Format: Hardback, height x width: 235x155 mm, Approx. 400 p.
Series: Undergraduate Texts in Mathematics
Pub. Date: 23-Nov-2023
ISBN-13: 9783031410253
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.
The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions.
No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
From the reviews of previous editions:
Altogether, the text is a didactic masterpiece. - zbMATH
The determinant-free proofs are elegant and intuitive. - American Mathematical Monthly
The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library - CHOICE
Preface for the Instructor-Preface for the Student-Acknowledgments-1.
Vector Spaces.-
2. Finite-Dimensional Vector Spaces.-
3. Linear Maps.-
4.
Polynomials.-
5. Eigenvalues, Eigenvectors, and Invariant Subspaces.-
6.
Inner Product Spaces.-
7. Operators on Inner Product Spaces.-
8. Operators on
Complex Vector Spaces.-
9. Operators on Real Vector Spaces.-
10. Trace and
Determinant-Photo Credits-Symbol Index-Index.
Format: Hardback, 528 pages, height x width: 235x155 mm, 1 Tables, color; 1 Illustrations, color; X, 528 p. 1 illus. in color
Series: Trends in the History of Science
Pub. Date: 15-Nov-2023
ISBN-13: 9783031326097
This book both articulates and responds to increasing scholarly interest in the materiality of the book. Taking as its base the unique collection of mathematical books in the Russell Library at Maynooth, it addresses questions related to printing techniques and print culture, book production, provenance, and reading practices. It considers the histories of individual items of the Russell Collection, their previous locations and owners, and explores ways in which annotations, underlinings, hand-drawn diagrams, and the like reveal patterns of reading and usage. Finally, it seeks to elicit more information on a previously under-researched topic: the historical role of mathematics in the extensive network of Irish colleges that once covered Catholic Europe, located in places such as Salamanca, Rome, Douai, and Prague. Alongside delivering important new insights into print culture as a medium for transmitting scientific ideas, Mathematical Book Histories is thus also intended to contribute to a broader understanding of the role and significance of mathematics in the context of clerical instruction and more broadly in the academic tradition of Ireland up to the beginning of the twentieth century. Many of the volumes in the Russell Library reflect the remarkably rich book-trade that flourished in seventeenth and early eighteenth century Dublin and which was quite distinct from that in London. Booksellers often bought in their wares directly from abroad, with the result that publications could enter collections that did not enter the purview of contemporary English or Scottish scholars in Britain.
Preface.- Introduction.- Section I: Origins and Reading Practices.-
Section II: Controversies and Mysteries.- Section III: Printing and
Booksellers.- Section IV: Mathematical Reform and Teaching.- Bibliography.-
Index.
Format: Hardback, 380 pages, height x width: 235x155 mm, 40 Tables, color; 40 Illustrations, color;
10 Illustrations, black and white; XX, 380 p. 50 illus., 40 illus. in color.
Series: Applied and Numerical Harmonic Analysis
Pub. Date: 14-Nov-2023
ISBN-13: 9783031411298
During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings - of which he was a Founding Member - is also included. The remaining articles are grouped into four sections - classical sampling, theoretical extensions, frame theory, and applications of sampling theory - and explore Higgins' contributions to these areas, as well as some of the latest developments.
PART I: Classical Sampling - Classical and approximate exponential
sampling formula: their interconnections in uniform and Mellin-Lebesgue norms
(Schmeisser).- Asymptotic theorems for Durrmeyer sampling operators with
respect to the L-norm (Vinti).- On generalized Shannon sampling operators in
the cosine operator function framework (Kivinukk).- Bernstein spaces,
sampling, and Riesz-Boas interpolation formulas in Mellin Analysis
(Pesenson).- The behavior of frequency band limited cardinal
interpolants(Madych).- The Balian-Low theorem for (Cq)-systems in
shift-invariant spaces (owell).- Whittaker - type derivative sampling and (p;
q) - order weighted diffrential operator (Pogany).- Shannon Sampling via
Poisson, Cauchy, Jacobi and Levin (Casey).- Part (II.) Theoretical Extensions
- Schoenberg's Theory of Totally Positive Functions and the Riemann Zeta
Function (Groechenig).- Sampling via the Banach Gelfand Triple
(Feichtinger).- Part (III.) Frame Theory - A Survey of Fusion Frames in
Hilbert Spaces (Koehldorfer).- Frames of iterations and vector-valued model
spaces (Cabrelli).- A survey on frame representations and operator orbits
(Christensen).- Three proofs of the Benedetto-Fickus theorem (Mixon).-
Clifford Prolate SpheroidalWavefunctions and Associated Shift Frames
(Lakey).- Part (IV.) Applications - Power Aware Analog To Digital Converters
(Mulleti).- Quaternionic coupled fractional Fourier transform on
Boehmians (Zayed).- Sampling : Theory and Applications - A History of the
SampTA Meetings (Casey).- Accelerartion Algorithms for Iterative Methods
(Marvasti).
*
Format: Hardback, height x width: 254x178 mm, Approx. 350 p., 1 Hardback
Series: Springer Texts in Statistics
Pub. Date: 29-Oct-2023
ISBN-13: 9783031421433
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Part I Linear Algebra
1 Basic Vector/Matrix Structure and Notation
2 Vectors and Vector Spaces
3 Basic Properties of Matrices
4 Vector/Matrix Derivatives and Integrals
5 Matrix Transformations and Factorizations
6 Solution of Linear Systems
Part II Applications in Data Analysis
8 Special Matrices and Operations Useful in Modeling andData Analysis
9 Selected Applications in Statistics
Part III Numerical Methods and Software
10 Numerical Methods
11 Numerical Linear Algebra
12 Software for Numerical Linear Algebra
Bibliography
Index
*
Format: Hardback, height x width: 240x168 mm, 35 Illustrations, color; Approx. 215 p.
35 illus. in color.; 35 Illustrations, color; Approx. 215 p. 35 illus. in color.,
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 18-Jan-2024
ISBN-13: 9783031428906
This book is a unified treatment of the most important core developments in the theory of completely regular semigroup theory as it stands today. This volume focuses on the lattice of varieties of completely regular semigroups. Since any in-depth study of the lattice of varieties requires an understanding of free completely regular semigroups, the book begins by describing the free object on countably infinite sets and the properties of the lattice of fully invariant congruences on the free object. The authors then introduce the various relations and operators on the lattice of varieties of completely regular semigroups. The book then covers the sublattice of varieties of bands with a focus on the influence of that sublattice on the structure of the whole lattice. The book concludes with the remarkable theorem due to Polak describing the whole lattice of varieties of completely regular as a subdirect product of lattices, some of which are well understood. The authors include recent advancements, insights, results, and techniques throughout the book.
Fully Invariant Relations.- Kernel and Trace Relations.- Bands.- Polak
Theorem.
Format: Hardback, 168 pages, height x width: 235x155 mm, 26 Tables, color;
26 Illustrations, color; 3 Illustrations, black and white; V, 168 p. 29 illus., 26 illus. in color
Series: Research Perspectives Ghent Analysis and PDE Center 1
Pub. Date: 08-Nov-2023
ISBN-13: 9783031416644
This collection consists of selected scientific results stemming from the conference "Methusalem Workshop on Classical Analysis and PDEs", held at the Ghent University from 27th February 2023 to 1st March 2023. The workshop was organized by the "Ghent Analysis & PDE Center". The presented materials mainly consist of scientific results on classical analysis and problems of PDEs. In particular, results on harmonic analysis, functional spaces, functional inequalities, inverse problems, non-local PDEs, non-classical problems of PDEs, integro-differential equations, hypoelliptic operators, pseudo-differential calculus, and others are given.
Preface.- I. Theory of Functional Analysis, Operator Theory, and
Applications.- Elena Afanaseva, Anatoly Golberg: Mappings of finite area
distortion: Hausdorff measures.- Alexander Cardona, Santiago Gomez Cobos: The
principal symbol of elliptic differential operators on Lie groups and
homogeneous spaces.- Arran Fernandez, Cihan Gueder, Walaa Yasin: On
fractional quaternionic d-bar derivatives.- Brian Grajales, Julieth Saavedra:
A note on homogeneous geometry of G2-type real flag manifolds.- Junqing
Huang: Semi-sparsity for Piecewise Constant Functions on Triangular Mesh
Denoising.- Mikhail Isaev, Roman G. Novikov, Grigory V. Sabinin:
Superresolution reconstruction from truncated Fourier transform.- Aitolkyn H.
Kalidolday, Erlan D. Nursultanov: Interpolation theorem for discrete net
spaces.- Vishvesh Kumar, Joel E. Restrepo: Titchmarsh theorem by modulus of
continuity for the deformed Hankel-Lipschitz classes.- Juan Pablo
Velasquez-Rodriguez: Titchmarsh Theorems for Hoelder- Lipschitz functions on
profinite groups.- Xuechao Wang, Sven Nomm, Junqing Huang, Marianna
Chatzakou, Michael Ruzhansky: An efficient neural network for the diagnosis
of Parkinson's disease using dynamic handwriting analysis.- II. Classical and
non-classical problems of PDEs.- Irfan Ali: On q2-analogue of the
one-dimensional non-homogeneous heat equation.- Ravshan Ashurov, Oqila
Mukhiddinova: Non-local and inverse problems for the Rayleigh-Stokes
equation.- Marianna Chatzakou, Abhilash Tushir: Very weak solution of the
discrete Heat Equation with irregular time-dependent thermal conductivity.-
Mulugeta A. Dagnaw: On a Mixed Stokes Problem with Variable Viscosity in the
2D Exterior Domain.- Nurbek Kakharman: The mixed initial-boundary value
problem for degenerate hyperbolic equation.- Tynysbek Sh. Kalmenov: A
criterion for minimality of the mixed type operators.- Baltabek Kanguzhin,
Zhalgas Kaiyrbek: An analogue of the d'Alembert formula for the Gurtin-Pipkin
equation with multipoint boundary conditions for zero initial data.- Bakytbek
Koshanov, Maksat Bakytbek: On Fredholm solvability and on the index of the
generalized Neumann problem for an elliptic equation of highorder on a
plane.- Nedyu Popivanov, Todor Popov, Ingo Witt: Solutions with power type
orexponential singularity for (3+1)-D Protter-Morawetz problems.- Makhmud
Sadybekov, Batirkhan Turmetov: Boundary Value Problems for Differential
Equations with a High-Order Derivative in the boundary condition.- Serikbol
Shaimardan: A Cauchy problem for q-heat equation.- Marian Slodicka:
Evolutionary PDEs with Volterra operators: direct and inverse source
problems.- Karel Van Bockstal: Inverse source problems in thermoelasticity.-
Rong Zhang: A Direct Method of Moving Planes for Logarithmic Schroedinger
Operator.
Format: Hardback, 608 pages, height x width: 235x155 mm, XVIII, 608 p., 1 Hardback
Series: Graduate Texts in Mathematics 300
Pub. Date: 26-Oct-2023
ISBN-13: 9783031411519
The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics.
The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields. The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed.
This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface.
1. Affine Algebraic Groups.-
2. Adeles.-
3. Discrete Automorphic Representations.-
4. Archimedean Representation Theory.-
5. Representations of Totally Disconnected Groups.-
6. Automorphic Forms.-
7. Unramified Representations.-
8. Nonarchimedean Representation Theory.-
9. The Cuspidal Spectrum.-
10. Einsenstein Series.-
11. Rankin-Selberg L-functions.-
12. Langlands Functoriality.-
13. Known Cases of Global Langlands Functoriality.-
14. Distinction and Period Integrals.-
15. The Cohomology of Locally Symmetric Spaces.-
16. Spectral Sides of the Trace Formulae.-
17. Orbital Integrals.-
18. Simple Trace Formulae.-
19. Applications of Trace Formulae.- A. Groups attached to involutions of algebras.- B. The Iwasawa Decomposition.- C. Poisson Summation.- D. Alternate conventions related to adelic quotients.- Hints to selected exercises.- References.- Index.