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Author: Zhiping Shi
Publisher: Springer Nature
ISBN: 9811572615
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.
Author: Zhiping Shi
Publisher: Springer Nature
ISBN: 9811572615
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.
Author: Frédéric Lang
Publisher: Springer
ISBN: 331910702X
Category : Computers
Languages : en
Pages : 213
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Book Description
This book constitutes the proceedings of the 19th International Conference on Formal Methods for Industrial Critical Systems, FMICS 2014, held in Florence, Italy, in September 2014. The 13 papers presented in this volume were carefully reviewed and selected from 26 submissions. They are organized in topical sections named: cyber-physical systems; computer networks; railway control systems; verification methods; and hardware and software testing.
Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages : 825
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Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author: John Chi-Kin Lee
Publisher: Taylor & Francis
ISBN: 1317616553
Category : Education
Languages : en
Pages : 344
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Book Description
There has been much debate in recent times between the Anglo American tradition of curriculum studies and the Continental and North European tradition of didactics (Didaktik). As important as such debate has been, this book seeks to add new voices to the debate representing ideas and traditions from a different part of the world. The focus is on Chinese curriculum thinking that has passed through a number of stages and currently represents a blend of some aspects of the American tradition and Chinese cultural traditions. How does Chinese thinking about curriculum, teaching and learning resonate with European didactic traditions and what are the implications for theorizing an expanded field of curriculum studies? This book deliberately transcends borders and cultures to explore new territory, to provide a platform for open dialogue and to open up new areas of investigation Chapters include, Curriculum Reform and Research in China: A Social-Historical Perspective What Mathematics Did Teachers Learn? Comparison of the School and the Pre-Service Teacher Mathematics Curricula in Germany and Taiwan Living in Parallel Worlds: A Transatlantic Dialogue between General Didactics and Instructional Design
Author: Tristan Needham
Publisher: Oxford University Press
ISBN: 9780198534464
Category : Mathematics
Languages : en
Pages : 620
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Book Description
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Author: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609
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Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Gerwin Klein
Publisher: Springer
ISBN: 3319089706
Category : Mathematics
Languages : en
Pages : 572
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Book Description
This book constitutes the proceedings of the 5th International Conference on Interactive Theorem Proving, ITP 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 35 papers presented in this volume were carefully reviewed and selected from 59 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematics.
Author: Joe Hurd
Publisher: Springer Science & Business Media
ISBN: 3540283722
Category : Computers
Languages : en
Pages : 418
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Book Description
This book constitutes the refereed proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2005, held in Oxford, UK, in August 2005. The 20 revised full papers presented together with 2 invited papers and 4 proof pearls (concise and elegant presentations of interesting examples) were carefully reviewed and selected from 49 submissions. All current issues in HOL theorem proving and formal verification of software and hardware systems are addressed. Among the topics of this volume are theorem proving, verification, recursion and induction, mechanized proofs, mathematical logic, proof theory, type systems, program verification, and proving systems like HOL, Coq, ACL2, Isabelle/HOL and Isabelle/HOLCF.
Author: University of Utah. Graduate School
Publisher:
ISBN:
Category :
Languages : en
Pages : 198
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Book Description
Author: Walter Carlsnaes
Publisher: SAGE
ISBN: 1473971195
Category : Political Science
Languages : en
Pages : 1131
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Book Description
The original Handbook of International Relations was the first authoritative and comprehensive survey of the field of international relations. In this eagerly-awaited new edition, the Editors have once again drawn together a team of the world′s leading scholars of international relations to provide a state-of-the-art review and indispensable guide to the field, ensuring its position as the pre-eminent volume of its kind. The Second Edition has been expanded to 33 chapters and fully revised, with new chapters on the following contemporary topics: - Normative Theory in IR - Critical Theories and Poststructuralism - Efforts at Theoretical Synthesis in IR: Possibilities and Limits - International Law and International Relations - Transnational Diffusion: Norms, Ideas and Policies - Comparative Regionalism - Nationalism and Ethnicity - Geopolitics in the 21st Century - Terrorism and International Relations - Religion and International Politics - International Migration A truly international undertaking, this Handbook reviews the many historical, philosophical, analytical and normative roots to the discipline and covers the key contemporary topics of research and debate today. The Handbook of International Relations remains an essential benchmark publication for all advanced undergraduates, graduate students and academics in politics and international relations.
