Many-sorted Algebras for Deep Learning and Quantum Technology

• Includes hundreds of well-designed examples to illustrate the intriguing concepts in quantum systems
• Provides precise description of all laws or equational identities that are needed in specifying an algebraic structure
• Illustrates all the inter and intra sort operations needed in describing algebras

Charles R. Giardina was born in the Bronx, NY, on December 29, 1942. He received the B.S. degree in mathematics from Fairleigh Dickinson University, Rutherford, NJ, and the M.S. degree in mathematics from Carnegie Institute of Technology, Pittsburgh, PA. He also received the M.E.E. degree in 1969, and the Ph.D. degree in mathematics and electrical engineering in 1970 from Stevens Institute of Technology, Hoboken, NJ. Dr. Giardina was Professor of Mathematics, Electrical Engineering, and Computer Science at Fairleigh Dickinson University from 1965 to 1982. From 1982 to 1986, he was a Professor at the Stevens Institute of Technology. From 1986 to 1996, he was a Professor at the College of Staten Island, City University of New York. From 1996, he was with Bell Telephone Laboratories, Whippany, NJ, USA. His research interests include digital signal and image processing, pattern recognition, artificial intelligence, and the constructive theory of functions. Dr. Giardina has authored numerous papers in these areas, and several books including, Mathematical Models for Artificial Intelligence and Autonomous Systems, Prentice Hall; Matrix Structure Image Processing, Prentice Hall; Parallel Digital Signal Processing: A Unified Signal Algebra Approach, Regency; Morphological Methods in Image and Signal Processing, Prentice Hall; Image Processing – Continuous to Discrete: Geometric, Transform, and Statistical Methods, Prentice Hall; and A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing, Chapman and Hall/CRC Press.