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Street-Fighting Mathematics

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ISBN: 9780262265591 9780262514293 Year: Pages: 152 Language: English
Publisher: The MIT Press
Subject: Science (General)
Added to DOAB on : 2019-01-17 11:41:37
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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.

Dynamics of decision making: from evidence to preference and belief

Authors: --- --- ---
Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889192700 Year: Pages: 259 DOI: 10.3389/978-2-88919-270-0 Language: English
Publisher: Frontiers Media SA
Subject: Science (General) --- Neurology --- Psychology
Added to DOAB on : 2015-12-03 13:02:24
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At the core of the many debates throughout cognitive science concerning how decisions are made are the processes governing the time course of preference formation and decision. From perceptual choices, such as whether the signal on a radar screen indicates an enemy missile or a spot on a CT scan indicates a tumor, to cognitive value-based decisions, such as selecting an agreeable flatmate or deciding the guilt of a defendant, significant and everyday decisions are dynamic over time. Phenomena such as decoy effects, preference reversals and order effects are still puzzling researchers. For example, in a legal context, jurors receive discrete pieces of evidence in sequence, and must integrate these pieces together to reach a singular verdict. From a standard Bayesian viewpoint the order in which people receive the evidence should not influence their final decision, and yet order effects seem a robust empirical phenomena in many decision contexts. Current research on how decisions unfold, especially in a dynamic environment, is advancing our theoretical understanding of decision making. This Research Topic aims to review and further explore the time course of a decision - from how prior beliefs are formed to how those beliefs are used and updated over time, towards the formation of preferences and choices and post-decision processes and effects. Research literatures encompassing varied approaches to the time-scale of decisions will be brought into scope: a) Speeded decisions (and post-decision processes) that require the accumulation of noisy and possibly non-stationary perceptual evidence (e.g., randomly moving dots stimuli), within a few seconds, with or without temporal uncertainty. b) Temporally-extended, value-based decisions that integrate feedback values (e.g., gambling machines) and internally-generated decision criteria (e.g., when one switches attention, selectively, between the various aspects of several choice alternatives). c) Temporally extended, belief-based decisions that build on the integration of evidence, which interacts with the decision maker's belief system, towards the updating of the beliefs and the formation of judgments and preferences (as in the legal context). Research that emphasizes theoretical concerns (including optimality analysis) and mechanisms underlying the decision process, both neural and cognitive, is presented, as well as research that combines experimental and computational levels of analysis.

25 Military Strategies for Samhandling in Unforeseen Situations (Book chapter)

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ISBN: 9788202535025 Year: Pages: 14 DOI: 10.23865/noasp.36.ch25 Language: English
Publisher: Cappelen Damm Akademisk/NOASP (Nordic Open Access Scholarly Publishing)
Subject: Sociology --- Social Sciences
Added to DOAB on : 2019-01-15 13:34:08
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"The purpose of this chapter is twofold. Firstly, a rather paradoxical situation
will be discussed. Even though most military practitioners seem to agree
on the characteristics of war, two almost diametrically-opposed norms for how to
samhandle have arisen: a centralized one and a decentralized one. We argue that the
decentralized approach, called Auftragstaktik, is the most effective. In the second
part of the chapter we discuss the pedagogical challenge of educating personnel to
thrive in a decentralized organization, which must operate effectively in unforeseen
and threatening environments. Based on the teachings of Moltke the Elder (1800–
1891) and the much more recent writings of Torgersen, Steiro and Saeverot (2015),
we argue that a crucial step in educating for the unforeseen is to give the students
the opportunity to solve new problems by themselves, gaining experience that is, as
far as possible, self-generated and thereby becoming more aware and confident in
dealing with new situations."

Complex Problem Solving Beyond the Psychometric Approach

Authors: --- --- ---
Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889455737 Year: Pages: 178 DOI: 10.3389/978-2-88945-573-7 Language: English
Publisher: Frontiers Media SA
Subject: Psychology --- Science (General)
Added to DOAB on : 2019-01-23 14:53:43
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Complex problem solving (CPS) and related topics such as dynamic decision-making (DDM) and complex dynamic control (CDC) represent multifaceted psychological phenomena. In abroad sense, CPS encompasses learning, decision-making, and acting in complex and dynamic situations. Moreover, solutions to problems that people face in such situations are often generated in teams or groups. This adds another layer of complexity to the situation itself because of the emerging issues that arise from the social dynamics of group interactions. This framing of CPS means that it is not a single construct that can be measured by using a particular type of CPS task (e.g. minimal complex system tests), which is a view taken by the psychometric community. The proposed approach taken here is that because CPS is multifaceted, multiple approaches need to be taken to fully capture and understand what it is and how the different cognitive processes associated with it complement each other.Thus, this Research Topic is aimed at showcasing the latest work in the fields of CPS, as well as DDM and CDC that takes a holist approach to investigating and theorizing about these abilities. The collection of articles encompasses conceptual approaches as well as experimental and correlational studies involving established or new tools to examine CPS, DDM and CDC. This work contributes to answering questions about what strategies and what general knowledge can be transferred from one type of complex and dynamic situation to another, what learning conditions result in transferable knowledge and skills, and how these features can be trained.

Principles and Practice of Case-based Clinical Reasoning Education: A Method for Preclinical Students

Authors: --- ---
Book Series: Innovation and Change in Professional Education ISSN: 1572-1957 / 2542-9957 ISBN: 9783319648279 9783319648286 Year: Pages: 207 DOI: https://doi.org/10.1007/978-3-319-64828-6 Language: English
Publisher: Springer
Subject: Medicine (General)
Added to DOAB on : 2017-11-24 17:20:23
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This volume describes and explains the educational method of Case-Based Clinical Reasoning (CBCR) used successfully in medical schools to prepare students to think like doctors before they enter the clinical arena and become engaged in patient care. Although this approach poses the paradoxical problem of a lack of clinical experience that is so essential for building proficiency in clinical reasoning, CBCR is built on the premise that solving clinical problems involves the ability to reason about disease processes. This requires knowledge of anatomy and the working and pathology of organ systems, as well as the ability to regard patient problems as patterns and compare them with instances of illness scripts of patients the clinician has seen in the past and stored in memory. CBCR stimulates the development of early, rudimentary illness scripts through elaboration and systematic discussion of the courses of action from the initial presentation of the patient to the final steps of clinical management.The book combines general backgrounds of clinical reasoning education and assessment with a detailed elaboration of the CBCR method for application in any medical curriculum, either as a mandatory or as an elective course. It consists of three parts: a general introduction to clinical reasoning education, application of the CBCR method, and cases that can used by educators to try out this method.

Understanding Society and Natural Resources: Forging New Strands of Integration Across the Social Sciences

Authors: --- --- ---
ISBN: 9789401789592 Year: Pages: 288 DOI: 10.1007/978-94-017-8959-2 Language: English
Publisher: Springer Grant: FP7 Ideas: European Research Council - 311819
Subject: Sociology
Added to DOAB on : 2016-12-29 13:22:42
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In this edited volume leading scholars from different disciplinary backgrounds wrestle with social science integration opportunities and challenges. This book explores the growing concern of how best to achieve effective integration of the social science disciplines as a means for furthering natural resource social science and environmental problem solving. The chapters provide an overview of the history, vision, advances, examples and methods that could lead to integration. The quest for integration among the social sciences is not new. Some argue that the social sciences have lagged in their advancements and contributions to society due to their inability to address integration related issues. Integration merits debate for a number of reasons. First, natural resource issues are complex and are affected by multiple proximate driving social factors. Single disciplinary studies focused at one level are unlikely to provide explanations that represent this complexity and are limited in their ability to inform policy recommendations. Complex problems are best explored across disciplines that examine social-ecological phenomenon from different scales. Second, multi-disciplinary initiatives such as those with physical and biological scientists are necessary to understand the scope of the social sciences. Too frequently there is a belief that one social scientist on a multi-disciplinary team provides adequate social science representation. Third, more complete models of human behavior will be achieved through a synthesis of diverse social science perspectives.

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