New Results from the Beginning of the 21st Century
This book, the first in its field to write about polynomial automorphisms
It is the first book containing the latest results concerning polynomial
automorphisms
It gives detailed accounts by leading researchers in the field
This book is an extension to Arno van den Essen's Polynomial Automorphisms and the
Jacobian Conjecture published in 2000. Many new exciting results have been obtained in the
past two decade, including the solution of Nagata's Conjecture, the complete solution of
Hilbert's fourteenth problem, the equivalence of the Jacobian Conjecture and the Dixmier
Conjecture, the symmetric reduction of the Jacobian Conjecture, the theory of Mathieu-Zhao
spaces and counterexamples to the Cancellation problem in positive characteristic. These and
many more results are discussed in detail in this work. The book is aimed at graduate students
and researchers in the field of Affine Algebraic Geometry. Exercises are included at the end of
each section.
Due 2021-01-14
1st ed. 2021, X, 191 p.
Softcover
ISBN 978-3-030-60533-9
Product category : Monograph
Series : Frontiers in Mathematics
Mathematics : Algebraic Geometry
Gathers a wealth of rigorously peer-reviewed contributions, written by
respected experts
Highlights the latest approaches to statistical distributions
Though chiefly focusing on theory, will also appeal to readers interested in
applied probabilities
This book highlights the forefront of research on statistical distribution theory, with a focus on
unconventional random quantities, and on phenomena such as random partitioning. The
respective papers reflect the continuing appeal of distribution theory and the lively interest in
this classic field, which owes much of its expansion since the 1960s to Professor Masaaki
Sibuya, to whom this book is dedicated. The topics addressed include a test procedure for
discriminating the(multivariate) Ewens distribution from the Pitman Sampling Formula,
approximation to the length of the Ewens distribution by discrete distributions and the normal
distribution, and the distribution of the number of levels in[s]-specified random permutations.
Also included are distributions associated with orthogonal polynomials with a symmetric matrix
argument and the characterization of the Jeffreys prior.
Due 2021-01-18
1st ed. 2020, IX, 112 p. 19 illus.
Softcover
ISBN 978-981-15-9662-9
Product category : Brief
Series : JSS Research Series in Statistics
Statistics : Applied Statistics
Focuses on various important areas of mathematics in which approximation
methods play an essential role
Reader will be exposed to convexity theory, polynomial inequalities, extremal
problems, prediction theory, fixed point theory for operators, PDEs, fractional
integral inequalities, multidimensional numerical integration, Gauss-Jacobi
and Hermite-Hadamard type inequalities, Hilbert-type inequalities, and Ulam’
s stability of functional equations
Provides up-to-date results which may be useful to graduate students and
researchers working in mathematics, physics, economics, operational research
This contributed volume focuses on various important areas of mathematics in which
approximation methods play an essential role. It features cutting-edge research on a wide
spectrum of analytic inequalities with emphasis on differential and integral inequalities in the
spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a
plethora of applications, making this work a valuable resource. The reader will be exposed to
convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point
theory for operators, PDEs, fractional integral inequalities, multidimensional numerical
integration, Gauss?Jacobi and Hermite?Hadamard type inequalities, Hilbert-type inequalities,
and Ulam’s stability of functional equations. Contributions have been written by eminent
researchers, providing up-to-date information and several results which may be useful to a
wide readership including graduate students and researchers working in mathematics, physics,
economics, operational research, and their interconnections.
Due 2021-01-29
1st ed. 2020, X, 490 p. 18 illus., 15 illus. in color.
Hardcover
ISBN 978-3-030-60621-3
Product category : Contributed volume
Mathematics : Optimization
Copyright Year 2018
ISBN 9780367657611
Published September 29, 2020 by Chapman and Hall/CRC
256 Pages
The Rogers--Ramanujan identities are a pair of infinite series?infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers?Ramanujan identities and will include related historical material that is unavailable elsewhere.
Background and the Pre-History. The Golden Age and its Modern Legacy. Infinite Families...Everywhere! From Infinite to Finite. Motivated Proofs, Connections to Lie Algebras, and More Identities. But wait...there's more!
Andrew Sills obtained his Ph.D. in 2002 from the University of Kentucky under. George E. Andrews, Evan Pugh Professor of Mathematics, Pennsylvania State University. He was Hill Assistant Professor of Mathematics, at Rutgers University between 2003- 2007 and a Tenure-track Assistant Professor at Georgia Southern University between 2007-2011. Since 2011 he has been Associate Professor of Mathematics at Georgia Southern, becoming a full Professor of Mathematics, effective August 1, 2015. He is a permanent Member of DIMACS (Center for Discrete Mathematics and Computer Science), since 2011. Research Grant: "Computer Assisted Research in Additive and Combinatorial Number Theory and Allied Areas," National Security Agency Grant, 2014-2015.
Copyright Year 2021
ISBN 9780367679354
December 15, 2020 Forthcoming by Chapman and Hall/CRC
380 Pages 25 B/W Illustrations
Hardback
The book contains selected problems aimed for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions. The problems are mostly selected from an extensive collection of problems from Polish Mathematical Olympics and many appear here in English for the first time. Each chapter consists of many sections devoted to a collection of related topics. Each of these sections starts with a problem followed by the necessary background (definitions and theorems used), careful and detailed solution, and discussion of possible generalizations.
List of Figures
Introduction
Chapter 1: Inequalities
Chapter 2: Equalities and Sequences
Chapter 3: Functions, Polynomials, and Functional Equations
Chapter 4: Combinatorics
Chapter 5: Number Theory
Chapter 6: Geometry
Chapter 7: Hints
Chapter 8: Solutions
Further Reading
Index
The book contains carefully selected, challenging problems to prepare readers for rigorous mathematics. Neither prior preparation nor any mathematical sophistication is required. The authors guide the readers to think and express themselves in a rigorous, mathematical way, to extract facts, analyze the problem, and identify main challenges. Moreover, they show how to draw appropriate, true conclusions and to see a big picture.
Readers are provided with a firm foundation in a diverse range of topics. Computer support is used to build a better intuition into discussed problems. The book can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses that are offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. It provides a solid foundation of various topics that would be useful for more advanced courses.
The content of this book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.
Copyright Year 2021
Available for pre-order. Item will ship after January 31, 2021
ISBN 9780367206932
Hardback
ISBN 9780367206925
Paperback
January 31, 2021 Forthcoming by A K Peters/CRC Press
516 Pages 160 B/W Illustrations
Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
A collection of the world’s best mathematical puzzles
Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof
Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not just exercises or contest problems.
The Puzzles. The Hints. 1. Out for the Count. 2. Achieving Parity. 3. Intermediate Math. 4. Graphography. 5. Algebra Too. 6. Safety in Numbers. 7. The Law of Small Numbers. 8. Weighs and Means. 9. The Power of Negative Thinking. 10. In All Probability. 11. Working for the System. 12. The Pigeonhole Principle. 13. Information, Please. 14. Great Expectation. 15. Brilliant Induction. 16. Journey Into Space. 17. Nimbers and the Hamming Code. 18. Unlimited Potentials. 19. Hammer and Tongs. 20. Let's Get Physical. 21. Back from the Future. 22. Seeing is Believing. 23. Infinite Choice. 24. Startling Transformation. Notes & Sources
Peter Winkler is the William Morrill Professor of Mathematics and Computer Science at Dartmouth College, and for 2019 - 2020, the Distinguished Visiting Professor for the Public Dissemination of Mathematics at the National Museum of Mathematics. He is the author of 160 research papers, a dozen patents, two previous puzzle books, a book on cryptographic techniques in the game of bridge, and a portfolio of compositions for ragtime piano.