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Formalization of Complex Analysis and Matrix Theory

Shi, Zhiping Guan Yong Li, Ximeng
Heftet / 2021 / Engelsk

Produktdetaljer

ISBN
9789811572630
Publisert
2021-08-12
Utgiver
Vendor
Springer Verlag, Singapore
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Orginaltittel
Fu Fen Xi He Ju Zhen Li Lun De Xing Shi Hua

Forfatter
Shi, Zhiping
Guan Yong
Li, Ximeng

Biographical note

Zhiping Shi is a Full Professor at the College of Information Engineering, Capital Normal University. Holding a Ph.D. from the Institute of Computing Technology, Chinese Academy of Sciences, his research interests include the formalization of mathematical theories, formal verification of IT systems, computer vision, and artificial intelligence. He has (co)authored over 100 peer-reviewed research papers and has led numerous research projects at national and international level.

Yong Guan is a Full Professor at the College of Information Engineering, Capital Normal University. His main research interests include formal verification, reliable embedded systems, and robotics. He has (co)authored over 180 research papers and has successfully conducted over 10 research projects at national and international level. He is a recipient of the “Special Government Allowance” issued by the state council and is the Head of the International Science and Technology Cooperation Base of Electronic System Reliability and Mathematical Interdisciplinary Research – a research center approved by the Ministry of Science and Technology of the People’s Republic of China.

Ximeng Li is a Lecturer at the College of Information Engineering, Capital Normal University. He holds a Ph.D. from the Technical University of Denmark (DTU) and was a Postdoctoral Researcher at DTU and TU Darmstadt, Germany. His research is mainly focused on the formal verification of software systems.  He has published in highly respected computer science conference proceedings and journals such as ESORICS, Logical Methods in Computer Science, and the Journal of Computer Languages. He has also participated in the European ARTEMIS project SESAMO and the German BMBF research project CRISP.

 


Formalization of Complex Analysis and Matrix Theory

Shi, Zhiping Guan Yong Li, Ximeng
Heftet / 2021 / Engelsk
Shi, Zhiping Guan Yong Li, Ximeng
Heftet / 2021 / Engelsk
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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 mathematicaltheories.
Les mer
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.
Les mer
Introduction.- Algebraic Systems.- Complex Numbers.- Gauge Integration.- FourierTransformation.- Discrete Fourier Transformation.- Matrices.
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.
Les mer
Describes the computer-assisted formalization of complex analysis and matrix theory Includes both the formalization of theoretical results and the verification of algorithms that are practically used Provides detailed information on related developments in the research community and outlines potential future directions, helping put the technical content into perspective
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

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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 mathematicaltheories.
Les mer
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.
Les mer
Introduction.- Algebraic Systems.- Complex Numbers.- Gauge Integration.- FourierTransformation.- Discrete Fourier Transformation.- Matrices.
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.
Les mer
Describes the computer-assisted formalization of complex analysis and matrix theory Includes both the formalization of theoretical results and the verification of algorithms that are practically used Provides detailed information on related developments in the research community and outlines potential future directions, helping put the technical content into perspective
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

Produktdetaljer

ISBN
9789811572630
Publisert
2021-08-12
Utgiver
Vendor
Springer Verlag, Singapore
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Orginaltittel
Fu Fen Xi He Ju Zhen Li Lun De Xing Shi Hua

Forfatter
Shi, Zhiping
Guan Yong
Li, Ximeng

Biographical note

Zhiping Shi is a Full Professor at the College of Information Engineering, Capital Normal University. Holding a Ph.D. from the Institute of Computing Technology, Chinese Academy of Sciences, his research interests include the formalization of mathematical theories, formal verification of IT systems, computer vision, and artificial intelligence. He has (co)authored over 100 peer-reviewed research papers and has led numerous research projects at national and international level.

Yong Guan is a Full Professor at the College of Information Engineering, Capital Normal University. His main research interests include formal verification, reliable embedded systems, and robotics. He has (co)authored over 180 research papers and has successfully conducted over 10 research projects at national and international level. He is a recipient of the “Special Government Allowance” issued by the state council and is the Head of the International Science and Technology Cooperation Base of Electronic System Reliability and Mathematical Interdisciplinary Research – a research center approved by the Ministry of Science and Technology of the People’s Republic of China.

Ximeng Li is a Lecturer at the College of Information Engineering, Capital Normal University. He holds a Ph.D. from the Technical University of Denmark (DTU) and was a Postdoctoral Researcher at DTU and TU Darmstadt, Germany. His research is mainly focused on the formal verification of software systems.  He has published in highly respected computer science conference proceedings and journals such as ESORICS, Logical Methods in Computer Science, and the Journal of Computer Languages. He has also participated in the European ARTEMIS project SESAMO and the German BMBF research project CRISP.

 


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