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This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH
A supplemental textbook for middle and high school students, Hoosiers and the American Story provides intimate views of individuals and places in Indiana set within themes from American history. During the frontier days when Americans battled with and exiled native peoples from the East, Indiana was on the leading edge of America’s westward expansion. As waves of immigrants swept across the Appalachians and eastern waterways, Indiana became established as both a crossroads and as a vital part of Middle America. Indiana’s stories illuminate the history of American agriculture, wars, industrialization, ethnic conflicts, technological improvements, political battles, transportation networks, economic shifts, social welfare initiatives, and more. In so doing, they elucidate large national issues so that students can relate personally to the ideas and events that comprise American history. At the same time, the stories shed light on what it means to be a Hoosier, today and in the past.
Winner of the Pulitzer Prize and a documentary from Ken Burns on PBS, this New York Times bestseller is “an extraordinary achievement” (The New Yorker)—a magnificent, profoundly humane “biography” of cancer—from its first documented appearances thousands of years ago through the epic battles in the twentieth century to cure, control, and conquer it to a radical new understanding of its essence. Physician, researcher, and award-winning science writer, Siddhartha Mukherjee examines cancer with a cellular biologist’s precision, a historian’s perspective, and a biographer’s passion. The result is an astonishingly lucid and eloquent chronicle of a disease humans have lived with—and perished from—for more than five thousand years. The story of cancer is a story of human ingenuity, resilience, and perseverance, but also of hubris, paternalism, and misperception. Mukherjee recounts centuries of discoveries, setbacks, victories, and deaths, told through the eyes of his predecessors and peers, training their wits against an infinitely resourceful adversary that, just three decades ago, was thought to be easily vanquished in an all-out “war against cancer.” The book reads like a literary thriller with cancer as the protagonist. Riveting, urgent, and surprising, The Emperor of All Maladies provides a fascinating glimpse into the future of cancer treatments. It is an illuminating book that provides hope and clarity to those seeking to demystify cancer.