Algebraic geometry Books
American Mathematical Society Sets Groups and Mappings An Introduction to
Book SynopsisIntroduces the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students who are looking for an entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry.Table of Contents Logic and proofs An introduction to sets The integers Mappings and relations Induction and recursion Binary operations Groups Divisibility and congruences Primes Multiplicative inverses of residue classes Linear transformations Isomorphism The symmetric group Examples of finite groups Cosets Homomorphisms Group actions Euclidean geometry Euler's formula Index
£71.10
MP-AMM American Mathematical Field Theory and Its Classical Problems
Book SynopsisAllows Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular $n$-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond.Trade ReviewThe presented book is a clear and concise introduction to classical results of Galois theory. The book is an excellent reading for everyone, especially for instructors and first year graduate students in Galois theory."" - Acta. Sci. Math.
£60.30
MP-AMM American Mathematical Intense Automorphisms of Finite Groups
Book SynopsisIn this paper the authors classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges that the structure of such groups is almost completely determined by their nilpotency class: for p > 3, they share a quotient, growing with their class, with a uniquely determined infinite 2-generated pro-p group.
£67.50
MP-AMM American Mathematical Arthur Packets for padic Groups by Way of
Book SynopsisProposes a geometric description of Arthur packets for padic groups using vanishing cycles of perverse sheaves. The approach is inspired by the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups and follows the direction indicated by Vogan in his paper on the Langlands correspondence.
£67.50
MP-AMM American Mathematical Tensors Asymptotic Geometry and Developments
Book SynopsisTensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. Numerous open problems appropriate for graduate students and post-docs are included throughout.Table of Contents Basics: Motivation, first definitions and properties Tensors via linear algebra: Rank and border rank Tensor networks The asymptotic geometry of tensors: Detour into probability and information theory Strassen's laser method and spectral theory Quantum mechanics for quantum information theory Quantum information theory and the asymptotic geometry of tensors Moment maps and moment polytopes Hints and answers to selected exercises Bibliography Index.
£45.90
MP-AMM American Mathematical Advances in Representation Theory of Algebras
Book SynopsisPapers in this volume cover theory, tame algebras, and the use of quadratic forms in representation theory. Also included are papers on the categorical approach to representations of algebras and relations to Lie theory, Cohen-Macaulay modules, quantum groups and other algebraic structures.Table of Contents Lectures on split-by-nilpotent extensions; A note on sequential walks; A characterization of representation infinite quiver settings; Dualities for modules of finite projective dimension; Frieze varieties are invariant under Coxeter mutation; On tame strongly simply connected algebras; A remark on Hochschild cohomology and Koszul duality; Thick subcategories of the stable category of modules over the exterior algebra; Finite direct sums of cyclic embeddings; The algebraic theory of Fuchsian singularities; Cycle-finite modules over Artin algebras; Piecewise hereditary incidence algebras; Derived categories of gentle algebras and surface dissections; Socle deformations of selfinjective orbit algebras of tilted type.
£96.30
MP-AMM American Mathematical Rings with Polynomial Identities and Finite
Book SynopsisA polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike.Table of Contents Introduction Foundations: Noncommutative algebra Universal algebra Symmetric functions and matrix invariants Polynomial maps Azumaya algebras and irreducible representations Tensor symmetry Combinatorial aspects of polynomial identities: Growth Shirshov's theorem $2\times2$ matrices The structure theorems Matrix identities Structure theorems Invariants and trace identities Involutions and matrices A geometric approach Spectrum and dimension The relatively free algebras: The nilpotent radical Finite-dimensional and affine PI algebras The relatively free algebras Identities and superalgebras The Specht problem The PI-exponent Codimension growth for matrices Codimension growth for algebras satisfying a Capelli identity The Golod-Shafarevich counterexamples Bibliography Index Index of Symbols.
£78.30
MP-AMM American Mathematical The Canonical Ring of a Stacky Curve
Book Synopsis
£67.50
MP-AMM American Mathematical A Study in Derived Algebraic Geometry Volume II
Book SynopsisDerived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry.Table of Contents Inf-schemes: Introduction Deformation theory Ind-schemes and inf-schemes Ind-coherent sheaves on ind-inf-schemes An application: Crystals Formal geometry: Introduction Formal moduli Lie algebras and co-commutative co-algebras Formal groups and Lie algebras Lie algebroids Infinitesimal differential geometry Bibliography Index of notations Index.
£101.70
MP-AMM American Mathematical Coefficient Systems on the BruhatTits Building
Book SynopsisIn general, this volume gives a description of the derived category of H-modules in terms of smooth G-representations and yields a functor to generalized (?, ?)-modules extending the constructions of Colmez, Schneider and Vigneras.
£67.50
American Mathematical Society Mackey Profunctors
Book SynopsisView the abstract.
£63.90
MP-AMM American Mathematical Planar Algebras in Braided Tensor Categories
Book SynopsisView the abstract.
£68.40
American Mathematical Society Iwasawa Theory and Its Perspective Volume 1
Book SynopsisThe goal of this publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt-Kubota $L$-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects.Table of Contents Motivation and utility of Iwasawa theory $\mathbb{Z}_p$-extension and Iwasawa algebra Cyclotomic Iwasawa theory for ideal class groups Bookguide Appendix A References Index
£96.30
MP-AMM American Mathematical Local Coefficients and Gamma Factors for
Book SynopsisView the abstract.
£68.40
MP-AMM American Mathematical Singularities Mirror Symmetry and the Gauged
Book SynopsisContains the proceedings of the workshop ‘Crossing the Walls in Enumerative Geometry’, held in May 2018. The volume features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model.Table of Contents R. Webb, Quasimaps and some examples of stacks for everybody E. Clader, Introduction to the gauged linear sigma model D. Ross, Localization and mirror symmetry W.-P. Li, A brief introduction to cosection localization and $P$-fields M. Shoemaker, Virtual classes for hypersurfaces via two-periodic complexes J. Oh, Localized Chern characters for 2-periodic complexes and virtual cycles T. Milanov, Singularity theory and mirror symmetry U. Whitcher, Counting points with Berglund-Hubsch-Kravitz mirror symmetry H. Fan and Y.-P. Lee, Variations on the theme of quantum Lefschetz R. Mi, Type II extremal transitions in Gromov-Witten theory C.-C. M. Liu, A lecture on holomorphic anomaly equations and extended holomorphic anomaly equation
£96.30
MP-AMM American Mathematical Weight Multiplicities and Young Tableaux Through
Book SynopsisView the abstract.
£68.40
MP-AMM American Mathematical Higher Ramanujan Equations and Periods of Abelian
Book SynopsisView the abstract.
£63.90
MP-AMM American Mathematical Cohomology of the Moduli Space of Cubic
Book SynopsisView the abstract.
£68.40
American Mathematical Society Multiplicative Invariant Fields of Dimension leq
Book SynopsisView the abstract.
£63.90
American Mathematical Society Inflectionary Invariants for Isolated Complete
Book SynopsisView the abstract.
£63.90
MP-AMM American Mathematical Linear Algebra Volumes I and II The Set
Book SynopsisThis two-volume set focuses on linear algebra for graduate students in mathematics, the sciences, and economics. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise.Table of Contents Part : Vector Spaces Over a Field $\mathbb{K}$ Linear Operators $T: V \to W$ Duality and the Dual Space $V^*$ Determinants The Diagonalization Problem Inner Product Spaces Index Part : Generalized Eigenspaces and the Jordon Decomposition Further Applications of Jordon Form Bilinear, Quadratic, and Multilinear Forms Tensor Fields, Manifolds, and Vector Calculus Matrix Lie Groups Bibliography.
£78.30
MP-AMM American Mathematical Representations of Semisimple Lie Algebras in the
Book Synopsis
£71.10
MP-AMM American Mathematical Analysis and Linear Algebra The Singular Value
Book SynopsisProvides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear algebra to data science. Four important applications relevant to data science are considered throughout the book.Table of Contents Introduction Linear algebra and normed vector spaces Main tools The spectral theorem The singular value decomposition Applications revisited A glimpse towards infinite dimensions Bibliography Index of notation Index
£46.80
American Mathematical Society Visual Group Theory
Book SynopsisThe more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups to advanced structural concepts.Trade ReviewCarter presents the group theory portion of abstract algebra in a way that allows students to actually see, using a multitude of examples and applications, the basic concepts of group theory … The numerous images (more than 300) are the heart of the text. As this work enables readers to see, experiment with, and understand the significance of groups, they will accumulate examples of groups and their properties that will serve them well in future endeavors in mathematics. Recommended.- J. T. Zerger, Choice;""If you teach abstract algebra, then this book should be a part of the resources you use. While the phrase “visual abstract algebra” may seem to be a contradiction, the diagrams in this book are an existence proof to the contrary. They are clear, colorful and concise, very easy to understand and sure to aid the students that have difficulty in internalizing the abstract nature of the subject matter …""- Charles Ashbacher, Journal of Recreational Mathematics
£999.99
MP-AMM American Mathematical Perfectoid Spaces Lectures from the 2017 Arizona
Book SynopsisProvides a broad introduction to perfectoid spaces. The book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.Table of Contents J. Weinstein, Arizona Winter School 2017: Adic spaces K. S. Kedlaya, Sheaves, stacks, and shtukas B. Bhatt, The Hodge-Tate decomposition via perfectoid spaces A. Caraiani, Perfectoid Shimura varieties
£78.30
MP-AMM American Mathematical Eigenfunctions of Transfer Operators and
Book SynopsisWe develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators.
£68.40
MP-AMM American Mathematical Total Positivity is a Quantum Phenomenon The
Book Synopsis
£68.40
American Mathematical Society On MediumRank Lie Primitive and Maximal Subgroups
Book Synopsis
£63.90
MP-AMM American Mathematical Comparison of Relatively Unipotent Log de Rham
Book Synopsis
£63.90
MP-AMM American Mathematical An Invitation to Arithmetic Geometry
Book Synopsis
£999.99
MP-AMM American Mathematical pAdic Analysis Arithmetic and Singularities
Book SynopsisProvides an introduction to an active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. The book introduces $p$-adic analysis, the theory of zeta functions, Archimedean, $p$-adic, motivic, singularities of plane curves and their Poincare series.Table of Contents Surveys: E. Leon-Cardenal, Archimedean zeta functions and oscillatory integrals J. J. Moyano-Fernandez, Generalized Poincare series for plane curve singularities N. Potemans and W. Veys, Introduction to $p$-adic Igusa zeta functions J. Viu-Sos, An introduction to $p$-adic and motivic integration, zeta functions and invariants of singularities W. A. Zuniga-Galindo, $p$-adic analysis: A quick introduction Articles: E. Artal Bartolo and M. Gonzalez Villa, On maximal order poles of generalized topological zeta functions J. I. Cogolludo-Agustin, T. Laszlo, J. Martin-Morales, and A. Nemethi, Local invariants of minimal generic curves on rational surfaces J. Nagy and A. Nemethi, Motivic Poincare series of cusp surface singularities C. D. Sinclair, Non-Archimedean electrostatics
£98.10
MP-AMM American Mathematical Algebras Lattices Varieties Volume II
Book SynopsisThe second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices.Table of Contents The classification of varieties Equational logic Rudiments of model theory Bibliography Index
£98.10
MP-AMM American Mathematical Algebras Lattices Varieties Volume III
Book SynopsisThe third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices.Table of Contents Finite algebras and their clones Abstract clone theory Commutator theory Bibliography Index
£98.10
MP-AMM American Mathematical Algebra and Coding Theory
Book SynopsisContains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, held in July 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held in July 2021. The articles cover topics in commutative and noncommutative algebra and applications to coding theory.Table of Contents R. R. de Araujo, A. L. M. Pereira, and C. Polcino Milies, A note on checkable codes over Frobenius and quasi-Frobenius rings N. Aydin, T. Guidotti, and P. Liu, Good classical and quantum codes from multi-twisted codes N. Bennenni and A. Leroy, Evaluation of iterated ore polynomials and skew Reed-Muller codes G. Blachar, L. H Rowen, and U. Vishne, Identities of the algebra $\mathbb{O}\otimes\mathbb{O}$ S. Breaz and Y. Zhou, When is every non central-unit a sum of two nilpotents? A. Chapman and K. McKinnie, Asymptotic Brauer $p$-dimension L. W. Christensen, S. Estrada, and P. Thompson, Five theorems on Gorenstein global dimensions S. T. Dougherty and S. Sahinkaya, Quasi-self-dual codes over a non-unital ring of order 4 S. T. Dougherty, S. Sahinkaya, and D. Ustun, Codes from the skew ring $M_2(\mathbb{F}_2\rtimes_\varphi G$ F. D'Este, The underlying vector spaces of certain endomorhism rings A. Facchini, Algebraic structures from the point of view of complete multiplicative lattices C. Fernandez-Cordoba and S. Szabo, $\mathbb{Z}_2\mathbb{Z}_4$-additive codes as codes over rings G. Lee, C. S. Roman, N. K. Tung, and X. Zhang, On Utumi rings and continuous regular Baer rings S. K. Jain and A. Leroy, Matrices representable as product of conjugates of a singular matrix F. Kaynarca, G. D'Este, and D. Keskin Tutuncu, Almost projective modules over non-hereditary algebras M. Salahuddin Khan, A. Abbasi, S. Ali, and M. Ayedh, On prime ideals with generalized derivations in rings with involution J. Krempa, On nil algebras and a problem of Passeman concerning nilpotent free algebras X. Mary, Rings with transitive chaining of idempotents J. K. Park and S. T. Rizvi, On continuous hulls of rings and modules
£103.50
MP-AMM American Mathematical A Friendly Introduction to Abstract Algebra
Book SynopsisOffers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics.Table of Contents Preliminaries: Introduction to proofs Sets and subsets Divisors Examples of groups: Modular arithmetic Symmetries Permutations Matrices Introduction to groups: Introduction to groups Groups of small size Matrix groups Subgroups Order of an element Cyclic groups, Part I Cyclic groups, Part II Group homomorphisms: Functions Isomorphisms Homomorphisms, Part I Homomorphisms, Part II Quotient groups: Introduction to cosets Lagrange's theorem Multiplying/adding cosets Quotient group examples Quotient group proofs Normal subgroups First isomorphism theorem Introduction to rings: Introduction to rings Integral domains and fields Polynomial rings, Part I Polynomial rings, Part II Factoring polynomials Quotient rings: Ring homomorphisms Introduction to quotient rings Quotient ring $\mathbb{Z}_7[x]/ \langle x^2-1\rangle$ Quotient ring $\mathbb{R}[x]/ \langle x^2 +1\rangle$ $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part I Maximal ideals $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part II Appendices: Proof of the GCD theorem Composition table for $D_4$ Symbols and notations Essential theorems Index: Index of terms
£54.90
American Mathematical Society Cyclic Cohomology at 40
Book SynopsisPresents survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc, in which cyclic homology plays the role of a unifying theme.Table of Contents A. Baldare, M. Benameur, and V. Nistor, Chern-Connes-Karoubi character isomorphisms and algebras of symbols of pseudodifferential operators J. Block, N. Higson, and J. Sanchez Jr., On Perrot's index cocycles P. Carrillo Rouse, The Chern-Baum Connes assembly map for Lie groupoids A. Connes and C. Consani, Hochschild homology, trace map and $\zeta$-cycles A. Connes and C. Consani, Cyclic theory and the pericyclic category J. Cuntz, The image of Bott peridocity in cyclic homology B. I. Dundas, Applications of topological cyclic homology to algebraic $K$-theory D. Gepner, Algebraic $K$-theory and generalized stable homotopy theory A. Gorokhovsky and E. van Erp, Cyclic cohomology and the extended Heisenberg calculus of Epstein and Melrose L. Hesselholt, Topological cyclic homology and the Fargues-Fontaine curve M. Khalkhali and I. Shapiro, Hopf cyclic cohomology and beyond M. Lorentz, The Hochschild cohomology of uniform Roe algebras E. McDonald, F. Sukochev, and X. Xiong, Quantum differntiability-The analytical perspective R. Meyer and D. Mukherjee, Local cyclic homology for nonarchimedean Banach algebras H. Moscovici, On the van Est analogy in Hopf cyclic cohomology P. Piazza and X. Tang, Primary and secondary invariants of Dirac operators on $G$-proper manifolds M. J. Pflaum, Localization in Hochschild homology R. Ponge, Cyclic homology and group actions E. Prodan, Cyclic cocycles and quantized pairings in materials science M. Puschnigg, Periodic cyclic homology of crossed products A. Savin and E. Schrohe, Trace expansions and equivariant traces on an algebra of Fourier integral operators on $\mathbb{R}^n$ Y. Song and X. Tang, Carton motion group and orbital integrals B. Tsygan, On noncommutative crystalline cohomology T. D. H. Van Nuland and W. D. van Suijlekom, Cyclic cocycles and one-loop corrections in the spectral action J. Wang, Z. Xie, and G. Yu, $\ell^1$-higher index, $\ell^1$-higher rho invariant and cyclic cohomology.
£109.80
American Mathematical Society (textbook) Applied Linear Algebra
Book SynopsisLinear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schroedinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to
£55.10
American Mathematical Society Homological Methods in Commutative Algebra
Book SynopsisDevelops the machinery of homological algebra and its applications to commutative rings and modules. The book assumes familiarity with basic commutative algebra. This is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra.Table of Contents Categories Abelian categories Derived functors Spectral sequences Projective and injective modules Flatness Koszul complexes and regular sequences Regularity Mild singularities Local cohomology and duality Background material Bibliography Index of notation Index
£106.20
MP-AMM American Mathematical Linear Algebra in Action
Book SynopsisPresents a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade.Table of Contents Prerequisites Dimension and rank Gaussian elimination Eigenvalues and eigenvectors Towards the Jordan decomposition The Jordan decomposition Determinants Companion matrices and circulants Inequalities Normed linear spaces Inner product spaces Orthogonality Normal matrices Projections, volumes, and traces Singular value decomposition Positive definite and semidefinite matrices Determinants redux Applications Discrete dynamical systems Continuous dynamical systems Vector-valued functions Fixed point theorems The implicit function theorem Extremal problems Newton's method Matrices with nonnegative entries Applications of matrices with nonnegative entries Eigenvalues of Hermitian matrices Singular values redux I Singular values redux II Approximation by unitary matrices Linear functionals A minimal norm problem Conjugate gradients Continuity of eigenvalues Eigenvalue location problems Matrix equations A matrix completion problem Minimal norm completions The numerical range Riccati equations Supplementary topics Toeplitz, Hankel, and de Branges Bibliography Notation index Subject index.
£106.20
MP-AMM American Mathematical Elementary Mathematical Models Order Aplenty and
Book SynopsisWith numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences.Trade ReviewKalman uses basic growth models...not only to convey the power of mathematics in solving real-world problems, but also to motivate the study of the elementary functions usually encountered in college algebra courses. There is a natural evolution from a simple hypotheses to difference equations, to their solutions, to the study of the elementary functions associated with the solutions. There is an emphasis on the ""why"" of algebra and on manipulation associated with applications rather than for its own sake.Numerical, graphical, and symbolic approaches are used throughout, and the numerous exercises include reading comprehension exercises and group selected exercises...Aimed at students at the college algebra or liberals arts mathematics level, the slow careful development should be clear even to those with a weak algebraic background. Highly recommended."" - Choice""An innovative alternative to introductory college mathematics intended for any student not headed for calculus. Uses discrete and continuous models of growth to introduce increasingly sophisticated algebraic patterns...An effective blend of narrative, motivation, calculation, and graphical representation that introduces algebraic thinking with a minimum of algebraic formalisms."" - The American Mathematical Monthly""The book is well balanced and succeeds in introducing the use of discrete models to students who might view a mathematics class with a weary eye...the author does a superb job of addressing a difficult audience. This is especially true of the problem sets. An excellent mix of reading, simple/short answer, and word problems of varying difficulties are given. Furthermore, complete answers to some of the problems are given in the same chapter, rather than in an appendix."" - Kelly Black, University of New Hampshire""This book can be described as the protocol of the ultimate (and apparently successful) teaching experiment, namely to lead students with hardly any mathematical background at all, to a respectable level in the fundamentals of mathematics in such a way, that they will always have positive thoughts about it. ...The expert reader may use this book as a rich source of growth problems."" - Springer-Verlag, Zentallblatt fur Mathematik""I found the book a refreshing alternative to college algebra textbooks and would recommend it to instructors who are seeking changes."" - The Mathematics Teacher
£52.20
American Mathematical Society Linear Algebra in Action
Book SynopsisPresents a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade.Table of Contents Prerequisites Dimension and rank Gaussian elimination Eigenvalues and eigenvectors Towards the Jordan decomposition The Jordan decomposition Determinants Companion matrices and circulants Inequalities Normed linear spaces Inner product spaces Orthogonality Normal matrices Projections, volumes, and traces Singular value decomposition Positive definite and semidefinite matrices Determinants redux Applications Discrete dynamical systems Continuous dynamical systems Vector-valued functions Fixed point theorems The implicit function theorem Extremal problems Newton's method Matrices with nonnegative entries Applications of matrices with nonnegative entries Eigenvalues of Hermitian matrices Singular values redux I Singular values redux II Approximation by unitary matrices Linear functionals A minimal norm problem Conjugate gradients Continuity of eigenvalues Eigenvalue location problems Matrix equations A matrix completion problem Minimal norm completions The numerical range Riccati equations Supplementary topics Toeplitz, Hankel, and de Branges Bibliography Notation index Subject index.
£66.60
MP-AMM American Mathematical Commutative Algebra
Book SynopsisProvides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered.Table of Contents Basics Finiteness conditions Factorization Computational methods Integral dependence Lattice methods Metric and topological methods Geometric dictionary Dimension theory Local structure Fields Bibliography Index of notation Index
£999.99
MP-AMM American Mathematical Homological Methods in Commutative Algebra
Book SynopsisDevelops the machinery of homological algebra and its applications to commutative rings and modules. The book assumes familiarity with basic commutative algebra. This is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra.Table of Contents Categories Abelian categories Derived functors Spectral sequences Projective and injective modules Flatness Koszul complexes and regular sequences Regularity Mild singularities Local cohomology and duality Background material Bibliography Index of notation Index
£70.20
American Mathematical Society The Versatility of Integrability
£104.40
MP-AMM American Mathematical The Classification of the Finite Simple Groups
Book SynopsisThe tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. This book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series.Table of Contents General group-theoretic lemmas Theorem $\mathscr{C}_6$ and $\mathscr{C}_6^*$ Theorems $\mathscr{C}_4$ and $\mathscr{C}_4^*$: Introduction Theorem $\mathscr{C}_4^*$: Stage A1. First steps Theorem $\mathscr{C}_4^*$: Stage A2. Nonconstrained $p$-rank 3 centralizers Theorem $\mathscr{C}_4^*$: Stage A3. $KM$-singularities Theorem $\mathscr{C}_4^*$: Stage A4. Setups for recognizing $G$ Theorem $\mathscr{C}_4^*$: Stage A5. Recognition Properties of $\mathscr{K}$-groups Bibliography Index
£96.30
Society for Industrial & Applied Mathematics,U.S. Solving Problems in Multiply Connected Domains
Book SynopsisWhenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected.This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author.This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time.Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
£78.20
Mathematical Association of America Learning Modern Algebra
Book SynopsisMuch of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practising mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high-school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalisations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.Trade ReviewThis book covers abstract algebra from a historical perspective by using mathematics from attempts to prove Fermat's last theorem, as the title indicates. The target audience is high school mathematics teachers. However, typical undergraduate students will also derive great benefit by studying this text. The book is permeated with fascinating mathematical nuggets that are clearly explained." - D. P. Turner, CHOICE"This book is destined for college students in the U.S. who intend to teach mathematics in high school. The reviewer finds it even more apt as a text for algebra courses. Special features in the book are side notes given and printed prominently at the margins of the pages, like: How to think about it, Historical notes, Etymology of notions and words. … The reviewer considers the book a refreshing read among the vast amount of books dealing with similar topics." - Robert W. van der Waall, Zentrallblatt MATH"Although this book is designed for college students who want to teach in high school," its mathematical richness fits it admirably as a text for a first abstract algebra course or a handbook for assiduous students working on their own. While definitions, examples, theorems and their proofs are organized formally, the book is enhanced by substantial historical notes, advice on "how to think about it," marginal comments, connections and etymology that are designed to "balance experience and formality." The book is tightly organized with the goal of elucidating developments leading to the solution of the Fermat conjecture and the theory of solvability by radicals." - E. J. Barbeau, Mathematical Reviews"The primary intended audience of the book is future high school teachers. The authors take great pains to relate the material covered here to subjects that are taught in high school mathematics classes. … In writing this book, the authors have obviously kept the needs of the student reader firmly in mind at all times. The writing style is not just clear; iit is often conversational and humorous. … There are lots of exercises covering a wide range of difficulty, some with hints (but none with complete solutions) and there is a pretty good 39-entry bibliography. … What might be a very interesting use for this book would be as a text for a senior seminar or “topics” course for students who already have some prior exposure to abstract algebra. And, of course, whatever may be the applicability of this book as a text for undergraduate course, it seems clear to me that it belongs in any good undergraduate library." - Mark Hunacek, MAA ReviewsTable of ContentsPreface; Some features of this book; A note to students; A note to instructors; Notation; 1. Early number theory; 2. Induction; 3. Renaissance; 4. Modular arithmetic; 5. Abstract algebra; 6. Arithmetic of polynomials; 7. Quotients, fields, and classical problems; 8. Cyclotomic integers; 9. Epilogue; References; Index.
£59.40
Springer Nature Switzerland AG The Brauer–Grothendieck Group
Book SynopsisThis monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.Trade Review“The book gives a comprehensive, clear, up-to date presentation of the theory, including most proofs. A particular strength is that it nicely collects many results, examples and counterexamples from various areas of algebraic and arithmetic geometry … . the book fills a wide gap and is a most welcome addition to the literature.” (Stefan Schröer, zbMATH 1490.14001, 2022)“This book has collected in one place much of the fundamental cohomological theory of the Brauer group, along with excellent references. It then gives some coverage of further results, especially on the two important topics of obstructions to rationality and obstructions to the Hasse principle. For whatever is not included in this book, it gives a thorough and coherent overview of the relevant literature. Approximately four hundred references are given.” (Thomas Benedict Williams, Mathematical Reviews, September, 2022)Table of Contents1 Galois Cohomology.- 2 Étale Cohomology.- 3 Brauer Groups of Schemes.- 4 Comparison of the Two Brauer Groups, II.- 5 Varieties Over a Field.- 6 Birational Invariance.- 7 Severi–Brauer Varieties and Hypersurfaces.- 8 Singular Schemes and Varieties.- 9 Varieties with a Group Action.- 10 Schemes Over Local Rings and Fields.- 11 Families of Varieties.- 12 Rationality in a Family.- 13 The Brauer–Manin Set and the Formal Lemma.- 14 Are Rational Points Dense in the Brauer–Manin Set?.- 15 The Brauer–Manin Obstruction for Zero-Cycles.- 16 Tate Conjecture, Abelian Varieties and K3 Surfaces.- Bibliography.- Index.
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