Format: Paperback / softback, 252 pages, height x width: 235x155 mm, 20 Illustrations,
black and white; XVIII, 252 p. 20 illus.
Series: Universitext
Pub. Date: 23-Mar-2022
ISBN-13: 9783030943592
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas
- Applies material to physics so students appreciate the applications of abstract mathematics
- Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates
- Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study
Introduction.-
1. General Facts About Groups.-
2. Representations of Finite Groups.-
3. Representations of Compact Groups.-
4. Lie Groups and Lie Algebras.-
5. Lie Groups SU(2) and SO(3).-
6. Representations of SU(2) and SO(3).-
7. Spherical Harmonics.-
8. Representations of SU(3) and Quarks.-
9. Spin Groups and Spinors.- Problems and Solutions.- Endnote.- Bibliography.-Index.
Format: Paperback / softback, 244 pages, height x width: 235x155 mm, 1 Tables, color;
1 Illustrations, color; 10 Illustrations, black and white; XX, 244 p. 11 illus., 1 illus. in color
Series: Springer Undergraduate Mathematics Series
Pub. Date: 05-Apr-2022
ISBN-13: 9783030949457
This textbook presents the theory of <i>Metric Spaces</i> necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at a pace appropriate to the material.<div><br></div><div>The book covers the main topics of metric space theory that the student of analysis is likely to need. Starting with an overview defining the principal examples of metric spaces in analysis (chapter 1), it turns to the basic theory (chapter 2) covering open and closed sets, convergence, completeness and continuity (including a treatment of continuous linear mappings). There is also a brief dive into general topology, showing how metric spaces fit into a wider theory. The following chapter is devoted to proving the completeness of the classical spaces. The text then embarks on a study of spaces with important special properties. Compact spaces, separable spaces, complete spaces and connected spaces each have a chapter devoted to them. A particular feature of the book is the occasional excursion into analysis. Examples include the Mazur?Ulam theorem, Picard’s theorem on existence of solutions to ordinary differential equations, and space filling curves.</div><div><br></div><div>This text will be useful to all undergraduate students of mathematics, especially those who require metric space concepts for topics such as multivariate analysis, differential equations, complex analysis, functional analysis, and topology. It includes a large number of exercises, varying from routine to challenging. The prerequisites are a first course in real analysis of one real variable, an acquaintance with set theory, and some experience with rigorous proofs.
1. Metric spaces.-
2. Basic theory of metric spaces.-
3. Completeness of the classical spaces.-
4. Compact spaces.-
5. Separable spaces.-
6. Properties of complete spaces.-
7. Connected spaces.- Index.
Format: Hardback, 361 pages, height x width: 235x155 mm, 4 Illustrations, color;
19 Illustrations, black and white; XI, 361 p. 23 illus., 4 illus. in color.
Pub. Date: 29-Mar-2022
ISBN-13: 9783030936341
This second edition textbook offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Calculus is a prerequisite for understanding the basic concepts, however the book is written with a sensitivity to students’ common difficulties with calculus that does not obscure the thorough treatment of the probability content. The first six chapters of this text neatly and concisely cover the material traditionally required by most undergraduate programs for a first course in probability.</p><p>The comprehensive text includes a multitude of new examples and exercises, and careful revisions throughout. Particular attention is given to the expansion of the last three chapters of the book with the addition of one entirely new chapter (9) on ’Finding and Comparing Estimators.’ The classroom-tested material presented in this second edition forms the basis for a second course introducing mathematical statistics.
Probability Space.- Conditional probabilities.- Discrete random variables.- Binomial random variables.- Poisson random variables.- Simulations of discrete random variables.- Combinatorics.- Continuous random variables.- The sample average and sample.- Estimating and testing proportions.- Estimating and testing means.- Small samples.- Chi-squared tests.- Design of experiments.- The cumulative distribution function.- Continuous joint distributions.- Covariance and independence.- Conditional distribution and expectation.- The bivariate normal distribution.- Sums of Bernoulli random variables.- Coupling random variables.- The moment generating function.- The chi-squared, Student and F distributions.- Sampling from a normal distribution.- Finding estimators.- Comparing estimators.- Best unbiased estimators.- Bayes' estimator.- Multiple linear regression.- List of common discrete distributions.- List of common continuous distributions.- Further reading.- Normal table.- Student table.- Chi-squared table.- Index.
Format: Hardback, 364 pages, height x width: 235x155 mm, 6 Illustrations, color;
13 Illustrations, black and white; XXII, 364 p. 19 illus., 6 illus. in colork
Series: Springer Monographs in Mathematics
Pub. Date: 28-Mar-2022
ISBN-13: 9783030941505
The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve as a text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.
1 Introduction.- 2 Extraction of coefficients and generating functions.- 3 The Riordan group.- 4 Characterization of Riordan arrays by special sequences.- 5 Combinatorial sums and inversions.- 6 Generalized Riordan arrays.- 7 Extensions of the Riordan group.- 8 q-analogs of Riordan arrays.- 9 Orthogonal polynomials. Solutions.- Index.
Format: Hardback, 382 pages, height x width: 235x155 mm, 115 Tables, color; 116 Illustrations, color;
38 Illustrations, black and white; X, 382 p. 154 illus., 116 illus. in color., 1 Hardback
Series: Springer INdAM Series 49
Pub. Date: 31-Mar-2022
ISBN-13: 9783030923129
This book collects selected contributions presented at the INdAM Workshop "Geometric Challenges in Isogeometric Analysis", held in Rome, Italy on January 27-31, 2020. It gives an overview of the forefront research on splines and their efficient use in isogeometric methods for the discretization of differential problems over complex and trimmed geometries. A variety of research topics in this context are covered, including (i) high-quality spline surfaces on complex and trimmed geometries, (ii) construction and analysis of smooth spline spaces on unstructured meshes, (iii) numerical aspects and benchmarking of isogeometric discretizations on unstructured meshes, meshing strategies and software. Given its scope, the book will be of interest to both researchers and graduate students working in the areas of approximation theory, geometric design and numerical simulation.<div><br></div><div>Chapter 10 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Ce livre presente la theorie spectrale des operateurs auto-adjoints en dimension infinie ainsi que son application ? la mecanique quantique. Le concept d"auto-adjonction, decouvert par John von Neumann dans les annees 1930, est bien plus subtil dans ce cadre que pour les matrices hermitiennes en dimension finie. Cet ouvrage peut aussi servir d"introduction mathematique ? la mecanique quantique. De multiples exemples physiques servent ainsi ? illustrer et motiver les theor?mes plus abstraits. Les deux derniers chapitres presentent des resultats plus recents concernant l"equation de Schrodinger pour les atomes, les molecules et les solides. Aucune connaissance physique n"est cependant requise pour lire ces pages.Premier livre en fran?ais sur le sujet destine aux etudiants de Master, ce livre pourra accompagner un cours ? ce niveau. Il devrait aussi ?tre utile aux lecteurs plus avances desirant en savoir plus sur cette theorie.This book presents th
e spectral theory of self-adjoint operators on Hilbert space, with applications to quantum mechanics. The concept of self-adjointness in infinite dimension was discovered by John von Neumann in the 1930s and it is much more involved than in the case of Hermitian matrices in finite dimension.The book also provides an introduction to quantum mechanics, suitable for students with a mathematics background. The presentation provides numerous physical examples illustrating the abstract theory. The last two chapters present recent results on Schrodinger"s equation for systems of particles. No previous knowledge of physics is required for the book.Based on the author"s teaching and intended for graduate courses, this French language textbook can also serve as a useful introduction to the topic for more advanced readers.
1 Carolina Vittoria Beccari and Hartmut Prautzsch, Quadrilateral Orbifold Splines.- 2 Timothy Boafo-Adade et al., B-Symmetric Univariate Splines and Euler Numbers.- 3 Nora Engleitner and Bert Juttler, DPB-Splines: The Decoupled Basis of Patchwork Splines.- 4 Antonella Falini et al., A Collocation IGA-BEM for 3D Potential Problems on Unbounded Domains.- 5 Tom Lyche et al., Simplex-Splines on the Clough-Tocher Split with Arbitrary Smoothness.- 6 Florian Martin and Ulrich Reif, Trimmed Spline Surfaces with Accurate Boundary Control.- 7 Benjamin Marussig, Fast Formation and Assembly of Isogeometric Galerkin Matrices for Trimmed Patches.- 8 Joerg Peters and Kestutis Karciauskas, Subdivision and G-Spline Hybrid Constructions for High-Quality Geometric and Analysis-Suitable Surfaces.- 9 Malcolm A. Sabin, Meshing as the Choice of Basis Functions for Finite Element Analysis.- 10 Vibeke Skytt and Tor Dokken, Scattered Data Approximation by LR B-Spline Surfaces: A Study on Refinement Strategies for Efficient Approximation.- 11 Roel Tielen et al., A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis.- 12 Nelly Villamizar et al., Completeness Characterization of Type-I Box Splines.- 13 Xiaodong Wei, THU-Splines: Highly Localized Refinement on Smooth Unstructured Splines.- 14 Yuxuan Yu et al., HexGen and Hex2Spline: Polycube-Based Hexahedral Mesh Generation and Spline Modeling for Isogeometric Analysis Applications in LS-DYNA.- 15 Mehrdad Zareh and Xiaoping Qian, C1 Triangular Isogeometric Analysis of the von Karman Equations.
Bibliog. data: 1 re d. 2022. 2022. x, 301 S. 1 SW-Abb., 30 Farbabb., 30 Farbtabellen. 235 mm
Format: Kartoniert
Series: Mathematiques et Applications 87
Publisher: SPRINGER, BERLIN; SPRINGER INTERNATIONAL PUBLISHING;
ISBN-13: 9783030934354
Ce livre presente la theorie spectrale des operateurs auto-adjoints en dimension infinie ainsi que son application ? la mecanique quantique. Le concept d"auto-adjonction, decouvert par John von Neumann dans les annees 1930, est bien plus subtil dans ce cadre que pour les matrices hermitiennes en dimension finie. Cet ouvrage peut aussi servir d"introduction mathematique ? la mecanique quantique. De multiples exemples physiques servent ainsi ? illustrer et motiver les theor?mes plus abstraits. Les deux derniers chapitres presentent des resultats plus recents concernant l"equation de Schrodinger pour les atomes, les molecules et les solides. Aucune connaissance physique n"est cependant requise pour lire ces pages.Premier livre en fran?ais sur le sujet destine aux etudiants de Master, ce livre pourra accompagner un cours ? ce niveau. Il devrait aussi ?tre utile aux lecteurs plus avances desirant en savoir plus sur cette theorie.This book presents th
e spectral theory of self-adjoint operators on Hilbert space, with applications to quantum mechanics. The concept of self-adjointness in infinite dimension was discovered by John von Neumann in the 1930s and it is much more involved than in the case of Hermitian matrices in finite dimension.The book also provides an introduction to quantum mechanics, suitable for students with a mathematics background. The presentation provides numerous physical examples illustrating the abstract theory. The last two chapters present recent results on Schrodinger"s equation for systems of particles. No previous knowledge of physics is required for the book.Based on the author"s teaching and intended for graduate courses, this French language textbook can also serve as a useful introduction to the topic for more advanced readers.
Preface.- Chapter. 1.- Introduction ? la mecanique quantique : l"atome d"hydrog?ne.- Chapter. 2.- Auto-adjonction.- Chapter. 3.- Crit?res d"auto-adjonction : Rellich, Kato & Friedrichs.- Chapter. 4.- Theor?me spectral et calcul fonctionnel.- Chapter. 5.- Spectre des operateurs auto-adjoints.- Chapter. 6.- Syst?mes ? N particules, atomes, molecules.- Chapter. 7.- Operateurs de Schrodinger periodiques et proprietes electroniques des materiaux.- Appendice A.- Espaces de Sobolev.- Appendice B. Probl?mes.-