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Every mathematician and student of mathematics needs a familiarity with mathematical induction. This volume provides advanced undergraduates and graduate students with an introduction and a thorough exposure to these proof techniques. 2017 edition.
Discusses the importance of training, supporting, and retaining new teachers, presents a step-by-step process for structuring an induction program, and features a list of replicable induction programs.
This book serves as a very good resource and teaching material for anyone who wants to discover the beauty of Induction and its applications, from novice mathematicians to Olympiad-driven students and professors teaching undergraduate courses. The authors explore 10 different areas of mathematics, including topics that are not usually discussed in an Olympiad-oriented book on the subject. Induction is one of the most important techniques used in competitions and its applications permeate almost every area of mathematics.
Practical reasoning is not just a matter of determining how to get what you want, but of working out what to want in the first place. In Practical Induction Elijah Millgram argues that experience plays a central role in this process of deciding what is or is not important or worth pursuing. He takes aim at instrumentalism, a view predominant among philosophers today, which holds that the goals of practical reasoning are basic in the sense that they are given by desires that are not themselves the product of practical reasoning. The view Millgram defends is "practical induction," a method of reasoning from experience similar to theoretical induction. What are the practical observations that teach us what to want? Millgram suggests they are pleasant and unpleasant experiences on the basis of which we form practical judgments about particular cases. By generalizing from these judgments--that is, by practical induction--we rationally arrive at our views about what matters. Learning new priorities from experience is necessary if we are to function in a world of ever-changing circumstances. And we need to be able to learn both from our own and from others' experience. It is this, Millgram contends, that explains the cognitive importance of both our capacity for pain and pleasure and our capacity for love. Pleasure's role in cognition is not that of a goal but that of a guide. Love's role in cognition derives from its relation to our trusting the testimony of others about what does and does not matter and about what merits our desire. Itself a pleasure to read, this book is full of inventive arguments and conveys Millgram's bold thesis with elegance and force. It will alter the direction of current debates on practical reasoning.
The second edition of the Handbook of Induction Heating reflects the number of substantial advances that have taken place over the last decade in theory, computer modeling, semi-conductor power supplies, and process technology of induction heating and induction heat treating. This edition continues to be a synthesis of information, discoveries, and technical insights that have been accumulated at Inductoheat Inc. With an emphasis on design and implementation, the newest edition of this seminal guide provides numerous case studies, ready-to-use tables, diagrams, rules-of-thumb, simplified formulas, and graphs for working professionals and students.
When is it better to induce labour than to let a woman's body or baby decide the best time for birth? What are the pros and cons of waiting and of being induced? What about after the due date? When the baby is thought to be bigger than average? When the woman is older? If she had IVF? Or when her waters have broken earlier than usual? Induction of labour is an increasingly common recommendation and more and more women find themselves having to decide whether to let their body and baby go into labour spontaneously or agree to medical intervention. This book explains the process of induction of labour and shares information from research studies, debates and women's, midwives' and doctors' experiences to help women and families become more informed and make the decision that is right for them.
Practical Induction Heat Treating, Second Edition is a quick reference source for induction heaters. This book ties-in the metallurgy, theory, and practice of induction heat treating from a hands-on explanation of what floor people need to know. This book includes practical tables and process analysis of induction heating.
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Induction in Geometry discusses the application of the method of mathematical induction to the solution of geometric problems, some of which are quite intricate. The book contains 37 examples with detailed solutions and 40 for which only brief hints are provided. Most of the material requires only a background in high school algebra and plane geometry; chapter six assumes some knowledge of solid geometry, and the text occasionally employs formulas from trigonometry. Chapters are self-contained, so readers may omit those for which they are unprepared. To provide additional background, this volume incorporates the concise text, The Method of Mathematical Induction. This approach introduces this technique of mathematical proof via many examples from algebra, geometry, and trigonometry, and in greater detail than standard texts. A background in high school algebra will largely suffice; later problems require some knowledge of trigonometry. The combination of solved problems within the text and those left for readers to work on, with solutions provided at the end, makes this volume especially practical for independent study.
It has been shown how the common structure that defines a family of proofs can be expressed as a proof plan [5]. This common structure can be exploited in the search for particular proofs. A proof plan has two complementary components: a proof method and a proof tactic. By prescribing the structure of a proof at the level of primitive inferences, a tactic [11] provides the guarantee part of the proof. In contrast, a method provides a more declarative explanation of the proof by means of preconditions. Each method has associated effects. The execution of the effects simulates the application of the corresponding tactic. Theorem proving in the proof planning framework is a two-phase process: 1. Tactic construction is by a process of method composition: Given a goal, an applicable method is selected. The applicability of a method is determined by evaluating the method's preconditions. The method effects are then used to calculate subgoals. This process is applied recursively until no more subgoals remain. Because of the one-to-one correspondence between methods and tactics, the output from this process is a composite tactic tailored to the given goal. 2. Tactic execution generates a proof in the object-level logic. Note that no search is involved in the execution of the tactic. All the search is taken care of during the planning process. The real benefits of having separate planning and execution phases become appar ent when a proof attempt fails.