Softcover ISBN: 978-1-4704-6444-8
Expected availability date: August 26, 2023
Student Mathematical Library,Volume: 103
2023; 375 pp
MSC: Primary 11;
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big O
, little o
, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet L
-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory.
The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field.
Undergraduate and graduate students interested in analytic number theory.
Hardcover ISBN: 978-1-4704-7065-4
Expected availability date: August 09, 2023
Graduate Studies in Mathematics, Volume: 23
2023; 336 pp
MSC: Primary 37;
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided.
In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.
Graduate students and researchers interested in smooth ergodic theory and ordinary differential equations.
Softcover ISBN: 978-1-4704-7220-7
Expected availability date: September 02, 2023
Classroom Resource Materials Volume: 70
2023
MSC: Primary 11;
Number Theory Through the Eyes of Sophie Germain: An Inquiry Course is an innovative textbook for an introductory number theory course.
Sophie Germain (1776?1831) was largely self-taught in mathematics and, two centuries ago, in solitude, devised and implemented a plan to prove Fermat's Last Theorem. We have only recently completely understood this work from her unpublished letters and manuscripts. David Pengelley has been a driving force in unraveling this mystery and here he masterfully guides his readers along a path of discovery. Germain, because of her circumstances as the first woman to do important original mathematical research, was forced to learn most of what we now include in an undergraduate number theory course for herself. Pengelley has taken excerpts of her writings (and those of others) and, by asking his readers to decipher them, skillfully leads us through an inquiry-based course in elementary number theory. It is a detective story on multiple levels. What is Sophie Germain thinking? What do her mathematical writings mean? How do we understand what she knew and what she was trying to do, where she succeeded and where she didn't?
Undergraduate students interested in learning number theory and math history.
Paperback ISBN: 9780443187827
Discrete Mathematics provides key concepts and a solid, rigorous foundation in mathematical reasoning. Appropriate for undergraduate as well as a starting point for more advanced class, the resource offers a logical progression through key topics without assuming any background in algebra or computational skills and without duplicating what they will learn in higher level courses. The book is designed as an accessible introduction for students in mathematics or computer science as it explores questions that test the understanding of proof strategies, such as mathematical induction. For students interested to dive into this subject, the text offers a rigorous introduction to mathematical thought through useful examples and exercises.
1. What is Discrete Mathematics?
2. Basic Set Theory
3. Formal Logic
4. Boolean Functions and Predicate Logic
5. Induction/Set Structures
6. Equivalence Relations/Number Theory
7. Chinese Remainder Theorem and Fermatfs Little Theorem
8. Searching and Sorting
9. Graphs and Planarity
10. Growth of Functions
available from August 2023
FORMAT: HardbackISBN: 9781009351454
The book is designed for undergraduates, graduates, and researchers of mathematics studying fixed point theory or nonlinear analysis. It deals with the fixed point theory for not only single-valued maps but also set-valued maps. The text is divided into three parts: fixed point theory for single-valued mappings, continuity and fixed point aspects of set-valued analysis, and variational principles and their equilibrium problems. It comprises a comprehensive study of these topics and includes all important results derived from them. The applications of fixed point principles and variational principles, and their generalizations to differential equations and optimization are covered in the text. An elementary treatment of the theory of equilibrium problems and equilibrium version of Ekeland's variational principle is also provided. New topics such as equilibrium problems, variational principles, Caristi's fixed point theorem, and Takahashi's minimization theorem with their applications are also included.
Dedicated coverage of fixed point principles, variational principles, and equilibrium problems in metric spaces
New and old results in metric fixed point theory for thorough understanding of concepts
Examples and exercises for strengthening grasp on fundamentals
Appendices on 'Some Basic Concepts and Inequalities' and 'Partial Ordering' for easy reference
Preface
Acknowledgements
Notations and Abbreviations
1. Basic Definitions and Concepts from Metric Spaces
2. Fixed Point Theory in Metric Spaces
3. Set-valued Analysis: Continuity and Fixed Point Theory
4. Variational Principles and their Applications
5. Equilibrium Problems and Extended Ekeland's Variational Principle
6. Some Applications of Fixed Point Theory
Appendix A. Some Basic Concepts and Inequalities
Appendix B. Partial Ordering
References
Index.