This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, in honor of Bang-Yen Chen's 75th birthday, held from October 20?21, 2018 at the University of Michigan, Ann Arbor, Michigan.
The development of contemporary geometry of submanifolds benefited greatly from Bang-Yen Chen's contributions, as several interesting questions actively pursued today originate in his work. Chen is known for several fundamental ideas in differential geometry, including Chen inequalities, Chen invariants, Chen's conjectures, Chen surface, Chen-Ricci inequality, Chen submanifolds, Chen equality, submanifolds of finite type, and slant submanifolds.
The papers in this volume represent a celebration of the geometry of submanifolds and its connections with other areas of mathematics and cover themes rooted in Chen's work, from investigations on the spectrum of the Laplacian on complete Riemannian manifolds to the geometry of symmetric spaces. These contributions are written with the hope to inform and inspire.
Graduate students and research mathematicians interested in differential geometry and geometry of submanifolds
Contemporary Mathematics, Volume: 756
2020; 269 pp; Softcover
Print ISBN: 978-1-4704-5092-2
Product Code: CONM/756
Part of Cambridge IISc Series
DATE PUBLISHED: October 2020AVAILABILITY: Available
FORMAT: HardbackISBN: 9781108839808
Suitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three important equations of mathematical physics ? Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen readers will benefit from more advanced topics and many references cited at the end of each chapter. In addition, the book covers advanced topics such as Conservation Laws and Hamilton-Jacobi Equation. Numerous real-life applications are interspersed throughout the book to retain readers' interest.
Highlights the importance of studying the equations outside the realm of classical solutions
Separate chapters on advanced topics such as the Hamilton-Jacobi equation and conservation laws
Explains the interplay between geometry and analysis in the existence and uniqueness of solutions in the treatment of first order equations
List of illustrations
Preface
Acknowledgements
Notations
1. Introduction
2. Preliminaries
3. First-order partial differential equations: method of characteristics
4. Hamilton?Jacobi equation
5. Conservation laws
6. Classification of second-order equations
7. Laplace and Poisson equations
8. Heat equation
9. One-dimensional wave equation
10. Wave equation in higher dimensions
11. Cauchy?Kovalevsky theorem and its generalization
12. A peep into weak derivatives, Sobolev spaces and weak formulation
References
Index.
PUBLICATION PLANNED FOR: December 2020
AVAILABILITY: Not yet published - available from December 2020
FORMAT: HardbackISBN: 9781733146630
Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.
Author is a world-renowned teacher of linear algebra who delivers the material in a clear and effective way that students will appreciate
Uses a highly accessible approach that enables students without a strong mathematics background to understand more advanced topics such as singular value decomposition (SVD)
Covers topics such as data science and deep learning that show why linear algebra isn't just for mathematicians
Comes with accompanying video lectures on the MIT OpenCourseWare website, giving students the option to self-study and learn at their own pace
Preface
1. Vectors and Matrices
2. Solving Linear Equations Ax = b
3. The Four Fundamental Subspaces
4. Orthogonality
5. Determinants and Linear Transformations
6. Eigenvalues and Eigenvectors
7. The Singular Value Decomposition (SVD)
8. Learning from Data
Appendix 1. The Ranks of AB and A + B
Appendix 2. Eigenvalues and Singular Values: Rank One
Appendix 3. Counting Parameters in the Basic Factorizations
Appendix 4. Codes and Algorithms for Numerical Linear Algebra
Appendix 5. Matrix Factorizations
Appendix 6. The Column-Row Factorization of a Matrix
Appendix 7. The Jordan Form of a Square Matrix
Appendix 8. Tensors
Appendix 9. The Condition Number
Appendix 10. Markov Matrices and Perron-Frobenius
Index
Index of Symbols
Six Great Theorems / Linear Algebra in a Nutshell.
Part of London Mathematical Society Student Texts
DATE PUBLISHED: October 2020AVAILABILITY:
Not yet published - available from December 2020
FORMAT: PaperbackISBN: 9781108413145
FORMAT: HardbackISBN: 9781108420150
This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.
A sleek introduction to the theory of forcing, which allows even those who do not have any background in set theory to understand the subject
Devotes the second part of the book to contemporary topics in the theory of forcing, including open questions
Includes previously unpublished results in the theory of forcing
Part I. Let's Be Independent:
1. Introduction
2. Axiomatic Systems
3. Zermelo-Fraenkel Axioms and the Axiom of Choice
4. Well Orderings and Ordinals
5. Cardinals
6. Models and Independence
7. Some Class Models of ZFC
8. Forcing
9. Violating CH
Part II. What Is New in Set Theory:
10. Introduction to Part Two
11. Classical Extensions
12. Iterated Forcing and Martin's Axiom
13. Some More Large Cardinals
14. Limitations of Martin's Axiom and Countable Supports
15. Proper Forcing and PFA
16. $aleph_2$ and other Successors of Regulars
17. Singular Cardinal Hypothesis and some PCF
18. Forcing at Singular Cardinals and their Successors
References
Index.
PUBLICATION PLANNED FOR: December 2020
AVAILABILITY: Not yet published - available from December 2020
FORMAT: HardbackISBN: 9781107012578
Is mathematics 'entangled' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the 'natural language moves' of Godel and Tarski, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. The treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with a new twist.
Presents Godel's and Tarski's mathematical research in a new light, emphasising previously neglected aspects of their work
Provides an overview of the current state of logical research in many different areas
Contributes to important contemporary debates in the philosophy of logic and mathematics, including naturalism and foundations
Part of Cambridge Mathematical Library
PUBLICATION PLANNED FOR: March 2021
AVAILABILITY: Not yet published - available from March 2021
FORMAT: PaperbackISBN: 9781108820288
Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition.
Assumes only a modest mathematical background (mainly linear algebra at undergraduate level)
Contains over 500 exercises, ranging from easy verifications to very challenging problems
Includes an addendum (with an extensive bibliography) describing major developments and open problems in symbolic dynamics since the original publication in 1995
1. Shift spaces
2. Shifts of finite type
3. Sofic shifts
4. Entropy
5. Finite-state codes
6. Shifts as dynamical systems
7. Conjugacy
8. Finite-to-one codes and finite equivalence
9. Degrees of codes and almost conjugacy
10. Embeddings and factor codes
11. Realization
12. Equal entropy factors
13. Guide to advanced topics
Addendum for the second edition
Bibliography
Addendum bibliography
Notation index
Index.