Notices of the American Mathematical Society

Differential Equations: Techniques, Theory, and Applications is designed for a modern first course in differential equations either one or two semesters in length. The organization of the book interweaves the three components in the subtitle, with each building on and supporting the others. Techniques include not just computational methods for producing solutions to differential equations, but also qualitative methods for extracting conceptual information about differential equations and the systems modeled by them. Theory is developed as a means of organizing, understanding, and codifying general principles. Applications show the usefulness of the subject as a whole and heighten interest in both solution techniques and theory. Formal proofs are included in cases where they enhance core understanding; otherwise, they are replaced by informal justifications containing key ideas of a proof in a more conversational format. Applications are drawn from a wide variety of fields: those in physical science and engineering are prominent, of course, but models from biology, medicine, ecology, economics, and sports are also featured. The 1,400+ exercises are especially compelling. They range from routine calculations to large-scale projects. The more difficult problems, both theoretical and applied, are typically presented in manageable steps. The hundreds of meticulously detailed modeling problems were deliberately designed along pedagogical principles found especially effective in the MAA study Characteristics of Successful Calculus Programs, namely, that asking students to work problems that require them to grapple with concepts (or even proofs) and do modeling activities is key to successful student experiences and retention in STEM programs. The exposition itself is exceptionally readable, rigorous yet conversational. Students will find it inviting and approachable. The text supports many different styles of pedagogy from traditional lecture to a flipped classroom model. The availability of a computer algebra system is not assumed, but there are many opportunities to incorporate the use of one. November 2019 Front Cover JMM Workshop for Math Administrators CIP Call for Proposals A Word From...Abbe Herzig AMS Short Course Table of Contents AMS Social at JMM 2020 Masthead Member Benefits at JMM MRC Letters to the Editor Statistical Numerical Approxiamtion by Houman Owhadi, Clint Scovel, and Florian Schafer From Operator Algebras to Complexity Theory and Back by Thomas Vidick Maps with Least Distortion Between Surfacse: From Geography to Brain Warping by Athanase Papadopoulos Join SIAM From Decoupling and Self-Normalization to Machine Learning by Victor H. de la Pena Early Career IPAM Sir Michael Atiyah, a Knight Mathematician--A Tribute to Michael Atiyah, an Inspiration and a Friend by Alain Connes and Joseph Kouneiher Ronald G. Douglas: A Mastering in the ARt of Transcending Problems by Guoliang Yu, Roger Howe, and Shana Hutchens Modeling Competitions and Gender Equity by Solomon Garfunkel Princeton University Press Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, a Review by John C. Baes London Mathematical Society Bookshelf AMS Bookshelf A Tale of Two Integrals by Jonathan Novak Face Numbers: Centrally Symmetric Spheres versus Centrally Symmetric Polytopes by Isabella Novik Operator Integrals in Theory and Applications by Anna Skripka Mathematics of Planet Earth by Hans G. Kaper and Christiane Rousseau AMS Congressional Fellowship Biennial Overview of AMS Honors Subscribe to Feature Column Backlog of Mathematics Research Journals Support MathSciNet for Developing Countries AMS Reciprocity Agreements AMS Department Chairs Workshop Fall 2017 Departmental Profile Report by Amanda L. Golbeck, Thomas H. Barr, and Colleen A. Rose Mathematics People Introducting an AMS Member Community Updates Mathematics Opportunities BIG Career Center Classified Advertising MathSciNet New Books Offered by the AMS JMM Child Care Grants Meetings & Conferences of the AMS November Table of Contents Meetings & Conferences of the AMS 2020 JMM Meeting Registration/Housing 2020 AMS Employment Center New Releases from the AMS In this text, the reader will learn that all the basic functions that arise in calculus such as powers and fractional powers, exponentials and logs, trigonometric functions and their inverses, as well as many new functions that the reader will meet are naturally defined for complex arguments. Furthermore, this expanded setting leads to a much richer understanding of such functions than one could glean by merely considering them in the real domain. For example, understanding the exponential function in the complex domain via its differential equation provides a clean path to Euler's formula and hence to a self-contained treatment of the trigonometric functions. Complex analysis, developed in partnership with Fourier analysis, differential equations, and geometrical techniques, leads to the development of a cornucopia of functions of use in number theory, wave motion, conformal mapping, and other mathematical phenomena, which the reader can learn about from material presented here. This book could serve for either a one-semester course or a two-semester course in complex analysis for beginning graduate students or for well-prepared undergraduates whose background includes multivariable calculus, linear algebra, and advanced calculus. What can you do with a degree in math? This book addresses this question with 125 career profiles written by people with degrees and backgrounds in mathematics. With job titles ranging from sports analyst to science writer to inventory specialist to CEO, the volume provides ample evidence that one really can do nearly anything with a degree in mathematics. These professionals share how their mathematical education shaped their career choices and how mathematics, or the skills acquired in a mathematics education, is used in their daily work. The degrees earned by the authors profiled here are a good mix of bachelors, masters, and PhDs. With 114 completely new profiles since the third edition, the careers featured within accurately reflect current trends in the job market. College mathematics faculty, high school teachers, and career counselors will all find this a useful resource. Career centers, mathematics departments, and student lounges should have a copy available for student browsing. In addition to the career profiles, the volume contains essays from career counseling professionals on the topics of job-searching, interviewing, and applying to graduate school. This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigué and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as $\mathrm{JB}^•$-triples and $\mathrm{JBW}^•$-triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis. What can you do with a degree in maths? This book addresses this question with 125 career profiles written by people with degrees and backgrounds in mathematics. With job titles ranging from sports analyst to science writer to inventory specialist to CEO, the volume provides ample evidence that you can do nearly anything with a maths degree. Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Explains that all the basic functions that arise in calculus - such as powers and fractional powers, exponentials and logs, trigonometric functions and their inverses, as well as many new functions that the reader will meet - are naturally defined for complex arguments. This leads to a richer understanding of such functions. Presents a systematic account of the developments in the theory of symmetric manifolds achieved over the past 50 years. The book contains detailed and friendly, but rigorous, proofs of the key results in the theory. "The book PDF contains a mock title page, mock copyright page, and the required materials marked as draft"-- Provided by publisher