Notices of the American Mathematical Society

Can we coexist with the other life forms that have evolved on this planet? Are there realistic alternatives to fossil fuels that would sustainably provide for human society's energy needs and have fewer harmful effects? How do we deal with threats such as emergent diseases? Mathematical models—equations of various sorts capturing relationships between variables involved in a complex situation—are fundamental for understanding the potential consequences of choices we make. Extracting insights from the vast amounts of data we are able to collect requires analysis methods and statistical reasoning. This book on elementary topics in mathematical modeling and data analysis is intended for an undergraduate “liberal arts mathematics”-type course but with a specific focus on environmental applications. It is suitable for introductory courses with no prerequisites beyond high school mathematics. A great variety of exercises extends the discussions of the main text to new situations and/or introduces new real-world examples. Every chapter ends with a section of problems, as well as with an extended chapter project which often involves substantial computing work either in spreadsheet software or in the ${\tt R}$ statistical package. It is great that mathematics is finally taught as a tool to understand the challenges that the planet will be facing and to participate in the debate. The book aims at developing skills in mathematical modeling and data analysis, with a focus on the environment. The projects encourage active learning. A wonderful book! —Christiane Rousseau, Initiator of Mathematics of Planet Earth (MPE2013) and Professor of Mathematics, Université de Montréal Using diverse examples with environmental science data, this text provides a lively review of high school math. Ideal for a quantitative literacy course, it offers an excellent alternative to the typical math rehash. —Louis J. Gross, Chancellor's Professor of Ecology and Evolutionary Biology and Mathematics, University of Tennessee, Knoxville May 2019 Front Cover Call for Nominations Programs That Make a Difference Call for Applications, Director of Education A Word From...Richard Schoen, AMS Vice President Table of Contents Front Matter Letters to the Editor Charitable Goals Hunting for Foxes with Sheaves by Michael Robinson On Turbulence and Geometry from Nash to Onsager by Camillo De Lellis and Laszlo Szekelyhidi Jr. Topological Time Series Analysis by Jose A. Perea Report from the Committee on Education Summer Break: Go Explore the Opportunities by Natalie Hobson Make a Difference This Summer by Melinda Lanius, Claire Merriman, and Simone Sisneros-Thiry You Should Organize Conferences and Workshops by Izzet Coskun Organizing Workshops and Programs at Math Institutes by Brendan Hassett AMS Membership for Early Careeer Mathematicians Anatole Katok--A Half-Century of Dynamics by Boris Hasselblatt Anatole Katok Center for Dynamical Systems and Geometry by Svetlana Katok and Yakov Pesin Mathematical Moments The Controversy over the AMS Publishing Original Investigations by Steve Batterson Call for Nominations Impact on the Teaching and Learning of Mathematics 2019 Award for Impact on the Teaching and Learning of Mathematics The Amazing Variet of Public Math by David Eisenbud and Kirsten Bohl What is...a Coleman integral? by Jennifer S. Balakrishnan Call for Applications and Nominations, Treasurer 2019 Mathematics Programs that Make a Difference Award GovMath 2019 Award for an Exemplary Program or Achievement in a Mathematics Department Maker of Patterns a Review by Steven J. Miller Bookshelf Call for Applications and Nominations, Secretary Who are you? by Edward Dunne Has Carmichael's Totient Conjecture Been Proven? No, No, It Has Not by Sophia D. Merow Mathematics People WAM: Fostering Excellence in Mathematics Research for Twenty-Five Years by Evelyn Lamb Mathematics Opportunities Classified Advertising New Books Offered by the AMS Call for Nomination, Bocher, Chevalley, Eisenbud, and Cole Prizes Meetings & Conferences of the AMS May Table of Contents Meetings & Conferences Call for Nominations Morgan Prize Recent Releases from the AMS Mathematical Modeling in Economics and Finance is designed as a textbook for an upper-division course on modeling in the economic sciences. The emphasis throughout is on the modeling process including post-modeling analysis and criticism. It is a textbook on modeling that happens to focus on financial instruments for the management of economic risk. The book combines a study of mathematical modeling with exposure to the tools of probability theory, difference and differential equations, numerical simulation, data analysis, and mathematical analysis. Students taking a course from Mathematical Modeling in Economics and Finance will come to understand some basic stochastic processes and the solutions to stochastic differential equations. They will understand how to use those tools to model the management of financial risk. They will gain a deep appreciation for the modeling process and learn methods of testing and evaluation driven by data. The reader of this book will be successfully positioned for an entry-level position in the financial services industry or for beginning graduate study in finance, economics, or actuarial science. The exposition in Mathematical Modeling in Economics and Finance is crystal clear and very student-friendly. The many exercises are extremely well designed. Steven Dunbar is Professor Emeritus of Mathematics at the University of Nebraska and he has won both university-wide and MAA prizes for extraordinary teaching. Dunbar served as Director of the MAA's American Mathematics Competitions from 2004 until 2015. His ability to communicate mathematics is on full display in this approachable, innovative text.-- Provided by publisher Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level. -- Provided by publisher The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. From the appearance of Gromov's original paper until today this approach has been the most important tool in global symplectic geometry. To produce numerical invariants of these manifolds using this method requires constructing a fundamental cycle associated with moduli spaces. This volume brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. Workers in the field will get a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. These techniques and results will be essential in further applications of this approach to producing invariants of symplectic manifolds. The author introduces basic techniques for constructing mathematical models, analyzing the information contained in data sets, and presenting data in numerical and graphical forms. This book explains how to use linear, exponential, and power functions to describe different environmental issues and how to select an appropriate model for a given situation. A project at the end of each chapter encourages students to access government data and develop their own answers to a series of questions Brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. The book offers a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. Mathematical models - equations of various sorts capturing relationships between variables involved in a complex situation - are fundamental for understanding the potential consequences of choices we make. This book on elementary topics in mathematical modeling and data analysis has a specific focus on environmental applications.