04186nam a22005415i 4500 978-3-031-66545-5 DE-He213 20251030113259.0 cr nn 008mamaa 241106s2024 sz | s |||| 0|eng d 9783031665455 978-3-031-66545-5 10.1007/978-3-031-66545-5 doi Q342 UYQ bicssc COM004000 bisacsh UYQ thema Manca, Vincenzo. author. aut http://id.loc.gov/vocabulary/relators/aut 87068 Python Arithmetic [electronic resource] : The Informational Nature of Numbers / by Vincenzo Manca. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. X, 104 p. 31 illus., 11 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Studies in Big Data, 2197-6511 ; 153 The Origins of Digital Age -- Mathematical notation and Python -- Counting Algorithms in Python -- Arithmetic Operations -- Square Root Algorithms -- Primality, Equations, Congruences -- Symbolic Computation. The book is a gentle introduction to Python using arithmetic, and vice versa, with a historical perspective encompassing programming languages within the wider process of development of mathematical notation. The revisitation of typical algorithms that are the core of elementary mathematical knowledge helps to grasp their essence and to clarify some assumptions that are often taken for granted but are very profound and of a very general nature. The first mathematician to define a systematic system for generating numbers was Archimedes of Syracuse in the third century B.C. The Archimedean system, which was defined in a book with the Latin title Arenarius, was not intended to define all numbers, but only very large numbers [13, 22, 23]. However, it can be considered the first system with the three main characteristics of a counting system that have the most important properties for complete arithmetic adequacy: creativity, infinity, and recursion. Creativity means that each numeral is new for numerals that precede it; infinity means that after any numeral there is always another numeral; recursion means that after an initial sequence of numerals coinciding with the digits of the system, digits repeat regularly in all subsequent numerals. Since the numerals are finite expressions of digits, their lengths increase along their generation. In the next chapter, Python is briefly introduced by linking this language to standard mathematical notation, which took its current form throughout a long process that extends from the introduction of decimal numerals to the eighteenth century, particularly within Euler’s notational and conceptual framework. The third chapter is devoted to counting algorithms, showing that something that is usually taken for granted has intriguing aspects that deserve a very subtle analysis: the authors will show that the Python representation of counting algorithms is very informative and demonstrates the informational nature of numbers. Computational intelligence. 64052 Python (Computer program language). 64608 Engineering Data processing. Computational Intelligence. 64052 Python. 47553 Data Engineering. 66059 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031665448 Printed edition: 9783031665462 Printed edition: 9783031665479 Studies in Big Data, 2197-6511 ; 153 68724 https://doi.org/10.1007/978-3-031-66545-5 ZDB-2-INR ZDB-2-SXIT 64735 64735