Forms Of Explanation
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Forms of Explanation
What makes one explanation better than another? How can we tell when an explanation has really answered our question? In a lively and readable discussion, Garfinkel argues that the key to understanding an explanation is to discover what question is really being answered. He then suggests criteria for a good explanation and goes on to examine some classic explanations in social and natural science.
Visual Differential Geometry and Forms
Author: Tristan Needham
language: en
Publisher: Princeton University Press
Release Date: 2021-07-13
An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Principles of Methodology
This book provides a comprehensive, accessible guide to social science methodology. In so doing, it establishes methodology as distinct from both methods and philosophy. Most existing textbooks deal with methods, or sound ways of collecting and analysing data to generate findings. In contrast, this innovative book shows how an understanding of methodology allows us to design research so that findings can be used to answer interesting research questions and to build and test theories. Most important things in social research (e.g., beliefs, institutions, interests, practices and social classes) cannot be observed directly. This book explains how empirical research can nevertheless be designed to make sound inferences about their nature, effects and significance. The authors examine what counts as good description, explanation and interpretation, and how they can be achieved by striking intelligent trade-offs between competing design virtues. Coverage includes: * why methodology matters; * what philosophical arguments show us about inference; * competing virtues of good research design; * purposes of theory, models and frameworks; * forming researchable concepts and typologies; * explaining and interpreting: inferring causation, meaning and significance; and * combining explanation and interpretation. The book is essential reading for new researchers faced with the practical challenge of designing research. Extensive examples and exercises are provided, based on the authors' long experience of teaching methodology to multi-disciplinary groups. Perri 6 is Professor of Social Policy in the Graduate School in the College of Business, Law and Social Sciences at Nottingham Trent University. Chris Bellamy is Emeritus Professor of Public Administration in the Graduate School, Nottingham Trent University.