{"title":"Algebra Books","description":"","products":[{"product_id":"the-cartoon-guide-to-algebra-9780062202697","title":"The Cartoon Guide to Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"HarperCollins Publishers Inc","offers":[{"title":"Default Title","offer_id":48732103410007,"sku":"9780062202697","price":13.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"algebra-9780198732822","title":"Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis Very Short Introduction invites readers to revisit algebra and appreciate the elegance and power of equations and inequalities. Offering a clear explanation of algebra through theory and example, Higgins shows how equations lead to complex numbers, matrices, groups, rings, and fields.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Numbers and algebra ; 2. The laws of algebra ; 3. Linear equations and inequalities ; 4. Quadratic equations ; 5. The algebra of polynomials ; 6. Introduction to matrices ; 7. Matrices and groups ; 8. Determinants and matrices ; 9. Algebra and the arithmetic of remainders ; 10. Vector spaces ; Further Reading ; Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732773155159,"sku":"9780198732822","price":8.54,"currency_code":"GBP","in_stock":true}]},{"product_id":"the-oxford-linear-algebra-for-scientists-9780198844921","title":"The Oxford Linear Algebra for Scientists","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook provides a modern introduction to linear algebra, a mathematical discipline every first year undergraduate student in physics and engineering must learn. A rigorous introduction into the mathematics is combined with many examples, solved problems, and exercises as well as scientific applications of linear algebra. These include applications to contemporary topics such as internet search, artificial intelligence, neural networks, and quantum computing, as well as a number of more advanced topics, such as Jordan normal form, singular value decomposition, and tensors, which will make it a useful reference for a more experienced practitioner. Structured into 27 chapters, it is designed as a basis for a lecture course and combines a rigorous mathematical development of the subject with a range of concisely presented scientific applications. The main text contains many examples and solved problems to help the reader develop a working knowledge of the subject and every chapter comes with exercises.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe authors are uniquely well qualified to produce a textbook suitable for first-year university students. * David Matravers, University of Portsmouth *\u003cbr\u003eLinear Algebra is a core undergraduate course not only in Mathematics but also in Physics, Chemistry, Biology and Computer Science. This textbook brilliantly succeeds in catering to such a wide audience by covering a broad range of formal developments along with concrete applications and is unique in its presentation of the topic. * Richard Joseph Szabo, Heriot-Watt University *\u003cbr\u003eLukas has written an impressive mathematical textbook that covers standard introductory linear algebra topics along with advanced concepts that will appeal to many readers. * Choice *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Linearity - an informal introduction 2: Sets and functions 3: Groups 4: Fields 5: Coordinate vectors 6: Vector spaces 7: Elementary vector space properties 8: Vector subspaces 9: The dot product 10: Vector and triple product 11: Lines and planes 12: Introduction to linear maps 13: Matrices 14: The structure of linear maps 15: Linear maps in terms of matrices 16: Computing with matrices 17: Linear systems 18: Determinants 19: Basics of eigenvalues 20: Diagonalising linear maps 21: The Jordan normal form 22: Scalar products 23: Adjoint and unitary maps 24: Diagonalisation - again 25: Bi-linear and sesqui-linear forms 26: The dual vector space 27: Tensors","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732809199959,"sku":"9780198844921","price":28.02,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198844921.jpg?v=1719998490"},{"product_id":"quicker-calculations-9780198852650","title":"Quicker Calculations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHow fast can you calculate? Would you like to be faster? This book presents the time honored  tricks and tips of calculation, from a fresh perspective,  to boost the speed at which you can add  whether a couple of numbers, or columns so long an accountant may faint. Find out how to subtract, multiply, divide, and find square roots more quickly.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eIf you think mental arithmetic is out of date in the 21st century, think again. This engaging book is about insight and interestingness beyond the simple utility of quicker calculations. The general style is original and characterful, and makes the book distinctive. * Prasenjit Saha, University of Zurich *\u003cbr\u003eThis book is about very elementary concepts that ought to be read by sophisticated people who appreciate that elementary does not mean trivial. The author's erudite scholarship shines in the prose, along with just the right level of dry wit. It's serious stuff he's writing about (without numbers and arithmetic, our modern world simply vanishes into the ancient past where numbers were limited to none, one, and many), but in such a way that the reader does not slowly nod-off into a coma. * Paul J. Nahin, University of New Hampshire *\u003cbr\u003eLipscombe's book is unusual, being, as it is, an expansive view of a small subject. The text he presents here is excellent, and is a model of everything a writer strives for: concision, simplicity, directness, accuracy, and surprise. * Don S. Lemons, Bethel College, Kansas *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface Introduction Challenge 1: Arithmetical Advice 2: Speedier Sums and Subtractions Interlude I: The Magic of 111,111 3: Accounting for Taste -- Adding Columns Quickly Interlude II: Checking, Check Digits, and Casting out Nines 4: Quicker Quotients and Pleasing Products -- Multiply and Divide by Specific Numbers Interlude III: Doomsday 5: Calculations with Constraints -- Multiply and Divide by Numbers with Specific Properties Interlude IV: Multicultural Multiplication 6: Super Powers -- Calculate Squares, Square Roots, Cube Roots, and More 7: Close-Enough Calculations -- Quick and Accurate Approximations Interlude V: Approximating the Number of Space Aliens 8: Multiplying Irrationally The Grand Finale Further Reading Appendix I: Calculating Doomsday Appendix II: The Squares from 1 to 100","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732813853015,"sku":"9780198852650","price":20.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198852650.jpg?v=1719998510"},{"product_id":"an-introduction-to-the-theory-of-numbers-9780199219865","title":"An Introduction to the Theory of Numbers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D.R. Heath-Brown this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today''s students through the key milestones and developments in number theory. Updates include a chapter by J.H. Silverman on one of the most important developments in number theory -- modular elliptic curves and their role in the proof of Fermat''s Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid readerThe text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eReview from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable. * Nature *\u003cbr\u003eThis fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory. * Mathematical Gazette *\u003cbr\u003e...an important reference work... which is certain to continue its long and successful life... * Mathematical Reviews *\u003cbr\u003e...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own. * Matyc Journal *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePREFACE TO THE SIXTH EDITION; PREFACE TO THE FIFTH EDITION; APPENDIX; LIST OF BOOKS; INDEX OF SPECIAL SYMBOLS AND WORDS; INDEX OF NAMES; GENERAL INDEX","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732836069719,"sku":"9780199219865","price":53.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199219865.jpg?v=1719998605"},{"product_id":"linear-algebra-9780199654444","title":"Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eLinear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader''s confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading p\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThis book gives an introduction to linear algebra for students with limited mathematical preparation. ... The steady pace of the book is so gentle that no student need be left behind. * Peter Macgregor, Mathematical Gazette *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Linear Equations and Matrices ; 2. Euclidean Space ; 3. General Vector Spaces ; 4. Inner Product Spaces ; 5. Linear Transformation ; 6. Determinants ; 7. Eigenvalues and Eigenvectors","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732876439895,"sku":"9780199654444","price":32.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199654444.jpg?v=1719998775"},{"product_id":"linear-algebra-9780387964126","title":"Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eI Vector Spaces.- II Matrices.- III Linear Mappings.- IV Linear Maps and Matrices.- V Scalar Products and Orthogonality.- VI Determinants.- VII Symmetric, Hermitian, and Unitary Operators.- VIII Eigenvectors and Eigenvalues.- IX Polynomials and Matrices.- X Triangulation of Matrices and Linear Maps.- XI Polynomials and Primary Decomposition.- XII Convex Sets.- Appendix I Complex Numbers.- Appendix II Iwasawa Decomposition and Others.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"The present textbook is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of finite-dimensional vector spaces and proceeds to explain the structure theorems for linear maps, including eigenvectors and eigenvalues, quadratic and Hermitian forms, diagonalization of symmetric, Hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. It also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem. The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants, and linear maps. In this third edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.\"  (S. Lajos, Mathematical Reviews) \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Vector Spaces; 2. Matrices; 3. Linear Mappings; 4. Linear Maps and Matrices; 5. Scalar Products and Orthogonality; 6. Determinants; 7. Symmetric, Hermitian, and Unitary Operators; 8. Eigenvectors and Eigenvalues; 9. Polynomials and Matrices; 10. Triangulation of Matrices and Linear Maps; 11. Polynomials and Primary Decomposition; 12. Convex Sets","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727162711,"sku":"9780387964126","price":39.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387964126.jpg?v=1720001407"},{"product_id":"introduction-to-linear-algebra-9780387962054","title":"Introduction to Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is a short text in linear algebra, intended for a one-term course. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eSecond Edition\u003c\/p\u003e \u003cp\u003e\u003cem\u003eS. Lang\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003eIntroduction to Linear Algebra\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"Excellent! Rigorous yet straightforward, all answers included!\"\u003c\/em\u003e—Dr. J. Adam, Old Dominion University\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI Vectors.- II Matrices and Linear Equations.- III Vector Spaces.- IV Linear Mappings.- V Composition and Inverse Mappings.- VI Scalar Products and Orthogonality.- VII Determinants.- VIII Eigenvectors and Eigenvalues.- Answers to Exercises.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727228247,"sku":"9780387962054","price":45.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387962054.jpg?v=1720001407"},{"product_id":"introduction-to-matrices-and-linear-transformations-third-edition-dover-books-on-mathematics-isbn-9780486481593-9780486481593","title":"Introduction to Matrices and Linear","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis versatile undergraduate-level text contains enough material for a one-year course and serves as a support text and reference. It combines formal theory and related computational techniques. Solutions to selected exercises. 1978 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733797777751,"sku":"9780486481593","price":18.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486481593.jpg?v=1720001738"},{"product_id":"algebraic-groups-and-number-theory-volume-1-9780521113618","title":"Algebraic Groups and Number Theory Volume 1","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is the first volume of a two-volume book that offers an in-depth, and essentially self-contained, treatment of the arithmetic theory of algebraic groups. It is accessible to graduate students and researchers in number theory, algebraic geometry, and related areas.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'The original English version of the book 'Algebraic Groups and Number Theory' by Platonov and Rapinchuk was a go to reference for graduate students and senior researchers alike working in areas of arithmetic and algebraic groups, discrete subgroups of Lie groups, and connections with number theory. The second edition, which will be split into two volumes, and also co-authored with I. Rapinchuk, is a welcome and timely update to the original. The first volume of the second edition, consists of an update to chapters 1-5 of the original with an additional section 4.9 to include new material on the structure of extensions of arithmetic groups. There is no doubt in my mind that this first volume of the second edition will again take on the role of a go to text for those working in an area of huge ongoing interest and importance, and be at the forefront training new generations of mathematicians working in the areas of arithmetic and algebraic groups, discrete subgroups of Lie groups, and connections with number theory.' Alan Reid, Rice University\u003cbr\u003e'The arithmetic theory of algebraic groups is a beautiful area of mathematics: a crossroad of number theory, groups, geometry, representation theory, and more. Not surprisingly it attracted some of the greatest mathematicians of the last few generations. The first edition of the book 'Algebraic Groups and Number Theory' by Vladimir Platonov and Andrei Rapinchuk which came out in the early 90s has quickly become the standard reference of the field. It presents in a clear way several deep topics. The book was one of the reasons the area attracted more researchers and expanded to new directions. This made an updated version much needed. The original authors and Igor Rapinchuk should be thanked by the mathematical community for carrying out this monumental job.' Alex Lubotzky, Hebrew University of Jerusalem\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Algebraic number theory; 2. Algebraic groups; 3. Algebraic groups over locally compact fields; 4. Arithmetic groups and reduction theory; 5. Adeles; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48733845225815,"sku":"9780521113618","price":52.24,"currency_code":"GBP","in_stock":true}]},{"product_id":"deep-down-things-the-breathtaking-beauty-of-particle-physics-9780801879715","title":"Deep Down Things  The Breathtaking Beauty of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntroducing readers to the world of particle physics, Deep Down Things opens new realms within which are many clues to unraveling the mysteries of the universe.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eA fascinating journey into the bizarre, subatomic world of particle physics. PhysOrg.com 2004 Quantum field theory, group theory, Lie algebras, internal symmetry spaces and gauge theory. [Schumm] does a remarkably good job of explaining all this, with a style that is mercifully plain. -- Peter de Groot New Scientist 2005 Explores the world of particle physics in terms laymen can understand. Santa Cruz Sentinel 2005 I expect that any physics undergraduate, bewildered by textbooks and lectures, would find this a delight. -- Stephen Battersby New Scientist 2005 One of several recently published books attempting to provide for interested nonphysicists a relatively nonmathematical account of what has come to be called the standard model of particle physics... Schumm's treatment is perhaps more detailed. Choice 2005 This is definitely a book for your Christmas list, and if it doesn't excite your mathematics colleagues too, they'll miss a treat. -- Rick Marshall School Science Review 2006 This book is beautifully written and is a didactic masterpiece. -- David Watts Science and Christian Belief 2006\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface\u003cbr\u003e1. Introduction\u003cbr\u003e2. The True Movers \u0026amp; Shakers: The Forces of Nature\u003cbr\u003e3. The Great Reawakening: The Modern Physics Revolution\u003cbr\u003e4. The Marriage of Relativity \u0026amp; Quantum Theory: Relativistic Quantum Field Theory\u003cbr\u003e5. Patterns in Nature: The Fundamental Building Blocks\u003cbr\u003e6. Mathematical Patterns: Lie Groups\u003cbr\u003e7. The World Within: Internal Symmetries\u003cbr\u003e8. Physics by Pure Thought: Gauge Theory\u003cbr\u003e9. The Current Paradigm: Hidden Symmetry, the Standard Model \u0026amp; the Higgs Boson\u003cbr\u003e10. Into the Unknown: What Lies Ahead\u003cbr\u003eAppendix: Exponential Notation\u003cbr\u003eNotes\u003cbr\u003eIndex\u003c\/p\u003e","brand":"Johns Hopkins University Press","offers":[{"title":"Default Title","offer_id":48737348780375,"sku":"9780801879715","price":29.92,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780801879715.jpg?v=1723811143"},{"product_id":"algebraic-number-theory-for-beginners-9781009001922","title":"Algebraic Number Theory for Beginners","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book introduces algebraic number theory through the problem of generalizing ''unique prime factorization'' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind''s concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'In Algebraic Number Theory for Beginners, John Stillwell once again displays his remarkable talent for using the history of mathematics to motivate and explore even the most abstract mathematical concepts at an accessible, undergraduate level. This book is another gem of the genre Stillwell has done so much to enhance.' Karen Hunger Parshall, University of Virginia\u003cbr\u003e'Stillwell, more than any author I know, helps us understand mathematics from its roots. In this book, he leads us into algebraic number theory along a historical route from concrete to abstract. In doing so, Stillwell makes a strong pedagogical case for flipping a typical algebraic number theory course — that students will understand number theory better if questions about numbers come before and throughout the abstract theory of rings and ideals. The treatments of mathematics and its history are crystal clear and meticulous. Stillwell's text is particularly well-suited for an advanced undergraduate or early graduate-level course in number theory. Experts also will find this text to be an incredible resource for its historical approach and well-motivated exercises. Stillwell has written another gem, this time for readers interested in number theory, abstract algebra, and their intertwined history.' Martin Weissman, University of California, Santa Cruz\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; 1. Euclidean arithmetic; 2. Diophantine arithmetic; 3. Quadratic forms; 4. Rings and fields; 5. Ideals; 6. Vector spaces; 7. Determinant theory; 8. Modules; 9. Ideals and prime factorization; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48737998340439,"sku":"9781009001922","price":29.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"surveys-in-combinatorics-2021-9781009018883","title":"Surveys in Combinatorics 2021","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, HasseWeil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. The partition complex: an invitation to combinatorial commutative algebra Karim Adiprasito and Geva Yashfe; 2. Hasse-Weil type theorems and relevant classes of polynomial functions Daniele Bartoli; 3. Decomposing the edges of a graph into simpler structures Marthe Bonamy; 4. Generating graphs randomly Catherine Greenhill; 5. Recent advances on the graph isomorphism problem Martin Grohe and Daniel Neuen; 6. Extremal aspects of graph and hypergraph decomposition problems Stefan Glock, Daniela Kühn and Deryk Osthus; 7. Borel combinatorics of locally finite graphs Oleg Pikhurko; 8. Codes and designs in Johnson graphs with high symmetry Cheryl E. Praeger; 9. Maximal subgroups of finite simple groups: classifications and applications Colva M. Roney-Dougal.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738000765271,"sku":"9781009018883","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"the-calabi-problem-for-fano-threefolds-9781009193399","title":"The Calabi Problem for Fano Threefolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book determines whether the general member of each family of smooth Fano threefolds admits a KählerEinstein metric, using K-stability. Complemented by appendices outlining results needed to understand this active area, it will be essential reading for researchers and graduate students working on algebraic and complex geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'The notion of K-stability for Fano manifold has origins in differential geometry and geometric analysis but is now also of fundamental importance in algebraic geometry, with recent developments in moduli theory. This monograph gives an account of a large body of research results from the last decade, studying in depth the case of Fano threefolds. The wealth of material combines in a most attractive way sophisticated modern theory and the detailed study of examples, with a classical flavour. The authors obtain complete results on the K-stability of generic elements of each of the 105 deformation classes. The concluding chapter contains some fascinating conjectures about the 34 families which may contain both stable and unstable manifolds, which will surely be the scene for much further work. The book will be an essential reference for many years to come.' Sir Simon Donaldson, F.R.S., Imperial College London\u003cbr\u003e'It is a difficult problem to check whether a given Fano variety is K-polystable. This book settles this problem for the general members of all the 105 deformation families of smooth Fano 3-folds. The book is recommended to anyone interested in K-stability and existence of Kähler-Einstein metrics on Fano varieties.' Caucher Birkar FRS, Tsinghua University and University of Cambridge\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; 1. K-stability; 2. Warm-up: smooth del Pezzo surfaces; 3. Proof of main theorem: known cases; 4. Proof of main theorem: special cases; 5. Proof of main theorem: remaining cases; 6. The big table; 7. Conclusion; Appendix. Technical results used in proof of main theorem; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738010202455,"sku":"9781009193399","price":71.25,"currency_code":"GBP","in_stock":true}]},{"product_id":"classroomready-rich-algebra-tasks-grades-612-9781071889268","title":"ClassroomReady Rich Algebra Tasks Grades 612","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003e\u003cem\u003eStop algebra from being a mathematical gatekeeper. With rich math tasks, all students can succeed.\u003c\/em\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eEvery teacher strives to make instruction effective and interesting, yet traditional methods of teaching algebra are not working for many students! That's a problem. But the answer isn't to supplement the curriculum with random tasks.\u003cstrong\u003e\u003cem\u003eClassroom Ready-Rich Math Tasks for Grades 6-12\u003c\/em\u003e\u003c\/strong\u003eequips you with a cohesive solution--50+ mathematical tasks that are rich, research-based, standards-aligned, and classroom-tested. The tasks:\u003c\/p\u003e\u003cul\u003e    \u003cli\u003eAre organized into learning progressions that help all students make the leap from arithmetic to algebra\u003c\/li\u003e\n\u003c\/ul\u003e\u003cul\u003e    \u003cli\u003eOffer students interesting mathematics problems to think about and solve so math is investigative, interactive, and engaging\u003c\/li\u003e    \u003cli\u003eProvide opportunities for you to connect new content to prior knowledge or focus on an underdeveloped concept\u003c\/li\u003e    \u003cli\u003eEngage students in conceptual understanding, procedural practice, and problem solving through critical thinking and application\u003c\/li\u003e    \u003cli\u003eCome with downloadable planning tools, student resource pages, and extension questions\u003c\/li\u003e    \u003cli\u003eInclude additional support for students who may be struggling\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eEvery learner deserves opportunities to engage in meaningful, rigorous mathematics. And every teacher can develop mathematical thinking and reasoning abilities in students. Part of the bestselling series spanning elementary and middle school,\u003cstrong\u003e\u003cem\u003eClassroom-Ready Rich Algebra Tasks, Grades 6-12\u003c\/em\u003e\u003c\/strong\u003eis a powerful add-on to any core mathematics program at your school.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eIn this astounding book, Dougherty and Venenciano skillfully illustrate tasks that develop students’\u003cbr\u003e reasoning, problem-solving, and communication skills. They thoughtfully include guiding and reflective\u003cbr\u003e questions along with suggestions for differentiation and extensions of each task. The wide range of topics\u003cbr\u003e makes this perfect for any algebra course! -- Laura Ashley Young\u003cbr\u003eBring the love of learning mathematics back into your classroom by implementing effective\u003cbr\u003e mathematical practices, building numeracy skills in your students, and providing rich algebra tasks that\u003cbr\u003e are engaging. Dougherty and Venenciano have done some great work to support educators that will\u003cbr\u003e enhance students’ learning and grit. -- Katie Majeres\u003cbr\u003eDougherty and Venenciano provoke us to reframe our thinking from, \"can my students get the correct\u003cbr\u003e answer for this task?\" to \"how can I use this task to help further my students’ understanding of the\u003cbr\u003e mathematics?\" The authors provide a vision, tools, and practical advice for strategically using engaging\u003cbr\u003e tasks to enhance students’ understanding of mathematical ideas and processes. -- Dewey Gottlieb\u003cbr\u003eThis is a treasure trove of amazing tasks and supporting materials! Framing the tasks in an overview of\u003cbr\u003e research-grounded practices promotes fidelity and provides access for all students. Tasks presented in Part\u003cbr\u003e 2 spell out the mathematical topics, content and practice alignments, watch-fors, anticipated solutions,\u003cbr\u003e prompts, and post-task notes that allow them to be efficiently integrated. -- Jessica Ivy\u003cbr\u003eIt’s important to implement rich tasks that support students’ math proficiency, drawing from their\u003cbr\u003e strengths and assets. It can be difficult locating or creating math tasks that are both rich and assetbased.\u003cbr\u003e I am excited to use tasks from this book in my work at the university with preservice teachers, in\u003cbr\u003e professional development with in-service teachers, and working with grades 6–12 students. -- Jonathan D. Bostie\u003cbr\u003eClassroom-Ready Rich Algebra Tasks is a must-have resource for all algebra teachers. Dougherty and\u003cbr\u003e Venenciano outline how to implement these tasks in your classroom and give numerous examples that\u003cbr\u003e could be used today. After more than a decade of teaching algebra and supporting algebra teachers, this\u003cbr\u003e is a resource I wish I had when I started. -- Nick Davies\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeword by Kevin Dykema Preface Acknowledgements About the Authors Part 1: GETTING STARTED WITH RICH ALGEBRA TASKS Chapter 1: RICH ALGEBRA TASKS: WHAT ARE THEY, WHY ARE THEY VALUABLE, AND HOW DO I PLAN FOR IMPLEMENTATION? Chapter 2: LAYING THE GROUNDWORK FOR TEACHING WITH RICH ALGEBRA TASKS Chapter 3: IMPLEMENTING RICH ALGEBRA TASK LESSONS Chapter 4: TASKS TO ESTABLISH MATHEMATICAL COMMUNITY Part 2: RICH ALGEBRA TASKS Chapter 5: RATIONAL NUMBER TASKS Chapter 6: EXPRESSIONS TASKS Chapter 7: EQUATIONS TASKS Chapter 8: LINEAR AND NON-LINEAR RELATIONSHIP TASKS Chapter 9: SYSTEMS OF EQUATIONS TASKS Chapter 10: POLYNOMIAL AND RATIONAL EXPRESSIONS AND EQUATIONS TASKS Chapter 11: Your Turn Appendix A References","brand":"SAGE Publications Inc","offers":[{"title":"Default Title","offer_id":48738219000151,"sku":"9781071889268","price":28.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781071889268.jpg?v=1723811830"},{"product_id":"high-school-algebra-ii-unlocked-9781101920077","title":"High School Algebra II Unlocked","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eUNLOCK THE SECRETS OF ALGEBRA II with THE PRINCETON REVIEW.\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003eAlgebra can be a daunting subject. That’s why our new High School Unlocked series focuses on giving you a wide range of key techniques to help you tackle subjects like Algebra II. If one method doesn''t click for you, you can use an alternative approach to understand the concept or problem, instead of painfully trying the same thing over and over without success. Trust us—unlocking the secrets of algebra doesn''t \u003ci\u003ehave \u003c\/i\u003eto hurt!\u003cbr\u003e\u003cbr\u003eWith this book, you’ll discover the link between abstract concepts and their real-world applications and build confidence as your skills improve. Along the way, you’ll get plenty of practice, from fully guided examples to independent end-of-chapter drills and test-like samples. \u003cbr\u003e\u003cbr\u003e\u003ci\u003eEverything You Need to Know About Algebra II.\u003c\/i\u003e\u003cbr\u003e• Complex concepts explained in clear, straightforward ways\u003cbr\u003e• Walk-throughs of sample problems for all topics\u003cbr\u003e• Clear goals and self-assessments to help you pinpoint areas for further review\u003cbr\u003e• Step-by-step examples of different ways to approach problems \u003cbr\u003e\u003ci\u003e\u003cbr\u003ePractice Your Way to Excellence.\u003c\/i\u003e\u003cbr\u003e• Drills and practice questions in every chapter\u003cbr\u003e• Complete answer explanations to boost understanding\u003cbr\u003e• ACT- and SAT-like questions for hands-on experience with how Algebra II may appear on major exams\u003cbr\u003e\u003cbr\u003e\u003cb\u003e\u003ci\u003eHigh School Algebra II Unlocked\u003c\/i\u003e covers:\u003c\/b\u003e\u003cbr\u003e• complex numbers and polynomials\u003cbr\u003e• graphing and solving systems of equations\u003cbr\u003e• radical and rational expressions and inequalities\u003cbr\u003e• trigonometric equations\u003cbr\u003e• logarithmic functions and operations\u003cbr\u003e• statistical modeling\u003cbr\u003e... and more!","brand":"Random House USA Inc","offers":[{"title":"Default Title","offer_id":48738233418071,"sku":"9781101920077","price":13.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781101920077.jpg?v=1723811844"},{"product_id":"modular-theory-in-operator-algebras-9781108489607","title":"Modular Theory in Operator Algebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by S.V. Stratila and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu''s result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to the second edition; Preface to the first edition; 1. Normal weights; 2. Conditional expectations and operator valued weights; 3. Groups of automorphisms; 4. Crossed products; 5. Continuous decompositions; 6. Discrete decompositions; Appendix; References; Subject Index; Notation Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738311012695,"sku":"9781108489607","price":108.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108489607.jpg?v=1723811915"},{"product_id":"matrix-analysis-and-entrywise-positivity-preservers-9781108792042","title":"Matrix Analysis and Entrywise Positivity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMatrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first book to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students, it presents an in-depth and comprehensive view of the subject, from early results to recent progress. Topics include: structural results about, and classifying the preservers of positive semidefiniteness and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry; classical connections to moment problems; and recent connections to combinatorics and Schur polynomials. Based on the author''s course, the book is stru\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'Positive definite matrices, kernels, sequences and functions, and operations on them that preserve their positivity, have been studied intensely for over a century. The techniques involved in their analysis and the variety of their applications both continue to grow. This book is an admirably comprehensive and lucid account of the topic. It includes some very recent developments in which the author has played a major role. This will be a valuable resource for researchers and an excellent text for a graduate course.' Rajendra Bhatia, Ashoka University\u003cbr\u003e'The opening notes of this symphony of ideas were written by Schur in 1911. Schoenberg, Loewner, Rudin, Herz, Hiai, FitzGerald, Jain, Guillot, Rajaratnam, Belton, Putinar, and others composed new themes and variations. Now, Khare has orchestrated a masterwork that includes his own harmonies in an elegant synthesis. This is a work of impressive scholarship.' Roger Horn, University of Utah, Retired\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I. Preliminaries, Entrywise Powers Preserving Positivity in Fixed Dimension: 1. The cone of positive semidefinite matrices; 2. The Schur product theorem and nonzero lower bounds; 3. Totally positive (TP) and totally non-negative (TN) matrices; 4. TP matrices – generalized Vandermonde and Hankel moment matrices; 5. Entrywise powers preserving positivity in fixed dimension; 6. Mid-convex implies continuous, and 2 x 2 preservers; 7. Entrywise preservers of positivity on matrices with zero patterns; 8. Entrywise powers preserving positivity, monotonicity, superadditivity; 9. Loewner convexity and single matrix encoders of preservers; 10. Exercises; Part II. Entrywise Functions Preserving Positivity in All Dimensions: 11. History – Shoenberg, Rudin, Vasudeva, and metric geometry; 12. Loewner's determinant calculation in Horn's thesis; 13. The stronger Horn–Loewner theorem, via mollifiers; 14. Stronger Vasudeva and Schoenberg theorems, via Bernstein's theorem; 15. Proof of stronger Schoenberg Theorem (Part I) – positivity certificates; 16. Proof of stronger Schoenberg Theorem (Part II) – real analyticity; 17. Proof of stronger Schoenberg Theorem (Part III) – complex analysis; 18. Preservers of Loewner positivity on kernels; 19. Preservers of Loewner monotonicity and convexity on kernels; 20. Functions acting outside forbidden diagonal blocks; 21. The Boas–Widder theorem on functions with positive differences; 22. Menger's results and Euclidean distance geometry; 23. Exercises; Part III. Entrywise Polynomials Preserving Positivity in Fixed Dimension: 24. Entrywise polynomial preservers and Horn–Loewner type conditions; 25. Polynomial preservers for rank-one matrices, via Schur polynomials; 26. First-order approximation and leading term of Schur polynomials; 27. Exact quantitative bound – monotonicity of Schur ratios; 28. Polynomial preservers on matrices with real or complex entries; 29. Cauchy and Littlewood's definitions of Schur polynomials; 30. Exercises.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738331066711,"sku":"9781108792042","price":66.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108792042.jpg?v=1723811937"},{"product_id":"matrix-mathematics-9781108837101","title":"Matrix Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eUsing a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student''s understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor''s resources are available.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'A broad coverage of more advanced topics, rich set of exercises, and thorough index make this stylish book an excellent choice for a second course in linear algebra.' Nick Higham, University of Manchester\u003cbr\u003e'This textbook thoroughly covers all the material you'd expect in a Linear Algebra course plus modern methods and applications. These include topics like the Fourier transform, eigenvalue adjustments, stochastic matrices, interlacing, power method and more. With 20 chapters of such material, this text would be great for a multi-part course and a reference book that all mathematicians should have.' Deanna Needell, University of California, Los Angeles\u003cbr\u003e'The original edition of Garcia and Horn's Second Course in Linear Algebra was well-written, well-organized, and contained several interesting topics that students should see - but rarely do in first-semester linear algebra - such as the singular value decomposition, Gershgorin circles, Cauchy's interlacing theorem, and Sylvester's inertia theorem. This new edition also has all of this, together with useful new material on matrix norms. Any student with the opportunity to take a second course on linear algebra would be lucky to have this book.' Craig Larson, Virginia Commonwealth University\u003cbr\u003e'An extremely versatile Linear Algebra textbook that allows numerous combinations of topics for a traditional course or a more modern and applications-oriented class. Each chapter contains the exact amount of information, presented in a very easy-to-read style, and a plethora of interesting exercises to help the students deepen their knowledge and understanding of the material.' Maria Isabel Bueno Cachadina, University of California, Santa Barbara\u003cbr\u003e'This is an excellent textbook. The topics flow nicely from one chapter to the next and the explanations are very clearly presented. The material can be used for a good second course in Linear Algebra by appropriately choosing the chapters to use. Several options are possible. The breadth of subjects presented makes this book a valuable resource.' Daniel B. Szyld, Temple University and President of the International Linear Algebra Society\u003cbr\u003e'With a careful selection of topics and a deft balance between theory and applications, the authors have created a perfect textbook for a second course on Linear Algebra. The exposition is clear and lively. Rigorous proofs are supplemented by a rich variety of examples, figures, and problems.' Rajendra Bhatia, Ashoka University\u003cbr\u003e'The authors have provided a contemporary, methodical, and clear approach to a broad and comprehensive collection of core topics in matrix theory. They include a wealth of illustrative examples and accompanying exercises to re-enforce the concepts in each chapter. One unique aspect of this book is the inclusion of a large number of concepts that arise in many interesting applications that do not typically appear in other books. I expect this text will be a compelling reference for active researchers and instructors in this subject area.' Shaun Fallat, University of Regina\u003cbr\u003e'It starts from scratch, but manages to cover an amazing variety of topics, of which quite a few cannot be found in standard textbooks. All matrices in the book are over complex numbers, and the connections to physics, statistics, and engineering are regularly highlighted. Compared with the first edition, two new chapters and 300 new problems have been added, as well as many new conceptual examples. Altogether, this is a truly impressive book.' Claus Scheiderer, University of Konstanz\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents; Preface; Notation; 1. Vector Spaces; 2. Bases and Similarity; 3. Block Matrices; 4. Rank, Triangular Factorizations, and Row Equivalence; 5. Inner Products and Norms; 6. Orthonormal Vectors; 7. Unitary Matrices; 8. Orthogonal Complements and Orthogonal Projections; 9. Eigenvalues, Eigenvectors, and Geometric Multiplicity; 10. The Characteristic Polynomial and Algebraic Multiplicity; 11. Unitary Triangularization and Block Diagonalization; 12. The Jordan Form: Existence and Uniqueness; 13. The Jordan Form: Applications; 14. Normal Matrices and the Spectral Theorem; 15. Positive Semidefinite Matrices; 16. The Singular Value and Polar Decompositions; 17. Singular Values and the Spectral Norm; 18. Interlacing and Inertia; 19. Norms and Matrix Norms; 20. Positive and Nonnegative Matrices; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738340471127,"sku":"9781108837101","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108837101.jpg?v=1723811949"},{"product_id":"algebra-a-complete-introduction-9781473678415","title":"Algebra A Complete Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAlgebra: A Complete Introduction\u003c\/i\u003e is the most comprehensive yet easy-to-use introduction to using Algebra.\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eWritten by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThe book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, law and sequences. \u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eEverything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions. \u003c\/div\u003e","brand":"John Murray Press","offers":[{"title":"Default Title","offer_id":48739541975383,"sku":"9781473678415","price":15.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781473678415.jpg?v=1720052545"},{"product_id":"basic-linear-algebra-9781852336622","title":"Basic Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eBasic Linear Algebra\u003c\/b\u003e is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers: this will take the form of a tutorial on the use of the \"LinearAlgebra\" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"It embodies a beautiful, concise and precise treatment of the subject, with succint numerical and algebra worked examples at the right points... an excellent textbook which is also eminently suitable for self-study...\" Zentralblatt MATH\u003c\/p\u003e \u003cp\u003e\"This is the second edition of a text for first-year students which covers the main themes of linear algebra in a succinct and readable way. … The book is well-written, with a very high standard of proof-reading, and there are full answers to all the exercises … . It should be welcomed as an excellent introductory textbook which could be used either for self-study and to complement a course of lectures.\" (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface Forward The Algebra of Matrices Some Applications of Matrices Systems of Linear Equations Invertible Matrices Vector Spaces Linear Mappings The Matrix Connection Determinants Eigenvalues and Eigenvectors The Minimum Polynomial Computer Assistance Solutions to the Exercises index","brand":"Springer London Ltd","offers":[{"title":"Default Title","offer_id":48742319194455,"sku":"9781852336622","price":31.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781852336622.jpg?v=1720060913"},{"product_id":"further-linear-algebra-9781852334253","title":"Further Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMost of the introductory courses on linear algebra develop the basic theory of finite­ dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num­ ber of illustrative and worked examples, as well as many exercises that are strategi­ cally placed throughout the text. Solutions to the exercises are also provided. Many applications of linear algebra require careful, and at times rather tedious, calculations by hand. Very often these are subject to error, so the assistance of a com­ puter is welcome. As far as computation in algebra is concerned, there are several packages available. Here we include, in the spirit of a tutorial, a chapter that gives 1 a brief introduction to the use of MAPLE in dealing with numerical and algebraic problems in linear algebra.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews of the first edition:\u003c\/p\u003e \u003cp\u003eMAA ONLINE\u003c\/p\u003e \u003cp\u003e\"This book will be of interest to anyone who wishes to have a good grasp of linear llgebra and matrix theory. It can also be used as an advanced undergraduate textbook. Although this book does not treat infinite dimensional linear spaces, it provides the reader with a deep understanding of finite dimensional linear spaces. Many aspects of the theory of finite dimensional linear spaces can easily be generalized to the infinite dimensional case. Therefore, this book will also be helpful to those who intend to study infinite dimensional spaces later. \"\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cp\u003eZENTRALBLATT MATH\u003c\/p\u003e \u003cp\u003e\"…it embodies a beautiful, concise and precise treatment of the subject, with succinct numerical and algebraic worked examples at the right points, and many exercises…This is an excellent textbook which, together with the earlier book, comprises a very nearly complete introduction to linear algebra which not only the undergraduate but also the advanced reader will enjoy studying.\"\u003c\/p\u003e \u003cp\u003e\"The present book is a contribution of the volume Basic Linear Algebra of the same authors, which appeared in the same Springer series. … It is a very interesting, accessible book for undergraduates (or teacher professors), and the many examples and exercises should really help the undergraduate to study its contents.\" (Koen Thas, Bulletin of the Belgian Mathematical Society, Vol. 11 (4), 2004)\u003c\/p\u003e \u003cp\u003e\"The book is a contribution of the authors’ Basic Linear Algebra published in the same series. … Besides numerous well-chosen examples scattered throughout the text, the reader can also enjoy short biographical profiles of twenty one eminent mathematicians associated with the subject.\" (European Mathematical Society Newsletter, December, 2003)\u003c\/p\u003e \u003cp\u003e\"The present book is a natural sequel to the same authors’ successful SUMS volume ‘Basic Linear Algebra’. The most advanced topics here take the reader to the very heart of the subject … . To sum up, this textbook is well suited for self-study or for a one- or two-semester course. Therefore, we warmly recommend it to undergraduate students studying as well as professors teaching Linear Algebra at any level.\" (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 69, 2003)\u003c\/p\u003e \u003cp\u003e\"Further Linear Algebra is a natural sequel to the authors’ highly acclaimed SUMS volume Basis Linear Algebra. … An introductory chapter recaps the prerequisites (for those readers unfamiliar with the first volume), and a wide range of worked examples and exercises (with solutions) are strategically placed throughout the text to consolidate understanding.\" (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe story so far.- 1. Inner Product Spaces.- 2. Direct Sums of Subspaces.- 3. Primary Decomposition.- 4. Reduction to Triangular Form.- 5. Reduction to Jordan Form.- 6. Rational and Classical Forms.- 7. Dual Spaces.- 8. Orthogonal Direct Sums.- 9. Bilinear and Quadratic Forms.- 10. Real Normality.- 11. Computer Assistance.- 12. …. but who were they?.- 13. Solutions to the Exercises.","brand":"Springer London Ltd","offers":[{"title":"Default Title","offer_id":48742319227223,"sku":"9781852334253","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"linear-model-theory-exercises-and-solutions-9783030520731","title":"Linear Model Theory: Exercises and Solutions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book contains 296 exercises and solutions covering a wide variety of topics in linear model theory, including generalized inverses, estimability, best linear unbiased estimation and prediction, ANOVA, confidence intervals, simultaneous confidence intervals, hypothesis testing, and variance component estimation. The models covered include the Gauss-Markov and Aitken models, mixed and random effects models, and the general mixed linear model. Given its content, the book will be useful for students and instructors alike. Readers can also consult the companion textbook \u003ci\u003eLinear Model Theory - \u003c\/i\u003e\u003ci\u003eWith Examples and Exercises\u003c\/i\u003e by the same author for the theory behind the exercises.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This volume contains solutions to the book's exercises … Many of those exercises stand as useful applications of results stated in the theory volume. Some of them go one step beyond and extend the theoretical results. I found this to be a very interesting and unique feature of the book on linear models, making the whole set particularly useful for both graduate students and instructors.” (Vassilis G. S. Vasdekis, Mathematical Reviews, August 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1 A Brief Introduction.- 2 Selected Matrix Algebra Topics and Results.- 3 Generalized Inverses and Solutions to Sytems of Linear Equations.- 4 Moments of a Random Vector and of Linear and Quadratic Forms in a Random Vector.- 5 Types of Linear Models.- 6 Estimability.- 7 Least Squares Estimation for the Gauss-Markov Model.- 8 Least Squares Geometry and the Overall ANOVA.- 9 Least Squares Estimation and ANOVA for Partitioned Models.- 10 Constrained Least Squares Estimation and ANOVA.- 11 Best Linear Unbiased Estimation for the Aitken Model.- 12 Model Misspecification.- 13 Best Linear Unbiased Prediction.- 14 Distribution Theory.- 15 Inference for Estimable and Predictable Functions.- 16 Inference for Variance-Covariance Parameters.- 17 Empirical BLUE and BLUP.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743039271255,"sku":"9783030520731","price":104.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"advanced-linear-and-matrix-algebra-9783030528171","title":"Advanced Linear and Matrix Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques.\u003c\/p\u003e  Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eAdvanced Linear and Matrix Algebra\u003c\/i\u003e offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author’s companion volume, \u003ci\u003eIntroduction to Linear and Matrix Algebra\u003c\/i\u003e.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book is well-organized. The main notions and results are well-presented, followed by a discussion and problems with detailed solutions. There are many helpful notes and examples. At the end of each section, the reader can frequently find several computational, true\/false, or proof exercises. … There are several illustrative and colorful figures. For instance, those illustrating the examples and remarks about the Gershgorin disc theorem or about the geometric interpretation of the positive semidefiniteness are really helpful.” (Carlos M. da Fonseca, zbMATH 1471.15001, 2021)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1: Vector Spaces.- Chapter 2: Matrix Decompositions.- Chapter 3: Tensors and Multilinearity.- Appendix A: Mathematical Preliminaries.- Appendix B: Additional Proofs.- Appendix C: Selected Exercise Solutions.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743039435095,"sku":"9783030528171","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"quaternion-algebras-9783030574673","title":"Quaternion Algebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike.\u003c\/p\u003e  Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eQuaternion Algebras\u003c\/i\u003e encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book contains a huge amount of interesting and very well-chosen exercises. … This ‘encyclopedic’ character of the text may play an important role both as a guide to some special topics and as a source of information for both students and those whose research in related fields creates a need to familiarize themselves with the knowledge of the case when quaternion algebras are relevant.” (Juliusz Brzeziński, Mathematical Reviews, September, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Beginnings.- 3. Involutions.- 4. Quadratic Forms.- 5. Ternary Quadratic Forms.- 6. Characteristic 2.- 7. Simple Algebras.- 8. Simple Algebras and Involutions.- 9. Lattices and Integral Quadratic Forms.- 10. Orders.- 11. The Hurwitz Order.- 12. Ternary Quadratic Forms Over Local Fields.- 13. Quaternion Algebras Over Local Fields.- 14. Quaternion Algebras Over Global Fields.- 15. Discriminants.- 16. Quaternion Ideals and Invertability.- 17. Classes of Quaternion Ideals.- 18. Picard Group.- 19. Brandt Groupoids.- 20. Integral Representation Theory.- 21. Hereditary and Extremal Orders.- 22. Ternary Quadratic Forms.- 23. Quaternion Orders.- 24. Quaternion Orders: Second Meeting.- 25. The Eichler Mass Formula.- 26. Classical Zeta Functions.- 27. Adelic Framework.- 28. Strong Approximation.- 29. Idelic Zeta Functions.- 30. Optimal Embeddings.- 31. Selectivity.- 32. Unit Groups.- 33. Hyperbolic Plane.- 34. Discrete Group Actions.- 35. Classical Modular Group.- 36. Hyperbolic Space.- 37. Fundamental Domains.- 38. Quaternionic Arithmetic Groups.- 39. Volume Formula.- 40. Classical Modular Forms.- 41. Brandt Matrices.- 42. Supersingular Elliptic Curves.- 43. Abelian Surfaces with QM.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743041204567,"sku":"9783030574673","price":26.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030574673.jpg?v=1720063852"},{"product_id":"around-the-unit-circle-mahler-measure-integer-matrices-and-roots-of-unity-9783030800307","title":"Around the Unit Circle: Mahler Measure, Integer","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book.\u003cp\u003eOne way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal  polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure.  All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eAround the Unit Circle\u003c\/i\u003e is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The reader at the graduate level having enough time and energy can learn a lot from this book about the Mahler measure, conjugate sets of algebraic integers, and related results. Some chapters of the book are quite accessible to undergraduate students as well, and may serve as an introduction to their research in this area.” (Arturas Dubickas, Mathematical Reviews, May, 2023)\u003cbr\u003e“It contains some material that is unavailable elsewhere. Each chapter is concluded by notes and a glossary of newly introduced definitions. … The reader at the graduate level having enough time and energy from this book can learn a lot about the Mahler measure, conjugate sets of algebraic integers and related results.” (Artūras Dubickas, zbMATH 1486.11003, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Mahler Measures of Polynomials in One Variable.- 2 Mahler Measures of Polynomials in Several Variables.- 3 Dobrowolski's Theorem.- 4 The Schinzel–Zassenhaus Conjecture.- 5 Roots of Unity and Cyclotomic Polynomials.- 6 Cyclotomic Integer Symmetric Matrices I: Tools and Statement of the Classification Theorem.- 7 Cyclotomic Integer Symmetric Matrices II: Proof of the Classification Theorem.- 8 The Set of Cassels Heights.- 9 Cyclotomic Integer Symmetric Matrices Embedded in Toroidal and Cylindrical Tesselations.- 10 The Transfinite Diameter and Conjugate Sets of Algebraic Integers.- 11 Restricted Mahler Measure Results.- 12 The Mahler Measure of Nonreciprocal Polynomials.- 13 Minimal Noncyclotomic Integer Symmetric Matrices.- 14 The Method of Explicit Auxiliary Functions.- 15 The Trace Problem For Integer Symmetric Matrices.- 16 Small-Span Integer Symmetric Matrices.- 17 Symmetrizable Matrices I: Introduction.- 18 Symmetrizable Matrices II: Cyclotomic Symmetrizable Integer Matrices.- 19 Symmetrizable Matrices III: The Trace Problem.- 20 Salem Numbers from Graphs and Interlacing Quotients.- 21 Minimal Polynomials of Integer Symmetric Matrices.- 22 Breaking Symmetry.- A Algebraic Background.- B Combinatorial Background.- C Tools from the Theory of Functions.- D Tables.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743049199959,"sku":"9783030800307","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"zero-product-determined-algebras-9783030802417","title":"Zero Product Determined Algebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a concise survey of the theory of zero product-determined algebras, which has been developed over the last 15 years. It is divided into three parts. The first part presents the purely algebraic branch of the theory, the second part presents the functional analytic branch, and the third part discusses various applications.\u003c\/p\u003e  \u003cp\u003eThe book is intended for researchers and graduate students in ring theory, Banach algebra theory, and nonassociative algebra.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book is about zero product determined algebras and is written in an attractive way. It deals with the introduction and study of this class of algebras. Most of this book is taken from research articles from the last 15 years and is suitable for researchers in this field and students with different backgrounds and can be used for self-study.” (Hoger Ghahramani, Mathematical Reviews, March, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e- \u003c\/b\u003e\u003cb\u003ePart I Algebraic Theory. - \u003c\/b\u003eZero Product Determined Nonassociative Algebras. - Zero Product Determined Rings and Algebras. - Zero Lie\/Jordan Product Determined Algebras. - \u003cb\u003ePart II Analytic Theory.\u003c\/b\u003e - Zero Product Determined Nonassociative Banach Algebras. - Zero Product Determined Banach Algebras. - Zero Lie\/Jordan Product Determined Banach Algebras. - \u003cb\u003ePart III Applications.\u003c\/b\u003e - Homomorphisms and Related Maps. - Derivations and Related Maps. - Miscellany.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743050838359,"sku":"9783030802417","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"relative-nonhomogeneous-koszul-duality-9783030895396","title":"Relative Nonhomogeneous Koszul Duality","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research. \u003c\/p\u003e  \u003cp\u003eThis book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare–Birkhoff–Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first time in the history of Koszul duality the derived D-\\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book under review is pretty self-contained, and it is not necessary to be familiar with all the background material before reading it. It also contains many examples to illustrate the main concepts.” (Dag Oskar Madsen, Mathematical Reviews, October, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Prologue.- Introduction.- Homogeneous Quadratic Duality over a Base Ring.- Flat and Finitely Projective Koszulity.- Relative Nonhomogeneous Quadratic Duality.- The Poincare-Birkhoff-Witt Theorem.- Comodules and Contramodules over Graded Rings.- Relative Nonhomogeneous Derived Koszul Duality: the Comodule Side.- Relative Nonhomogeneous Derived Koszul Duality: the Contramodule Side.- The Co-Contra Correspondence.- Koszul Duality and Conversion Functor.- Examples.- References.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743056900439,"sku":"9783030895396","price":39.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030895396.jpg?v=1720063922"},{"product_id":"a-quantum-computation-workbook-9783030912161","title":"A Quantum Computation Workbook","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eTeaching quantum computation and information is notoriously difficult, because it requires covering subjects from various fields of science, organizing these subjects consistently in a unified way despite their tendency to favor their specific languages, and overcoming the subjects’ abstract and theoretical natures, which offer few examples of actual realizations. \u003cbr\u003eIn this book, we have organized all the subjects required to understand the principles of quantum computation and information processing in a manner suited to physics, mathematics, and engineering courses as early as undergraduate studies.In addition, we provide a supporting package of quantum simulation software from Wolfram Mathematica, specialists in symbolic calculation software. \u003cbr\u003eThroughout the book’s main text, demonstrations are provided that use the software package, allowing the students to deepen their understanding of each subject through self-practice. Readers can change the code so as to experiment with their own ideas and contemplate possible applications. The information in this book reflects many years of experience teaching quantum computation and information. The quantum simulation-based demonstrations and the unified organization of the subjects are both time-tested and have received very positive responses from the students who have experienced them.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The book provides an extensive bibliography and index. … this volume is well suited for a advanced graduate or first-year PhD course in quantum mechanics, with ample time available for self-study.” (L.-F. Pau, Computing Reviews, January 30, 2023)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 The Postulates of Quantum Mechanics.- 2 Virtual Realization of Quantum Computers.- 3 Quantum Computation: Overview.- 4 Quantum Algorithms: Introduction.- 5 Quantum Information: Introduction.- 6 Quantum Error Correction Codes: Introduction.- Appendix A Linear Algebra.- Appendix B Mathematica Application Q3.- References.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743057523031,"sku":"9783030912161","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030912161.jpg?v=1723812626"},{"product_id":"explorations-in-number-theory-commuting-through-the-numberverse-9783030989309","title":"Explorations in Number Theory: Commuting through","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis innovative undergraduate textbook approaches number theory through the lens of abstract algebra.  Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory.  Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics.  The text is organized around three core themes: the notion of what a “number” is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems.  Other aspects of modern number theory – including the study of elliptic curves, the analogs between integer and polynomial arithmetic, \u003ci\u003ep\u003c\/i\u003e-adic arithmetic, and relationships between the spectra of primes in various rings – are included in smaller but persistent threads woven through chapters and exercise sets.\u003cbr\u003eEach chapter concludes with exercises organized in four categories: Calculations and Informal Proofs, Formal Proofs, Computation and Experimentation, and General Number Theory Awareness.  IBL “Exploration” worksheets appear in many sections, some of which involve numerical investigations.  To assist students who may not have experience with programming languages, Python worksheets are available on the book’s website.  The final chapter provides five additional IBL explorations that reinforce and expand what students have learned, and can be used as starting points for independent projects.  The topics covered in these explorations are public key cryptography, Lagrange’s four-square theorem, units and Pell’s Equation, various cases of the solution to Fermat’s Last Theorem, and a peek into other deeper mysteries of algebraic number theory.\u003cbr\u003eStudents should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the “numberverse.”\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- What is a Number?- A Quick Survey of the Last Two Millenia.- Number Theory in $\\mathcal{Z}$ Beginning.- Number Theory in the Mod-n Era.- Gaussian Number Theory: $\\mathcal{Z}[i]$ of the Storm.- Number Theory: From Where We $\\mathcal{R}$ to across the $mathcal{C}$.- Cyclotomic Number Theory: Roots and Reciprocity. Number Theory Unleashed: Release $\\mathcal{Z}_p$!- The Adventure Continues.- Appendix: Number Systems.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743061782871,"sku":"9783030989309","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030989309.jpg?v=1723812628"},{"product_id":"drinfeld-modules-9783031197062","title":"Drinfeld Modules","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory.\u003cbr\u003eAfter the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized.\u003cbr\u003e\u003ci\u003eDrinfeld Modules\u003c\/i\u003e guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Acknowledgements.- Notation and Conventions.- Chapter 1. Algebraic Preliminaries.- Chapter 2. Non-Archimedean Fields.- Chapter 3. Basic Properties of Drinfeld Modules.- Chapter 4. Drinfeld Modules over Finite Fields.- Chapter 5. Analytic Theory of Drinfeld Modules.- Chapter 6. Drinfeld Modules over Local Fields.- Chapter 7. Drinfeld Modules over Global Fields.- Appendix A. Drinfeld modules for general function rings.- Appendix B. Notes on exercises.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743075086679,"sku":"9783031197062","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031197062.jpg?v=1720064000"},{"product_id":"putnam-and-beyond-9783319589862","title":"Putnam and Beyond","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad\u003c\/p\u003eratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eUsing the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. \u003ci\u003ePutnam and Beyond\u003c\/i\u003e is organized for independent study by undergraduate and gradu\u003c\/p\u003eate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to the Second Edition.- Preface to the First Edition.- A Study Guide.- 1. Methods of Proof.- 2. Algebra.- 3. Real Analysis.- 4. Geometry and Trigonometry.- 5. Number Theory.- 6. Combinatorics and Probability.- Solutions.- Index of Notation.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743099466071,"sku":"9783319589862","price":46.74,"currency_code":"GBP","in_stock":true}]},{"product_id":"homological-methods-representation-theory-and-cluster-algebras-9783319745848","title":"Homological Methods, Representation Theory, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study.\u003c\/p\u003e\u003cp\u003eThe six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003eThe courses held were:\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eAdvanced homological algebra\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eIntroduction to the representation theory of algebras\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eAuslander-Reiten theory for algebras of infinite representation type\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eCluster algebras arising from surfaces\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eCluster tilted algebras\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eCluster characters\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eIntroduction to K-theory\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eBrauer graph algebras and applications to cluster algebras\u003cbr\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction to the Representation Theory of  Finite-Dimensional Algebras: The Functorial Approach (M. I. Platzeck).- Auslander–Reiten Theory for Finite-Dimensional Algebras  (P. Malicki).-  Cluster Algebras From Surfaces (R. Schiffler).- Cluster Characters (P.-G. Plamondon).- A Course on Cluster Tilted Algebras (I. Assem).- Brauer Graph Algebras (S. Schroll). ","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743104151895,"sku":"9783319745848","price":41.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319745848.jpg?v=1723812632"},{"product_id":"groups-rings-and-fields-9783540761778","title":"Groups, Rings and Fields","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Sets and Mappings.- 2 The Integers.- 3 Introduction to Rings.- 4 Introduction to Groups.- 5 Rings.- 6 Topics in Group Theory.- Hints to Solutions.- Suggestions for Further Study.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743131611479,"sku":"9783540761778","price":28.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540761778.jpg?v=1720064249"},{"product_id":"linear-algebra-and-optimization-with-applications-to-machine-learning-volume-ii-fundamentals-of-optimization-theory-with-applications-to-machine-learning-9789811216565","title":"Linear Algebra And Optimization With Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eVolume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743276839255,"sku":"9789811216565","price":162.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811216565.jpg?v=1720064887"},{"product_id":"introduction-to-abstract-algebra-an-sets-groups-rings-and-fields-9789811247552","title":"Introduction To Abstract Algebra, An: Sets,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743282114903,"sku":"9789811247552","price":63.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811247552.jpg?v=1723812656"},{"product_id":"linear-algebra-ii-advanced-topics-for-applications-9789811257056","title":"Linear Algebra Ii: Advanced Topics For","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course.The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory.The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743285490007,"sku":"9789811257056","price":81.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811257056.jpg?v=1720064925"},{"product_id":"linear-algebra-ii-advanced-topics-for-applications-9789811257988","title":"Linear Algebra Ii: Advanced Topics For","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course.The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory.The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743285686615,"sku":"9789811257988","price":52.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811257988.jpg?v=1720064926"},{"product_id":"linear-algebra-i-basic-concepts-9789811257971","title":"Linear Algebra I: Basic Concepts","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course.The objective of this volume is to present, from the engineering viewpoint, the standard mathematical results in linear algebra such as those on systems of equations and eigenvalue problems. In addition to giving mathematical theorems and formulas, it explains how the mathematical concepts such as rank, eigenvalues, and singular values are linked to engineering applications and numerical computations.In particular, the following four aspects are emphasized.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743285948759,"sku":"9789811257971","price":52.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811257971.jpg?v=1720064926"},{"product_id":"advanced-linear-algebra-with-applications-9789811621666","title":"Advanced Linear Algebra with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides a comprehensive knowledge of linear algebra for graduate and undergraduate courses. As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical, bilinear, quadratic, sesquilinear, Hermitian forms of operators and tensor products of vector spaces with their algebras. The last three chapters focus on empowering readers to pursue interdisciplinary applications of linear algebra in numerical methods, analytical geometry and in solving linear system of differential equations. A rich collection of examples and exercises are present at the end of each section to enhance the conceptual understanding of readers. Basic knowledge of various notions, such as sets, relations, mappings, etc., has been pre-assumed.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Algebraic Structures\u003cbr\u003e2. Matrices and Systems of Linear Equations\u003cbr\u003e3. Vector Spaces\u003cbr\u003e4. Linear Transformations\u003cbr\u003e5. Dual Spaces\u003cbr\u003e6. Inner Product Spaces\u003cbr\u003e7. Canonical Forms of an Operator\u003cbr\u003e8. Bilinear and Quadratic Forms\u003cbr\u003e9. Sesquilinear and Hermitian Forms\u003cbr\u003e10. Applications of Linear Algebra to Numerical Methods\u003cbr\u003e11. Affine and Euclidean Spaces and the Applications of Linear Algebra to Geometry\u003cbr\u003e12. Ordinary differential equations and linear systems of ordinary differential equations","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743290372439,"sku":"9789811621666","price":40.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811621666.jpg?v=1720064947"},{"product_id":"linear-algebra-from-the-beginnings-to-the-jordan-normal-forms-9789811669965","title":"Linear Algebra: From the Beginnings to the Jordan","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe purpose of this book is to explain linear algebra clearly for beginners. In doing so, the author states and explains somewhat advanced topics such as Hermitian products and Jordan normal forms. Starting from the definition of matrices, it is made clear with examples that matrices and matrix operation are abstractions of tables and operations of tables. The author also maintains that systems of linear equations are the starting point of linear algebra, and linear algebra and linear equations are closely connected. The solutions to systems of linear equations are found by solving matrix equations in the row-reduction of matrices, equivalent to the Gauss elimination method of solving systems of linear equations. The row-reductions play important roles in calculation in this book. To calculate row-reductions of matrices, the matrices are arranged vertically, which is seldom seen but is convenient for calculation. Regular matrices and determinants of matrices are defined and explained. Furthermore, the resultants of polynomials are discussed as an application of determinants. Next, abstract vector spaces over a field \u003ci\u003eK\u003c\/i\u003e are defined. In the book, however, mainly vector spaces are considered over the real number field and the complex number field, in case readers are not familiar with abstract fields. Linear mappings and linear transformations of vector spaces and representation matrices of linear mappings are defined, and the characteristic polynomials and minimal polynomials are explained. The diagonalizations of linear transformations and square matrices are discussed, and inner products are defined on vector spaces over the real number field. Real symmetric matrices are considered as well, with discussion of quadratic forms. Next, there are definitions of Hermitian inner products. Hermitian transformations, unitary transformations, normal transformations and the spectral resolution of normal transformations and matrices are explained. The book ends with Jordan normal forms. It is shown that any transformations of vector spaces over the complex number field have matrices of Jordan normal forms as representation matrices.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Matrices.- 2. Linear Equations.- 3. 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Starting from the definition of matrices, it is made clear with examples that matrices and matrix operation are abstractions of tables and operations of tables. The author also maintains that systems of linear equations are the starting point of linear algebra, and linear algebra and linear equations are closely connected. The solutions to systems of linear equations are found by solving matrix equations in the row-reduction of matrices, equivalent to the Gauss elimination method of solving systems of linear equations. The row-reductions play important roles in calculation in this book. To calculate row-reductions of matrices, the matrices are arranged vertically, which is seldom seen but is convenient for calculation. Regular matrices and determinants of matrices are defined and explained. Furthermore, the resultants of polynomials are discussed as an application of determinants. Next, abstract vector spaces over a field \u003ci\u003eK\u003c\/i\u003e are defined. 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The book explains many basic techniques for proving inequalities such as direct comparison, method of magnifying and reducing, substitution method, construction method, and so on.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743300464983,"sku":"9789814696456","price":25.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789814696456.jpg?v=1720064993"},{"product_id":"linear-algebra-with-python-theory-and-applications-9789819929504","title":"Linear Algebra with Python: Theory and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook is for those who want to learn linear algebra from the basics. After a brief mathematical introduction, it provides the standard curriculum of linear algebra based on an abstract linear space. It covers, among other aspects: linear mappings and their matrix representations, basis, and dimension; matrix invariants, inner products, and norms; eigenvalues and eigenvectors; and Jordan normal forms. Detailed and self-contained proofs as well as descriptions are given for all theorems, formulas, and algorithms.\u003c\/p\u003e  \u003cp\u003eA unified overview of linear structures is presented by developing linear algebra from the perspective of functional analysis. Advanced topics such as function space are taken up, along with Fourier analysis, the Perron–Frobenius theorem, linear differential equations, the state transition matrix and the generalized inverse matrix, singular value decomposition, tensor products, and linear regression models. These all provide a bridge to more specialized theories based on linear algebra in mathematics, physics, engineering, economics, and social sciences.\u003c\/p\u003e  Python is used throughout the book to explain linear algebra. Learning with Python interactively, readers will naturally become accustomed to Python coding.  By using Python’s libraries NumPy, Matplotlib, VPython, and SymPy,  readers can easily perform large-scale matrix calculations, visualization of calculation results, and symbolic computations.  All the codes in this book can be executed on both Windows and macOS and also on Raspberry Pi.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eMathematics and Python.- Linear Spaces and Linear Mappings.- Basis and Dimension.- Matrices.- Elementary Operations and Matrix Invariants.- Inner Product and Fourier Expansion.- Eigenvalues and Eigenvectors.- Jordan Normal Form and Spectrum.- Dynamical Systems.- Applications and Development of Linear Algebra.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743302103383,"sku":"9789819929504","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819929504.jpg?v=1720065001"},{"product_id":"at-sixes-and-sevens-9780008491079","title":"At Sixes and Sevens","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn engaging, accessible introduction into how numbers work and why we shouldn't be afraid of them, frommaths expertRachel Riley.Do you know your fractions from your percentages? Your adjacent to your hypotenuse? And who really knows how to do long division, anyway?Puzzled already? Don't blame youBut fret not! You won't be At Sixes and Sevens for long. In this brilliant, well-rounded guide, Countdown''s Rachel Riley will take you back to the very basics, allow you to revisit what you learnt at school (and may have promptly forgotten, *ahem*), build your understanding of maths from the get-go and provide you with the essential toolkit to gain confidence in your numerical abilities.Discover how to divide and conquer, make your decimal debut, become a pythagoras professional and so much more with these easy-to-learn tips and tricks. Packed full of working examples, fool-proof methods, quirky trivia and brainteasers to try from puzzle-pro Dr Gareth Moore, this book is an absolute must-read for anyone and everyone who ever thought maths was above' them. Because the truth is: you can do it. What's more, it can be pretty fun too!","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863995789655,"sku":"9780008491079","price":13.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008491079.jpg?v=1722269914"},{"product_id":"how-to-think-about-abstract-algebra-9780198843382","title":"How to Think About Abstract Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHow to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eI'd very strongly recommend it to undergraduates studying maths, Sixth formers about to study maths, and anyone who did a maths degree a while ago and wants to revisit groups, rings and fields. I also recommend that any first year pure maths lecturers reading this should add this book to their course's reading list. * Chalkdust *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: What is Abstract Algebra? 2: Axioms and Denitions 3: Theorems and Proofs 4: Studying Abstract Algebra 5: Binary Operations 6: Groups and Subgroups 7: Quotient Groups 8: Isomorphisms and Homomorphisms 9: Rings References","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48864218349911,"sku":"9780198843382","price":21.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198843382.jpg?v=1722270944"},{"product_id":"abstract-algebra-9780471433347","title":"Abstract Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWidely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003ePreliminaries.\u003c\/p\u003e \u003cp\u003ePART I: GROUP THEORY.\u003c\/p\u003e \u003cp\u003eChapter 1. Introduction to Groups.\u003c\/p\u003e \u003cp\u003eChapter 2. Subgroups.\u003c\/p\u003e \u003cp\u003eChapter 3. Quotient Group and Homomorphisms.\u003c\/p\u003e \u003cp\u003eChapter 4. Group Actions.\u003c\/p\u003e \u003cp\u003eChapter 5. Direct and Semidirect Products and Abelian Groups.\u003c\/p\u003e \u003cp\u003eChapter 6. Further Topics in Group Theory.\u003c\/p\u003e \u003cp\u003ePART II: RING THEORY.\u003c\/p\u003e \u003cp\u003eChapter 7. Introduction to Rings.\u003c\/p\u003e \u003cp\u003eChapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.\u003c\/p\u003e \u003cp\u003eChapter 9. Polynomial Rings.\u003c\/p\u003e \u003cp\u003ePART III: MODULES AND VECTOR SPACES.\u003c\/p\u003e \u003cp\u003eChapter 10. Introduction to Module Theory.\u003c\/p\u003e \u003cp\u003eChapter 11. Vector Spaces.\u003c\/p\u003e \u003cp\u003eChapter 12. Modules over Principal Ideal Domains.\u003c\/p\u003e \u003cp\u003ePART IV: FIELD THEORY AND GALOIS THEORY.\u003c\/p\u003e \u003cp\u003eChapter 13. Field Theory.\u003c\/p\u003e \u003cp\u003eChapter 14. Galois Theory.\u003c\/p\u003e \u003cp\u003ePART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA.\u003c\/p\u003e \u003cp\u003eChapter 15. Commutative Rings and Algebraic Geometry.\u003c\/p\u003e \u003cp\u003eChapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.\u003c\/p\u003e \u003cp\u003eChapter 17. Introduction to Homological Algebra and Group Cohomology.\u003c\/p\u003e \u003cp\u003ePART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS.\u003c\/p\u003e \u003cp\u003eChapter 18. Representation Theory and Character Theory.\u003c\/p\u003e \u003cp\u003eChapter 19. Examples and Applications of Character Theory.\u003c\/p\u003e \u003cp\u003eAppendix I: Cartesian Products and Zorn's Lemma.\u003c\/p\u003e \u003cp\u003eAppendix II: Category Theory.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864648659287,"sku":"9780471433347","price":128.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471433347.jpg?v=1722272888"},{"product_id":"linear-algebra-and-its-applications-9780471751564","title":"Linear Algebra and Its Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis set features\u003cbr\u003e\u003cbr\u003e\u003ci\u003eLinear Algebra and Its Applications, Second Edition\u003c\/i\u003e (978-0-471-75156-4)\u003cbr\u003e\u003ci\u003eLinear Algebra and Its Applications\u003c\/i\u003e, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book''s accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.\u003cbr\u003e\u003cbr\u003eBeginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.\u003cbr\u003e\u003cbr\u003eFurther updates and revisions have been i\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"...an informative and useful book, distinguished by its blend of theory and applications, which fulfills its goals admirably.\" (\u003ci\u003eMAA Review\u003c\/i\u003e March 2008)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003ePreface to the First Edition.\u003c\/p\u003e \u003cp\u003e1. Fundamentals.\u003c\/p\u003e \u003cp\u003e2. Duality.\u003c\/p\u003e \u003cp\u003e3. Linear Mappings.\u003c\/p\u003e \u003cp\u003e4. Matrices.\u003c\/p\u003e \u003cp\u003e5. Determinant and Trace.\u003c\/p\u003e \u003cp\u003e6. Spectral Theory.\u003c\/p\u003e \u003cp\u003e7. Euclidean Structure.\u003c\/p\u003e \u003cp\u003e8. Spectral Theory of Self-Adjoint Mappings.\u003c\/p\u003e \u003cp\u003e9. Calculus of Vector- and Matrix-Valued Functions.\u003c\/p\u003e \u003cp\u003e10. Matrix Inequalities.\u003c\/p\u003e \u003cp\u003e11. Kinematics and Dynamics.\u003c\/p\u003e \u003cp\u003e12. Convexity.\u003c\/p\u003e \u003cp\u003e13. The Duality Theorem.\u003c\/p\u003e \u003cp\u003e14. Normed Linear Spaces.\u003c\/p\u003e \u003cp\u003e15. Linear Mappings Between Normed Linear Spaces.\u003c\/p\u003e \u003cp\u003e16. Positive Matrices.\u003c\/p\u003e \u003cp\u003e17. How to Solve Systems of Linear Equations.\u003c\/p\u003e \u003cp\u003e18. How to Calculate the Eigenvalues of Self-Adjoint Matrices.\u003c\/p\u003e \u003cp\u003e19. Solutions.\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eAppendix 1. Special Determinants.\u003c\/p\u003e \u003cp\u003eAppendix 2. The Pfaffian.\u003c\/p\u003e \u003cp\u003eAppendix 3. Symplectic Matrices.\u003c\/p\u003e \u003cp\u003eAppendix 4. Tensor Product.\u003c\/p\u003e \u003cp\u003eAppendix 5. Lattices.\u003c\/p\u003e \u003cp\u003eAppendix 6. Fast Matrix Multiplication.\u003c\/p\u003e \u003cp\u003eAppendix 7. Gershgorin's Theorem.\u003c\/p\u003e \u003cp\u003eAppendix 8. The Multiplicity of Eigenvalues.\u003c\/p\u003e \u003cp\u003eAppendix 9. The Fast Fourier Transform.\u003c\/p\u003e \u003cp\u003eAppendix 10. The Spectral Radius.\u003c\/p\u003e \u003cp\u003eAppendix 11. The Lorentz Group.\u003c\/p\u003e \u003cp\u003eAppendix 12. Compactness of the Unit Ball.\u003c\/p\u003e \u003cp\u003eAppendix 13. A Characterization of Commutators.\u003c\/p\u003e \u003cp\u003eAppendix 14. Liapunov's Theorem.\u003c\/p\u003e \u003cp\u003eAppendix 15. The Jordan Canonical Form.\u003c\/p\u003e \u003cp\u003eAppendix 16. Numerical Range.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864652296535,"sku":"9780471751564","price":75.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471751564.jpg?v=1722272905"},{"product_id":"basic-algebra-i-9780486471891","title":"Basic Algebra I","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864736117079,"sku":"9780486471891","price":21.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486471891.jpg?v=1722273004"}],"url":"https:\/\/bookcurl.com\/collections\/algebra.oembed?page=39","provider":"Book Curl","version":"1.0","type":"link"}