Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina

An engaging portrait of a community of biologists, The Tapir's Morning Bathis a behind-the-scenes account of life at a tropical research station that"conveys the uncertainties, frustrations, and joys of [scientific] fieldwork" (Science). On Panama's Barro Colorado Island, Elizabeth Royte worksalongside the scientists -- counting seeds, sorting insects, collectingmonkey dung, radiotracking fruit bats -- as they struggle to parse theintricate workings of the tropical rain forest. While showing the humanside of the scientists at work, Royte explores the tensions between the slow pace of basic research and the reality of a world that may not have time to wait for answers.

Biodiversity has been a key concept in international conservation since the 1980s, yet historians have paid little attention to its origins. Uncovering its roots in tropical fieldwork and the southward expansion of U.S. empire at the turn of the twentieth century, Megan Raby details how ecologists took advantage of growing U.S. landholdings in the circum-Caribbean by establishing permanent field stations for long-term, basic tropical research. From these outposts of U.S. science, a growing community of American "tropical biologists" developed both the key scientific concepts and the values embedded in the modern discourse of biodiversity. Considering U.S. biological fieldwork from the era of the Spanish-American War through the anticolonial movements of the 1960s and 1970s, this study combines the history of science, environmental history, and the history of U.S.–Caribbean and Latin American relations. In doing so, Raby sheds new light on the origins of contemporary scientific and environmentalist thought and brings to the forefront a surprisingly neglected history of twentieth-century U.S. science and empire.

Whether in a small backyard or a larger farm or forest, trees are vital to the web of life. Protecting and planting trees can restore wildlife habitat, heal degraded land, conserve soil, protect watersheds, diversify farm or garden products, beautify landscapes, and enhance the economic and ecological viability of land use systems. Careful planning and sound information is needed to reach these goals. The Overstory Book distills essential information about working with trees into 134 short, easy-to-read, single-subject chapters. Each chapter shares key concepts and useful information, so readers can get back to planting and protecting more trees, gardens, and forests, more effectively. * Discover time-tested agricultural and conservation techniques from indigenous and traditional peoples * Work with beneficial microorganisms, from mycorrhizal fungi to nitrogen-fixing bacteria and more * Create abundance with fruit trees, timber trees, vine crops, vegetables, mushrooms, and more * Form alliances with animals, from wildlife, birds, and insects to integrated, free-range livestock * Design effective tree-based windbreaks, noise barriers, live fences, and erosion buffers * Understand how to grow or obtain the highest quality seeds, seedlings, and plant materials * Restore fertility, productivity, and biodiversity with trees * Work with multipurpose plants including trees, palms, bamboos, and more * Market products effectively to improve economic returns sustainably * Locate helpful internet sites, organizations, people, and publications * And much more!

The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.

A New York Times Notable Book for 2011 A Boston Globe Best Fiction Book of 2011 The great panoramic social novel that Los Angeles deserves—a twenty-first century, West Coast Bonfire of the Vanities by the only writer qualified to capture the city in all its glory and complexity With The Barbarian Nurseries, Héctor Tobar gives our most misunderstood metropolis its great contemporary novel, taking us beyond the glimmer of Hollywood and deeper than camera-ready crime stories to reveal Southern California life as it really is, across its vast, sunshiny sprawl of classes, languages, dreams, and ambitions. Araceli is the live-in maid in the Torres-Thompson household—one of three Mexican employees in a Spanish-style house with lovely views of the Pacific. She has been responsible strictly for the cooking and cleaning, but the recession has hit, and suddenly Araceli is the last Mexican standing—unless you count Scott Torres, though you'd never suspect he was half Mexican but for his last name and an old family photo with central L.A. in the background. The financial pressure is causing the kind of fights that even Araceli knows the children shouldn't hear, and then one morning, after a particularly dramatic fight, Araceli wakes to an empty house—except for the two Torres-Thompson boys, little aliens she's never had to interact with before. Their parents are unreachable, and the only family member she knows of is Señor Torres, the subject of that old family photo. So she does the only thing she can think of and heads to the bus stop to seek out their grandfather. It will be an adventure, she tells the boys. If she only knew . . . With a precise eye for the telling detail and an unerring way with character, soaring brilliantly and seamlessly among a panorama of viewpoints, Tobar calls on all of his experience—as a novelist, a father, a journalist, a son of Guatemalan immigrants, and a native Angeleno—to deliver a novel as broad, as essential, as alive as the city itself.