Mathematical Foundations of Advanced Informatics Volume 1: Inductive Approaches /

• Κύριοι συγγραφείς: Steffen, Bernhard (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Rüthing, Oliver (http://id.loc.gov/vocabulary/relators/aut), Huth, Michael (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Θέματα: Computer science-Mathematics.; Computers.; Computer mathematics.; Software engineering.; Mathematics of Computing.; Theory of Computation.; Mathematical Applications in Computer Science.; Software Engineering/Programming and Operating Systems.

 The books in this trilogy capture the foundational core of advanced informatics. The authors make the foundations accessible, enabling students to become effective problem solvers. This first volume establishes the inductive approach as a fundamental principle for system and domain analysis. After a brief introduction to the elementary mathematical structures, such as sets, propositional logic, relations, and functions, the authors focus on the separation between syntax (representation) and semantics (meaning), and on the advantages of the consistent and persistent use of inductive definitions. They identify compositionality as a feature that not only acts as a foundation for algebraic proofs but also as a key for more general scalability of modeling and analysis. A core principle throughout is invariance, which the authors consider a key for the mastery of change, whether in the form of extensions, transformations, or abstractions. This textbook is suitable for undergraduate and graduate courses in computer science and for self-study. Most chapters contain exercises and the content has been class-tested over many years in various universities. 

 Introduction -- Propositions and Sets -- Relations and Functions -- Inductive Definitions -- Inductive Proofs -- Inductive Approach: Potential, Limitations, and Pragmatics.