Mathematics and Plausible Reasoning [Two Volumes in One]
Mathematics and Plausible Reasoning [Two Volumes in One]

Author: George Polya

Publisher:

Published: 2014-01

Total Pages: 498

ISBN-13: 9781614275572

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2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.

Patterns of Plausible Inference
Patterns of Plausible Inference

Author: George Pólya

Publisher:

Published: 1954

Total Pages: 200

ISBN-13: 9780691080062

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A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics.

Probabilistic Reasoning in Intelligent Systems
Probabilistic Reasoning in Intelligent Systems

Author: Judea Pearl

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 573

ISBN-13: 0080514898

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Probabilistic Reasoning in Intelligent Systems is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertainty--and offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognition--in short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Mathematics and Plausible Reasoning: Patterns of plausible inference
Mathematics and Plausible Reasoning: Patterns of plausible inference

Author: G. Polya

Publisher: Princeton University Press

Published: 1990-08-23

Total Pages: 242

ISBN-13: 9780691025100

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"Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines."--Book cover.

Data and Evidence in Linguistics
Data and Evidence in Linguistics

Author: András Kertész

Publisher: Cambridge University Press

Published: 2012-02-09

Total Pages:

ISBN-13: 1107378427

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The question of what types of data and evidence can be used is one of the most important topics in linguistics. This book is the first to comprehensively present the methodological problems associated with linguistic data and evidence. Its originality is twofold. First, the authors' approach accounts for a series of unexplained characteristics of linguistic theorising: the uncertainty and diversity of data, the role of evidence in the evaluation of hypotheses, the problem solving strategies as well as the emergence and resolution of inconsistencies. Second, the findings are obtained by the application of a new model of plausible argumentation which is also of relevance from a general argumentation theoretical point of view. All concepts and theses are systematically introduced and illustrated by a number of examples from different linguistic theories, and a detailed case-study section shows how the proposed model can be applied to specific linguistic problems.

Street-Fighting Mathematics
Street-Fighting Mathematics

Author: Sanjoy Mahajan

Publisher: MIT Press

Published: 2010-03-05

Total Pages: 152

ISBN-13: 0262265591

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An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Poisson Structures and Their Normal Forms
Poisson Structures and Their Normal Forms

Author: Jean-Paul Dufour

Publisher: Springer Science & Business Media

Published: 2006-01-17

Total Pages: 332

ISBN-13: 3764373350

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The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.

Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving
Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving

Author: George Pólya

Publisher:

Published: 2009

Total Pages: 236

ISBN-13: 9784871878319

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George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Polya Gyorg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It." However, "How to Solve It" is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife ). Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.

Patterns, Predictions, and Actions: Foundations of Machine Learning
Patterns, Predictions, and Actions: Foundations of Machine Learning

Author: Moritz Hardt

Publisher: Princeton University Press

Published: 2022-08-23

Total Pages: 321

ISBN-13: 0691233721

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An authoritative, up-to-date graduate textbook on machine learning that highlights its historical context and societal impacts Patterns, Predictions, and Actions introduces graduate students to the essentials of machine learning while offering invaluable perspective on its history and social implications. Beginning with the foundations of decision making, Moritz Hardt and Benjamin Recht explain how representation, optimization, and generalization are the constituents of supervised learning. They go on to provide self-contained discussions of causality, the practice of causal inference, sequential decision making, and reinforcement learning, equipping readers with the concepts and tools they need to assess the consequences that may arise from acting on statistical decisions. Provides a modern introduction to machine learning, showing how data patterns support predictions and consequential actions Pays special attention to societal impacts and fairness in decision making Traces the development of machine learning from its origins to today Features a novel chapter on machine learning benchmarks and datasets Invites readers from all backgrounds, requiring some experience with probability, calculus, and linear algebra An essential textbook for students and a guide for researchers