Softcover ISBN: 978-1-4704-6977-1
Product Code: PSPUM/105
This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27?October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada.
Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory.
The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme.
The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.
Graduate students and researchers interested in cyclic cohomology and applications to arithmetic geometry, global analysis, topological and algebraic K
-theory, and physics.
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7184-2
A Panoply of Polygons presents and organizes hundreds of beautiful, surprising and intriguing results about polygons with more than four sides. (A Cornucopia of Quadrilaterals, a previous volume by the same authors, thoroughly explored the properties of four-sided polygons.) This panoply consists of eight chapters, one dedicated to polygonal basics, the next ones dedicated to pentagons, hexagons, heptagons, octagons and many-sided polygons. Then miscellaneous classes of polygons are explored (e.g., lattice, rectilinear, zonogons, cyclic, tangential) and the final chapter presents polygonal numbers (figurate numbers based on polygons). Applications, real-life examples, and uses in art and architecture complement the presentation where many proofs with a visual nature are included.
A Panoply of Polygons can be used as a supplement to a high school or college geometry course. It can also be used as a source for group projects or extra-credit assignments. It will appeal, and be accessible to, anyone with an interest in plane geometry. Claudi Alsina and Roger Nelsen are, jointly and individually, the authors of thirteen previous MAA/AMS books. Those books, and this one, celebrate and illuminate the power of visualization in learning, teaching, and creating mathematics.
Undergraduate and graduate students and researchers interested in classical geometry.
Cover
1/2 title page
title page
copyright
Contents
Preface
1. Polygon Basics
2. Pentagons
3. Hexagons
4. Heptagaons
5. Octagons
6. Many-sided Polygons
7. Miscellaneous Classes of Polygons
8. Polygonal Numbers
Solutions to the Challenges
Credits & Permissions
Bibliography
Index
Softcover ISBN: 978-1-4704-6604-6
Product Code: CONM/782
This volume contains the proceedings of the conference on Formal and Analytic Solutions of Diff. Equations, held from June 28?July 2, 2021, and hosted by University of Alcala, Alcala de Henares, Spain.
The manuscripts cover recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, q
-difference equations, partial differential equations, moment differential equations, etc. Also discussed are related topics such as summability of formal solutions and the asymptotic study of their solutions.
The volume is intended not only for researchers in this field of knowledge but also for students who aim to acquire new techniques and learn recent results.
Graduate students and research mathematicians interested in equations in complex domain.
Softcover ISBN: 978-1-4704-7027-2
Product Code: AMSTEXT/61
Lighten up about mathematics! Have fun. If you read this book, you will have to endure bad math puns and jokes and out-of-date pop culture references. You'll learn some really cool mathematics to boot. In the process, you will immerse yourself in living, thinking, and breathing logical reasoning. We like to call this proofs, which to some is a bogey word, but to us it is a boogie word. You will learn how to solve problems, real and imagined. After all, math is a game where, although the rules are pretty much set, we are left to our imaginations to create. Think of this book as blueprints, but you are the architect of what structures you want to build. Make sure you lay a good foundation, for otherwise your buildings might fall down. To help you through this, we guide you to think and plan carefully. Our playground consists of basic math, with a loving emphasis on number theory. We will encounter the known and the unknown. Ancient and modern inquirers left us with elementary-sounding mathematical puzzles that are unsolved to this day. You will learn induction, logic, set theory, arithmetic, and algebra, and you may one day solve one of these puzzles.
Appropriate for a course serving as a transition to advanced mathematics and for undergraduate students interested in mathematical reasoning and an introduction to proofs.
Hardcover ISBN: 978-1-4704-6898-9
Product Code: GSM/229
This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian.
The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part, to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.
Graduate students and researchers interested in fractional Sobolev spaces.