The Heart Of Calculus
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The Heart of Calculus
Author: Philip M. Anselone
language: en
Publisher: American Mathematical Soc.
Release Date: 2015-12-31
This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs. The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives. The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth. A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.
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The Heart of Altruism
Author: Kristen Renwick Monroe
language: en
Publisher: Princeton University Press
Release Date: 1998-07-01
Is all human behavior based on self-interest? Many social and biological theories would argue so, but such a perspective does not explain the many truly heroic acts committed by people willing to risk their lives to help others. In The Heart of Altruism, Kristen Renwick Monroe boldly lays the groundwork for a social theory receptive to altruism by examining the experiences described by altruists themselves: from Otto, a German businessman who rescued over a hundred Jews in Nazi Germany, to Lucille, a newspaper poetry editor, who, armed with her cane, saved a young girl who was being raped. Monroe's honest and moving interviews with these little-known heroes enable her to explore the causes of altruism and the differences between altruists and other people. By delineating an overarching perspective of humanity shared by altruists, Monroe demonstrates how social theories may begin to account for altruism and debunks the notions of scientific inevitability that stem from an overemphasis on self-interest. As Monroe has discovered, the financial and religious backgrounds of altruists vary greatly--as do their views on issues such as welfare, civil rights, and morality. Altruists do, however, share a certain way of looking at the world: where the rest of us see a stranger, altruists see a fellow human being. It is this perspective that many social theories overlook. Monroe restores altruism to a general theory of ethical political behavior. She argues that to understand what makes one person act out of concern for others and not the self, we need to ask how that individual's perspective sets the range of options he or she finds available.