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Formalization of complex analysis an...

Guan, Yong.

Formalization of complex analysis and matrix theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Formalization of complex analysis and matrix theoryby Zhiping Shi, Yong Guan, Ximeng Li.
作者:	Shi, Zhiping.
其他作者:	Guan, Yong.
出版者:	Singapore :Springer Singapore :2020.
面頁冊數:	x, 168 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematical analysis.
電子資源:	https://doi.org/10.1007/978-981-15-7261-6
ISBN:	9789811572616$q(electronic bk.)

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$q(electronic bk.)

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

186133
Mathematical analysis.

LC Class. No.: QA300 / .S559 2020

Dewey Class. No.: 515

Formalization of complex analysis and matrix theory
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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.
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