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Applications of Polynomial Systems
Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border...
Aspiring and Inspiring
Aspiring and Inspiring is a collection of essays from successful women and gender minority mathematicians on what it takes to build a career in mathematics. The individual essays are intended to advise, encourage, and inspire mathematicians throughout different stages of their careers. Themes emerge as these prominent individuals describe how they managed to persist and rise to positions of leadership in a field which can still be forbidding to many. We read, repeatedly, that individual mentorship matters, that networks of support can be critical, and that finding fulfillment can mean formulating one's own definition of success. Those who aspire to leadership in the field will find much usef...
Multidimensional Residue Theory and Applications
Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to...
Residues and Duality for Projective Algebraic Varieties
"This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D. A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."--BOOK JACKET.
Mathematical Congress of the Americas
This volume contains the proceedings of the First Mathematical Congress of the Americas, held from August 5-9, 2013, in Guanajuato, México. With the participation of close to 1,000 researchers from more than 40 countries, the meeting set a benchmark for mathematics in the two continents. The papers, written by some of the plenary and invited speakers, as well as winners of MCA awards, cover new developments in classic topics such as Hopf fibrations, minimal surfaces, and Markov processes, and provide recent insights on combinatorics and geometry, isospectral spherical space forms, homogenization on manifolds, and Lagrangian cobordism, as well as applications to physics and biology.
The Best Writing on Mathematics 2010
The year’s most memorable writing on mathematics This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freema...
