TEXTBOOK
PUBLICATION PLANNED FOR: November 2022
AVAILABILITY: Not yet published - available from November 2022
FORMAT: Paperback ISBN: 9781009159692
Calculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role. The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition. The author has restructured the subject matter in the book by using Tarski's version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity. The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem. Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.
Lucid and structured presentation of concepts for better understanding
Sufficient practice exercises at the end of each section for self-study
Additional exercises called tasks and thematic questions for more hands-on practice
Signage for ease of identification for various sections
ntroduction
1. Real Numbers and Functions
2. Integration
3. Limits and Continuity
4. Differentiation
5. Techniques of Integration
6. Mean Value Theorems and Applications
7. Sequences and Series
8. Taylor and Fourier Series
A. Solutions to Odd-Numbered Exercises
Bibliography
Index.
Part of Institute of Mathematical Statistics Textbooks
PUBLICATION PLANNED FOR: December 2022
AVAILABILITY: Not yet published - available from November 2022
FORMAT: HardbackISBN: 9781108488907
During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.
Provides an accessible course on a central player in modern statistical practice, connecting models with methodology without the need for advanced math
Connects with modern computational-intensive applications: survival analysis and proportional hazards, bootstrap, Bayes and empirical Bayes, and false discovery rates
Emphasizes geometric reasoning
Close
1. One-parameter exponential families
2. Multiparameter exponential families
3. Generalized linear models
4. Curved exponential families, eb, missing data, and the em algorithm
5. Bootstrap confidence intervals
Bibliography
Index.
Part of Institute of Mathematical Statistics Textbooks
PUBLICATION PLANNED FOR: December 2022
AVAILABILITY: Not yet published - available from November 2022
FORMAT: Hardback ISBN: 9781108488907
During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.
Provides an accessible course on a central player in modern statistical practice, connecting models with methodology without the need for advanced math
Connects with modern computational-intensive applications: survival analysis and proportional hazards, bootstrap, Bayes and empirical Bayes, and false discovery rates
Emphasizes geometric reasoning
1. One-parameter exponential families
2. Multiparameter exponential families
3. Generalized linear models
4. Curved exponential families, eb, missing data, and the em algorithm
5. Bootstrap confidence intervals
Bibliography
Index.
DATE PUBLISHED: November 2022
AVAILABILITY: Not yet published - available from January 2024
FORMAT: Paperback ISBN: 9781108714006
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In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.
Makes a strong case for pluralism in logic and mathematics, with different frameworks serving different legitimate purposes.
Furthers the development of the modal-structural approach in philosophy and foundations of mathematics.
Explores the key benefits and limitations of restrictive approaches to mathematics, nominalism, predicativism, and constructivism
Part of Lecture Notes in Logic
PUBLICATION PLANNED FOR: November 2022
AVAILABILITY: Not yet published - available from November 2022
FORMAT: Hardback ISBN: 9781108840682
This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by proving a comparison theorem for mouse pairs parallel to the FSIT comparison theorem for pure extender mice, and then using the underlying comparison process to develop a fine structure theory for strategy mice. Great effort has been taken to make the book accessible to non-experts so that it may also serve as an introduction to the higher reaches of inner model theory. It contains a good deal of background material, some of it unpublished folklore, and includes many references to the literature to guide further reading. An introductory essay serves to place the new results in their broader context. This is a landmark work in inner model theory that should be in every set theorist's library.
Proves important new theorems in inner model theory for large cardinal hypotheses in set theory
Includes a good deal of background material, references to the wider literature, and an introductory essay placing the new results in context
The first accessible introduction to the higher reaches of inner model theory
1. Introduction
2. Preliminaries
3. Background-induced iteration strategies
4. More mice and iteration trees
5. Some properties of induced strategies
6. Normalizing stacks of iteration trees
7. Strategies that condense and normalize well
8. Comparing iteration strategies
9. Fine structure for the least branch hierarchy
10. Phalanx iteration into a construction
11. HOD in the derived model of a HOD mouse
References
Index.
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TEXTBOOK
PUBLICATION PLANNED FOR: December 2022
AVAILABILITY: Not yet published - available from December 2022
FORMAT: HardbackISBN: 9781009158121
Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in the solutions of polynomial equations. Because groups may act as permutations of a set, as linear transformations on a vector space, or as automorphisms of a field, the deeper structure of a group may emerge from these viewpoints, two different groups can be distinguished, or a polynomial equation can be shown to be solvable by radicals. By developing the properties of these group actions, readers encounter essential algebra topics like the Sylow theorems and their applications, Galois theory, and representation theory. Warmup chapters that review and build on the first course and active learning modules help students transition to a deeper understanding of ideas.
Presents unified narratives around fundamental concepts in modern algebra, allowing readers to anticipate and develop methods that are related but widely applicable
Features active learning modules, “Getting to Know…,” where readers work out ideas for themselves, offering opportunities for mathematical discourse among students in group settings
Discusses representation theory ? an often-overlooked topic for undergraduates ? while illustrating its importance, depth, and remarkable applications
Provides a more motivated narrative of Galois theory, developed with group actions to hand, and exposes readers to concrete examples of Galois theory in action
Preface
1. Warmup: more group theory
2. Groups acting on sets
3. Warmup: some linear algebra
4. Representation theory
5. Warmup: fields and polynomials
6. Galois theory
7. Epilogue
References
Index.
Part of Cambridge Studies in Advanced Mathematics
PUBLICATION PLANNED FOR: January 2023
AVAILABILITY: Not yet published - available from January 2023
FORMAT: Hardback ISBN: 9781316510872
This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderon problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding section discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.
Gives an up-to-date account of the developments in geometric inverse problems in the past two decades
Focuses on the two-dimensional case and with ample background material to keep pre-requisites to a minimum
Includes many proofs that have not appeared elsewhere in the literature and provides a unified approach to the subject
Contents
Foreword Andras Vasy
Preface
1. The Radon transform in the plane
2. Radial sound speeds
3. Geometric preliminaries
4. The geodesic X-ray transform
5. Regularity results for the transport equation
6. Vertical Fourier analysis
7. The X-ray transform in non-positive curvature
8. Microlocal aspects, surjectivity of $I^{*}_{0}$
9. Inversion formulas and range
10. Tensor tomography
11. Boundary rigidity
12. The attenuated geodesic X-ray transform
13. Non-Abelian X-ray transforms
14. Non-Abelian X-ray transforms II
15. Open problems and related topics
References
Index.