XYZ Series Volume: 31
2018; 340 pp; Hardcover
MSC: Primary 00; 97;
Print ISBN: 978-0-9993428-1-7
The main areas covered are: (1) telescoping sums and products in algebra and trigonometry; (2) the use of complex numbers and de Moivre's formula; (3) Abel's summation formula; (4) mathematical induction; (5) combinatorial identities; and (6) multiplicative functions and the use of Mobius function.
The theory is presented together with rich examples. At the end, readers are invited to solve problems from a list of 125 questions divided into three levels.
Students who participate in mathematics competitions at the AIME and USAMO levels, their teachers, and anyone with an interest in mathematics.
Anneli Lax New Mathematical Library Volume: 50
2018; 275 pp; Softcover
Print ISBN: 978-1-4704-4783-0
MAA Press: An Imprint of the American Mathematical Society
Winner of a CHOICE Outstanding Academic Title Award for 2017!
What does style mean in mathematics? Style is both how one does something and how one communicates what was done. In this book, the author investigates the worlds of the well-known numbers, the binomial coefficients. The author follows the example of Raymond Queneau's Exercises in Style. Offering the reader 99 stories in various styles. The book celebrates the joy of mathematics and the joy of writing mathematics by exploring the rich properties of this familiar collection of numbers. For any one interested in mathematics, from high school students on up.
By examining and extending binomial coefficients from seemingly every possible direction, the author provides an amazing concoction of ideas, prompting readers to say "Wow, I forgot that connection," or "Wow, I did not know that," or just "Wow!..McCleary's effort is exceptional, as it reaches into the realm of elan, clearly demonstrating the energy and enthusiasm that can pervade mathematical writing and mathematics itself.
-- J. Johnson, CHOICE
2009; 199 pp; Softcover
MSC: Primary 01;
Print ISBN: 978-1-4704-4838-7
Mathematicians is a remarkable collection of ninety-two photographic portraits, featuring a selection of the most impressive mathematicians of our time. Acclaimed photographer Mariana Cook captures the exuberance and passion of these brilliant thinkers. The superb images are accompanied by autobiographical texts written by each mathematician. Together, the photographs and words illuminate a diverse group of men and women dedicated to the absorbing pursuit of mathematics.
The compelling black-and-white portraits introduce readers to mathematicians who are both young and old and from notably diverse backgrounds. They include Fields Medal winners, those at the beginning of major careers, and those who are long-established celebrities in the discipline. Their candid personal essays reveal unique and wide-ranging thoughts, opinions, and humor. The mathematicians discuss how they became interested in mathematics, why they love the subject, how they remain motivated in the face of mathematical challenges, and how their greatest contributions have paved new directions for future generations. Mathematicians in the book include Jean-Pierre Serre, Henri Cartan, Karen Uhlenbeck, David Blackwell, Eli Stein, John Conway, Timothy Gowers, Frances Kirwan, Peter Lax, William Massey, John Milnor, Cathleen Morawetz, John Nash, Pierre Deligne, and James Simons.
This book conveys the beauty and joy of mathematics to readers outside the field as well as those in it. These pictures and their texts are an inspiration, and a perfect gift for those who love mathematics as well as for those who think they can't do it!
Undergraduate and graduate students and researchers interested in biographies of mathematicians.
The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics.
This volume is based on lectures delivered at the 2017 AMS Short Course
gRandom Growth Modelsh, held January 2-3, 2017 in Atlanta, GA.
The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Graduate Students and researchers interested in various models of random growth in percolation theory, cell growth, and particle systems.
Mathematical Surveys and Monographs Volume: 235
2018; 509 pp; Hardcover
MSC: Primary 47; 31; 34; 35; 45; 30;
Print ISBN: 978-1-4704-4800-4
The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics.
An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.
Graduate students and researchers interested in recent development in mathematical and computational advances in photonics and phononics (light and sound propagation on complex structures).
Contemporary Mathematics Volume: 716
2018; 203 pp; Softcover
MSC: Primary 16; 18;
Print ISBN: 978-1-4704-3679-7
This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years.
Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.
Graduate students and research mathematicians interested in functor categories, triangulated categories, module theory, homological algebras, and combinatorial methods in representation theory of quivers.