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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Grundlagen Mathematics as a Foreign Language
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Mathematics as a Foreign Language
Nikolay I. Kazimirov (Gebundene Ausgabe, Englisch)
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Beschreibung
This text, structured in two parts, presents a distinctive pedagogical approach to the foundations of mathematics by treating the subject as a formal language to be learned. Its central thesis is that mastery of modern mathematics, logic, and computer science requires fluency in a precise and structured mode of thinking—an “architecture of thought” grounded in a rigorous and expressive language.… The book develops a method for learning mathematical language in a way aligned with contemporary foreign language pedagogy, enabling readers to interpret mathematical texts with clarity and precision while gaining insight into their underlying patterns, structures, capabilities, and limitations. In doing so, it bridges the gap between intuitive understanding and formal rigor, complementing standard courses in logic, set theory, algebra, and philosophy. The text includes approximately 190 exercises of varying difficulty, each accompanied by detailed solutions to support independent study and self-assessment. It also explicitly connects the formal language of mathematics with the operational logic of artificial intelligence. Undergraduate students in mathematics, computer science, philosophy, and linguistics—as well as graduate students seeking a clear and structured review of foundational concepts—will find the book a valuable contribution to their understanding of mathematical formalism. Those interested in the logical principles underlying computer science and AI will likewise find it an engaging resource for deepening their grasp of formal structures. Part I, The Ascent, serves as a conceptual and intuitive guide, using the metaphor of language acquisition levels (A1 to C1) to develop understanding from the basic syntax of mathematical expressions (the “Matryoshka principle”) to advanced ideas in formal logic and set theory, enriched by analogies, historical context, and philosophical motivation. Part II, Proof-Theoretical Basis, provides the rigorous definitions and proofs underpinning these concepts, completing the transition from intuition to formal precision. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
23.10.2026
Sprache
Englisch
EAN
9783032307200
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Mathematics in Mind
Sonderedition
Nein
Autor
Nikolay I. Kazimirov
Seitenanzahl
441
Einbandart
Gebundene Ausgabe
Schlagwörter
mathematical logic, linguica franca, MathLogic Nexus, Matryoshka Principle, sets, logic and semantics, syllogism, propositional logic, Peano arithmetic, prolegomena, Zermelo-Fraenkel set theory, induction, recursion, von Neumann heirarchy, ordinal arithmetic, cardinal arithmetic, countable choice
Thema-Inhalt
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
PBCH - Mengenlehre
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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