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Algebraic topology --- Knot theory. --- Théorie des noeuds --- Théorie des noeuds

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Algebraic topology --- Differential geometry. Global analysis --- Knot theory --- Surfaces --- Théorie des noeuds --- Théorie des noeuds --- Topologie combinatoire --- Topologie algebrique --- Theorie des noeuds --- Homotopie

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This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral­ lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge­ ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory.

Algebraic geometry --- Algebraic topology --- Knot theory --- Théorie des noeuds --- Knot theory. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Théorie des noeuds --- Manifolds (Mathematics). --- Complex manifolds. --- Group theory. --- Mathematical physics. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Group Theory and Generalizations. --- Theoretical, Mathematical and Computational Physics. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Physical mathematics --- Physics --- Variétés topologiques --- Topologie combinatoire --- Theorie des noeuds

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The closed orbits of three-dimensional flows form knots and links. This book develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-smale, Smale, and integrable Hamiltonian flows. The necesssary background theory is sketched; however, some familiarity with low-dimensional topology and differential equations is assumed.

Differential geometry. Global analysis --- Flows (Differentiable dynamical systems) --- Knot theory --- Link theory --- Geometry --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Flows (Differentieerbare systemen) --- Flows (Systèmes dynamiques différentiables) --- Knopentheorie --- Noeuds [Theorie des ] --- Manifolds (Mathematics). --- Complex manifolds. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Link theory. --- Knot theory. --- Knots (Topology) --- Low-dimensional topology --- Piecewise linear topology

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The Analyze, Design, Develop, Implement, and Evaluate (ADDIE) process is used to introduce an approach to instruction design that has a proven record of success. Instructional Design: The ADDIE Approach is intended to serve as an overview of the ADDIE concept. The primary rationale for this book is to respond to the need for an instruction design primer that addresses the current proliferation of complex educational development models, particularly non-traditional approaches to learning, multimedia development and online learning environments. Many entry level instructional designers and students enrolled in related academic programs indicate they are better prepared to accomplish the challenging work of creating effective training and education materials after they have a thorough understanding of the ADDIE principles. However, a survey of instructional development applications indicate that the overwhelming majority of instructional design models are based on ADDIE, often do not present the ADDIE origins as part of their content, and are poorly applied by people unfamiliar with the ADDIE paradigm. The purpose of this book is to focus on fundamental ADDIE principles, written with a minimum of professional jargon. This is not an attempt to debate scholars or other educational professionals on the finer points of instructional design, however, the book's content is based on sound doctrine and supported by valid empirical research. The only bias toward the topic is that generic terms will be used as often as possible in order to make it easy for the reader to apply the concepts in the book to other specific situations.

Instructional systems --- Curriculum planning. --- Design. --- Curriculum development --- Education --- Planning --- Instructional design --- Curricula --- Design --- Knot theory. --- Link theory. --- Manifolds (Mathematics). --- Topology --- 515.1 --- 515.1 Topology --- Knot theory --- Link theory --- Manifolds (Mathematics) --- Théorie des noeuds --- Variétés (Mathématiques) --- Education. --- Business. --- Educational Technology. --- Learning & Instruction. --- Business and Management, general. --- Education, general. --- Trade --- Economics --- Management --- Commerce --- Industrial management --- Children --- Education, Primitive --- Education of children --- Human resource development --- Instruction --- Pedagogy --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Training --- Educational innovations --- Learning systems --- Educational technology --- Educational technology. --- Learning. --- Instruction. --- Management science. --- Quantitative business analysis --- Problem solving --- Operations research --- Statistical decision --- Learning process --- Comprehension --- Instructional technology --- Technology in education --- Technology --- Aids and devices --- Topologie algébrique --- Topologie algébrique --- Variétés topologiques