Explorations in Topology

The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material.

Author: David Gay

Publisher: Elsevier

ISBN: 9780124166400

Category: Mathematics

Page: 332

View: 431

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Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Students begin to solve substantial problems from the start Ideas unfold through the context of a storyline, and students become actively involved The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material
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Explorations in Topology Map Coloring Surfaces and Knots

The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material.

Author: David Gay

Publisher: Elsevier

ISBN: 0128101709

Category: Mathematics

Page: 332

View: 540

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"Explorations in Topology, Second Edition," provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. "Explorations in Topology, Second Edition," enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Students begin to solve substantial problems from the startIdeas unfold through the context of a storyline, and students become actively involvedThe text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material
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Explorations in Analysis Topology and Dynamics An Introduction to Abstract Mathematics

This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs.

Author: Alejandro Uribe A.

Publisher: American Mathematical Soc.

ISBN: 9781470452704

Category: Education

Page: 178

View: 593

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This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.
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Topological in Hegel

Topological Notions of Qualitative quantity and Multiplicity in Hegel's Fourfold of Infinities Borislav G. Dimitrov. author of the books - “Heidegger and the Thinking of Place: Explorations in the Topology of Being”60and “Heidegger's ...

Author: Borislav G. Dimitrov

Publisher: Borislav Dimitrov

ISBN: 9781370071210

Category: Philosophy

Page: 500

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The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.
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Topology Through Inquiry

The definition of a topological space opens the door for the explorations that make up the rest of this book. After defining a mathematical object that is as fundamental as a topological space, the next steps are to see the consequences ...

Author: Michael Starbird

Publisher: American Mathematical Soc.

ISBN: 9781470462611

Category: Education

Page: 313

View: 105

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Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.
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Network Fundamentals CCNA Exploration Companion Guide

CCNA Exploration Companion Guide Mark Dye, Rick McDonald, Antoon Rufi. The topology of a network is the arrangement or relationship of the network devices and the interconnections between them. Network topologies can be viewed at the ...

Author: Mark Dye

Publisher: Cisco Press

ISBN: 0132877430

Category: Computers

Page: 560

View: 870

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Network Fundamentals, CCNA Exploration Companion Guide is the official supplemental textbook for the Network Fundamentals course in the Cisco® Networking Academy® CCNA® Exploration curriculum version 4. The course, the first of four in the new curriculum, is based on a top-down approach to networking. The Companion Guide, written and edited by Networking Academy instructors, is designed as a portable desk reference to use anytime, anywhere. The book’s features reinforce the material in the course to help you focus on important concepts and organize your study time for exams. New and improved features help you study and succeed in this course: Chapter objectives–Review core concepts by answering the focus questions listed at the beginning of each chapter. Key terms–Refer to the updated lists of networking vocabulary introduced and highlighted in context in each chapter. Glossary–Consult the comprehensive glossary with more than 250 terms. Check Your Understanding questions and answer key–Evaluate your readiness with the updated end-of-chapter questions that match the style of questions you see on the online course quizzes. The answer key explains each answer. Challenge questions and activities–Strive to ace more challenging review questions and activities designed to prepare you for the complex styles of questions you might see on the CCNA exam. The answer key explains each answer. How To–Look for this icon to study the steps you need to learn to perform certain tasks. Packet Tracer Activities– Explore networking concepts in activities interspersed throughout some chapters using Packet Tracer v4.1 developed by Cisco. The files for these activities are on the accompanying CD-ROM. Also available for the Network Fundamentals Course Network Fundamentals, CCNA Exploration Labs and Study Guide ISBN-10: 1-58713-203-6 ISBN-13: 978-1-58713-203-2 Companion CD-ROM **See instructions within the ebook on how to get access to the files from the CD-ROM that accompanies this print book.** The CD-ROM provides many useful tools and information to support your education: Packet Tracer Activity exercise files v4.1 VLSM Subnetting Chart Structured Cabling Exploration Supplement Taking Notes: a .txt file of the chapter objectives A Guide to Using a Networker’s Journal booklet IT Career Information Tips on Lifelong Learning in Networking This book is part of the Cisco Networking Academy Series from Cisco Press®. The products in this series support and complement the Cisco Networking Academy online curriculum.
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Mineral Exploration

3.4.6 Topology Building Topology defines the mathematical representation of the spatial relationship between geographical features. It describes the relationships between connecting or adjacent coverage attributes.

Author: Swapan Kumar Haldar

Publisher: Elsevier

ISBN: 9780128140239

Category: Science

Page: 378

View: 741

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Mineral Exploration: Principles and Applications, Second Edition, presents an interdisciplinary approach on the full scope of mineral exploration. Everything from grass root discovery, objective base sequential exploration, mining, beneficiation, extraction, economic evaluation, policies and acts, rules and regulations, sustainability, and environmental impacts is covered. Each topic is presented using theoretical approaches that are followed by specific applications that can be used in the field. This new edition features updated references, changes to rules and regulations, and new sections on oil and gas exploration and classification, air-core drilling, and smelting and refining techniques. This book is a key resource for both academics and professionals, offering both practical and applied knowledge in mineral exploration. Offers important updates to the previous edition, including sections on the cyclical nature of mineral industry, exploration for oil and gas, CHIM-electro-geochemical survey, air-core drilling, classification of oil and gas resources, smelting, and refining technologies Presents global case studies that allow readers to quickly apply exploration concepts to real-world scenarios Includes 385 illustrations and photographs to aid the reader in understanding key procedures and applications
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Design Space Exploration and Resource Management of Multi Many Core Systems

Simulator Team Language Abstraction Level Topologies Heterogeneous Ref Benchmark Support BookSim DARSIM HNOCS Nigram Noxim + - University of Stanford MIT Technion Israel Institute of Technology University of Southampton University of ...

Author: Amit Kumar Singh

Publisher: MDPI

ISBN: 9783036508764

Category: Technology & Engineering

Page: 218

View: 543

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The increasing demand of processing a higher number of applications and related data on computing platforms has resulted in reliance on multi-/many-core chips as they facilitate parallel processing. However, there is a desire for these platforms to be energy-efficient and reliable, and they need to perform secure computations for the interest of the whole community. This book provides perspectives on the aforementioned aspects from leading researchers in terms of state-of-the-art contributions and upcoming trends.
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Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration

Listing 10.11 shows a small Java program that creates the job schedule network, prints out the topology in backward and forward order, performs a topological sort, and displays the results. This small Java driver for the topology ...

Author: Earl Cox

Publisher: Elsevier

ISBN: 9780080470597

Category: Computers

Page: 540

View: 730

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Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration is a handbook for analysts, engineers, and managers involved in developing data mining models in business and government. As you’ll discover, fuzzy systems are extraordinarily valuable tools for representing and manipulating all kinds of data, and genetic algorithms and evolutionary programming techniques drawn from biology provide the most effective means for designing and tuning these systems. You don’t need a background in fuzzy modeling or genetic algorithms to benefit, for this book provides it, along with detailed instruction in methods that you can immediately put to work in your own projects. The author provides many diverse examples and also an extended example in which evolutionary strategies are used to create a complex scheduling system. Written to provide analysts, engineers, and managers with the background and specific instruction needed to develop and implement more effective data mining systems Helps you to understand the trade-offs implicit in various models and model architectures Provides extensive coverage of fuzzy SQL querying, fuzzy clustering, and fuzzy rule induction Lays out a roadmap for exploring data, selecting model system measures, organizing adaptive feedback loops, selecting a model configuration, implementing a working model, and validating the final model In an extended example, applies evolutionary programming techniques to solve a complicated scheduling problem Presents examples in C, C++, Java, and easy-to-understand pseudo-code Extensive online component, including sample code and a complete data mining workbench
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