p\u003e \u003cp\u003e\"During the last twenty-five years problems from written preliminary examinations that are required for the Ph.D. degree at the Mathematics Department of the University of California, Berkeley, have been assembled. … The book is suited for students in mathematics, physics or engineering. Solutions are well explained, making the book valuable for self-study. The problems have a satisfactory high level, so the book is a rich resource of examples for lecturers as well, who need exercises … . This book certainly is to be recommended.\" \u003cem\u003e(Paula Bruggen, Bulletin of the Belgian Mathematical Society, 12:4, 2005)\u003c\/em\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents Preface  I Problems  1 Real Analysis  1.1 Elementary Calculus  1.2 Limitsand Continuity  1.3 Sequences, Series, and Products  1.4 Differential Calculus  1.5 Integral Calculus  1.6 Sequences of Functions  1.7 Fourier Series  1.8 Convex Functions 2 Multivariable Calculus  2.1 Limitsand Continuity  2.2 Differential Calculus  2.3 Integral Calculus 3 Differential Equations  3.1 First Order Equations  3.2 SecondOrder Equations  3.3 Higher Order Equations  3.4 Systems of Differential Equations 4 Metric Spaces  4.1 Topology of Rn  4.2 General Theory  4.3 Fixed Point Theorem 5 Complex Analysis  5.1 Complex Numbers  5.2 Series and Sequences of Functions  5.3 Conformal Mappings  5.4 Functions on the Unit Disc  5.5 Growth Conditions  5.6 Analytic and Meromorphic Functions  5.7 Cauchy’s Theorem  5.8 Zeros and Singularities  5.9 Harmonic Functions  5.10 Residue Theory  5.11 Integrals Along the Real Axis 6 Algebra  6.1 Examples of Groups and General Theory  6.2 Homomorphisms and Subgroups  6.3 Cyclic Groups  6.4 Normality, Quotients, and Homomorphisms  6.5 Sn, An , Dn, .. 6.6 Direct Products  6.7 Free Groups, Generators, and Relations  6.8 Finite Groups  6.9 Ringsand Their Homomorphisms  6.10 Ideals  6.11 Polynomials  6.12 Fields and Their Extensions  6.13 Elementary Number Theory 7 Linear Algebra  7.1 Vector Spaces  7.2 Rankand Determinants  7.3 Systems of Equations  7.4 Linear Transformations  7.5 Eigenvalues and Eigenvectors  7.6 Canonical Forms  7.7 Similarity  7.8 Bilinear, Quadratic Forms, and Inner Product Spaces  7.9 General Theory ofMatrices II Solutions  1 Real Analysis  1.1 Elementary Calculus  1.2 Limits and Continuity  1.3 Sequences, Series, and Products  1.4 Differential Calculus  1.5 Integral Calculus  1.6Sequences of Functions  1.7 Fourier Series  1.8 Convex Functions 2 Multivariable Calculus  2.1 Limitsand Continuity  2.2 Differential Calculus  2.3 Integral Calculus  3 Differential Equations  3.1 First Order Equations  3.2 Second Order Equations  3.3 Higher Order Equations  3.4 Systems of Differential Equations 4 Metric Spaces  4.1 Topology of Rn  4.2 General Theory  4.3 Fixed Point Theorem 5 Complex Analysis  5.1 Complex Numbers  5.2 Series and Sequences of Functions  5.3 Conformal Mappings  5.4 Functions on the Unit Disc  5.5 Growth Conditions  5.6 Analytic and Meromorphic Functions  5.7 Cauchy’s Theorem  5.8 Zeros and Singularities  5.9 Harmonic Functions  5.10 Residue Theory  5.11 Integrals Along the Real Axis 6 Algebra  6.1 Examples of Groups and General Theory  6.2 Homomorphisms and Subgroups  6.3 Cyclic Groups  6.4 Normality, Quotients, and Homomorphisms  6.5 Sn, An , Dn, .. 6.6 Direct Products  6.7 Free Groups, Generators, and Relations  6.8 Finite Groups  6.9 Rings and Their Homomorphisms  6.10 Ideals  6.11 Polynomials  6.12 Fields and Their Extensions  6.13 Elementary Number Theory 7 Linear Algebra  7.1 Vector Spaces  7.2 Rankand Determinants  7.3 Systems of Equations  7.4 Linear Transformations  7.5 Eigenvalues and Eigenvectors  7.6 Canonical Forms  7.7 Similarity  7.8 Bilinear, Quadratic Forms, and Inner Product Spaces  7.9 General Theory of Matrices III Appendices  A How to Get the Exams  A.1 On-line  A.2 Off-line, the Last Resort  B Passing Scores  C The Syllabus  References  Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733723754839,"sku":"9780387008929","price":56.24,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387008929.jpg?v=1791459023"},{"product_id":"naive-lie-theory-9780387782140","title":"Naive Lie Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eGeometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of Lie algebras.- The matrix logarithm.- Topology.- Simply connected Lie groups.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“An excellent read. In just 200 pages the author explains what Lie groups and algebras actually are. … An undergraduate who has taken the calculus series, had a course in linear algebra that discusses matrices, has some knowledge of complex variables and some understanding of group theory should easily follow the material to this point. … the best book to get you going.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)\u003c\/p\u003e\u003cp\u003e“There are several aspects of Stillwell’s book that I particularly appreciate. He keeps the sections very short and straightforward, with a few exercises at the end of each to cement understanding. The theory is built up in small bites. He develops an intuition for what is happening by starting with very simple examples and building toward more complicated groups. … In short, if you want to teach an undergraduate course on Lie theory, I recommend Stillwell.”(David Bressoud, The UMAP Journal, Vol. 31 (4), 2010)\u003c\/p\u003e\u003cp\u003e\"Lie theory, basically the study of continuous symmetry, certainly occupies a central position in modern mathematics … . In Naive Lie Theory, Stillwell (Univ. of San Franciso) concentrates on the simplest examples and stops short of representation theory … . Summing Up: Recommended. Upper-division undergraduates and graduate students.\" (D. V. Feldman, Choice, Vol. 46 (9), May, 2009)\u003c\/p\u003e\u003cp\u003e\"This book provides an introduction to Lie groups and Lie algebras suitable for undergraduates having no more background than calculus and linear algebra. … Each chapter concludes with a lively and informative account of the history behind the mathematics in it. The author writes in a clear and engaging style … . The book is a welcome addition to the literature in representation theory.\" (William M. McGovern, Mathematical Reviews, Issue 2009 g)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"This is a beautifully clear exposition of the main points of Lie theory, aimed at undergraduates who have … calculus and linear algebra. … The book is well equipped with examples … . The book has a very strong geometric flavor, both in the use of rotation groups and in the connection between Lie algebras and Lie groups.\" (Allen Stenger, The Mathematical Association of America, October, 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGeometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of Lie algebras.- The matrix logarithm.- Topology.- Simply connected Lie groups.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726409047,"sku":"9780387782140","price":33.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387782140.jpg?v=1791459035"},{"product_id":"groups-matrices-and-vector-spaces-a-group-theoretic-approach-to-linear-algebra-universitext-9780387794273","title":"Groups Matrices and Vector Spaces A Group","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symmetry groups, determinants, linear coding theory and cryptography are interwoven throughout.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This is an introductory text on linear algebra and group theory from a geometric viewpoint. The topics, largely standard, are presented in brief, well-organized one- and two-page subsections written in clear, if rather pedestrian, language, with detailed examples.” (R. J. Bumcrot, Mathematical Reviews, February, 2018)\u003cbr\u003e\u003cbr\u003e“It is particularly applicable for anyone who is familiar with vector spaces and wants to learn about groups – and also for anyone who is familiar with groups and wants to learn about vector spaces. This book is well readable and therefore suitable for self-studying. Each chapter begins with a concise and informative summary of its content, guiding the reader to choose the chapters with most interest to him\/her.” (Jorma K. Merikoski, zbMATH 1380.15001, 2018)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Preliminaries.- 2. Groups and Fields: The Two Fundamental Notions of Algebra.- 3. Vector Spaces.- 4. Linear Mappings.- 5. Eigentheory.- 6. Unitary Diagonalization and Quadratic Forms.- 7. The Structure Theory of Linear Mappings.- 8. Theorems on Group Theory.- 9. Linear Algebraic Groups: An Introduction.- Bibliography.- Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726474583,"sku":"9780387794273","price":61.74,"currency_code":"GBP","in_stock":false}]},{"product_id":"commutative-algebra-9780387942698","title":"Commutative Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eD. Eisenbud\u003c\/p\u003e \u003cp\u003e\u003cem\u003eCommutative Algebra with a View Toward Algebraic Geometry\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"This text has personality—Those familiar with Eisenbud\"s own research will recognize its traces in his choice of topics and manner of approach. The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible.\u003c\/em\u003e\"—MATHEMATICAL REVIEWS\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; 0. Elementary Definitions; I. Basic Constructions; 1. Roots and Commutative Algebra; 2. Localization; 3. Associated Primes and Primary Decomposition; 4. Integral Dependence and the Nullstellensatz; 5. Filtrations and the Artin-Rees Lemma; 6. Flat Families; 7. Completions and Hensel's Lemma; II. Dimension Theory; 8. Introduction to Dimension Theory; 9. Fundamental Definitions of Dimension Theory; 10. The Principal Ideal Theorem and Systems of Parameters;  11. Dimension and Codimension One; 12. Dimension and Hilbert- Samuel Polynomials; 13. Dimension of Affine Rings; 14. Elimination Theory, Generic Freeness and the Dimension of Fibers; 15. Grobner Bases; 16. Modules of Differentials; III. Homological Methods; 17. Regular Sequence and the Koszul Complex; 18. Depth, Codimension and Cohen-Macaulay Rings; 19. Homological Theory of Regular Local Rings; 20. Free Resolutions and Fitting Invariants; 21. Duality, Canonical Modules and Gorenstein Rings; Appendix 1. Field Theory; Appendix 2. Multilinear Algebra; Appendix 3. Homological Algebra; Appendix 4. A Sketch of Local Cohomology; Appendix 5. Category Theory; Appendix 6. Limits and Colimits; Appendix 7. Where Next?; Hints and Solutions for Selected Exercises; References; Index of Notations; Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726802263,"sku":"9780387942698","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387942698.jpg?v=1720001406"},{"product_id":"algebra-9780387953854","title":"Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOne The Basic Objects of Algebra.- I Groups.- II Rings.- III Modules.- IV Polynomials.- Two Algebraic Equations.- V Algebraic Extensions.- VI Galois Theory.- VII Extensions of Rings.- VIII Transcendental Extensions.- IX Algebraic Spaces.- X Noetherian Rings and Modules.- XI Real Fields.- XII Absolute Values.- Three Linear Algebra and Representations.- XIII Matrices and Linear Maps.- XIV Representation of One Endomorphism.- XV Structure of Bilinear Forms.- XVI The Tensor Product.- XVII Semisimplicity.- XVIII Representations of Finite Groups.- XIX The Alternating Product.- Four Homological Algebra.- XX General Homology Theory.- XXI Finite Free Resolutions.- Appendix 2 Some Set Theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cem\u003eS. Lang\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003eAlgebra\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"Lang’s Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books.\"—\u003c\/em\u003eNOTICES OF THE AMS \u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the ‘right’ way, and he never gets bogged down in the dry formalism which pervades some parts of algebra.\"\u003c\/em\u003e—MATHEMATICAL REVIEWS\u003c\/p\u003e \u003cp\u003eFrom the reviews of the third edition:\u003c\/p\u003e \u003cp\u003e\"The current third edition has grown again … dealing with topics close to the author’s heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields … . This makes it a fascinating book to read … . a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items.\" (Paul M. Cohn, Zentralblatt MATH, Vol. 984, 2003)\u003c\/p\u003e \u003cp\u003e\"Lang’s Algebra … has gained an iconic status, due both to the comprehensiveness of its coverage and its ability to be authoritative and lively at the same time. … a revolutionary work, changing the way in which graduate algebra was taught. … the author describes the book as ‘very stable’, indicating that there is little that he has wished to change. This confidence is reflected in the wider mathematical community, and ... this new printing deserves a place in every university departmental library.\" (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeword * Groups * Rings * Modules * Polynomials * Algebraic Equations * Galois Theory * Extensions of Rings * Transcendental Extensions * Algebraic Spaces * Noetherian Rings and Modules * Real Fields * Absolute Values * Matrices and Linear Maps * Representation of One Endomorphism * Structure of Bilinear Forms * The Tensor Product * Semisimplicity * Representations of Finite Groups * The Alternating Product * General Homology Theory * Finite Free Resolutions * Appendices * Bibliography","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726966103,"sku":"9780387953854","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387953854.jpg?v=1720001407"},{"product_id":"applications-of-lie-groups-to-differential-equations-9780387950006","title":"Applications of Lie Groups to Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e1 Introduction to Lie Groups.- 1.1. Manifolds.- 1.2. Lie Groups.- 1.3. Vector Fields.- 1.4. Lie Algebras.- 1.5. Differential Forms.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- 3.5. Group-Invariant Prolongations and Reduction.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- 4.2. Variational Symmetries.- 4.3. Conservation Laws.- 4.4. Noether's Theorem.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- 5.4. The Variational Complex.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- 6.2. Symplectic Structures and Foliations.- 6.3. Symmetries, First Integrals and Reduction of Order.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- 7.2. Symmetries and Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Notes.- Exercises.- References.- Symbol Index.- Author Index.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and Connectedness.- 1.2. Lie Groups.- Lie Subgroups.- Local Lie Groups.- Local Transformation Groups.- Orbits.- 1.3. Vector Fields.- Flows.- Action on Functions.- Differentials.- Lie Brackets.- Tangent Spaces and Vectors Fields on Submanifolds.- Frobenius’ Theorem.- 1.4. Lie Algebras.- One-Parameter Subgroups.- Subalgebras.- The Exponential Map.- Lie Algebras of Local Lie Groups.- Structure Constants.- Commutator Tables.- Infinitesimal Group Actions.- 1.5. Differential Forms.- Pull-Back and Change of Coordinates.- Interior Products.- The Differential.- The de Rham Complex.- Lie Derivatives.- Homotopy Operators.- Integration and Stokes’ Theorem.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- Invariant Subsets.- Invariant Functions.- Infinitesimal Invariance.- Local Invariance.- Invariants and Functional Dependence.- Methods for Constructing Invariants.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- Systems of Differential Equations.- Prolongation of Group Actions.- Invariance of Differential Equations.- Prolongation of Vector Fields.- Infinitesimal Invariance.- The Prolongation Formula.- Total Derivatives.- The General Prolongation Formula.- Properties of Prolonged Vector Fields.- Characteristics of Symmetries.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- First Order Equations.- Higher Order Equations.- Differential Invariants.- Multi-parameter Symmetry Groups.- Solvable Groups.- Systems of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Local Solvability.- In variance Criteria.- The Cauchy—Kovalevskaya Theorem.- Characteristics.- Normal Systems.- Prolongation of Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- The Adjoint Representation.- Classification of Subgroups and Subalgebras.- Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- Dimensional Analysis.- 3.5. Group-Invariant Prolongations and Reduction.- Extended Jet Bundles.- Differential Equations.- Group Actions.- The Invariant Jet Space.- Connection with the Quotient Manifold.- The Reduced Equation.- Local Coordinates.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- The Variational Derivative.- Null Lagrangians and Divergences.- Invariance of the Euler Operator.- 4.2. Variational Symmetries.- Infinitesimal Criterion of Invariance.- Symmetries of the Euler—Lagrange Equations.- Reduction of Order.- 4.3. Conservation Laws.- Trivial Conservation Laws.- Characteristics of Conservation Laws.- 4.4. Noether’s Theorem.- Divergence Symmetries.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- Differential Functions.- Generalized Vector Fields.- Evolutionary Vector Fields.- Equivalence and Trivial Symmetries.- Computation of Generalized Symmetries.- Group Transformations.- Symmetries and Prolongations.- The Lie Bracket.- Evolution Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- Frechet Derivatives.- Lie Derivatives of Differential Operators.- Criteria for Recursion Operators.- The Korteweg—de Vries Equation.- Master Symmetries.- Pseudo-differential Operators.- Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- Adjoints of Differential Operators.- Characteristics of Conservation Laws.- Variational Symmetries.- Group Transformations.- Noether’s Theorem.- Self-adjoint Linear Systems.- Action of Symmetries on Conservation Laws.- Abnormal Systems and Noether’s Second Theorem.- Formal Symmetries and Conservation Laws.- 5.4. The Variational Complex.- The D-Complex.- Vertical Forms.- Total Derivatives of Vertical Forms.- Functionals and Functional Forms.- The Variational Differential.- Higher Euler Operators.- The Total Homotopy Operator.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- Hamiltonian Vector Fields.- The Structure Functions.- The Lie-Poisson Structure.- 6.2. Symplectic Structures and Foliations.- The Correspondence Between One-Forms and Vector Fields.- Rank of a Poisson Structure.- Symplectic Manifolds.- Maps Between Poisson Manifolds.- Poisson Submanifolds.- Darboux’ Theorem.- The Co-adjoint Representation.- 6.3. Symmetries, First Integrals and Reduction of Order.- First Integrals.- Hamiltonian Symmetry Groups.- Reduction of Order in Hamiltonian Systems.- Reduction Using Multi-parameter Groups.- Hamiltonian Transformation Groups.- The Momentum Map.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- The Jacobi Identity.- Functional Multi-vectors.- 7.2. Symmetries and Conservation Laws.- Distinguished Functionals.- Lie Brackets.- Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Recursion Operators.- Notes.- Exercises.- References.- Symbol Index.- Author Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727064407,"sku":"9780387950006","price":39.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387950006.jpg?v=1720001407"},{"product_id":"groups-and-symmetry-9780387966755","title":"Groups and Symmetry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e1 Symmetries of the Tetrahedron.- 2 Axioms.- 3 Numbers.- 4 Dihedral Groups.- 5 Subgroups and Generators.- 6 Permutations.- 7 Isomorphisms.- 8 Plato's Solids and Cayley's Theorem.- 10 Products.- 11 Lagrange's Theorem.- 12 Partitions.- 13 Cauchy's Theorem.- 14 Conjugacy.- 15 Quotient Groups.- 16 Homomorphisms.- 17 Actions, Orbits, and Stabilizers.- 18 Counting Orbits.- 19 Groups.- 20 The Sylow Theorems.- 21 Finitely Generated Abelian Groups.- 22 Row and Column Operations.- 23 Automorphisms.- 24 The Euclidean Group.- 25 Lattices and Point Groups.- 26 Wallpaper Patterns.- 27 Free Groups and Presentations.- 28 Trees and the Nielsen-Schreier Theorem.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eM.A. Armstrong\u003c\/p\u003e \u003cp\u003e\u003cem\u003eGroups and Symmetry\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author’s plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed\u003c\/em\u003e.\u003cem\u003e\u003cstrong\u003e\"—\u003c\/strong\u003e\u003c\/em\u003eMATHEMATICAL REVIEWS\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface. 1: Symmetries of the Tetrahedron. 2: Axioms. 3: Numbers. 4: Dihedral Groups. 5: Subgroups and Generators. 6: Permutations. 7: Isomorphisms. 8: Plato's Solids and Cayley's Theorem. 9: Matrix Groups. 10: Products. 11: Lagrange's Theorem. 12: Partitions. 13: Cauchy's Theorem. 14: Conjugacy. 15: Quotient Groups. 16: Homomorphisms. 17: Actions, Orbits, and Stabalizers. 18: Counting Orbits. 19: Finite Rotation Groups. 20: The Sylow Theorems. 21: Finitely Generated Abelian Groups. 22: Row and Column Operations. 23: Automorphisms. 24: The Euclidean Group. 25: Lattices and Point Groups. 26: Wallpaper Patterns. 27: Free Groups and Presentations. 28: Trees and the Nielsen-Schreier Theorem. Bibliography. Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727261015,"sku":"9780387966755","price":40.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387966755.jpg?v=1720001407"},{"product_id":"representation-theory-9780387974958","title":"Representation Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eI: Finite Groups.- 1. Representations of Finite Groups.- \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI: Finite Groups.-","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727719767,"sku":"9780387974958","price":72.91,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387974958.jpg?v=1791459041"},{"product_id":"sphere-packings-lattices-and-groups-grundlehren-der-mathematischen-wissenschaften-v-290-9780387985855","title":"Sphere Packings Lattices and Groups Grundlehren","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e1 Sphere Packings and Kissing Numbers.- 2 Coverings, Lattices and Quantizers.- 3 Codes, Designs and Groups.- 4 Certain Important Lattices and Their Properties.- 5 Sphere Packing and Error-Correcting Codes.- 6 Laminated Lattices.- 7 Further Connections Between Codes and Lattices.- 8 Algebraic Constructions for Lattices.- 9 Bounds for Codes and Sphere Packings.- 10 Three Lectures on Exceptional Groups.- 11 The Golay Codes and the Mathieu Groups.- 12 A Characterization of the Leech Lattice.- 13 Bounds on Kissing Numbers.- 14 Uniqueness of Certain Spherical Codes.- 15 On the Classification of Integral Quadratic Forms.- 16 Enumeration of Unimodular Lattices.- 17 The 24-Dimensional Odd Unimodular Lattices.- 18 Even Unimodular 24-Dimensional Lattices.- 19 Enumeration of Extremal Self-Dual Lattices.- 20 Finding the Closest Lattice Point.- 21 Voronoi Cells of Lattices and Quantization Errors.- 22 A Bound for the Covering Radius of the Leech Lattice.- 23 The Covering Radius of the Leech Lattice.- 24 Twenty-Three Constructions for the Leech Lattice.- 25 The Cellular Structure of the Leech Lattice.- 26 Lorentzian Forms for the Leech Lattice.- 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice.- 28 Leech Roots and Vinberg Groups.- 29 The Monster Group and its 196884-Dimensional Space.- 30 A Monster Lie Algebra?.- Supplementary Bibliography.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThird Edition\u003c\/p\u003e \u003cp\u003eJ.H. Conway and N.J.A. Sloane\u003c\/p\u003e \u003cp\u003e\u003cem\u003eSphere Packings, Lattices and Groups\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"This is the third edition of this reference work in the literature on sphere packings and related subjects. In addition to the content of the preceding editions, the present edition provides in its preface a detailed survey on recent developments in the field, and an exhaustive supplementary bibliography for 1988-1998. A few chapters in the main text have also been revised.\"—\u003c\/em\u003eMATHEMATICAL REVIEWS\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Sphere Packings and Kissing Numbers.- 2 Coverings, Lattices and Quantizers.- 3 Codes, Designs and Groups.- 4 Certain Important Lattices and Their Properties.- 5 Sphere Packing and Error-Correcting Codes.- 6 Laminated Lattices.- 7 Further Connections Between Codes and Lattices.- 8 Algebraic Constructions for Lattices.- 9 Bounds for Codes and Sphere Packings.- 10 Three Lectures on Exceptional Groups.- 11 The Golay Codes and the Mathieu Groups.- 12 A Characterization of the Leech Lattice.- 13 Bounds on Kissing Numbers.- 14 Uniqueness of Certain Spherical Codes.- 15 On the Classification of Integral Quadratic Forms.- 16 Enumeration of Unimodular Lattices.- 17 The 24-Dimensional Odd Unimodular Lattices.- 18 Even Unimodular 24-Dimensional Lattices.- 19 Enumeration of Extremal Self-Dual Lattices.- 20 Finding the Closest Lattice Point.- 21 Voronoi Cells of Lattices and Quantization Errors.- 22 A Bound for the Covering Radius of the Leech Lattice.- 23 The Covering Radius of the Leech Lattice.- 24 Twenty-Three Constructions for the Leech Lattice.- 25 The Cellular Structure of the Leech Lattice.- 26 Lorentzian Forms for the Leech Lattice.- 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice.- 28 Leech Roots and Vinberg Groups.- 29 The Monster Group and its 196884-Dimensional Space.- 30 A Monster Lie Algebra?.- Supplementary Bibliography.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733728178519,"sku":"9780387985855","price":67.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387985855.jpg?v=1791459041"},{"product_id":"topics-in-operator-semigroups-281-progress-in-mathematics-9780817649319","title":"Topics in Operator Semigroups 281 Progress in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato''s unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone''s representation of unitary semigroups. Part II explores generalizations of spectral theory''s connection to operator semigroups.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e\u003cp\u003e“This monograph is suitable for second-year graduate students, but it can be recommended also to any researcher interested in operator semigroups.” (László Kérchy, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)\u003c\/p\u003e\u003cp\u003e“The present graduate level text expands the previous lecture notes from the same author, Semigroups of operators and spectral theory … . It begins with a succinct introduction to operator semigroups covering classical topics such as generators, the Hille-Yosida theorem, dissipative operators and the Lumer–Phillips theorem, the Trotter convergence theorem, exponential formulas, perturbation theory, Stone’s theorem, and analytic semigroups. … The text is also intended for second-year graduate students … . it will be a valuable source for researchers working in this area.” (G. Teschl, Monatshefte für Mathematik, Vol. 162 (4), April, 2011)\u003c\/p\u003e\u003cp\u003e“This book is based on the author’s lecture notes … in which the more advanced parts concentrated on spectral representations. … There is also a presentation of a well-known stability theorem for semigroups under countable spectral conditions. … The increased variety of topics covered will make the book more useful … . Other advantages are the inclusion of an index and some exercises, considerable extensions of the bibliography and the list of contents, and more attractive typesetting.”­­­ (C. J. K. Batty, Mathematical Reviews, Issue 2010 k)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGeneral Theory.- Basic Theory.- The Semi-Simplicity Space for Groups.- Analyticity.- The Semigroup as a Function of its Generator.- Large Parameter.- Boundary Values.- Pre-Semigroups.- Integral Representations.- The Semi-Simplicity Space.- The Laplace#x2013;Stieltjes Space.- Families of Unbounded Symmetric Operators.- A Taste of Applications.- Analytic Families of Evolution Systems.- Similarity.","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":48737454457175,"sku":"9780817649319","price":82.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817649319.jpg?v=1791467660"},{"product_id":"algebraic-groups-9781009018586","title":"Algebraic Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAlgebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the BarsottiChevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the BorelChevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'All together, this excellent text fills a long-standing gap in the textbook literature on algebraic groups. It presents the modern theory of group schemes in a very comprehensive, systematic, detailed and lucid manner, with numerous illustrating examples and exercises. It is fair to say that this reader-friendly textbook on algebraic groups is the long-desired modern successor to the old, venerable standard primers …' Werner Kleinert, zbMath\u003cbr\u003e'The author invests quite a lot to make difficult things understandable, and as a result, it is a real pleasure to read the book. All in all, with no doubt, Milne's new book will remain for decades an indispensable source for everybody interested in algebraic groups.' Boris È. Kunyavskiĭ, MathSciNet\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; 1. Definitions and basic properties; 2. Examples and basic constructions; 3. Affine algebraic groups and Hopf algebras; 4. Linear representations of algebraic groups; 5. Group theory: the isomorphism theorems; 6. Subnormal series: solvable and nilpotent algebraic groups; 7. Algebraic groups acting on schemes; 8. The structure of general algebraic groups; 9. Tannaka duality: Jordan decompositions; 10. The Lie algebra of an algebraic group; 11. Finite group schemes; 12. Groups of multiplicative type: linearly reductive groups; 13. Tori acting on schemes; 14. Unipotent algebraic groups; 15. Cohomology and extensions; 16. The structure of solvable algebraic groups; 17. Borel subgroups and applications; 18. The geometry of algebraic groups; 19. Semisimple and reductive groups; 20. Algebraic groups of semisimple rank one; 21. Split reductive groups; 22. Representations of reductive groups; 23. The isogeny and existence theorems; 24. Construction of the semisimple groups; 25. Additional topics; Appendix A. Review of algebraic geometry; Appendix B. Existence of quotients of algebraic groups; Appendix C. Root data; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738000666967,"sku":"9781009018586","price":40.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009018586.jpg?v=1723811670"},{"product_id":"modern-trends-in-algebra-and-representation-theory-9781009097352","title":"Modern Trends in Algebra and Representation","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eExpanding on lectures given at the LMS Autumn Algebra School 2020, this text gives a guided tour of modern developments in algebra and representation theory. It includes many worked examples and applications, providing graduate students and researchers in related disciplines with a springboard into the vast literature in each area.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction David Jordan, Nadia Mazza and Sibylle Schroll; 1. Auslander-Reiten theory of finite-dimensional algebras Raquel Coelho Simões; 2. τ-Tilting theory – an introduction Hipolito Treffinger; 3. From frieze patterns to cluster categories Matthew Pressland; 4. Infinite-dimensional representations of algebras Rosanna Laking; 5. The Springer correspondence Sam Gunningham; 6. An introduction to diagrammatic Soergel bimodules Amit Hazi; 7. A companion to quantum groups Bart Vlaar; 8. Infinite-dimensional Lie algebras and their multivariable generalizations Brian Williams; 9. An introduction to crowns in finite groups Gareth Tracey; 10. An introduction to totally disconnected locally compact groups and their finiteness conditions Ilaria Castellano; 11. Locally analytic representations of p-adic groups Andreas Bode and Nicolas Dupré.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738004009303,"sku":"9781009097352","price":70.0,"currency_code":"GBP","in_stock":true}]},{"product_id":"quantum-theory-for-mathematicians-9781461471158","title":"Quantum Theory for Mathematicians","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAlthough ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book''s conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stonevon Neumann Theorem; the WentzelKramersBrillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics.\u003c\/p\u003e\u003cp\u003eThe numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basi\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“This book is an introduction to quantum mechanics intended for mathematicians and mathematics students who do not have a particularly strong background in physics. … A well-qualified graduate student can learn a lot from this book. I found it to be clear and well organized, and I personally enjoyed reading it very much.” (David S. Watkins, SIAM Review, Vol. 57 (3), September, 2015)\u003c\/p\u003e\u003cp\u003e“This textbook is meant for advanced studies on quantum mechanics for a mathematical readership. The exercises at the end of each chapter make the book especially valuable.” (A. Winterhof, Internationale Mathematischen Nachrichten, Issue 228, 2015)\u003c\/p\u003e\u003cp\u003e“There are a few textbooks on quantum theory for mathematicians who are alien to the physical culture … but this modest textbook will surely find its place. All in all, the book is well written and accessible to any interested mathematicians and mathematical graduates.” (Hirokazu Nishimura, zbMATH, Vol. 1273, 2013)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 The Experimental Origins of Quantum Mechanics.- 2 A First Approach to Classical Mechanics.- 3 A First Approach to Quantum Mechanics.- 4 The Free Schrödinger Equation.- 5 A Particle in a Square Well.- 6 Perspectives on the Spectral Theorem.- 7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements.- 8 The Spectral Theorem for Bounded Sef-Adjoint Operators: Proofs.- 9 Unbounded Self-Adjoint Operators.- 10 The Spectral Theorem for Unbounded Self-Adjoint Operators.- 11 The Harmonic Oscillator.- 12 The Uncertainty Principle.- 13 Quantization Schemes for Euclidean Space.- 14 The Stone–von Neumann Theorem.- 15 The WKB Approximation.- 16 Lie Groups, Lie Algebras, and Representations.- 17 Angular Momentum and Spin.- 18 Radial Potentials and the Hydrogen Atom.- 19 Systems and Subsystems, Multiple Particles.- V Advanced Topics in Classical and Quantum Mechanics.- 20 The Path-Integral Formulation of Quantum Mechanics.- 21 Hamiltonian Mechanics on Manifolds.- 22 Geometric Quantization on Euclidean Space.- 23 Geometric Quantization on Manifolds.- A Review of Basic Material.- References.​- Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739349397847,"sku":"9781461471158","price":56.69,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461471158.jpg?v=1791471582"},{"product_id":"the-body-of-the-group-sexuality-and-gender-in-group-analysis-9781912691906","title":"The Body of the Group: Sexuality and Gender in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cem\u003eThe Body in the Group\u003c\/em\u003e has been structured around the formation of a group analytic concept of sexuality, using the archaeology of Michel Foucault to move away from psychoanalytic theory, with its association to heteronormativity and pathology, on which group analysis has historically relied. The failure of group analysis to have its own theory of sexuality is, in fact, its greatest potential. It is a psychosocial theory that is able to contain failure in language and gaps in discourse, and, furthermore, can mobilise its creative potential in relation to the discourse of sexuality. Furthermore, using queer theory enables the failure of the term ‘homosexual’ by disrupting its association to heteronormativity and psychopathology that traditional psychoanalysis has emphasised.\u003cbr\u003e The potential of the group analytic matrix to disrupt and change discourse by conceiving of it using figurations and their associated political radicalism within language and discourse permits a radical conception of space and time. Bi-logic removes the potentially unhelpful competitive splits in power associated with the politics of sexuality and gender and, by doing so, enables multiple and contradictory positions of sexuality and gender to be held simultaneously. In addition, group analysis radically alters typical notions of ethics by being able to conceive of a psychosocial form of ethics. Likewise, queer theory raises an awareness for group analysis of the potential violence of its textual representation. Finally, analytic groups are ‘figurations in action’ when terms such as group polyphony, embodiment, discursive gaps, and norms (or no-norms) are mobilised alongside spatio-temporality and bi-logic. The group analytic literature so far has delimited sexuality and gender by over-reliance on psychoanalysis. Daniel Anderson, by utilising group analytic theory alongside the archaeology of Foucault and feminist, queer and education theory, has created an exciting and innovative way of working with sexuality in a group analysis setting.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e'If it takes courage and clarity for an individual to know their shadows and to embrace change, this is equally true for organisations, like psychotherapy institutions. Daniel Anderson’s book, written with courage and clarity, beautifully deconstructs many of the assumptions and (dubious) comforts of our historical orthodoxies as group analysts. In the words of gay pioneer Harvey Milk, \"once you have dialogue starting, you know you can break down prejudice\".'\u003c\/p\u003e -- Martin Weegmann, psychologist, group analyst and author\u003cbr\u003e\u003cp\u003e‘This is a well-written, well-informed and well-argued academic book providing the reader with an overview of the fundamentals of queer theory. It then proceeds to thoughtfully integrate this into group analytic theory. I highly recommend it as a textbook for all course modules on gender and sexuality. It should be essential reading for teaching trainees on psychotherapy and group analytic trainings. It would also be highly relevant to those training to work in the field of couple counselling and family therapy and as a reference book for clinical supervisors.’\u003c\/p\u003e -- Margaret Smith, group analyst, psychodynamic psychotherapist and former course convenor of the Institute of Group Analysis supervision course\u003cbr\u003e\u003cp\u003e‘Here, at last, is a book that successfully puts academic debates about gender and sexuality studies into dialogue with group analytic theory and practice. In \u003cem\u003eThe Body of the Group\u003c\/em\u003e, Daniel Anderson meticulously maps the “field imaginary of group analysis” – from the historical parameters of its therapeutic project to the current protocols of its knowledge production. Using historical and contemporary case studies, this new study brings to light the blind spots as well as the remarkable achievements of group analysis. Drawing on his own professional training and experiences, the author offers a fascinating route through how and why group analysis has – and importantly has not – addressed questions of gender and sexuality. Putting feminist and queer studies into dialogue with debates in group analysis, this book urges us to explore what might happen if we were to hold these diverse fields within the same frame.’\u003c\/p\u003e -- Jackie Stacey, Professor of Media and Cultural Studies and Director of the Centre for the Study of Sexuality and Culture, The University of Manchester\u003cbr\u003e\u003cp\u003e‘Daniel Anderson has started a much needed conversation around sexuality and gender. I have witnessed his bravery, vulnerability and questioning of himself and others to explore their own shadows in our training together. He has respectfully challenged the complacency we all, including institutions, fall into. We all need to take responsibility for addressing the gaps we have in analytic training around difference, in particular, around sexuality and gender. Our training as therapists centres around language and putting words to often very difficult and sensitive situations, yet we have struggled to challenge traditional thoughts around what is normative and we continue to normalise dated and dangerous language around sexuality. It was a privilege to have trained alongside Dan, he continues to push me to be better. This book evidences he has much more to contribute to the development of analytical training.’\u003c\/p\u003e -- Baljit Kaur, group analyst and social worker\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface\u003c\/p\u003e  \u003cp\u003eAbout the author\u003c\/p\u003e  \u003cp\u003ePermissions\u003c\/p\u003e  \u003cp\u003eAcknowledgements\u003c\/p\u003e  \u003cp\u003eIntroduction\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003ePart I: Failure and the embodied field\u003c\/strong\u003e\u003c\/p\u003e  \u003cp\u003e1. The field imaginary of sexuality in group analysis\u003c\/p\u003e  \u003cp\u003e2. The discursive failure of the ‘homosexual’\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003ePart II: The group as figuration\u003c\/strong\u003e\u003c\/p\u003e  \u003cp\u003e3. Figurations in group polyphony\u003c\/p\u003e  \u003cp\u003e4. “Something is missing”\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003ePart III: Re-reading sources and curricula\u003c\/strong\u003e\u003c\/p\u003e  \u003cp\u003e5. Queering the group analytic paradigm\u003c\/p\u003e  \u003cp\u003e6. The discursive production of group analysts in the UK\u003c\/p\u003e  \u003cp\u003e\u003cbr\u003e Conclusion: Mobilising a generative dialogue\u003c\/p\u003e  \u003cp\u003eReferences \u003c\/p\u003e  \u003cp\u003eIndex\u003c\/p\u003e","brand":"Karnac Books","offers":[{"title":"Default Title","offer_id":48742688457047,"sku":"9781912691906","price":36.18,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781912691906.jpg?v=1791479591"},{"product_id":"symmetry-a-mathematical-exploration-9783030516680","title":"Symmetry: A Mathematical Exploration","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas.  It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem.  All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us.\u003c\/p\u003e\u003cp\u003eThe exposition is engaging, precise and rigorous.  The theorems are visually motivated with intuitive proofs appropriate for the intended audience.  Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book has much to recommend it. The material is presented clearly and enthusiastically … . there are a lot of well-chosen exercises, ranging from very easy to more challenging. … this is a well-written book, covering interesting material, that can serve a number of possible audiences. … many math majors will never have seen many of the topics discussed in this book … technical details by the instructor, serve as a useful text for a capstone course for majors.” (Mark Hunacek MAA Reviews, November 14, 2021)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Introduction to Symmetry.- 2. The Algebra of Symmetry.- 3. The Classification Theorems.- 4. Isomorphic Groups.- 5. Subgroups \u0026amp; Product Groups.- 6. Permutation Groups.- 7. Symmetries of 3D Objects.- 8. The Five Platonic Solids.- 9. Symmetry and Optimization.- 10. What is a Number?.- 11. Excursions in Numbers.- 12. Rigid Motions as Functions.- 13. Rigid Motions as Matrices.- Image Credits.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743038779735,"sku":"9783030516680","price":42.74,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030516680.jpg?v=1791480495"},{"product_id":"interactions-of-quantum-affine-algebras-with-cluster-algebras-current-algebras-and-categorification-in-honor-of-vyjayanthi-chari-on-the-occasion-of-her-60th-birthday-9783030638481","title":"Interactions of Quantum Affine Algebras with","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including:\u003cul\u003e\n\u003cli\u003eString diagrams and categorification\u003c\/li\u003e\n\u003cli\u003eQuantum affine algebras and cluster algebras\u003c\/li\u003e\n\u003cli\u003eSteinberg groups for Jordan pairs\u003c\/li\u003e\n\u003cli\u003eDynamical quantum determinants and Pfaffians\u003c\/li\u003e\n\u003c\/ul\u003e\u003ci\u003eInteractions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification\u003c\/i\u003e will be an ideal resource for researchers in the fields of representation theory and mathematical physics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePublications of Vyjayanthi Chari.- Students of Vyjayanthi Chari.- Part I: Courses.- String Diagrams and Categorification.- Quantum Affine Algebras and Cluster Algebras.- Part II: Surveys.- Work of Vyjayanthi Chari.- Steinberg Groups for Jordan Pairs - An Introduction with Open Problems.- On the Hecke-Algebraic Approach for General Linear Groups over a p-adic Field.- Part III: Papers.- Categorical Representations and Classical p-adic Groups.- Formulae of \u003ci\u003el\u003c\/i\u003e-Divided Powers in Uq(sl2),II.- Longest Weyl Group Elements in Action.- Dual Kashiwara Functions for the B(∞) Crystal in the Bipartite Case.- Lusztig's t-Analogue of weight multiplicity via Crystals.- Conormal Varieties on the Cominuscule Grassmannian.- Evaluation Modules for Quantum Toroidal \u003ci\u003egln\u003c\/i\u003e Algebras.- Dynamical Quantum Determinants and Pfaffians.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743043465559,"sku":"9783030638481","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030638481.jpg?v=1720063862"},{"product_id":"algebraic-topology-9783030706074","title":"Algebraic Topology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003ci\u003eAlgebraic Topology\u003c\/i\u003e is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the preliminaries needed for the formal definition of a surface. Other topics covered in the book include the classification of surfaces, group theory, the fundamental group, and homology.\u003cbr\u003e \u003cbr\u003e This book assumes no background in abstract algebra or real analysis, and the material from those subjects is presented as needed in the text. This makes the book readable to undergraduates or high-school students who do not have the background typically assumed in an algebraic topology book or class. The book contains many examples and exercises, allowing it to be used for both self-study and for an introductory undergraduate topology course.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“Algebraic topology provides a self-contained introduction to the field … . the book thus provides a particularly well-organized, interesting, and smooth exposition of its subject. … This particular book unique is that it provides a clear, elementary, but mathematically solid introduction to algebraic topology that keeps the subject interesting throughout. … provides a clear, readable, and detailed treatment of the ideas and proofs in the subject … .” (Thomas Mack, Mathematical Reviews, July, 2022)\u003c\/p\u003e“The book could easily be used in an undergraduate course or read by a bright high school student. It should certainly be in any high school library.” (Jonathan Hodgson, zbMATH 1481.55001, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- 1. Surface Preliminaries.- 2. Surfaces.- 3. The Euler Characteristic and Identification Spaces.- 4. Classification Theorem of Compact Surfaces.- 5. Introduction to Group Theory.- 6. Structure of Groups.- 7. Cosets, Normal Subgroups, and Quotient Groups.- 8. The Fundamental Group.- 9. Computing the Fundamental Group.- 10. Tools for Fundamental Groups.- 11. Applications of Fundamental Groups.- 12. The Seifert-Van Kampen Theorem.- 13. Introduction to Homology.- 14. The Mayer-Vietoris Sequence.- A. Topological Notions.- Bibliography.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743046414679,"sku":"9783030706074","price":31.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030706074.jpg?v=1720063874"},{"product_id":"excursions-in-number-theory-algebra-and-analysis-9783031130168","title":"Excursions in Number Theory, Algebra, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland’s path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics.\u003c\/p\u003e  \u003cp\u003eA pool of 200 ‘Dialing In’ problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eExcursions in Number Theory, Algebra, and Analysis\u003c\/i\u003e invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and \u003ci\u003edo some mathematics\u003c\/i\u003e.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Rather than being a book that one reads from cover to cover, Excursions is a curated collection problems followed by expository material aimed at providing background material useful for solving these problems. I imagine it would be a great experience to have a course taught out of this book. The second author clearly enjoyed the experience of studying this material under the guidance of the first author and wanted to make that experience available to others.” (John D. Cook, MAA Reviews, June 17, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Dialing In Problems.- 2. Polygons and Modular Arithmetic.- 3. The Fundamental Theorem of Arithmetic.- 4. The Fundamental Theorem of Algebra.- 5. Irrational, Algebraic and Transcendental Numbers.- 6. Fourier Series and Gauss Sums.- Epilogue.- Notation.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743071351127,"sku":"9783031130168","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031130168.jpg?v=1720063984"},{"product_id":"linear-fractional-transformations-an-illustrated-introduction-9783031250019","title":"Linear Fractional Transformations: An Illustrated","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. \u003c\/p\u003e This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eMotivation.- I Euclidean and Inversive Geometry.- Euclidean Isometries and Similarities.- Inversive Geometry.- Applications of Inversive Geometry.- II Non-Euclidean Geometry.- Spherical Geometry.- Appendix: Set Theory.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743077183831,"sku":"9783031250019","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031250019.jpg?v=1720064009"},{"product_id":"university-of-toronto-mathematics-competition-2001-2015-9783319281049","title":"University of Toronto Mathematics Competition","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto. Problems cover areas of single-variable differential and integral calculus, linear algebra, advanced algebra, analytic geometry, combinatorics, basic group theory, and number theory. The problems of the competitions are given in chronological order as presented to the students. The solutions appear in subsequent chapters according to subject matter. Appendices recall some background material and list the names of students who did well.  \u003cbr\u003e\u003cp\u003eThe University of Toronto Undergraduate Competition was founded to provide additional competition experience for undergraduates preparing for the Putnam competition, and is particularly useful for the freshman or  sophomore undergraduate. Lecturers, instructors, and coaches for mathematics competitions will find this presentation useful. Many of the problems are of intermediate difficulty and relate to the first two years of the undergraduate curriculum. The problems presented may be particularly useful for regular class  assignments. Moreover, this text contains problems that lie outside the regular syllabus and may interest students who are eager to learn beyond the classroom.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The book under review is mainly intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay among applied analysis, mathematical physics, and numerical analysis.” (Teodora-Liliana Rădulescu, zbMATH 1357.97001, 2017)\u003c\/p\u003e\u003cp\u003e“This book is the compilation of the problems from those competitions from 2001 to 2015, along with their solutions, an appendix of notation and key results, and an appendix listing the top ranking students. … This books seems most useful as a supplementary resource for a problem solving or Putnam prep group, class, or math club.” (Megan Patnott, MAA Reviews, maa.org, August, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Problems of the Contests.- 2. Algebra.- 3. Inequalities.- 4. Sequences and Series.- 5. Calculus and its Applications.- 6. Other Topics in Analysis.- 7. Linear Algebra.- 8. Geometry.- 9. Group Theory.- 10. Combinatorics and Finite Mathematics.- 11. Number Theory.- Appendix A: Definitions, Conventions, Notation, and Basics.- Appendix B: Top-Ranking Students.- Index. ","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743093764439,"sku":"9783319281049","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319281049.jpg?v=1791481714"},{"product_id":"ergodic-theory-independence-and-dichotomies-9783319498454","title":"Ergodic Theory: Independence and Dichotomies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy.\u003cbr\u003e \u003cbr\u003e The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Introduction.- General Framework and Notational Conventions.- Part 1 Weak Mixing Comactness.- Basic Concepts in Ergodic Theory.- Structure Theory for P.M.P. Actions.- Amenability.- Property (T).- Orbit Equivalence Beyond Amenability.- Topological Dynamics.- Tameness and Independence.- Part 2 Entropy.- Entropy for Actions of Amenable Groups.- Entropy for Actions of Sofic Groups.- The f-invariant.- Entropy and Independence.- Algebraic Actions: Expansiveness, Homoclinicity, and Entropy.- Algebraic Actions: Entropy and the Fuglede-Kadison Determinant.- Appendix A. Polish Spaces and Standard Borel Spaces.- Appendix B. Positive Definite Functions and Weak Containment.- Appendix C. Hilbert Modules.- Appendix D. Weakly Almost Periodic Functions.- Appendix E. Gaussian Actions.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743096451415,"sku":"9783319498454","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319498454.jpg?v=1791481721"},{"product_id":"introduction-to-the-theory-of-lie-groups-9783319543734","title":"Introduction to the Theory of Lie Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory.\u003cbr\u003eWritten by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book draws many very interesting connections, say to topological groups, that are rarely found in more recent books. Hence I believe it is a valuable source for material for courses on the topic.” (A. Cap, Monatshefte für Mathematik, Vol. 192 (4), August, 2020)\u003cbr\u003e“This book is an educational text, in which practically all statements, which are contained in it, are proved. Therefore it is written for students, who want not only to study the theory of Lie groups and Lie algebras and to pass an examination, but to study the foundation of Lie theory for effectively using it in further scientific work.” (V. V. Gorbatsevich, zbMATH 1367.22001, 2017)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTopological Groups.- Simply Connected Spaces and Groups.- Analytic Properties of Linear Groups.- Manifolds and Lie Group.- The Lie Algebra of a Lie Group.- The Exponential Map for Lie Groups.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743097958743,"sku":"9783319543734","price":61.74,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319543734.jpg?v=1791481724"},{"product_id":"a-primer-for-undergraduate-research-from-groups-and-tiles-to-frames-and-vaccines-9783319660646","title":"A Primer for Undergraduate Research: From Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading.\u003c\/p\u003e\u003cp\u003eThe content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book is a superb resource for students and faculty mentors embarking on undergraduate research in mathematics. Its focus is on topics and applications rarely covered in the traditional undergraduate math curriculum, offering novice researchers a sturdy jumping-off point to a broad array of research problems. … A valuable resource for students and faculty mentors interested in undergraduate research.” (V. K. Chellamuthu, Choice, Vol. 56 (2), October, 2018)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCoxeter Groups and the Davis Complex (T.A. Schroeder).- A Tale of Two Symmetries: Embeddable and Non-Embeddable Group Actions on Surfaces (V. Peterson, A. Wootton).- Tile Invariants for Tackling Tiling Questions (M.P. Hitchman).- Forbidden Minors: Finding the Finite Few (T.W. Mattman).- Introduction to competitive graph coloring (C. Dunn, V. Larsen, J.F. Nordstrom).- Matrioids (E. McNicholas, N.A. Neudauer, C. Starr).- Finite Frame Theory (S. Datta, J. Oldroyd).- Mathematical decision-making with linear and convex programming (J. Kotas).- Computing weight multiplicities (P. E. Harris).- Vaccination strategies for small worlds. (W. Just, H. C. Highlander).- Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations (R. C. Harwood).","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743101366615,"sku":"9783319660646","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"pseudocompact-topological-spaces-a-survey-of-classic-and-new-results-with-open-problems-9783319916798","title":"Pseudocompact Topological Spaces: A Survey of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. Basic and Classic Results on Pseudocompact Spaces.- 2. Pseudocompact Topological Groups.- 3. Pseudocompactness and Ultrafilters.- 4. Bounded Subsets of Tychonoff Spaces: A Survey of Results and Problems.- 5. Weakly Pseudocompact Spaces.- 6. Maximal Pseudocompact Spaces.- 7. Pseudocompactness in the Realm of Topological Transformation Groups.- 8. Topology of Mrówka-Isbell Spaces.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743109296471,"sku":"9783319916798","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"poisson-structures-9783642310898","title":"Poisson Structures","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePoisson structures appear in a large variety of contexts, ranging from string theory, classical\/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.​\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e\u003cp\u003e“Each chapter contains a series of exercises as well as a number of notes aimed at giving further hints as to how the various items in the book are interrelated and, furthermore, at placing the material in the literature. … The book is a timely and courageous attempt to make accessible a flourishing research area to a wider audience in the form of a research monograph\/textbook and as such it is very welcome.” (Johannes Huebschmann, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 116, 2014)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e“This book is an excellent presentation of Poisson geometry, its applications and related topics. … This book is suitable for those who have a solid foundation of differential geometry and Lie algebras. The reader will understand why Poisson geometry is such an interesting and important subject.” (Zhuo Chen, zbMATH, Vol. 1284, 2014)\u003c\/p\u003e\u003cp\u003e“This book provides a comprehensive introduction to Poisson structures. … Exercises are given at the end of each chapter … to help readers understand the basic theory. … This is a nice introductory book for both entry level graduate students and advanced researchers who are interested in the subject.” (Xiang Tang, Mathematical Reviews, August, 2013)\u003c\/p\u003e\u003cp\u003e“The book under review deals with very exciting (and current) material presented from a fascinating vantage point and should be welcomed by any scholar whose work touches upon the matters … . its thirteen chapters are peppered with sets of exercises and each chapter comes equipped with supplemental notes that go a bit beyond the text, introduce some historical material, and point to other relevant sources.” (Michael Berg, MAA Reviews, November, 2012)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e​\u003cp\u003ePart I Theoretical Background:1.Poisson Structures: Basic Definitions.- 2.Poisson Structures: Basic Constructions.- 3.Multi-Derivations and Kähler Forms.- 4.Poisson (Co)Homology.- 5.Reduction.- Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds.- 7.Linear Poisson Structures and Lie Algebras.- 8.Higher Degree Poisson Structures.- 9.Poisson Structures in Dimensions Two and Three.- 10.\u003ci\u003eR\u003c\/i\u003e-Brackets and \u003ci\u003er\u003c\/i\u003e-Brackets.- 11.Poisson–Lie Groups.- Part III Applications:12.Liouville Integrable Systems.- 13.Deformation Quantization.- A Multilinear Algebra.- B Real and Complex Differential Geometry.- References.- Index.- List of Notations.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743135019351,"sku":"9783642310898","price":109.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783642310898.jpg?v=1791482051"},{"product_id":"basic-algebraic-topology-and-its-applications-9788132228417","title":"Basic Algebraic Topology and its Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike.\u003cbr\u003eFocusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“Adhikari’s work is an excellent resource for any individual seeking to learn more about algebraic topology. By no means will this text feel like an introduction to algebraic topology, but it does offer much for both beginners and experts. … the text will be a valuable reference on the bookshelf of any reader with an interest in algebraic topology. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (A. Misseldine, Choice, Vol. 54 (9), May, 2017)\u003c\/p\u003e\u003cp\u003e“I am pretty enthusiastic about this book. … it shows very good taste on the author’s part as far as what he’s chosen to do and how he’s chosen to do it. … Wow! What a nice book. I’m glad I have a copy.” (Michael Berg, MAA Reviews, maa.org, February, 2017)\u003c\/p\u003e“This is a comprehensive textbook on algebraic topology. … accessible to students of all levels of mathematics, so suitable for anyone wanting and needing to learn about algebraic topology. It can also offer a valuable resource for advanced students with a specialized knowledge in other areas who want to pursue their interest in this area. … further readings are provided at the end of each of them, which also enables students to study the subject discussed therein in more depth.” (Haruo Minami, zbMATH 1354.55001, 2017)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePrerequisite Concepts and Notations.- Basic Homotopy.- The Fundamental Groups.-Covering Spaces.- Fibre Bundles, Vector Bundles and K-theory.- Geometry of Simplicial Complexes and Fundamental Groups.- Higher Homotopy Groups.- Products in Higher Homotopy Groups.- CW-complexes and Homotopy.- Eilenberg-MacLane Spaces.- Homology and Cohomology Theories.- Eilenberg-Steenrod Axioms for Homology and Cohomology Theories.- Consequences of the Eilenberg-Steenrod Axioms.- Some Applications of Homology Theory.- Spectral Homology and Cohomology Theories.- Obstruction Theory.- More Relations Between Homotopy and Homology Groups.- A Brief Historical Note.\u003c\/p\u003e","brand":"Springer, India, Private Ltd","offers":[{"title":"Default Title","offer_id":48743198622039,"sku":"9788132228417","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788132228417.jpg?v=1720064544"},{"product_id":"infinite-group-theory-from-the-past-to-the-future-9789813204041","title":"Infinite Group Theory: From The Past To The","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743296860503,"sku":"9789813204041","price":72.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789813204041.jpg?v=1720064976"},{"product_id":"contemporary-abstract-algebra-9780367651787","title":"Contemporary Abstract Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eContemporary Abstract Algebra, Tenth Edition\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eFor more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.\u003c\/p\u003e\u003cp\u003eThe author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop but rarely do. Applications are included to illustrate the utility of the abstract concepts.\u003c\/p\u003e\u003cp\u003eExamples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\"It has now been 35 years since Gallian's classic textbook Contemporary Abstract Algebra was first published. The book is deservedly popular with instructors of abstract algebra courses. It is written at an appropriate level for junior and senior undergraduates, has lucid coverage of all of the standard topics and several nonstandard ones (Frieze Groups and Crystallographic Groups, Coding Theory, Greek Geometric Construction Problems, etc), is example-driven, and contains thousands of exercises at various levels of difficulty. Moreover, every chapter begins with an interesting quote or two (by as diverse a group of people as Einstein, Miguel de Cervantes, Ralph Waldo Emerson, Bob Dylan, etc) and most conclude with a mini- biography of a mathematician whose work relates to the chapter's content. This is an interesting book that is a pleasure to read.\u003cbr\u003e \u003cbr\u003eAccording to the Preface, changes made for the tenth edition include:\u003cbr\u003e \u003cbr\u003e1. Approximately 200 new exercises\u003cbr\u003e2. Many new examples\u003cbr\u003e3. New quotes\u003cbr\u003e4. A freshening of the discussion portions\"\u003c\/p\u003e\u003cp\u003e- \u003cstrong\u003eBenjamin Linowitz\u003c\/strong\u003e, Oberlin College, Published in MAA\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1 Introduction to Groups\u003cbr\u003e 2 Groups\u003cbr\u003e 3 Finite Groups; Subgroups\u003cbr\u003e 4 Cyclic Groups\u003cbr\u003e 5 Permutation Groups\u003cbr\u003e 6 Ismorphisms\u003cbr\u003e 7 Cosets and Lagrange's Theorem\u003cbr\u003e 8 External Direct Products\u003cbr\u003e 9 Normal Subgroups and Factor Groups\u003cbr\u003e 10 Group Homomorphisms\u003cbr\u003e 11 Fundamental Theorem of Finite Abelian Groups\u003cbr\u003e 12 Introduction to Rings\u003cbr\u003e 13 Integral Domains\u003cbr\u003e 14 Ideals and Factor Rings\u003cbr\u003e 15 Ring Homomorphisms\u003cbr\u003e 16 Polynomial Rings\u003cbr\u003e 17 Factorization of Polynomials\u003cbr\u003e 18 Divisibilty in Integral Domains\u003cbr\u003e 19 Extension Fields\u003cbr\u003e 20 Algebraic Extensions\u003cbr\u003e 21 Finite Fields\u003cbr\u003e 22 Geometric Constructions\u003cbr\u003e 23 Sylow Theorems\u003cbr\u003e 24 Finite Simple Groups\u003cbr\u003e 25 Generators and Relations\u003cbr\u003e 26 Symmetry Groups\u003cbr\u003e 27 Symmetry and Counting\u003cbr\u003e 28 Cayley Digraphs of Groups\u003cbr\u003e 29 Introduction to Algebraic Coding Theory\u003cbr\u003e 30 An Introduction to Galois Theory\u003cbr\u003e 31 Cyclotomic Extensions\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":48864513851735,"sku":"9780367651787","price":84.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780367651787.jpg?v=1722272274"},{"product_id":"fourier-analysis-on-groups-9780486813653","title":"Fourier Analysis on Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSelf-contained treatment by a master mathematical expositor ranges from introductory chapters on basic theorems of Fourier analysis and structure of locally compact Abelian groups to extensive appendixes on topology, topological groups, more. 1962 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864743653719,"sku":"9780486813653","price":13.04,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486813653.jpg?v=1722273041"},{"product_id":"mathematical-aspects-of-quantum-field-theory-9780521115773","title":"Mathematical Aspects of Quantum Field Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOver the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. This graduate-level introduction presents the basic ideas and tools of quantum field theory to a mathematical audience.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'… a brief, but careful, reasonably balanced, and representative introduction for mathematicians to QFT as it is used in physics.' The Mathematical Intelligencer\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeword Dennis Sullivan; Preface; 1. Classical mechanics; 2. Quantum mechanics; 3. Relativity, the Lorentz group and Dirac's equation; 4. Fiber bundles, connections and representations; 5. Classical field theory; 6. Quantization of classical fields; 7. Perturbative quantum field theory; 8. Renormalization; 9. The standard model; Appendix A. Hilbert spaces and operators; Appendix B. C* algebras and spectral theory; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48864935772503,"sku":"9780521115773","price":62.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780521115773.jpg?v=1791463076"},{"product_id":"group-theory-in-a-nutshell-for-physicists-9780691162690","title":"Group Theory in a Nutshell for Physicists","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eAlthough group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-co\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eHonorable Mention for the 2017 PROSE Award in Textbook\/Best in Physical Sciences and Mathematics, Association of American Publishers \"Another excellent entry in the 'Nutshell' series, Zee's latest has it all: broad scope, depth, thorough explanations, history, and an appealing sense of humor. The author's knowledge of mathematics and physics is encyclopedic, and he leavens the text generously with episodes and asides drawn from the life and work of the major figures in the development of group theory and its applications in physics.\"--Choice \"In Group Theory in a Nutshell for Physicists, Anthony Zee ... combines clarity of presentation with mathematical detail at a level of rigor acceptable to physicists. The result is a tour de force that guides readers through the universe of group theory and leads them to recent particle physics, cosmology, and condensed matter. The book is unique in its laid-back presentation.\"--Physics Today \"This book lives up to my high expectations and can stand shoulder to shoulder with Zee's other two Nutshell books.\"--Johannes Koelman, Science 2.0","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865530773847,"sku":"9780691162690","price":78.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691162690.jpg?v=1722274416"},{"product_id":"group-theoretical-foundations-of-quantum-mechanics-9781560722489","title":"Group Theoretical Foundations of Quantum","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eGroup Theoretical Foundations of Quantum Mechanics","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886317678935,"sku":"9781560722489","price":83.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781560722489.jpg?v=1722539598"},{"product_id":"new-topics-in-theoretical-physics-9781600213557","title":"New Topics in Theoretical Physics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAlthough the various branches of physics differ in their experimental methods and theoretical approaches, certain general principles apply to all of them. 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According to quantum theory, electromagnetic radiation does not always consist of continuous waves; instead it must be viewed under some circumstances as a collection of particle-like photons, the energy and momentum of each being directly proportional to its frequency (or inversely proportional to its wavelength, the photons still possessing some wavelike characteristics). This book presents state-of-the-art research from around the world.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886593126743,"sku":"9781600213557","price":187.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781600213557.jpg?v=1722540773"},{"product_id":"group-theory-classes-representation-connections-applications-9781608761753","title":"Group Theory: Classes, Representation \u0026","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eGroup theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced tremendous advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, can be modelled by symmetry groups. Thus group theory and the closely related representation theory have many applications in physics and chemistry. This new and important book gathers the latest research from around the globe in the study of group theory and highlights such topics as: application of symmetry analysis to the description of ordered structures in crystals, a survey of Lie Group analysis, graph groupoids and representations, and others.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886761029975,"sku":"9781608761753","price":198.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781608761753.jpg?v=1722541440"},{"product_id":"representations-of-finite-and-lie-groups-9781860944826","title":"Representations Of Finite And Lie Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides an introduction to representations of both finite and compact groups. The proofs of the basic results are given for the finite case, but are so phrased as to hold without change for compact topological groups with an invariant integral replacing the sum over the group elements as an averaging tool. Among the topics covered are the relation between representations and characters, the construction of irreducible representations, induced representations and Frobenius reciprocity. Special emphasis is given to exterior powers, with the symmetric group Sn as an illustrative example. The book concludes with a chapter comparing the representations of the finite group SL2(p) and the non-compact Lie group SL2(P).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The author took care to always keep close to his main topic, which is the representations, and to give the reader an impression of a variety of results without loading the book with extensive theory ... The booklet can be recommended as a short introduction to what representation theory is about.\"Mathematical Reviews\"This is a straight, very readable introduction to representation theory of finite groups in characteristic 0 case ... this nice booklet can be recommended warmly to anyone who wants to become familiar quickly with group representations.\"Monatshefte fur Mathematik\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBasic Representation Theory-I; Induced Representations and Their Characters; Multilinear Algebra and  U-rings; Representations of Compact Groups; Lie Groups and Algebras; SL2(p) and SL2( A).","brand":"Imperial College Press","offers":[{"title":"Default Title","offer_id":48888193909079,"sku":"9781860944826","price":65.55,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781860944826.jpg?v=1791479097"},{"product_id":"geometry-dynamics-and-foliations-2013-in-honor-of-steven-hurder-and-takashi-tsuboi-on-the-occasion-of-their-60th-birthdays-9784864970402","title":"Geometry, Dynamics, And Foliations 2013: In Honor","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume is an outcome of the conference 'Geometry and Foliations 2013' held in Tokyo in September 2013 and associated meetings, aimed for providing a good overview of the present studies as well as some perspective for further studies.The aspects and quality of the volume is represented by B Deroin's survey on Brownian motions on foliated complex surfaces which contains many essential results and ideas.Other articles cover wide topics of foliations and groups of diffeomorphisms old and new; some discuss characteristic classes such as Godbillon-Vey class or homotopy theory of foliations while others deal with topological and differential geometrical aspects, particularly in the holomorphic setting.Also, several articles shows relationship to the geometric group theory.Highly recommended to researchers and graduate students who are interested in and going to study the theories of foliations and related topics such as diffeomorphism groups, geometric group theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889418809687,"sku":"9784864970402","price":80.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784864970402.jpg?v=1791482571"},{"product_id":"group-theory-an-intuitive-approach-9789810233655","title":"Group Theory: An Intuitive Approach","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe physical principles of group theory; examples of groups; groups as mathematical objects; groups, combinations, subsets; the group as a representation of itself; properties of representations; the symmetric group and its representations; applications of symmetric group representations; the rotation groups and their relatives; representations of groups SO(3) and SU(2); applications of representations of SO(3) and O(3); Lie algebras; representations of Lie algebras; groups of crystals and molecules.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48890168803671,"sku":"9789810233655","price":38.95,"currency_code":"GBP","in_stock":false}]},{"product_id":"a-gentle-introduction-to-group-theory-9789819901494","title":"A Gentle Introduction to Group Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBackground Results in Set Theory.- Algebraic Operations on Integers.- The Integers Modulo.- Semigroups.- Groups.- The Symmetric Group.- Subgroups.- Groups Homomorphisms and Isomorphic Groups.- Classification of Finite Abelian Groups.- Group Theory and SageMath.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48890227753303,"sku":"9789819901494","price":40.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819901494.jpg?v=1791484547"},{"product_id":"creating-high-performance-teams-9780415538411","title":"Creating High Performance Teams","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cem\u003eCreating High Performance Teams\u003c\/em\u003e is an accessible and thorough new introduction to this key area of business education. Written by teams experts Ray Aldag and Loren Kuzuhara, this book provides students with both a firm grounding in the key concepts of the field and the practical tools to become successful team managers and members. Built on a solid foundation of the most up to date research and theory, chapters are packed with case studies, real-world examples, tasks and discussion questions, while a companion website supports the book with a wealth of useful resources for students, team members, and instructors.\u003c\/p\u003e\u003cp\u003eCentered around an original model for high performance teams, topics covered include:\u003c\/p\u003e\u003cul\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eBuilding and developing effective teams\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eManaging diversity\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eEffective communication\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eTeam processes â meetings, performance management\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eDealing with change and team problems\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eCurrent issues â virtual teams, globalization\u003c\/li\u003e \u003c\/ul\u003e\u003cp\u003eWith its combined emphasis on principles and application, interwoven with the tools, topics, and teams most relevant today, \u003ci\u003eCreating High Performance Teams\u003c\/i\u003e is perfectly placed to equip upper-level undergraduate and MBA students with the knowledge and skills necessary to take on teams in any situation.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e‘Aldag and Kuzuhara have written the book I've been wanting: beyond its thorough coverage of the latest teams-related literature, it provides skill-building exercises, and plenty of examples from work organizations; it is engaging to read and filled with practical wisdom. Students and managers of teams will love it.’\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eMarianne J. Koch,\u003c\/strong\u003e Associate Dean and Professor of Management, Golden Gate University, USA\u003c\/p\u003e\u003cp\u003e‘Aldag and Kuzuhara have created an exceptional framework for understanding and building high performance teams. Each chapter builds incrementally to facilitate student insight and adaptive behaviour within teams. The footnotes\/references and callouts for cases are a great resource for further analysis by the learners. To me the chapter on Socializing, Building Trust, Training, Motivating, and Leading Teams provided significant wisdom into the challenges of sharing, communication, and authentic trust amongst members of a team. Too often integrating these concepts into a textbook falls flat; but not with this text.’\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eMichael J.D. Sutton,\u003c\/strong\u003e Associate Professor, Bill and Vieve Gore School of Business, Westminster College, USA\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. Teams: Opportunities and Challenges 2. Designing the Team System 3. Building and Developing the Team 4. Socializing, Building Trust, Training Motivating, and Leading Teams 5. Managing Team Diversity 6. Fostering Effective Communication in Teams 7. Facilitating Team Processes 8. Managing Change in Teams 9. Dealing with Team Problems 10. Evaluating Team Effectiveness 11. The New Teams: Virtual, Global, Connected, and Self-Managing 12. Designing and Implementing Team-Based Organizations 13. Teams Summary and Integration\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":49083498987863,"sku":"9780415538411","price":80.74,"currency_code":"GBP","in_stock":false}]},{"product_id":"continuous-symmetry-from-euclid-to-klein-from-euclid-to-klein-9780821839003","title":"Continuous Symmetry from Euclid to Klein  from","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe fundamental idea of geometry is that of symmetry. With that principle as the starting point, this book presents a study of Euclidean geometry. It focuses on transformations of the plane. It contains hundreds of exercises. It is suitable for a one-semester undergraduate course on geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFoundations of geometry in the plane Isometries in the plane: Products of reflections Isometries in the plane: Classification and structure Similarities in the plane Conjugacy and geometric equivalence Applications to plane geometry Symmetric figures in the plane Frieze and wallpaper groups Area, volume, and scaling References Index.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":49083683307863,"sku":"9780821839003","price":67.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780821839003.jpg?v=1725549708"},{"product_id":"symmetry-broken-symmetry-and-topology-in-modern-physics-9781316518618","title":"Symmetry Broken Symmetry and Topology in Modern","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWritten for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'The whole of theoretical physics, and our general picture of the world, are based on symmetries. This book is devoted to symmetries and their manifestations in nature, and it allows students to develop a theoretical and experimental understanding of the fundamental properties of the Universe. This path is carefully paved by the authors.' Professor Vladimir Zelevinsky, Michigan State University\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Part I. Symmetry Groups and Algebras: 1. Introduction; 2. Some properties of groups; 3. Introduction to lie groups; 4. Permutation groups; 5. Electrons on periodic lattices; 6. The rotation group; 7. Classification of lie algebras; 8. Unitary and special unitary groups; 9. SU(3) flavor symmetry; 10. Harmonic oscillators and SU(3); 11. SU(3) matrix elements; 12. Introduction to non-compact groups; 13. The Lorentz group; 14. Lorentz covariant fields; 15. Poincaré invariance; 16. Gauge invariance; Part II. Broken Symmetry: 17. Spontaneous symmetry breaking; 18. The Higgs mechanism; 19. The standard model; 20. Dynamical symmetry; 21. Generalized coherent states; 22. Restoring symmetry by projection; 23. Quantum phase transitions; Part III. Topology and Geometry: 24. Topology, manifolds, and metrics; 25. Topological solitons; 26. Geometry and gauge theories; 27. Geometrical phases; 28. Topology of the quantum Hall effect; 29. Topological matter; Part IV. A Variety of Physical Applications: 30. Angular momentum recoupling; 31. Nuclear fermion dynamical symmetry; 32. Superconductivity and superfluidity; 33. Current algebra; 34. Grand unified theories; Appendix A. Second quantization; Appendix B. Natural units; Appendix C. Angular momentum tables; Appendix D. Lie algebras; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49083862384983,"sku":"9781316518618","price":62.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781316518618.jpg?v=1725550250"},{"product_id":"from-rings-and-modules-to-hopf-algebras-one-flew-over-the-algebraists-nest-9783031500619","title":"From Rings and Modules to Hopf Algebras: One Flew","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups.\u003cbr\u003eThroughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory — whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld–Lusztig double of a group algebra, appearing for the first time in a textbook at this level.\u003cbr\u003eBased on over twenty years of teaching various aspects of algebra, mainly at the École Normale Supérieure (Paris) and at Peking University, the book reflects the audiences of the author's courses. In particular, foundations of abstract algebra, like linear algebra and elementary group theory, are assumed of the reader. Each of the of four parts can be used for a course — with a little \u003ci\u003ead hoc\u003c\/i\u003e complement on the language of categories. Thanks to its rich choice of topics, the book can also serve students as a reference throughout their studies, from undergraduate to advanced graduate level.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Prerequisites and Preliminaries.- Part I Rings and Modules.- 2 Rings, Polynomials, Divisibility.- 3 Polynomial Rings in Several Indeterminates.- 4 More on Modules.- 5 On Representations of Finite Groups.- Part II Integral Domains, Polynomials, Fields.- 6 Prime and Maximal Ideals, Integral Domains.- 7 Fields, Division Rings.- Part III Finitely Generated Modules.- 8 Integrality, Noetherianity.- 9 Finitely Generated Projective Modules.- 10 Finitely Generated Modules Over Dedekind Domains.- 11 Complement on Dedekind Domains.- Part IV Characteristic Zero Linear Representations of Finite Groups.- 12 Monoidal Categories: An Introduction.- 13 Characteristic 0 Representations.- 14 Playing With the Base Field.- 15 Induction and Restriction: Some Applications to Finite Groups.- 16 Brauer’s Theorem and Some Applications.- 17 Graded Representations and Characters.- 18 The Drinfeld–Lusztig Double of a Group Algebra.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084759048535,"sku":"9783031500619","price":71.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"interpersonal-communication-9780815386971","title":"Interpersonal Communication","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis fully revised text demystifies interpersonal communication skills by bringing the latest research together with practical guidance that prepares students to discern key communication dynamics and communicate more effectively in all areas of their lives.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe new edition draws on current theory and research to guide students through the foundations of the discipline, recent developments in scientific research, and tips for improving their own interpersonal communication skills. In addition, readers will find:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cul\u003e\u003cul\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cli\u003eExpanded coverage of technology and computer-mediated communication, including explicit examples of what interpersonal communication looks like online. \u003c\/li\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cli\u003eInvitations to engage with elaborated descriptions of theories and related resources on the companion website whenever prominent theories of interpersonal communication are mentioned in the text. \u003c\/li\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cli\u003eA commitment to gender inclusive language a\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"As might be expected from two of the field’s leading scholars, Solomon and Theiss have produced a first-rate survey of research and theory in interpersonal communication. Their treatment is comprehensive, current, and goes beyond exposition of foundational concepts by challenging students to consider the practical, ethical, and skill-development implications of the material covered in each chapter.\"\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eJohn O. Greene\u003c\/b\u003e, \u003ci\u003ePurdue University, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cp\u003eIn \u003ci\u003eInterpersonal Communication: Putting Theory into Practice (2nd ed.), \u003c\/i\u003eSolomon and Theiss provide a well-balanced and theory-oriented approach to highlighting the multiple dimensions of interpersonal communication influences, processes, and outcomes in a variety of socially relevant and timely contexts. Presented in an easy-to-read logical format with a multitude of examples pertinent to undergraduate students, Solomon and Theiss’s thorough coverage of theory and research is accessible and will be enjoyable to anyone interested in better understanding the multi-faceted nature of communication.\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eJennifer A. Samp\u003c\/b\u003e, \u003ci\u003eUniversity of Georgia, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cp\u003e“This book provides a solid foundation to teach interpersonal communication skills that facilitate solutions to complex human problems. The authors find a great balance between density and presentation of core concepts. The book provides well-presented content for students to understand core concepts and significant issues, and to reflect on their own communication practices, experiences, and possibilities for making a difference through skillful interpersonal communication.”\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eAshley P. Duggan\u003c\/b\u003e, \u003ci\u003eBoston College, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cp\u003e\"Solomon and Theiss have done a terrific job translating complex theories and social science into practical language without sacrificing intellectual depth. The textbook reflects the latest social scientific knowledge about interpersonal communication and is chock-full of important real-life applications that encourage students to think about interpersonal communication. Solomon and Theiss speak directly to students with engaging examples and provocative questions. Every chapter contains crucial exercises for students to hone their social competencies and to reflect on their strengths.\"\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eSusanne M. Jones\u003c\/b\u003e, \u003ci\u003eUniversity of Minnesota, USA and Associate Editor of \u003c\/i\u003eMindfulness\u003c\/p\u003e\n\u003cp\u003e\"Solomon and Theiss thoughtfully translate interpersonal communication research and theory into everyday life and examples. My students are left enchanted by the ways the text intersects with their own relationships and experiences, enabling them to be deliberate and thoughtful in their encounters and equipping them with relational skills that enrich their own lives and careers.\"\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eKeli Fazio\u003c\/b\u003e, \u003ci\u003eThe College of New Jersey, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cbr\u003e\u003cp\u003e\"As might be expected from two of the field’s leading scholars, Solomon and Theiss have produced a first-rate survey of research and theory in interpersonal communication. Their treatment is comprehensive, current, and goes beyond exposition of foundational concepts by challenging students to consider the practical, ethical, and skill-development implications of the material covered in each chapter.\"\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eJohn O. Greene\u003c\/b\u003e, \u003ci\u003ePurdue University, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cp\u003eIn \u003ci\u003eInterpersonal Communication: Putting Theory into Practice (2nd ed.), \u003c\/i\u003eSolomon and Theiss provide a well-balanced and theory-oriented approach to highlighting the multiple dimensions of interpersonal communication influences, processes, and outcomes in a variety of socially relevant and timely contexts. Presented in an easy-to-read logical format with a multitude of examples pertinent to undergraduate students, Solomon and Theiss’s thorough coverage of theory and research is accessible and will be enjoyable to anyone interested in better understanding the multi-faceted nature of communication.\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eJennifer A. Samp\u003c\/b\u003e, \u003ci\u003eUniversity of Georgia, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cp\u003e“This book provides a solid foundation to teach interpersonal communication skills that facilitate solutions to complex human problems. The authors find a great balance between density and presentation of core concepts. The book provides well-presented content for students to understand core concepts and significant issues, and to reflect on their own communication practices, experiences, and possibilities for making a difference through skillful interpersonal communication.”\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eAshley P. Duggan\u003c\/b\u003e, \u003ci\u003eBoston College, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cp\u003e\"Solomon and Theiss have done a terrific job translating complex theories and social science into practical language without sacrificing intellectual depth. The textbook reflects the latest social scientific knowledge about interpersonal communication and is chock-full of important real-life applications that encourage students to think about interpersonal communication. Solomon and Theiss speak directly to students with engaging examples and provocative questions. Every chapter contains crucial exercises for students to hone their social competencies and to reflect on their strengths.\"\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eSusanne M. Jones\u003c\/b\u003e, \u003ci\u003eUniversity of Minnesota, USA and Associate Editor of \u003c\/i\u003eMindfulness\u003c\/p\u003e\n\u003cp\u003e\"Solomon and Theiss thoughtfully translate interpersonal communication research and theory into everyday life and examples. My students are left enchanted by the ways the text intersects with their own relationships and experiences, enabling them to be deliberate and thoughtful in their encounters and equipping them with relational skills that enrich their own lives and careers.\"\u003c\/p\u003e\n\u003cp\u003e\u003cb\u003eKeli Fazio\u003c\/b\u003e, \u003ci\u003eThe College of New Jersey, USA\u003c\/i\u003e\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. What Is Interpersonal Communication? \u003cb\u003ePart 1: Foundations \u003c\/b\u003e2. Culture and Interpersonal Communication 3. Identity and Interpersonal Communication 4. Perception and Interpersonal Communication \u003cb\u003ePart 2: Interpersonal Interaction \u003c\/b\u003e5. Language and Interpersonal Communication 6. Nonverbal Communication 7. Emotions and Communication 8. Listening and Responding \u003cb\u003ePart 3: Interpersonal Relating \u003c\/b\u003e9. Developing and Ending Relationships 10. Intimacy and Interpersonal Communication 11. Communication in Families \u003cb\u003ePart 4: Strategic Interpersonal Communication \u003c\/b\u003e12. Interpersonal Influence 13. Interpersonal Conflict 14. Communicating Comfort and Support \u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/ul\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49371772813655,"sku":"9780815386971","price":71.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780815386971.jpg?v=1730154496"},{"product_id":"lie-groups-lie-algebras-and-representations-an-elementary-introduction-9783319134666","title":"Lie Groups, Lie Algebras, and Representations: An","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.\u003c\/p\u003e\u003cp\u003eIn addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ea treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras\u003c\/li\u003e\n\u003cli\u003emotivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;\u003cb\u003eC\u003c\/b\u003e)\u003c\/li\u003e\n\u003cli\u003ean unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras\u003c\/li\u003e\n\u003cli\u003ea self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe second edition of \u003ci\u003eLie Groups, Lie Algebras, and Representations\u003c\/i\u003e contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eReview of the first edition\u003c\/b\u003e:\u003c\/p\u003e\u003cp\u003e\u003ci\u003eThis is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e— The Mathematical Gazette\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The first edition of this book was very good; the second is even better, and more versatile. This text remains one of the most attractive sources available from which to learn elementary Lie group theory, and is highly recommended.” (Mark Hunacek, The Mathematical Gazette, Vol. 101 (551), July, 2017)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I: General Theory.-Matrix Lie Groups.- The Matrix Exponential.- Lie Algebras.- Basic Representation Theory.- The Baker–Campbell–Hausdorff Formula and its Consequences.- Part II: Semisimple Lie Algebras.- The Representations of sl(3;C).-Semisimple Lie Algebras.- Root Systems.- Representations of Semisimple Lie Algebras.- Further Properties of the Representations.- Part III: Compact lie Groups.- Compact Lie Groups and Maximal Tori.- The Compact Group Approach to Representation Theory.- Fundamental Groups of Compact Lie Groups.- Appendices.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49372698837335,"sku":"9783319134666","price":48.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319134666.jpg?v=1730163857"},{"product_id":"visual-group-theory-9783662693643","title":"Visual Group Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49372704211287,"sku":"9783662693643","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783662693643.jpg?v=1791482270"},{"product_id":"topics-in-geometric-group-theory-9780226317212","title":"Topics in Geometric Group Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis work seeks to offer a concise introduction to geometric group theory - a method for studying infinite groups via their intrinsic geometry. Basic combinatorial and geometric group theory is presented, along with research on the growth of groups, and exercises and problems.","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":49399993008471,"sku":"9780226317212","price":36.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226317212.jpg?v=1730469377"}],"url":"https:\/\/bookcurl.com\/collections\/groups-and-group-theory.oembed?page=11","provider":"Book Curl","version":"1.0","type":"link"}