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Rigor And Structure
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Book Synopsis Rigor and Structure by : John P. Burgess
Download or read book Rigor and Structure written by John P. Burgess and published by . This book was released on 2015 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.
Book Synopsis Reason & Rigor by : Sharon M. Ravitch
Download or read book Reason & Rigor written by Sharon M. Ravitch and published by SAGE Publications. This book was released on 2016-01-04 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for novice as well as more experienced researchers, Reason & Rigor by Sharon M. Ravitch and Matthew Riggan presents conceptual frameworks as a mechanism for aligning literature review, research design, and methodology. The book explores the conceptual framework—defined as both a process and a product—that helps to direct and ground researchers as they work through common research challenges. Focusing on published studies on a range of topics and employing both quantitative and qualitative methods, the updated Second Edition features two new chapters and clearly communicates the processes of developing and defining conceptual frameworks.
Download or read book Structure written by Geoffrey Bourne and published by Elsevier. This book was released on 2013-10-22 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Structure and Function of Muscle, Second Edition: Volume II: Structure, Part 2 deals with various aspects of muscle structure, including physiology and microanatomy. The structure of the motor end plate is discussed, together with muscle regeneration and postmortem changes in muscle. Membranous systems in muscle fibers as well as the ultrastructural and physiological aspects of heart muscle are also considered. This volume is comprised of nine chapters and begins with an overview of how basic studies in uterine function and regulation promoted developments in reproduction, obstetrics, and regulatory biology, with emphasis on the basic mechanism of function and regulation of smooth muscles. The following chapters explore the capacitative, resistive, and syncytial properties of heart muscle; contractile structures in some Protozoa such as ciliates and gregarines; the microanatomy of smooth muscle, cardiac muscle, and voluntary, somatic, or skeletal muscle; postmortem changes in the physical characteristics of muscle; and morphology of spontaneous degeneration and regeneration in skeletal muscle. The morphology, ultrastructure, and cytochemistry of the muscle spindle are also outlined. The final chapter deals with membraneous systems in muscle fibers and includes a discussion on correlation between physiology and morphology of fiber types in vertebrates and invertebrates. This book will be a useful resource for students, researchers, and practitioners of anatomy, physiology, biology, and medicine.
Book Synopsis Introduction · to Mathematical Structures and · Proofs by : Larry Gerstein
Download or read book Introduction · to Mathematical Structures and · Proofs written by Larry Gerstein and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.
Book Synopsis Structure and Interpretation of Classical Mechanics, second edition by : Gerald Jay Sussman
Download or read book Structure and Interpretation of Classical Mechanics, second edition written by Gerald Jay Sussman and published by MIT Press. This book was released on 2015-02-06 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation. We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated. This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.
Book Synopsis Berry Phases in Electronic Structure Theory by : David Vanderbilt
Download or read book Berry Phases in Electronic Structure Theory written by David Vanderbilt and published by Cambridge University Press. This book was released on 2018-11-01 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These 'Berry phases' describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.
Book Synopsis Statistical Mechanics of Lattice Systems by : Sacha Friedli
Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Book Synopsis Leadership Rigor! by : Erica Peitler
Download or read book Leadership Rigor! written by Erica Peitler and published by Circle Takes the Square. This book was released on 2014-07-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transform the Way You Lead! Leadership Rigor offers innovation in leadership through its breakthrough approaches for transforming the way you lead. The simple truth is that "how" you lead is the precursor to "what" you can achieve as a leader, yet it is often underestimated, dismissed, or not given a conscious consideration. In March 2014, Bersin by Deloitte published their latest Global Human Capital Trend Survey stating: Building leadership capability is by far the most urgent need for companies today... and companies see the need for leadership at all levels, in all geographies, and across all functional areas. In addition, this continuous need for new and better leaders has accelerated. Leadership Rigor views your development as a journey with a road map rather than a black-box mystery! It is both a practice and a philosophy designed to accelerate your leadership performance and productivity across the life cycle of your career. Already becoming a movement, Leadership Rigor prepares you to lead yourself, teams, and organizations. The essence of Leadership Rigor is creating "change-ready" leaders who can embrace challenges because they have the tools, models, and language to assess, structure, and facilitate aligned actions. They also have the mindset and emotional skills to lean into the change process despite its uncomfortable nature. By innovating on their preparedness first, these "change-ready" leaders are equipped to realize the growth in themselves and in their teams or organizations. Are you ready to take on your personal journey of Leadership Rigor?
Book Synopsis Problems in Argument Analysis and Evaluation by : Trudy Govier
Download or read book Problems in Argument Analysis and Evaluation written by Trudy Govier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-05 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Problems in Argument Analysis and Evaluation".
Book Synopsis Visual Group Theory by : Nathan Carter
Download or read book Visual Group Theory written by Nathan Carter and published by American Mathematical Soc.. This book was released on 2021-06-08 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Book Synopsis The Structural Basis of Muscular Contraction by : John Squire
Download or read book The Structural Basis of Muscular Contraction written by John Squire and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Muscular contraction provides one of the most fascinating topics for a biophysicist to study. Although muscle comprises a molecular machine whereby chemical energy is converted to mechanical work, its action in producing force is something that is readily observable in everyday life, a feature that does not apply to most other structures of biophysical inter est. In addition, muscle is so beautifully organized at the microscopic level that those important structural probes, electron microscopy (with the associated image analysis methods) and X-ray diffraction, have pro vided a wealth of information about the arrangements of the constituent proteins in a variety of muscle types. But, despite all this, the answer to the question "How does muscle work?" is still uncertain, especially with regard to the molecular events by which force is actually generated, and the question remains one of the major unsolved problems in biology. With this problem in mind, this book has been written to collect together the available evidence on the structures of the muscle fila ments and on their arrangements in different muscle cells, to extract the common structural features of these cells, and thus to attempt to define a possible series of mechanical steps that will describe at molecular resolu tion the process by which force is generated. The book cannot be considered to be an introductory text; in fact, it presents a very detailed account of muscle structure as gleaned mainly from electron microscopy and X-ray diffraction.
Book Synopsis Structure and Being by : Lorenz B. Puntel
Download or read book Structure and Being written by Lorenz B. Puntel and published by Penn State Press. This book was released on 2010-11-01 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Structured Analytic Techniques for Intelligence Analysis by : Randolph H. Pherson
Download or read book Structured Analytic Techniques for Intelligence Analysis written by Randolph H. Pherson and published by CQ Press. This book was released on 2019-12-05 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Excellent publication for the study of intelligence analysis, structured analytical techniques and their application in this increasingly dangerous environment. A must read for anyone entering the intelligence community as an analyst, practitioner, stakeholder and leader." —Charles E. Wilson, University of Detroit Mercy The Third Edition of Structured Analytic Techniques for Intelligence Analysis showcases sixty-six structured analytic techniques—nine new to this edition—that represent the most current best practices in intelligence, law enforcement, homeland security, and business analysis. With more depth, detail, and utility than existing handbooks, each technique is clearly and systematically explained. Logically organized and richly illustrated, and with spiral binding and tabs that separate techniques into categories, this book is an easy-to-use, comprehensive reference.
Download or read book Structure written by and published by . This book was released on 2007 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hodge Theory and Complex Algebraic Geometry I: by : Claire Voisin
Download or read book Hodge Theory and Complex Algebraic Geometry I: written by Claire Voisin and published by Cambridge University Press. This book was released on 2007-12-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.
Book Synopsis Quantum Mechanics by : Gregory L. Naber
Download or read book Quantum Mechanics written by Gregory L. Naber and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-09-20 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions. The author addresses all these topics with utter mathematical rigor. The high number of instructive Appendices and numerous Remark sections supply the necessary background knowledge.
Book Synopsis Homogenization of Reticulated Structures by : Doina Cioranescu
Download or read book Homogenization of Reticulated Structures written by Doina Cioranescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Materials science is an area of growing research as composite materials become widely used in such areas as civil engineering, electrotechnics, and the aerospace industry. This mathematically rigorous treatment of lattice-type structures will appeal to both applied mathematicians, as well as engineers looking for a solid mathematical foundation of the methodology.
