{"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}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780062202697.jpg?v=1791378608"},{"product_id":"introduction-to-modern-analysis-9780192849557","title":"Introduction to Modern Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAimed at advanced undergraduate and graduate students this textbook provides an introduction to  the vast and crucial area of modern analysis. This new edition begins by covering the theoretical bases, gradually moving on to more advanced subjects and practical applications, supplementing the material with many exercises.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eMost chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills. * MathSciNet *","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732595945815,"sku":"9780192849557","price":51.3,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192849557.jpg?v=1791454079"},{"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}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198732822.jpg?v=1791378722"},{"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":29.49,"currency_code":"GBP","in_stock":false}],"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":"berkeley-problems-in-mathematics-9780387008929","title":"Berkeley Problems in Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews of the third edition:\u003c\/p\u003e \u003cp\u003e\"This new edition has been updated with the most recent exams … . There are numerous new problems and solutions which were not included in previous editions. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph. D program. … this book will develop problem-solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. … Tags with the exact exam year provide the opportunity to rehearse complete examinations. … This new edition has been updated with the most recent exams … .\" \u003cem\u003e(Zentralblatt für Didaktik der Mathematik, November 2004)\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"The Mathematics department of the University of California, Berkeley, has set a written preliminary examination to determine whether first year Ph.D. students have mastered enough basic mathematics to succeed in the doctoral program. Berkeley Problems in Mathematics is a compilation of all the … questions, together with worked solutions … . All the solutions I looked at are complete … . Some of the solutions are very elegant. … This is an impressive piece of work and a welcome addition to any mathematician’s bookshelf.\" \u003cem\u003e(Chris Good, The Mathematical Gazette, 90:518, 2006)\u003c\/em\u003e \u003c\/p\u003e \u003cp\u003e\"During the last twenty-five years problems from written preliminary examinations that are required for the Ph.D. degree at the Mathematics Department of the University of California, Berkeley, have been assembled. … The book is suited for students in mathematics, physics or engineering. Solutions are well explained, making the book valuable for self-study. The problems have a satisfactory high level, so the book is a rich resource of examples for lecturers as well, who need exercises … . This book certainly is to be recommended.\" \u003cem\u003e(Paula Bruggen, Bulletin of the Belgian Mathematical Society, 12:4, 2005)\u003c\/em\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents Preface  I Problems  1 Real Analysis  1.1 Elementary Calculus  1.2 Limitsand Continuity  1.3 Sequences, Series, and Products  1.4 Differential Calculus  1.5 Integral Calculus  1.6 Sequences of Functions  1.7 Fourier Series  1.8 Convex Functions 2 Multivariable Calculus  2.1 Limitsand Continuity  2.2 Differential Calculus  2.3 Integral Calculus 3 Differential Equations  3.1 First Order Equations  3.2 SecondOrder Equations  3.3 Higher Order Equations  3.4 Systems of Differential Equations 4 Metric Spaces  4.1 Topology of Rn  4.2 General Theory  4.3 Fixed Point Theorem 5 Complex Analysis  5.1 Complex Numbers  5.2 Series and Sequences of Functions  5.3 Conformal Mappings  5.4 Functions on the Unit Disc  5.5 Growth Conditions  5.6 Analytic and Meromorphic Functions  5.7 Cauchy’s Theorem  5.8 Zeros and Singularities  5.9 Harmonic Functions  5.10 Residue Theory  5.11 Integrals Along the Real Axis 6 Algebra  6.1 Examples of Groups and General Theory  6.2 Homomorphisms and Subgroups  6.3 Cyclic Groups  6.4 Normality, Quotients, and Homomorphisms  6.5 Sn, An , Dn, .. 6.6 Direct Products  6.7 Free Groups, Generators, and Relations  6.8 Finite Groups  6.9 Ringsand Their Homomorphisms  6.10 Ideals  6.11 Polynomials  6.12 Fields and Their Extensions  6.13 Elementary Number Theory 7 Linear Algebra  7.1 Vector Spaces  7.2 Rankand Determinants  7.3 Systems of Equations  7.4 Linear Transformations  7.5 Eigenvalues and Eigenvectors  7.6 Canonical Forms  7.7 Similarity  7.8 Bilinear, Quadratic Forms, and Inner Product Spaces  7.9 General Theory ofMatrices II Solutions  1 Real Analysis  1.1 Elementary Calculus  1.2 Limits and Continuity  1.3 Sequences, Series, and Products  1.4 Differential Calculus  1.5 Integral Calculus  1.6Sequences of Functions  1.7 Fourier Series  1.8 Convex Functions 2 Multivariable Calculus  2.1 Limitsand Continuity  2.2 Differential Calculus  2.3 Integral Calculus  3 Differential Equations  3.1 First Order Equations  3.2 Second Order Equations  3.3 Higher Order Equations  3.4 Systems of Differential Equations 4 Metric Spaces  4.1 Topology of Rn  4.2 General Theory  4.3 Fixed Point Theorem 5 Complex Analysis  5.1 Complex Numbers  5.2 Series and Sequences of Functions  5.3 Conformal Mappings  5.4 Functions on the Unit Disc  5.5 Growth Conditions  5.6 Analytic and Meromorphic Functions  5.7 Cauchy’s Theorem  5.8 Zeros and Singularities  5.9 Harmonic Functions  5.10 Residue Theory  5.11 Integrals Along the Real Axis 6 Algebra  6.1 Examples of Groups and General Theory  6.2 Homomorphisms and Subgroups  6.3 Cyclic Groups  6.4 Normality, Quotients, and Homomorphisms  6.5 Sn, An , Dn, .. 6.6 Direct Products  6.7 Free Groups, Generators, and Relations  6.8 Finite Groups  6.9 Rings and Their Homomorphisms  6.10 Ideals  6.11 Polynomials  6.12 Fields and Their Extensions  6.13 Elementary Number Theory 7 Linear Algebra  7.1 Vector Spaces  7.2 Rankand Determinants  7.3 Systems of Equations  7.4 Linear Transformations  7.5 Eigenvalues and Eigenvectors  7.6 Canonical Forms  7.7 Similarity  7.8 Bilinear, Quadratic Forms, and Inner Product Spaces  7.9 General Theory of Matrices III Appendices  A How to Get the Exams  A.1 On-line  A.2 Off-line, the Last Resort  B Passing Scores  C The Syllabus  References  Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733723754839,"sku":"9780387008929","price":56.24,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387008929.jpg?v=1791459023"},{"product_id":"groups-matrices-and-vector-spaces-a-group-theoretic-approach-to-linear-algebra-universitext-9780387794273","title":"Groups Matrices and Vector Spaces A Group","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symmetry groups, determinants, linear coding theory and cryptography are interwoven throughout.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This is an introductory text on linear algebra and group theory from a geometric viewpoint. The topics, largely standard, are presented in brief, well-organized one- and two-page subsections written in clear, if rather pedestrian, language, with detailed examples.” (R. J. Bumcrot, Mathematical Reviews, February, 2018)\u003cbr\u003e\u003cbr\u003e“It is particularly applicable for anyone who is familiar with vector spaces and wants to learn about groups – and also for anyone who is familiar with groups and wants to learn about vector spaces. This book is well readable and therefore suitable for self-studying. Each chapter begins with a concise and informative summary of its content, guiding the reader to choose the chapters with most interest to him\/her.” (Jorma K. Merikoski, zbMATH 1380.15001, 2018)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Preliminaries.- 2. Groups and Fields: The Two Fundamental Notions of Algebra.- 3. Vector Spaces.- 4. Linear Mappings.- 5. Eigentheory.- 6. Unitary Diagonalization and Quadratic Forms.- 7. The Structure Theory of Linear Mappings.- 8. Theorems on Group Theory.- 9. Linear Algebraic Groups: An Introduction.- Bibliography.- Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726474583,"sku":"9780387794273","price":61.74,"currency_code":"GBP","in_stock":false}]},{"product_id":"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486481593.jpg?v=1720001738"},{"product_id":"on-riemanns-theory-of-algebraic-functions-and-their-integrals-9780486828336","title":"On Riemanns Theory of Algebraic Functions and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733819339095,"sku":"9780486828336","price":10.44,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486828336.jpg?v=1791462942"},{"product_id":"introduction-to-linear-algebra-9780486834122","title":"Introduction to Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733826416983,"sku":"9780486834122","price":15.29,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486834122.jpg?v=1791462947"},{"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780521113618.jpg?v=1791463075"},{"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":"topics-in-operator-semigroups-281-progress-in-mathematics-9780817649319","title":"Topics in Operator Semigroups 281 Progress in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato''s unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone''s representation of unitary semigroups. Part II explores generalizations of spectral theory''s connection to operator semigroups.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e\u003cp\u003e“This monograph is suitable for second-year graduate students, but it can be recommended also to any researcher interested in operator semigroups.” (László Kérchy, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)\u003c\/p\u003e\u003cp\u003e“The present graduate level text expands the previous lecture notes from the same author, Semigroups of operators and spectral theory … . It begins with a succinct introduction to operator semigroups covering classical topics such as generators, the Hille-Yosida theorem, dissipative operators and the Lumer–Phillips theorem, the Trotter convergence theorem, exponential formulas, perturbation theory, Stone’s theorem, and analytic semigroups. … The text is also intended for second-year graduate students … . it will be a valuable source for researchers working in this area.” (G. Teschl, Monatshefte für Mathematik, Vol. 162 (4), April, 2011)\u003c\/p\u003e\u003cp\u003e“This book is based on the author’s lecture notes … in which the more advanced parts concentrated on spectral representations. … There is also a presentation of a well-known stability theorem for semigroups under countable spectral conditions. … The increased variety of topics covered will make the book more useful … . Other advantages are the inclusion of an index and some exercises, considerable extensions of the bibliography and the list of contents, and more attractive typesetting.”­­­ (C. J. K. Batty, Mathematical Reviews, Issue 2010 k)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGeneral Theory.- Basic Theory.- The Semi-Simplicity Space for Groups.- Analyticity.- The Semigroup as a Function of its Generator.- Large Parameter.- Boundary Values.- Pre-Semigroups.- Integral Representations.- The Semi-Simplicity Space.- The Laplace#x2013;Stieltjes Space.- Families of Unbounded Symmetric Operators.- A Taste of Applications.- Analytic Families of Evolution Systems.- Similarity.","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":48737454457175,"sku":"9780817649319","price":82.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817649319.jpg?v=1791467660"},{"product_id":"102-combinatorial-problems-9780817643171","title":"102 Combinatorial Problems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCovers such topics as: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"Andreescu's 51 'introductory problems' and 51 'advanced problems,' all novel, would nicely supplement any university course in combinatorics or discrete mathematics. This volume contains detailed solutions, sometimes multiple solutions, for all the problems, and some solutions offer additional twists for further thought . . . \" \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—CHOICE\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"Another excellent effort towards building combinatorial skills especially for students engaged in mathematical competitions is presented in this book through 102 selected Combinatorial problems.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—ZENTRALBLATT MATH\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"Each solution is given in full, and often with alternative versions as well. Some solutions introduce standard combinatorial tools like inclusion-exclusion, generating functions, and graphs. Others stray into probability, number theory, complex numbers, inequalities and functional equations. The book will be useful for teachers looking for challenging problems for able students and for those preparing for Olympiads.\"\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—The MATHEMATICAL GAZETTE\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"This book contains 102 highly selected combinatorial problems used in the training and testing of the USA International Mathematical Olympiad team. Half of the problems are introductory, while the rest are more difficult. All problems have complete solutions. . . It is not a collection of very difficult, impenetrable questions. Instead, the book gradually builds students' combinatorial skills and techniques. It aims to broaden a student's view of mathematics in perparation for possible participation in mathematical competitions.\" \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003e—IASI POLYTECHNIC MAGAZINE\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"Both of the two authors serves as a coach of the USA International Mathematical Olympiad (IMO) Team for several years. … the book gradually builds students’ combinatorial skills and techniques. It aims to broaden a student’s view of mathematics in preparation for possible participation in mathematical competitions. … this is a book for problem-solvers. … The present collection of problems and the presented solutions are carefully designed to develop the readers’ problem-solving abilities. … Have fun working on them!\" (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 69, 2003)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface and Introduction * Acknowledgments * Abbreviations and Notations * Introductory Problems * Advanced Problems * Solutions to Introductory Problems * Solutions to Advanced Problems * Glossary * Further Reading","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":48737459831127,"sku":"9780817643171","price":49.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817643171.jpg?v=1791467660"},{"product_id":"a-new-approach-to-differential-geometry-using-cliffords-geometric-algebra-9780817682828","title":"A New Approach to Differential Geometry using","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDifferential geometry is the study of the curvature and calculus of curves and surfaces. \u003ci\u003eA New Approach to Differential Geometry using Clifford''s Geometric Algebra\u003c\/i\u003e simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.\u003c\/p\u003e\u003cp\u003e\u003ci\u003e\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003eComplete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“The book is written in a very pedagogical style and seems to be the mirror of the original ideas of its author in the area of mathematical physics. … The typography is excellent and the figures are beautiful. … Graduate and advanced undergraduate students in physics and even in mathematics will find in this book an understanding of the contribution of Clifford algebras to the field of differential geometry as well as motivation to continue their study.” (Pierre Anglès, Mathematical Reviews, March, 2014)\u003c\/p\u003e\u003cp\u003e“The book under review is perfectly organized textbook for undergraduate students in mathematics and physics due to the large experience of the author. … The author provides quite interesting historical analysis … . This book is a natural continuation of the previous book of the author … .” (Milen Hristov, JGSP Journal of Geometry and Symmetry in Physics, Vol. 33, 2014)\u003c\/p\u003e\u003cp\u003e“The author develops the differential geometry of curves and surfaces by using Clifford’s geometric algebra. … The book is enriched with several very interesting and extensive historical and biographical presentations. … it can serve as an accompanying source for someone who studies differential geometry, or for someone who wants to look at known facts from a different viewpoint. Also, it is ideal for studying geometry through historical development, and thus this book could also be useful for reading courses on certain aspects of geometry.” (A. Arvanitoyeorgos, Zentralblatt MATH, Vol. 1232, 2012)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Introduction.- Clifford Algebra in Euclidean 3-Space.- Clifford Algebra in Minkowski 4-Space.- Clifford Algebra in Flat n-Space.- Curved Spaces.- The Gauss-Bonnet Formula.- Non-Euclidean (Hyperbolic) Geometry.- Some Extrinsic Geometry in E^n.- Ruled Surfaces Continued.- Lines of Curvature.- Minimal Surfaces.- Some General Relativity.- Matrix Representation of a Clifford Algebra.- Construction of Coordinate Dirac Matrices.- A Few Terms of the Taylor's Series for the Urdī-Copernican Model for the Outer Planets.- A Few Terms of the Taylor's Series for Kepler's Orbits.- References.- Index.","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":48737459929431,"sku":"9780817682828","price":75.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817682828.jpg?v=1791467661"},{"product_id":"103-trigonometry-problems-9780817643348","title":"103 Trigonometry Problems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIncludes problem-solving tactics and practical test-taking techniques that provide enrichment and preparation for various math competitions. This title provides comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"The way chosen by the authors of this book is one that goes directly to the interested student. The theoretical facts are presnented at the beginning of each paragraph and then problems with solutions are discussed...Most of the themes are from so-called trigonometric goemetry, making the book more pleasant for the interested student. Each topic is punctured by a lot of examples. I [note] the beautiful topics on spheric trigonometry which is nowadays forgetten in schools...To conclude, I enjoyed a wonderful text in trigonometry which contains also a lot of real important mathematical ideas. I recommend it as a basic text for all students and teachers involved in high school competitions as competitors or coaches.\" ---\u003cstrong\u003eRevue Roumaine de Mathématiques Pures et Appliquées\u003c\/strong\u003e\u003c\/p\u003e \u003cp\u003e\"The title of this book already says everything about the content: 103 trigonometry problems that were given in the training and testing of the US International Mathematical Olympiad team are presented along with their solutions. … The presentation is clear, accurate and extensive. For these reasons the book is very easy to read and leads the reader to astonishing insights in an elementary field of mathematics. It is therefore also very appropriate as a textbook … .\" (St. Götz, Monatshefte für Mathematik, Vol. 149 (3), 2006)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e* Preface * Abbreviations and Notations * Trigonometric Problems * Introductory Problems * Advanced Problems * Solutions to Introductory Problems * Solutions to Advanced Problems * Glossary * Further Reading","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":48737463206231,"sku":"9780817643348","price":49.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817643348.jpg?v=1791467660"},{"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":36.38,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009001922.jpg?v=1791378855"},{"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":62.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009018883.jpg?v=1791468890"},{"product_id":"modern-trends-in-algebra-and-representation-theory-9781009097352","title":"Modern Trends in Algebra and Representation","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eExpanding on lectures given at the LMS Autumn Algebra School 2020, this text gives a guided tour of modern developments in algebra and representation theory. It includes many worked examples and applications, providing graduate students and researchers in related disciplines with a springboard into the vast literature in each area.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction David Jordan, Nadia Mazza and Sibylle Schroll; 1. Auslander-Reiten theory of finite-dimensional algebras Raquel Coelho Simões; 2. τ-Tilting theory – an introduction Hipolito Treffinger; 3. From frieze patterns to cluster categories Matthew Pressland; 4. Infinite-dimensional representations of algebras Rosanna Laking; 5. The Springer correspondence Sam Gunningham; 6. An introduction to diagrammatic Soergel bimodules Amit Hazi; 7. A companion to quantum groups Bart Vlaar; 8. Infinite-dimensional Lie algebras and their multivariable generalizations Brian Williams; 9. An introduction to crowns in finite groups Gareth Tracey; 10. An introduction to totally disconnected locally compact groups and their finiteness conditions Ilaria Castellano; 11. Locally analytic representations of p-adic groups Andreas Bode and Nicolas Dupré.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738004009303,"sku":"9781009097352","price":70.0,"currency_code":"GBP","in_stock":true}]},{"product_id":"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":75.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009193399.jpg?v=1791468905"},{"product_id":"coxeter-bialgebras-9781009243773","title":"Coxeter Bialgebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; 1. Coxeter groups and reflection arrangements; Part I. Coxeter Species: 2. Coxeter species and Coxeter bimonoids; 3. Basic theory of Coxeter bimonoids; 4. Examples of Coxeter bimonoids; 5. Coxeter operads; 6. Coxeter Lie monoids; 7. Structure theory of Coxeter bimonoids; Part II. Coxeter Spaces: 8. Coxeter spaces and Coxeter bialgebras; 9. Basic theory of Coxeter bialgebras; 10. Examples of Coxeter bialgebras; 11. Coxeter operad algebras; 12. Coxeter Lie algebras; 13. Structure theory of Coxeter bialgebras; Part III. Fock Functors: 14. Fock functors; 15. Coxeter bimonoids and Coxeter bialgebras; 16. Adjoints of Fock functors; 17. Structure theory under Fock functors; 18. Examples of Fock spaces; Appendix A. Category theory; References; List of Notations; List of Tables; List of Figures; List of Summaries; Author Index; Subject Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738029044055,"sku":"9781009243773","price":182.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009243773.jpg?v=1791468913"},{"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":114.0,"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":70.29,"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":999.99,"currency_code":"GBP","in_stock":false}],"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}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781852334253.jpg?v=1791478948"},{"product_id":"encountering-algebra-a-comparative-study-of-classrooms-in-finland-norway-sweden-and-the-usa-9783030175764","title":"Encountering Algebra: A Comparative Study of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book reports a comparative research project about algebra teaching and learning in four countries. Algebra is a central topic of learning across the world, and it is well-known that it represents a hurdle for many students. The book presents analyses built on extensive video-recordings of classrooms documenting the first introduction to symbolic algebra (students aged 12 to 14). While the content addressed in all classrooms is variables, expressions and equations, the teaching approaches are diverse. The chapters bring the reader into different algebra classrooms, discussing issues such as mathematization and social norms, the role of mediating tools and designed examples, and teacher beliefs. By comparing classrooms, new insights are generated about how students understand the algebraic content, how teachers instruct, and how both parties deal with difficulties in learning elementary algebra. The book also describes a research methodology using video in search of taken-for-granted aspects of algebra lessons.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This book is a valuable resource for those who are interested in studying either the teaching and learning of algebra or similarities and differences in mathematics instruction around the world. … the book provides an interesting and enlightening glimpse into how algebra is introduced to students around the world.” (Erica R. Miller, MAA Reviews, May 24, 2020)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eChapter 1: School Algebra.- Chapter 2: Researching Classrooms in Search of Learning: Theoretical and Methodological Considerations.- Chapter 3: The VIDEOMAT Project: Theoretical Considerations and Methodological Procedures.- Chapter 4: Participation and Mathematization in Introductory Algebra Classrooms: The Case of Sweden.- Chapter 5: Designed Examples as Mediating Tools: Introductory Algebra in Two Norwegian Grade 8 Classrooms.- Chapter 6: Learning to Solve Equations in Three Swedish-speaking Classrooms in Finland.- Chapter 7: How Teachers Introduce Algebra and How it Might Affect Students’ Beliefs About What it Means to “Do” Mathematics.- Chapter 8: The Fifth Lesson: Students’ Responses to a Patterning Task Across the Four Countries.- Chapter 9: Encouraging Algebraic Reasoning in Contemporary Classrooms: Some Observations and a Synthesis.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743025770839,"sku":"9783030175764","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030175764.jpg?v=1791480460"},{"product_id":"basic-representation-theory-of-algebras-9783030351175","title":"Basic Representation Theory of Algebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander–Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander–Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. \u003cbr\u003eIntended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This text is a well-conceived and accessible entry point to the representation theory of finite-dimensional algebras, taking the modern perspective of focussing on morphisms between modules rather than just modules themselves.” (Ryan David Kinser, Mathematical Reviews, December, 2021)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Chapter 1: Modules, algebras and quivers.- Chapter 2: The radical and almost split sequences.- Chapter 3: Constructing almost split sequences.- Chapter 4: The Auslander–Reiten quiver of an algebra.- Chapter 5: Endomorphism algebras.- Chapter 6: Representation-finite algebras.- Bibliography.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743033995607,"sku":"9783030351175","price":49.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030351175.jpg?v=1791480475"},{"product_id":"advanced-linear-and-matrix-algebra-9783030528140","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":48743038943575,"sku":"9783030528140","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030528140.jpg?v=1723812623"},{"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":999.99,"currency_code":"GBP","in_stock":false}]},{"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030528171.jpg?v=1791480495"},{"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030574673.jpg?v=1720063852"},{"product_id":"interactions-of-quantum-affine-algebras-with-cluster-algebras-current-algebras-and-categorification-in-honor-of-vyjayanthi-chari-on-the-occasion-of-her-60th-birthday-9783030638481","title":"Interactions of Quantum Affine Algebras with","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including:\u003cul\u003e\n\u003cli\u003eString diagrams and categorification\u003c\/li\u003e\n\u003cli\u003eQuantum affine algebras and cluster algebras\u003c\/li\u003e\n\u003cli\u003eSteinberg groups for Jordan pairs\u003c\/li\u003e\n\u003cli\u003eDynamical quantum determinants and Pfaffians\u003c\/li\u003e\n\u003c\/ul\u003e\u003ci\u003eInteractions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification\u003c\/i\u003e will be an ideal resource for researchers in the fields of representation theory and mathematical physics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePublications of Vyjayanthi Chari.- Students of Vyjayanthi Chari.- Part I: Courses.- String Diagrams and Categorification.- Quantum Affine Algebras and Cluster Algebras.- Part II: Surveys.- Work of Vyjayanthi Chari.- Steinberg Groups for Jordan Pairs - An Introduction with Open Problems.- On the Hecke-Algebraic Approach for General Linear Groups over a p-adic Field.- Part III: Papers.- Categorical Representations and Classical p-adic Groups.- Formulae of \u003ci\u003el\u003c\/i\u003e-Divided Powers in Uq(sl2),II.- Longest Weyl Group Elements in Action.- Dual Kashiwara Functions for the B(∞) Crystal in the Bipartite Case.- Lusztig's t-Analogue of weight multiplicity via Crystals.- Conormal Varieties on the Cominuscule Grassmannian.- Evaluation Modules for Quantum Toroidal \u003ci\u003egln\u003c\/i\u003e Algebras.- Dynamical Quantum Determinants and Pfaffians.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743043465559,"sku":"9783030638481","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030638481.jpg?v=1720063862"},{"product_id":"elements-of-mathematics-a-problem-centered-approach-to-history-and-foundations-9783030750503","title":"Elements of Mathematics: A Problem-Centered","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed.\u003c\/p\u003e  \u003cp\u003eBeginning with a thorough treatment of the natural numbers via Peano’s axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff’s axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eElements of Mathematics\u003c\/i\u003e is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Elements of mathematics is a curious book. The most challenging aspect of this volume to assess is its purpose.” (Jeff Johannes, Mathematical Reviews, October, 2022)\u003cbr\u003e“Transparency of explanation and gradually built material are outstanding features of the textbook. In addition, solutions to some problems are designed using more than one approach, making it adaptable to various students' backgrounds. … The book makes itself accessible to a vast population of students. The book can enhance the undergraduate curriculum or serve as a reflective resource for graduate mathematics students.” (Andrzej Sokolowski, MAA Reviews, March 20, 2022)\u003cbr\u003e“A historical concern is present throughout, with pieces of information on the history of concepts and theorems.” (Victor V. Pambuccian, zbMATH 1479.00002, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e0. Preliminaries: Sets, Relations, Maps.- 1. Natural, Integral and Rational Numbers.- 2. Real Numbers.- 3. Rational and Real Exponentiation.- 4. Limits of Real Functions.- 5. Real Analytic Plane Geometry.- 6. Polynomial Expressions.- 7. Polynomial Functions.- 8. Conics.- 9. Rational and Algebraic Expressions and Functions.- 10. Exponential and Logarithmic Functions.- 11. Trigonometry.- Further Reading.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743048315223,"sku":"9783030750503","price":52.24,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030750503.jpg?v=1791480529"},{"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030800307.jpg?v=1791480537"},{"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030802417.jpg?v=1791480537"},{"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":44.99,"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031197062.jpg?v=1720064000"},{"product_id":"introduction-to-matrix-analysis-and-applications-9783319041490","title":"Introduction to Matrix Analysis and Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eMatrices can be studied in different ways. They are a linear algebraic structure and have a topological\/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis.\u003c\/p\u003e\u003cp\u003eThis book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eIntroduction to Matrix Analysis and Applications\u003c\/i\u003e is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This volume, written in a clear and elegant style, provides a nice introduction to this actively studied area. It is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.” (László Kérchy, Acta Scientiarum Mathematicarum, Vol. 82 (1-2), 2016)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFundamentals of operators and matrices.- Mappings and algebras.- Functional calculus and derivation.- Matrix monotone functions and convexity.- Matrix means and inequalities.- Majorization and singular values.- Some applications.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743091568983,"sku":"9783319041490","price":58.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319041490.jpg?v=1791481704"},{"product_id":"homotopical-topology-9783319234878","title":"Homotopical Topology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This book is a treasure trove for every mathematician who has to deal with classical algebraic topology and homotopy theory on the research level. … Its style is refreshing and informative, and the reader can feel the authors’ joy at sharing their insight into algebraic topology. … will be a useful addition to any mathematical bookshelf.” (Thomas Hüttemann, Mathematical Reviews, March, 2017)\u003c\/p\u003e\u003cp\u003e“This book covers all the basic material necessary for complete understanding of the fundamentals of algebraic topology … . This increase in the number of topics has made the book more convenient for serious students not only to extend their knowledge but also to gain insight into the interplay between these three subjects. … This book is designed to help students to select the level of learning subjects they want to reach … .” (Haruo Minami, zbMATH 1346.55001, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Homotopy.- Homology.- Spectral Sequences of Fibrations.- Cohomology Operations.- The Adams Spectral Sequence.- K-Theory and Other Extraordinary Cohomology Theories.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743093043543,"sku":"9783319234878","price":47.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319234878.jpg?v=1791379134"},{"product_id":"an-excursion-through-elementary-mathematics-volume-i-real-numbers-and-functions-9783319538709","title":"An Excursion through Elementary Mathematics,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003eAs part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003eThe book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book develops several basic concepts in elementary mathematics and which are needed in the preparation of mathematical Olympiads around the world. … Throughout the book, the author puts great emphasis on explaining the issues discussed. … The presentation is pedagogical and coherent throughout with emphasis on concepts and underlying ideas … . The author has succeeded in crafting a comprehensive book to give a well-rounded picture of the role of real numbers and functions in elementary mathematics.” (Teodora Liliana Rădulescu, zbMATH 1371.97002, 2017)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eChapter 1 The Set of Real Numbers.- Chapter 2 Algebraic Identities, Equations and Systems.- Chapter 3 Elementary Sequences.- Chapter 4 Induction and the Binomial Formula.- Chapter 5 Elementary Inequalities.- Chapter 6 The Concept of Function.- Chapter 7 More on Real Numbers.- Chapter 8 Continuous Functions.- Chapter 9 Limits and Derivatives.- Chapter 10 Riemann’s Integral.- Chapter 11 Series of Functions.- Bibliography.- Appendix A Glossary.- Appendix B Hints and Solutions.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743097762135,"sku":"9783319538709","price":58.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319538709.jpg?v=1791481724"}],"url":"https:\/\/bookcurl.com\/collections\/algebra.oembed?page=60","provider":"Book Curl","version":"1.0","type":"link"}