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Author: Steven H. Weintraub Publisher: Courier Dover Publications ISBN: 0486821234 Category : Mathematics Languages : en Pages : 128
Book Description
Mathematical induction — along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle — constitute essential proof techniques. Every mathematician is familiar with mathematical induction, and every student of mathematics requires a grasp of its concepts. This volume provides an introduction and a thorough exposure to these proof techniques. Geared toward students of mathematics at all levels, the text is particularly suitable for courses in mathematical induction, theorem-proving, and problem-solving. The treatment begins with both intuitive and formal explanations of mathematical induction and its equivalents. The next chapter presents many problems consisting of results to be proved by induction, with solutions omitted to enable instructors to assign them to students. Problems vary in difficulty; the majority of them require little background, and the most advanced involve calculus or linear algebra. The final chapter features proofs too complicated for students to find on their own, some of which are famous theorems by well-known mathematicians. For these beautiful and important theorems, the author provides expositions and proofs. The text concludes with a helpful Appendix providing the logical equivalence of the various forms of induction.
Author: Steven H. Weintraub Publisher: Courier Dover Publications ISBN: 0486821234 Category : Mathematics Languages : en Pages : 128
Book Description
Mathematical induction — along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle — constitute essential proof techniques. Every mathematician is familiar with mathematical induction, and every student of mathematics requires a grasp of its concepts. This volume provides an introduction and a thorough exposure to these proof techniques. Geared toward students of mathematics at all levels, the text is particularly suitable for courses in mathematical induction, theorem-proving, and problem-solving. The treatment begins with both intuitive and formal explanations of mathematical induction and its equivalents. The next chapter presents many problems consisting of results to be proved by induction, with solutions omitted to enable instructors to assign them to students. Problems vary in difficulty; the majority of them require little background, and the most advanced involve calculus or linear algebra. The final chapter features proofs too complicated for students to find on their own, some of which are famous theorems by well-known mathematicians. For these beautiful and important theorems, the author provides expositions and proofs. The text concludes with a helpful Appendix providing the logical equivalence of the various forms of induction.
Author: Annette L. Breaux Publisher: ISBN: 9780962936043 Category : Education Languages : en Pages : 0
Book Description
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.
Author: Titu Andreescu Publisher: ISBN: 9780996874595 Category : Induction (Mathematics) Languages : en Pages : 432
Book Description
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.
Author: Elijah Millgram Publisher: Harvard University Press ISBN: 9780674695979 Category : Philosophy Languages : en Pages : 204
Book Description
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.
Author: Steven H. Weintraub Publisher: Courier Dover Publications ISBN: 0486811999 Category : Mathematics Languages : en Pages : 129
Book Description
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.
Author: Sara Wickham Publisher: ISBN: 9781999806439 Category : Languages : en Pages : 168
Book Description
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.
Author: Valery Rudnev Publisher: CRC Press ISBN: 1351643762 Category : Science Languages : en Pages : 816
Book Description
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.
Author: Makoto Sei Watanabe Publisher: Springer Science & Business Media ISBN: 9783764366414 Category : Architecture Languages : en Pages : 100
Book Description
City planning is a concept which usually covers the wide range of events, processes and developments taking place in our cities, but individual plans and designs cannot do justice to the complex realities of the city. In "Induction Cities" the author aims to take the reader beyond our traditional understanding of city design to redefine our perception of design in this context. With the assistance of computers, a dynamic mechanism will be created which generates a result corresponding to the specific conditions and requirements stipulated. By this form of "meta-design" a greater degree of freedom is obtained than the conventional design methods provide. In this publication, this new theory and process is analysed, looking at the first computer-generated architecture in the world, the underground station "Iidabashi"in Tokyo. Makoto Sei Watanabe studied architecture and worked in the office of Arata Isozaki in Tokyo. In 1984 he founded his own architectural office which has realised numerous projects.
Author: L.I. Golovina Publisher: Courier Dover Publications ISBN: 0486838560 Category : Mathematics Languages : en Pages : 177
Book Description
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.
Author: Hantao Zhang Publisher: Springer Science & Business Media ISBN: 9400916752 Category : Computers Languages : en Pages : 223
Book Description
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.
Author: Steven H. Weintraub
Author: Steven H. Weintraub
Author: Annette L. Breaux
Author: Titu Andreescu
Author: Elijah Millgram
Author: Steven H. Weintraub
Author: Sara Wickham
Author: Valery Rudnev
Author: Makoto Sei Watanabe
Author: L.I. Golovina
Author: Hantao Zhang