This stunning YA debut is a timely and heartfelt speculative narrative about healing, faith, and freedom. Seventeen-year-old Marisol has always dreamed of being American, learning what Americans and the US are like from television and Mrs. Rosen, an elderly expat who had employed Marisol's mother as a maid. When she pictured an American life for herself, she dreamed of a life like Aimee and Amber's, the title characters of her favorite American TV show. She never pictured fleeing her home in El Salvador under threat of death and stealing across the US border as "an illegal", but after her brother is murdered and her younger sister, Gabi's, life is also placed in equal jeopardy, she has no choice, especially because she knows everything is her fault. If she had never fallen for the charms of a beautiful girl named Liliana, Pablo might still be alive, her mother wouldn't be in hiding and she and Gabi wouldn't have been caught crossing the border. But they have been caught and their asylum request will most certainly be denied. With truly no options remaining, Marisol jumps at an unusual opportunity to stay in the United States. She's asked to become a grief keeper, taking the grief of another into her own body to save a life. It's a risky, experimental study, but if it means Marisol can keep her sister safe, she will risk anything. She just never imagined one of the risks would be falling in love, a love that may even be powerful enough to finally help her face her own crushing grief. The Grief Keeper is a tender tale that explores the heartbreak and consequences of when both love and human beings are branded illegal.

This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

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Updated to include a new chapter about the influence of social media and the Internet—the 20th anniversary edition of Bowling Alone remains a seminal work of social analysis, and its examination of what happened to our sense of community remains more relevant than ever in today’s fractured America. Twenty years, ago, Robert D. Putnam made a seemingly simple observation: once we bowled in leagues, usually after work; but no longer. This seemingly small phenomenon symbolized a significant social change that became the basis of the acclaimed bestseller, Bowling Alone, which The Washington Post called “a very important book” and Putnam, “the de Tocqueville of our generation.” Bowling Alone surveyed in detail Americans’ changing behavior over the decades, showing how we had become increasingly disconnected from family, friends, neighbors, and social structures, whether it’s with the PTA, church, clubs, political parties, or bowling leagues. In the revised edition of his classic work, Putnam shows how our shrinking access to the “social capital” that is the reward of communal activity and community sharing still poses a serious threat to our civic and personal health, and how these consequences have a new resonance for our divided country today. He includes critical new material on the pervasive influence of social media and the internet, which has introduced previously unthinkable opportunities for social connection—as well as unprecedented levels of alienation and isolation. At the time of its publication, Putnam’s then-groundbreaking work showed how social bonds are the most powerful predictor of life satisfaction, and how the loss of social capital is felt in critical ways, acting as a strong predictor of crime rates and other measures of neighborhood quality of life, and affecting our health in other ways. While the ways in which we connect, or become disconnected, have changed over the decades, his central argument remains as powerful and urgent as ever: mending our frayed social capital is key to preserving the very fabric of our society.