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Formalization of complex analysis an...

Shi, Zhiping.

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Formalization of complex analysis and matrix theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Formalization of complex analysis and matrix theory/ by Zhiping Shi, Yong Guan, Ximeng Li.
Author:	Shi, Zhiping.
other author:	Guan, Yong.
Published:	Singapore :Springer Singapore : : 2020.,
Description:	x, 168 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Algebraic Systems -- Complex Numbers -- Gauge Integration -- FourierTransformation -- Discrete Fourier Transformation -- Matrices.
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-981-15-7261-6
ISBN:	9789811572616

Formalization of complex analysis and matrix theory
Shi, Zhiping.

Formalization of complex analysis and matrix theory[electronic resource] /by Zhiping Shi, Yong Guan, Ximeng Li. - Singapore :Springer Singapore :2020. - x, 168 p. :ill., digital ;24 cm.

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.

ISBN: 9789811572616

Standard No.: 10.1007/978-981-15-7261-6doiSubjects--Topical Terms:

516833
Mathematical analysis.

LC Class. No.: QA300 / .S559 2020

Dewey Class. No.: 515

Formalization of complex analysis and matrix theory
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100 1 $a Shi, Zhiping. $3 3525993
245 1 0 $a Formalization of complex analysis and matrix theory $h [electronic resource] / $c by Zhiping Shi, Yong Guan, Ximeng Li.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a x, 168 p. : $b ill., digital ; $c 24 cm.
505 0 $a Introduction -- Algebraic Systems -- Complex Numbers -- Gauge Integration -- FourierTransformation -- Discrete Fourier Transformation -- Matrices.
520 $a 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.
650 0 $a Mathematical analysis. $3 516833
650 0 $a Matrices. $3 516894
650 1 4 $a Applications of Mathematics. $3 890893
650 2 4 $a Mathematical and Computational Engineering. $3 3226306
650 2 4 $a Mathematics of Computing. $3 891213
700 1 $a Guan, Yong. $3 3525994
700 1 $a Li, Ximeng. $3 3525995
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-981-15-7261-6
950 $a Mathematics and Statistics (SpringerNature-11649)