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Proof Patterns

Author: Mark Joshi

Publisher: Springer

Published: 2015-03-17

Total Pages: 190

ISBN-13: 3319162500

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This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Book Synopsis Proof Patterns by : Mark Joshi

Download or read book Proof Patterns written by Mark Joshi and published by Springer. This book was released on 2015-03-17 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Test Pattern Generation using Boolean Proof Engines

Author: Rolf Drechsler

Publisher: Springer Science & Business Media

Published: 2009-04-22

Total Pages: 196

ISBN-13: 9048123607

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In Test Pattern Generation using Boolean Proof Engines, we give an introduction to ATPG. The basic concept and classical ATPG algorithms are reviewed. Then, the formulation as a SAT problem is considered. As the underlying engine, modern SAT solvers and their use on circuit related problems are comprehensively discussed. Advanced techniques for SAT-based ATPG are introduced and evaluated in the context of an industrial environment. The chapters of the book cover efficient instance generation, encoding of multiple-valued logic, usage of various fault models, and detailed experiments on multi-million gate designs. The book describes the state of the art in the field, highlights research aspects, and shows directions for future work.

Book Synopsis Test Pattern Generation using Boolean Proof Engines by : Rolf Drechsler

Download or read book Test Pattern Generation using Boolean Proof Engines written by Rolf Drechsler and published by Springer Science & Business Media. This book was released on 2009-04-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Test Pattern Generation using Boolean Proof Engines, we give an introduction to ATPG. The basic concept and classical ATPG algorithms are reviewed. Then, the formulation as a SAT problem is considered. As the underlying engine, modern SAT solvers and their use on circuit related problems are comprehensively discussed. Advanced techniques for SAT-based ATPG are introduced and evaluated in the context of an industrial environment. The chapters of the book cover efficient instance generation, encoding of multiple-valued logic, usage of various fault models, and detailed experiments on multi-million gate designs. The book describes the state of the art in the field, highlights research aspects, and shows directions for future work.

Proof and Knowledge in Mathematics

Author: Michael Detlefsen

Publisher: Routledge

Published: 2005-08-18

Total Pages: 170

ISBN-13: 1134916760

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Distinguished contributors tackle the main problem that arizes when considering an epistemology for mathematics, the nature and sources of mathematical justification.

Book Synopsis Proof and Knowledge in Mathematics by : Michael Detlefsen

Download or read book Proof and Knowledge in Mathematics written by Michael Detlefsen and published by Routledge. This book was released on 2005-08-18 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguished contributors tackle the main problem that arizes when considering an epistemology for mathematics, the nature and sources of mathematical justification.

Teaching and Learning Proof Across the Grades

Author: Despina A. Stylianou

Publisher: Routledge

Published: 2010-09-23

Total Pages: 515

ISBN-13: 1135856745

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A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. By building and extending on existing research and by allowing a variety of voices from the field to be heard, Teaching and Learning Proof Across the Grades not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.

Book Synopsis Teaching and Learning Proof Across the Grades by : Despina A. Stylianou

Download or read book Teaching and Learning Proof Across the Grades written by Despina A. Stylianou and published by Routledge. This book was released on 2010-09-23 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. By building and extending on existing research and by allowing a variety of voices from the field to be heard, Teaching and Learning Proof Across the Grades not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.

Advances in Mathematics Education Research on Proof and Proving

Author: Andreas J. Stylianides

Publisher: Springer

Published: 2018-01-10

Total Pages: 301

ISBN-13: 3319709968

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This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.

Book Synopsis Advances in Mathematics Education Research on Proof and Proving by : Andreas J. Stylianides

Download or read book Advances in Mathematics Education Research on Proof and Proving written by Andreas J. Stylianides and published by Springer. This book was released on 2018-01-10 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.

The Mathematics of Love

Author: Hannah Fry

Publisher: Simon and Schuster

Published: 2015-02-03

Total Pages: 128

ISBN-13: 1476784884

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Uses math as a tool for explaining the complicated patterns of love, tackling such common questions as the chance of finding love that will last, how online dating works, and when to compromise.

Book Synopsis The Mathematics of Love by : Hannah Fry

Download or read book The Mathematics of Love written by Hannah Fry and published by Simon and Schuster. This book was released on 2015-02-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uses math as a tool for explaining the complicated patterns of love, tackling such common questions as the chance of finding love that will last, how online dating works, and when to compromise.

Security Engineering with Patterns

Author: Markus Schumacher

Publisher: Springer

Published: 2003-09-09

Total Pages: 215

ISBN-13: 3540451803

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For quite some time, in systems and software design, security only came as a second thought or even as a nice-to-have add-on. However, since the breakthrough of the Internet as a virtual backbone for electronic commerce and similar applications, security is now recognized as a fundamental requirement. This book presents a systematic security improvement approach based on the pattern paradigm. The author first clarifies the key concepts of security patterns, defines their semantics and syntax, demonstrates how they can be used, and then compares his model with other security approaches. Based on the author's model and best practice in security patterns, security novices are now in a position to understand how security experts solve problems and can basically act like them by using the patterns available as building blocks for their designs.

Book Synopsis Security Engineering with Patterns by : Markus Schumacher

Download or read book Security Engineering with Patterns written by Markus Schumacher and published by Springer. This book was released on 2003-09-09 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: For quite some time, in systems and software design, security only came as a second thought or even as a nice-to-have add-on. However, since the breakthrough of the Internet as a virtual backbone for electronic commerce and similar applications, security is now recognized as a fundamental requirement. This book presents a systematic security improvement approach based on the pattern paradigm. The author first clarifies the key concepts of security patterns, defines their semantics and syntax, demonstrates how they can be used, and then compares his model with other security approaches. Based on the author's model and best practice in security patterns, security novices are now in a position to understand how security experts solve problems and can basically act like them by using the patterns available as building blocks for their designs.

Future-Proof Software-Systems

Author: Frank J. Furrer

Publisher: Springer

Published: 2019-09-25

Total Pages: 376

ISBN-13: 3658199385

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This book focuses on software architecture and the value of architecture in the development of long-lived, mission-critical, trustworthy software-systems. The author introduces and demonstrates the powerful strategy of “Managed Evolution,” along with the engineering best practice known as “Principle-based Architecting.” The book examines in detail architecture principles for e.g., Business Value, Changeability, Resilience, and Dependability. The author argues that the software development community has a strong responsibility to produce and operate useful, dependable, and trustworthy software. Software should at the same time provide business value and guarantee many quality-of-service properties, including security, safety, performance, and integrity. As Dr. Furrer states, “Producing dependable software is a balancing act between investing in the implementation of business functionality and investing in the quality-of-service properties of the software-systems.” The book presents extensive coverage of such concepts as: Principle-Based Architecting Managed Evolution Strategy The Future Principles for Business Value Legacy Software Modernization/Migration Architecture Principles for Changeability Architecture Principles for Resilience Architecture Principles for Dependability The text is supplemented with numerous figures, tables, examples and illustrative quotations. Future-Proof Software-Systems provides a set of good engineering practices, devised for integration into most software development processes dedicated to the creation of software-systems that incorporate Managed Evolution.

Book Synopsis Future-Proof Software-Systems by : Frank J. Furrer

Download or read book Future-Proof Software-Systems written by Frank J. Furrer and published by Springer. This book was released on 2019-09-25 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on software architecture and the value of architecture in the development of long-lived, mission-critical, trustworthy software-systems. The author introduces and demonstrates the powerful strategy of “Managed Evolution,” along with the engineering best practice known as “Principle-based Architecting.” The book examines in detail architecture principles for e.g., Business Value, Changeability, Resilience, and Dependability. The author argues that the software development community has a strong responsibility to produce and operate useful, dependable, and trustworthy software. Software should at the same time provide business value and guarantee many quality-of-service properties, including security, safety, performance, and integrity. As Dr. Furrer states, “Producing dependable software is a balancing act between investing in the implementation of business functionality and investing in the quality-of-service properties of the software-systems.” The book presents extensive coverage of such concepts as: Principle-Based Architecting Managed Evolution Strategy The Future Principles for Business Value Legacy Software Modernization/Migration Architecture Principles for Changeability Architecture Principles for Resilience Architecture Principles for Dependability The text is supplemented with numerous figures, tables, examples and illustrative quotations. Future-Proof Software-Systems provides a set of good engineering practices, devised for integration into most software development processes dedicated to the creation of software-systems that incorporate Managed Evolution.

Book of Proof

Author: Richard H. Hammack

Publisher:

Published: 2016-01-01

Total Pages: 314

ISBN-13: 9780989472111

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This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Book Synopsis Book of Proof by : Richard H. Hammack

Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Proofs from THE BOOK

Author: Martin Aigner

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 194

ISBN-13: 3662223430

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According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Book Synopsis Proofs from THE BOOK by : Martin Aigner

Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.