Format: Hardback, 514 pages, height x width: 235x155 mm, 2 Illustrations, color; 72 Illustrations, black and white; X, 510 p. 33 illus., 2 illus. in color., 1 Hardback
Series: Springer Texts in Statistics
Pub. Date: 17-Nov-2024
ISBN-13: 9783031690372
This book examines statistical models for frequency data. The primary focus is on log-linear models for contingency tables but also includes extensive discussion of logistic regression. Topics such as logistic discrimination, generalized linear models, and correspondence analysis are also explored.
The treatment is designed for readers with prior knowledge of analysis of variance and regression. It builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data. While emphasizing similarities between methods for discrete and continuous data, this book also carefully examines the differences in model interpretations and evaluation that occur due to the discrete nature of the data. Numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises. A major addition to the third edition is the availability of a companion online manual providing R code for the procedures illustrated in the book.
The book begins with an extensive discussion of odds and odds ratios as well as concrete illustrations of basic independence models for contingency tables. After developing a sound applied and theoretical basis for frequency models analogous to ANOVA and regression, the book presents, for contingency tables, detailed discussions of the use of graphical models, of model selection procedures, and of models with quantitative factors. It then explores generalized linear models, after which all the fundamental results are reexamined using powerful matrix methods. The book then gives an extensive treatment of Bayesian procedures for analyzing logistic regression and other regression models for binomial data. Bayesian methods are conceptually simple and unlike traditional methods allow accurate conclusions to be drawn without requiring large sample sizes. The book concludes with two new chapters: one on exact conditional tests for small sample sizes and another on the graphical procedure known as correspondence analysis.
Two-Dimensional Tables and Simple Logistic Regression.- Three-Dimensional Tables.- Logistic Regression, Logit Models, and Logistic Discrimination.- Independence Relationships and Graphical Models.- Model Selection Methods and Model Evaluation.- Models for Factors with Quantitative Levels.- Fixed and Random Zeros.- Generalized Linear Models.- The Matrix Approach to Log-Linear Models.- The Matrix Approach to Logit Models.- Maximum Likelihood Theory for Log-Linear Models.- Bayesian Binomial Regression. Exact Conditional Tests. - Correspondence Analysis.
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Format: Hardback, 799 pages, height x width: 235x155 mm, 33 Illustrations, color; 58 Illustrations, black and white; Approx. 750 p., 1 Hardback
Pub. Date: 19-Nov-2024
ISBN-13: 9783031687105
This is the seventh volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.
This volume consists of fourteen chapters that provide an in-depth and reader-friendly introduction to various important aspects of singularity theory. The volume begins with an outstanding exposition on Jim Damonfs contributions to singularity theory and its applications. Jim passed away in 2022 and he was one of the greatest mathematicians of recent times, having made remarkable contributions to singularity theory and its applications, mostly to medical image computing.
The next chapter focuses on the singularities of real functions and their bifurcation sets. Then, we look at the perturbation theory of polynomials and linear operators, complex analytic frontal singularities, the global singularity theory of differentiable maps, and the singularities of holomorphic functions from a global point of view.
The volume continues with an overview of new tools in singularity theory that spring from symplectic geometry and Floer-type homology theories. Then, it looks at the derivation of Lie algebras of isolated singularities and the three-dimensional rational isolated complete intersection singularities, as well as recent developments in algebraic K-stability and the stable degeneration conjecture.
This volume also contains an interesting survey on V-filtrations, a theory began by Malgrange and Kashiwara that can be used to study nearby and vanishing cycle functors and introduced by Deligne. Then, we present a panoramic view of the Hodge, toric, and motivic methods in the study of Milnor fibers in singularity theory, both from local and global points of view.
The Monodromy conjecture is also explained; this is a longstanding open problem in singularity theory that lies at the crossroads of number theory, algebra, analysis, geometry, and topology. This volume closes with recent developments in the study of the algebraic complexity of optimization problems in applied algebraic geometry and algebraic statistics.
The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
1 Bill Bruce, Peter Giblin, David Mond, Stephen Pizer and Les
Wilson, Jim Damons Contributions to Singularity Theory and Its
Applications.- 2 Viktor A. Vassiliev, Real Function Singularities and Their
Bifurcation Sets.- 3 Adam Parusinski and Armin Rainer, Perturbation Theory of
Polynomials and Linear Operators.- 4 Goo Ishikawa, Frontal Singularities and
Related Problems.- 5 Osamu Saeki, Introduction to Global Singularity Theory
of Differentiable Maps.- 6 Claude Sabbah, Singularities of Functions: A
Global Point of View.- 7 Mark McLean, Floer Theory, Arc Spaces and
Singularities.- 8 Stephen S.-T. Yau and Huaiqing Zuo, Various Derivation Lie
Algebras of Isolated Singularities.- 9 Bingyi Chen, Stephen S.-T. Yau and
Huaiqing Zuo, Three-Dimensional Rational Isolated Complete Intersection
Singularities.- 10 Ziquan Zhuang, Stability of klt Singularities.- 11 Qianyu
Chen, Bradley Dirks and Mircea Mustata, An introduction to V-Filtration.-
12 Kiyoshi Takeuchi, Geometric Monodromies, Mixed Hodge Numbers of Motivic
Milnor Fibers and Newton Polyhedra.- 13 Willem Veys, Introduction to the
Monodromy Conjecture.- 14 Laurentiu G. Maxim, Jose Israel Rodriguez and
Botong Wang, Applications of Singularity Theory in Applied Algebraic Geometry
and Algebraic Statistics.
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Format: Hardback, 155 pages, height x width: 235x155 mm, X, 140 p., 1 Hardback
Series: RSME Springer Series 15
Pub. Date: 19-Oct-2024
ISBN-13: 9783031688577
This book presents progress on two open problems within the framework of algebraic geometry and commutative algebra: Grobner's problem regarding the arithmetic Cohen-Macaulayness (aCM) of projections of Veronese varieties, and the problem of determining the structure of the algebra of invariants of finite groups. We endeavour to understand their unexpected connection with the weak Lefschetz properties (WLPs) of artinian ideals. In 1967, Grobner showed that the Veronese variety is aCM and exhibited examples of aCM and nonaCM monomial projections. Motivated by this fact, he posed the problem of determining whether a monomial projection is aCM. In this book, we provide a comprehensive state of the art of Grobners problem and we contribute to this question with families of monomial projections parameterized by invariants of a finite abelian group called G-varieties. We present a new point of view in the study of Grobners problem, relating it to the WLP of Artinian ideals. GT varieties are a subclass of G varieties parameterized by invariants generating an Artinian ideal failing the WLP, called the Galois-Togliatti system. We studied the geometry of the G-varieties; we compute their Hilbert functions, a minimal set of generators of their homogeneous ideals, and the canonical module of their homogeneous coordinate rings to describe their minimal free resolutions. We also investigate the invariance of nonabelian finite groups to stress the link between projections of Veronese surfaces, the invariant theory of finite groups and the WLP. Finally, we introduce a family of smooth rational monomial projections related to G-varieties called RL-varieties. We study the geometry of this family of nonaCM monomial projections and we compute the dimension of the cohomology of the normal bundle of RL varieties. This book is intended to introduce Grobners problem to young researchers and provide new points of view and directions for further investigations.
- Introduction.- Algebraic Preliminaries.- Invariants of finite abelian groups and aCM projections of Veronese varieties. Applications.- The geometry of -varieties.- Invariants of finite groups and the weak Lefschetz property.- Normal bundle of RL-varieties.
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Format: Hardback, 454 pages, height x width: 235x155 mm, 47 Illustrations, black and white; XXII, 500 p. 70 illus., 20 illus. in color., 1 Hardback
Series: IMPA Monographs
Pub. Date: 05-Nov-2024
ISBN-13: 9783031674945
This book explores recent developments in the dynamics of invertible circle maps, a rich and captivating topic in one-dimensional dynamics. It focuses on two main classes of invertible dynamical systems on the circle: global diffeomorphisms and smooth homeomorphisms with critical points. The latter is the book's core, reflecting the authors' recent research interests.
Organized into four parts and 14 chapters, the content covers rigid rotations, circle homeomorphisms, and the concept of rotation number in the first part. The second part delves into circle diffeomorphisms, presenting classical results. The third part introduces multicritical circle maps?smooth homeomorphisms of the circle with a finite number of critical points. The fourth and final part centers on renormalization theory, analyzing the fine geometric structure of orbits of multicritical circle maps. Complete proofs for several fundamental results in circle dynamics are provided throughout. The book concludes with a list of open questions.
Primarily intended for graduate students and young researchers in dynamical systems, this book is also suitable for mathematicians from other fields with an interest in the subject. Prerequisites include familiarity with the content of a standard graduate course in real analysis, along with some understanding of ergodic theory and dynamical systems. Basic knowledge of complex analysis is needed for specific chapters.
Preface.-
Part I - Basic Theory:
1 Rotations.- 2 Homeomorphisms of the Circle.-
Part II - Diffeomorphisms:
3 Diffeomorphisms: Denjoy Theory.- 4 Smooth Conjugacies to Rotations.-
Part III - Multicritical Circle Maps.- 5 Cross-ratios and Distortion Tools.- 6 Topological Classification and the Real
Bounds.- 7 Quasisymmetric Rigidity.- 8 Ergodic Aspects.- 9 Orbit Flexibility.-
Part IV - Renormalization Theory:
10 Smooth Rigidity and Renormalization..- 11 Quasiconformal Deformations.- 12 Lipschitz Estimates
for Renormalization.- 13 Exponential Convergence: the Smooth Case.- 14 Renormalization: Holomorphic Methods.- Epilogue.- Appendices.- Bibliography.
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Format: Hardback, 332 pages, height x width: 235x155 mm, 64 Illustrations, black and white; X, 350 p. 250 illus., 1 Hardback
Pub. Date: 27-Nov-2024
ISBN-13: 9789819765676
This book is a straightforward and comprehensive presentation of the concepts and methodology of elementary real analysis. Targeted to undergraduate students of mathematics and engineering, it serves as the foundation for mathematical reasoning and proofs. The topics discussed are logic, methods of proof, functions, real number properties, sequences and series, limits and continuity and differentiation and integration (Riemann integral and Lebesgue integral). The book explains the concepts and theorems through geometrical and pictorial representation. Limits of sequences and functions, topology of metric spaces, continuity of functions and the Cauchy sequence have been thoroughly discussed in the book.
Chapter 1 The System of Real Numbers.
Chapter 2 Real Sequences.
Chapter 3 Infinite Series of Numbers.
Chapter 4 Limits, Continuity and Differentiability.
Chapter 5 Metric Spaces.
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Format: Hardback, 190 pages, height x width: 235x155 mm, Approx. 200 p., 1 Hardback
Series: Association for Women in Mathematics Series 34
Pub. Date: 15-Nov-2024
ISBN-13: 9783031664014
This volume contains the proceedings from the first Women in MathArt Research Collaboration Conference for Women, showcasing women mathematicians researching and curating creative pedagogies at the intersection of mathematics and the arts. This volume contains contributions to mathart projects from student-mentor teams and researchers in all stages of their careers. The volume also contains survey articles on new mathart intersections such as neuroaesthetics, generative design, generative adversarial networks, and Langlands Program. New results of particular interest are: diamond Langlands; generative design in the geometrization of the local Langlands Program; investigations of the grammatology and visual epistemology of perfectoid diamonds in mathematics as grammatological metaphor; infinity-category constructions of pro-Generative Adversarial Networks; infinity-stackification of mathematical exigency; condensing temporal logic with entropic categorizations; perfectoid diamond holography; neuroaesthetics in immunology. Also included is the result to foster a more inclusive work community of mathematicians using the arts as a tool to bring more vulnerability and integrity to each individual's research life. Readers are herein provided a rigorous overview of current mathart developments and future mathart projects.
Chapter 1: Making Up Our Minds: Imaginative Deconstruction in MathArt,
1920 Present .
Chapter 2: What is a Mathematical Ode? .
Chapter 3:
Venice, Glass, and Math .
Chapter 4: A Topological Journal of the Plague
Year .
Chapter 5: Artistic Mediation in Mathematized Phenomenology. -Chapter
6: History. -Chapter 7: The Making of a Mathematician: Personal and
Professional Growth Through Writing. -Chapter 8: MathLIKE: Coining a New
Word, Using It in Teaching, and in Interpreting Some of My Own Math-Poetry.
-Chapter 9: A Meaningful Intersection: Mathematics, Computer Programming, and
Art. -Chapter 10: Twas the Functorial Night. -Chapter 11: Sonnets. -Chapter
12: Categorical Colors in Diamonds: Sight as Site: Categorical Ozma and
Cinderella. -Chapter 13: Old Math. -Chapter 14: Design of Strips with
Geometry Shapes and Mathematical Analysis. -Chapter 15: Imagination as
Mathematics. -Chapter 16: The Long Fraction line: Mathematical Concepts
Rhymers. -Chapter 17: Solving with Sherlock. -Chapter 18: Qurio:
Meta-Learning Curiosity Algorithms and Agentive AI Tutors. -Chapter 19:
Marvels. -Chapter 20: Decembris: My Emerald Winter Color Walk.
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Format: Hardback, 409 pages, height x width: 235x155 mm, 2 Illustrations, color; 16 Illustrations, black and white; XXII, 399 p. 12 illus., 1 Hardback
Pub. Date: 07-Nov-2024
ISBN-13: 9783031682667
This monograph explores the history of the contribution to ballistics by the American mathematician Gilbert Ames Bliss during World War I. Drawing on the then-evolving calculus of variations, Bliss pioneered a novel technique for solving the problem of differential variations in ballistic trajectory. Called Blissf adjoint method, this technique was both hailed and criticized at the time: it was seen as both a triumphant application of pure mathematics to an applied problem and as a complex intrusion of higher mathematics into the jobs of military personnel not particularly interested in these matters. Although he received much praise immediately after the War, the details of Blissf work, its furthering of pure mathematical thought, and its absorption into mainstream ballistic work and instruction have never been adequately examined.
Gluchoff explores the mathematics of Blissf work and the strands from which his technique was developed. He then documents the efforts to make the adjoint method accessible to military officers and the conflicts that emerged as a result both between mathematicians and officers and among mathematicians themselves. The eventual absorption of the adjoint method into range firing table construction is considered by looking at later technical books which incorporate it, and, finally, its influence on the ongoing development of functional calculus is detailed.
From Frechet Differentials to Firing Tables will appeal to historians of mathematics, physics, engineering, and warfare, as well as current researchers, professors, and students in these areas.
Introduction.- First Appearances of Bliss' Method.- Four Sources of Bliss' Method: Existence and Smoothness of Solutions to Differential Equations.- Four Sources of Bliss' Method: The Mayer Problem.- Four Sources of Bliss' Method: Embedding and Implicit Function Theorems.- Four Sources of Bliss' Method: Functions of a Line.- Bliss' Two 1920 Papers.- Introduction of Bliss' Method into Military Settings.- Bliss' Results as Part of the Development of the Functional Calculus at the University of Chicago.- Conclusion.