Copyright Year 2021
ISBN 9780815354369
648 Pages 50 B/W Illustrations
Hardback
Look for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections,
topics, and exercises. The authors present the core principles of modern
cryptography, with emphasis on formal definitions, rigorous proofs of security
Jonathan Katz is Director, Maryland Cybersecurity Center and Professor, Department of Computer Science and UMIACS Department of Electrical and Computer Engineering at University of Maryland. He is the co-author with Yehuda Lindell of Introdution to Modern Cryptography, Second Edition, published by CRC Press.Vadim
Yehuda Lindell is a professor in the Department of Computer Science at Bar-Ilan University where he conducts research on cryptography with a focus on the theory of secure computation and its application in practice. Lindell received a Raviv Fellowship[1] and spent two years at IBM's cryptography research group at the T.J. Watson Research Center.
Copyright Year 2021
ISBN 9780367569327
April 28, 2021 Forthcoming
292 Pages 21 B/W Illustrations
This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree of knowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix.
* Serves to find analogies between classical results (Cramer, Wold, Kolmogorov, Wiener, Kalman, Rozanov) and up-to-date methods for dimension reduction in multidimensional time series.
* Provides a unified treatment for time and frequency domain inferences by using machinery of complex and harmonic analysis, spectral and Smith--McMillan decompositions. Establishes analogies between the time and frequency domain notions and calculations.
* Discusses the Wold's decomposition and the Kolmogorov's classification together, by distinguishing between different types of singularities. Understanding the remote past helps us to characterize the ideal situation where there is a regular part at present. Examples and constructions are also given.
* Establishes a common outline structure for the state space models, prediction, and innovation algorithms with unified notions and principles, which is applicable to real-life high frequency time series.
It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.
1. Harmonic analysis of stationary time series. 2. ARMA, regular, and singular time series in 1D. 3. Linear system theory, state space models. 4. Multidimensional time series. 5. Dimension reduction and prediction in the time and frequency domain. Appendices.
Marianna Bolla, DSc is professor in the Institute of Mathematics, Budapest University of Technology and Economics. She authored the book Spectral Clustering and Biclustering, Learning Large Graphs and Contingency Tables, Wiley (2013) and the article Factor Analysis, Dynamic in Wiley StatsRef: Statistics Reference Online (2017). She is coauthor of a Hungarian book on Multivariate Statistical Analysis and a textbook Theory of Statistical Inference; further, provides lectures on these topics at her home institution and in the Budapest Semesters in Mathematics program. Research interest: spectral clustering, graphical models, time series, application of spectral and block matrix techniques in multivariate regression and prediction, based on classical works of CR Rao.
Tamas Szabados, PhD is a retired associate professor in the Institute of Mathematics, Budapest University of Technology and Economics. He used to give lectures on stochastic analysis and probability theory in his home institute and on probability theory in the Budapest Semesters in Mathematics program as well. He is a coauthor of a Hungarian textbook (1983) on vector analysis. He holds master’s degrees in electrical engineering and applied mathematics and PhD in mathematics. Research interests: discrete approximations in stochastic calculus, theory of time series, and mathematical immunology.
Copyright Year 2021
Hardback ISBN 9781032010779
paperback ISBN 9780367761455
June 14, 2021 Forthcoming by Chapman and Hall/CRC
166 Pages 25 B/W Illustrations
This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic.
The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry.
About the Author
Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.
1 Genesis-What is Number Theory?
2 Review of the Prerequisite Material
3 Basic Concepts
4 Arithmetic in Relative Extensions
5 Geometry of Numbers
6 Analytic Methods
7 Arithmetic in Galois Extensions
8 Cyclotomic Fields
9 The Kronecker-Weber Theorem
10 Passage to Algebraic Geometry
11 Epilogue-Fermat’s Last Theorem
Bibliography
Index
ISBN 9780367703127
June 10, 2021 Forthcoming by Chapman and Hall/CRC
136 Pages 78 B/W Illustrations
Hardback
One cannot watch or read about any news these days without hearing about the models for COVID-19 or the testing that must occur to approve vaccines or treatments for the disease.
This book’s purpose is to shed some light on the meaning and interpretations of many of the types of models that are or might be used in the presentation of analysis. Understanding the concepts presented is essential in the entire modeling process of a pandemic.
From the virus itself and its infectious rates and deaths rates to explain the process for testing a vaccine or eventually a cure, the author builds, presents, and shows model testing.
This book is an attempt, based on available data, to add some validity to the models developed and used, showing how close to reality the models are to predicting "results" from previous pandemics such as the Spanish flu in 1918 and more recently the Honk Kong flu. Then the author applies those same models to Italy, New York City, and the United States as a whole.
Modeling is a process. It is essential to understand that there are many assumptions that go into the modeling of each type of model. The assumptions influence the interpretation of the results. Regardless of the modeling approach the results generally indicate approximately the same results. This book reveals how these interesting results are obtained.
Preface
1. Modeling as a Process
2. DISCRETE DYNAMICAL SYSTEM MODELS
3. Modeling Coupled Systems of Discrete Dynamical Systems
4. Modeling with Differential Equation
5. Systems of Differential Equations
6. Probabilistic Models
7. Hypothesis Tests
8. Two Samples Hypothesis test (means and proportions)
9. Agent Based Model with NetLogo
10. Concluding Remarks and Epilogue
References
Index
Dr. William P. Fox is an Emeritus Professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is a Visitng Professor of Computational Operations Research in the Department of Mathematics at the College of William and Mary. He received his BS degree from the United States Military Academy at West Point, New York, his MS in operations research from the Naval Postgraduate School, and his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy, at Francis Marion University where he was the chair of mathematics for eight years, and twelve years at the Naval Postgraduate School. He has many publications and scholarly activities including over twenty books (6 with CRC Press), twenty-two chapters of books & technical reports, one hundred and fifty journal articles, and over one hundred and fifty conference presentations and mathematical modeling workshops.
ISBN 9781032021935
ISBN 9780367766801 Paperback
June 15, 2021 Forthcoming by Chapman and Hall/CRC
136 Pages
Whereas many partial solutions and sketches for the odd-numbered exercises appear in the book, the Student Solutions Manual, written by the author, has comprehensive solutions for all odd-numbered exercises and large number of even-numbered exercises. This Manual also offers many alternative solutions to those appearing in the text. These will provide the student with a better understanding of the material.
This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Tenth Edition and is designed to supplement that text.
Integers and Equivalence Relations
0. Preliminaries
Groups
1. Introduction to Groups
2. Groups
3. Finite Groups; Subgroups
4. Cyclic Groups
5. Permutation Groups
6. Isomorphisms
7. Cosets and Lagrange's Theorem
8. External Direct Products
9. Normal Subgroups and Factor Groups
10. Group Homomorphisms
11. Fundamental Theorem of Finite Abelian Groups
Rings
12. Introduction to Rings
13. Integral Domains
14. Ideals and Factor Rings
15. Ring Homomorphisms
16. Polynomial Rings
17. Factorization of Polynomials
18. Divisibility in Integral Domains Fields
Fields
19. Extension Fields
20. Algebraic Extensions
21. Finite Fields
22. Geometric Constructions
Special Topics
23. Sylow Theorems
24. Finite Simple Groups
25. Generators and Relations
26. Symmetry Groups
27. Symmetry and Counting
28. Cayley Digraphs of Groups
29. Introduction to Algebraic Coding Theory
30. An Introduction to Galois Theory
31. Cyclotomic Extensions
Joseph A. Gallian earned his PhD from Notre Dame. In addition to receiving numerous national awards for his teaching and exposition, he has served terms as the Second Vice President, and the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in the national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.