MAA Press: An Imprint of the American Mathematical Society
AMS/MAA Textbooks Volume: 52
1994; 192 pp; Softcover
Print ISBN: 978-1-4704-5182-0
Product Code: TEXT/52
The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained?no background in complex numbers is assumed?and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.
Provides a self-contained introduction to complex numbers and college geometry written in an informal style with an emphasis on the motivation behind the ideas ... The author engages the reader with a casual style, motivational questions, interesting problems and historical notes.
-- Mathematical Reviews
Contemporary Mathematics Volume: 731
2019; Softcover
MSC: Primary 11; 26; 28; 30; 31; 35; 37; 52; 60;
Print ISBN: 978-1-4704-3581-3
This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21?29, 2016, at California Polytechnic State University, San Luis Obispo, California.
The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).
Graduate students and research mathematicians interested in fractal geometry, dynamical systems, and related areas.
Contemporary Mathematics Volume: 732
2019; 286 pp; Softcover
MSC: Primary 11; 14; 22; 32;
Print ISBN: 978-1-4704-3525-7
This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11?22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop.
These articles address various aspects of the theory of automorphic forms and its relations with the theory of L
-functions, the theory of elliptic curves, and representation theory.
In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well.
This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to gbuild bridgesh to mathematical questions in other fields.
Graduate students and research mathematicians interested in number theory, representation theory, and arithmetic geometry.
MSRI Mathematical Circles Library Volume: 23
2019; 262 pp; Softcover
MSC: Primary 00;
Print ISBN: 978-1-4704-5115-8
This book is a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general math enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking. The essays are self-contained and rely only on tools from high-school mathematics (with only a few pieces that ever-so-briefly brush up against high-school calculus).
The gist of each essay is easy to pick up with a cursory glance?the reader should feel free to simply skim through some essays and dive deep into others. This book is an invitation to play with mathematics and to explore its wonders. Much joy awaits!
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Math circles students and organizers, participants and organizers of math summer camps for high-school students, and anyone interested in learning or teaching mathematics at the high-school level.
Graduate Studies in Mathematics Volume: 200
2019; Hardcover
MSC: Primary 58; 35; 34; 81;
Print ISBN: 978-1-4704-4366-5
Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either 0
or 14
. An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves.
This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Graduate students and researchers interested in scattering resonances.