Notices of the American Mathematical Society

The theory of complex dynamics in one variable, initiated by Fatou and Julia in the early twentieth century, concerns the iteration of a rational function acting on the Riemann sphere. Building on foundational investigations of $p$-adic dynamics in the late twentieth century, dynamics in one non-archimedean variable is the analogous theory over non-archimedean fields rather than over the complex numbers. It is also an essential component of the number-theoretic study of arithmetic dynamics. This textbook presents the fundamentals of non-archimedean dynamics, including a unified exposition of Rivera-Letelier's classification theorem, as well as results on wandering domains, repelling periodic points, and equilibrium measures. The Berkovich projective line, which is the appropriate setting for the associated Fatou and Julia sets, is developed from the ground up, as are relevant results in non-archimedean analysis. The presentation is accessible to graduate students with only first-year courses in algebra and analysis under their belts, although some previous exposure to non-archimedean fields, such as the $p$-adic numbers, is recommended. The book should also be a useful reference for more advanced students and researchers in arithmetic and non-archimedean dynamics. Noticed March 2019 Front Cover Coll for Nominations Leroy P. Steele Prizes A Word From...Catherine A. Roberts, AMS Executive Director Table of Contents Front Matter Letters to the Editor Karen Uhlenbeck and the Calculus of Variations by Simon Donaldson AMS Textbook Course Adaptation Celebratio Mathematica: An Interview with Karen Uhlenbeck and Three New Volumes on Women Mathematicians by Sheila Newbery Gertrude M. Cox and Statistical Design by Sharon L. Lohr The Life and Pioneering Contributions of an African American Centenarian: Mathematician Katherine G. Johnson by Johnny L. Houston The Mathematics of Grace Murray Hopper by Asher Auel The Mathematics of Joan Birman by Dan Margalit Outward-Facing Mathematics: A Pitch by Jordan Ellenberg To Write or Not to Write...a Book, and When? by Joseph H. Silverman Preparing Your Results for Publication The Art of Writing Introductions by John Etnyre Writing, and Reading, Referee Reports by Arend Bayer AMS Membership for Early Career Mathematicians AMS Graduate Student Chapers In Memory of Marina Ratner 1938-2017 Marina Ratner by S. G. Dani Ratner's Work on Unipotent Flows and Its Impact by Elon Lindenstrauss, Peter Sarnak, and Amie Wilkinson To the Memory of Marina Ratner by Yakov Sinai Meetings: For almost All of Our Lives by Boris Gurevich In Memory by D. Ornstein Marina Ratner, quelques evocations by Jean-Paul Thouvenot Remembering Marina Ratner by Hee Oh Mathematical Moments Creating Opportunities and Building Confidence: Clare Boothe Luce's Unexpected Support of Women in Math and Science by Della Dumbaugh Women in Mathematics, A Review by Katie Spurrier Quertermous Call for Applications & Nominations, Secretary of the American Mathematical Society Bookshelf AMS Bookshelf MathPrograms.org Sectional Sampler Do Sums of Squares Dream of Free Resolutions? by Grigoriy Blekherman Invariant Markov Processes Under Actions of Lie Groups by Ming Liao Analysis of Nonlinear Geometric Equations by Aaron Naber Data Analysis Techniques with Applications to Lyme Date by Deanna Needell An Illustration in Number Theory by Katherine E. Stange Maria Gaetana Agnesi 1718-1799 by Della Dumbaugh A Mathematician Hosts NOVA Wonders Washington Update by Karen Saxe An Interview with Immediate Past President Kenneth A. Ribet by Evelyn Lamb Lafforgue Awarded 2019 Breakthrough Prize in Mathematics Mathematics People 2018 Class of Fellows of the AMS Call for Applications & Nominations Treasurer of the American Mathematical Society Community Updates Mathematics Opportunities Classified Advertising New Books Offered by the AMS Meetings & Conferences of the AMS March Table of Contents Meetings & Conferences of the AMS Upcoming Features and Memorial Tributes Position Available Director of Education American Mathematical Society Recent Releases from the AMS A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme. Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information. Linear Algebra: Concepts and Applications is designed to be used in a first linear algebra course taken by mathematics and science majors. It provides a complete coverage of core linear algebra topics, including vectors and matrices, systems of linear equations, general vector spaces, linear transformations, eigenvalues, and eigenvectors. All results are carefully, clearly, and rigorously proven. The exposition is very accessible. The applications of linear algebra are extensive and substantial—several of those recur throughout the text in different contexts, including many that elucidate concepts from multivariable calculus. Unusual features of the text include a pervasive emphasis on the geometric interpretation and viewpoint as well as a very complete treatment of the singular value decomposition. The book includes over 800 exercises and numerous references to the author's custom software Linear Algebra Toolkit. A student's solutions manual is freely available electronically: click here. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information. Linear Concepts and Applications is designed to be used in a first linear algebra course taken by mathematics and science majors. It provides a complete coverage of core linear algebra topics, including vectors and matrices, systems of linear equations, general vector spaces, linear transformations, eigenvalues, and eigenvectors. All results are carefully, clearly, and rigorously proven. The exposition is very accessible. The applications of linear algebra are extensive and substantial several of those recur throughout the text in different contexts, including many that elucidate concepts from multivariable calculus. Unusual features of the text include a pervasive emphasis on the geometric interpretation and viewpoint as well as a very complete treatment of the singular value decomposition. The book includes over 800 exercises and numerous references to the author's custom software Linear Algebra Toolkit. Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. The materials in Linear Algebra and Geometry have been used, field tested, and refined for over two decades. It is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. Secondary teachers will find the emphasis on developing effective habits of mind especially helpful. The book is written in a friendly, approachable voice and contains nearly a thousand problems. Organised around carefully sequenced problems, Linear Algebra and Geometry will help students build both the tools and the habits that provide a solid basis for further study in mathematics. This volume uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. A thoroughly modern textbook for a differential equations course. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature.