Contemporary Mathematics,Volume: 736
2019; 265 pp; Softcover
MSC: Primary 37; 34; 35; 55;
Print ISBN: 978-1-4704-4831-8
This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13?15, 2018, at Agnes Scott College, Decatur, Georgia.
The papers cover various topics in dynamics and randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages.
The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.
Graduate students and research mathematicians interested in dynamical systems and random processes.
Classroom Resource Materials, Volume: 64
2019; 282 pp; Softcover
MSC: Primary 00; 01; 97;
Print ISBN: 978-1-4704-5085-4
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.
Undergraduate and graduate students interested in career possibilities in mathematics.
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.
Undergraduate students interested in differential equations.
IAS/Park City Mathematics Series, Volume: 26
2019; 498 pp; Hardcover
MSC: Primary 15; 60; 82; 35; 46;
Print ISBN: 978-1-4704-5280-3
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. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory.
This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.
Graduate students and researchers interested in random matrix theory and its many applications.
Graduate Studies in Mathematics, Volume: 202
2019; 480 pp; Hardcover
MSC: Primary 30;
Print ISBN: 978-1-4704-5286-5
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.
Graduate students interested in complex analysis.
Mathematical Surveys and Monographs, Volume: 243
2019; Hardcover
MSC: Primary 46; 58; 53; 32; 17; 57; 22;
Print ISBN: 978-1-4704-5083-0
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 (Vigue 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 JB?JB?-triples and JBW?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.
Graduate students interested in complex analysis and the theory of Banach spaces.