Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
Author: Zhiyong Zheng
Publisher: Springer Nature
Published: 2024
Total Pages: 191
ISBN-13: 9464634634
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A Functorial Model Theory
Author: Cyrus F. Nourani
Publisher: CRC Press
Published: 2016-04-19
Total Pages: 296
ISBN-13: 1482231506
DOWNLOAD EBOOKThis book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Inverse Limits
Author: W.T. Ingram
Publisher: Springer Science & Business Media
Published: 2011-11-06
Total Pages: 229
ISBN-13: 146141797X
DOWNLOAD EBOOKInverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families. This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.
Fundamentals of Computation Theory
Author: Maciej Liskiewicz
Publisher: Springer Science & Business Media
Published: 2005-08-04
Total Pages: 590
ISBN-13: 3540281932
DOWNLOAD EBOOKThis book constitutes the refereed proceedings of the 15th International Symposium Fundamentals of Computation Theory, FCT 2005, held in Lübeck, Germany in August 2005. The 46 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 105 submissions. The papers are organized in topical sections on circuits, automata, complexity, approximability, computational and structural complexity, graphs and complexity, computational game theory, visual cryptography and computational geometry, query complexity, distributed systems, automata and formal languages, semantics, approximation algorithms, average case complexity, algorithms, graph algorithms, and pattern matching.
Algebraic Computability and Enumeration Models
Author: Cyrus F. Nourani
Publisher: CRC Press
Published: 2016-02-24
Total Pages: 304
ISBN-13: 1771882484
DOWNLOAD EBOOKThis book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples
Topological Groups and the Pontryagin-van Kampen Duality
Author: Lydia Außenhofer
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2021-11-22
Total Pages: 392
ISBN-13: 3110654938
DOWNLOAD EBOOKThis book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.
Basic Algebraic Topology and its Applications
Author: Mahima Ranjan Adhikari
Publisher: Springer
Published: 2016-09-16
Total Pages: 628
ISBN-13: 813222843X
DOWNLOAD EBOOKThis book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.
Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial
Author: Anatoly M. Vershik
Publisher: American Mathematical Soc.
Published: 2021-08-30
Total Pages: 345
ISBN-13: 1470456648
DOWNLOAD EBOOKVladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.
