03569nam a22005055i 4500 978-981-97-2432-1 DE-He213 20251030112623.0 cr nn 008mamaa 240711s2024 si | s |||| 0|eng d 9789819724321 978-981-97-2432-1 10.1007/978-981-97-2432-1 doi QA75.5-76.95 UYA bicssc COM014000 bisacsh UYA thema Liu, Xinyu. author. aut http://id.loc.gov/vocabulary/relators/aut 80363 Mathematics in Programming [electronic resource] / by Xinyu Liu. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. XII, 383 p. 197 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Chapter 1 Numbers -- Chapter 2 Recursion -- Chapter 3 Symmetry -- Chapter 4 Category -- Chapter 5 Fusion -- Chapter 6 Infinity -- Chapter 7 Paradox. The book presents the mathematical view and tools of computer programming with broad and friendly context. It explains the basic concepts such as recursion, computation model, types, data, and etc. The book serves as an introductory and reference guide to the engineers, students, researchers, and professionals who are interested in functional programming, type system, and computer programming languages. The book covers seven topics. Firstly, it lays out the number system based on Peano Axioms and demonstrates the isomorphic computer data structures. Then, it introduces Lambda calculus as a computing model and recursion, an important programming structure, with the Y-combinator. It next presents the basic abstract algebra, including group and fields, and provides a friendly introduction to Galois theory. After that, it uses category theory as a tool to explain several concepts in computer programming, including the type system, polymorphism, null handler, and recursive data types, then followed by an application of program optimization. In the last two chapters, the author shows how to program with the concept of infinity through stream and lazy evaluation, and then explains the naïve set theory and transfinite numbers, from which the logic paradox arises. Finally, it introduces four historical views of mathematical foundation, as well as Gödel’s incompleteness theorems developed in 1930s, and how they define the boundaries of computer programming. Additionally, the book provides biographies, stories, and anecdotes of 25 mathematicians, along with over 130 exercises and their corresponding answers. Computer science. 58552 Computer science Mathematics. 64041 Mathematics. 65523 Computer Science Logic and Foundations of Programming. 68173 Mathematical Applications in Computer Science. 65518 Mathematics in Popular Science. 75252 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819724314 Printed edition: 9789819724338 https://doi.org/10.1007/978-981-97-2432-1 ZDB-2-SCS ZDB-2-SXCS 61505 61505