Handbook of Cognitive Mathematics

ISBN-13: 9783031039447 / Angielski / Twarda / 2022 / 1410 str.

Marcel Danesi

Opis

Cognitive mathematics provides insights into how mathematics works inside the brain and how it is interconnected with other faculties through so-called blending and other associative processes. This handbook is the first large collection of various aspects of cognitive mathematics to be amassed into a single title, covering decades of connection between mathematics and other figurative processes as they manifest themselves in language, art, and even algorithms. It will be of use to anyone working in math cognition and education, with each section of the handbook edited by an international leader in that field.

Spis treści

Introduction: Marcel Danesi: What Is Cognitive Mathematics?.- BASIC NOTIONS: Rafael Núnez.- Embodied Cognition and Mathematics.- Numeracy.- Numerosity.- Spatial Reasoning in a Cognitive Mathematical Framework.- Mathematics, Culture, and History.- CONCEPTUAL BLENDING IN MATHEMATICS: Mark Turner.- Conceptual Metaphor Theory.- Conceptual Blending.- Conceptual Integration.- Compression.- Mathematical Modeling.- NEURIOSCIENTIFIC ASPECTS OF MATHEMATICS: Brian Butterworth.- Computational Neuroscience.- Creativity in Mathematics.- Modularity Theory.- Parallel Processing.- Species-Specificities.- MATHEMATICS AND LANGUAGE: Keith Devlin.- Metaphor in Language and Mathematics.- Metonymy in Language and Mathematics.- Overlapping Sign Systems.- Theories of Syntax and the Nature of Equations.- Semantics in Language and Mathematics.- V. MATHEMATICS AND THE ARTS: Gizem Karaali.- Drawing.- Music.- Poetry.- Dance.- Literature.- VI. LEARNING MATHEMATICS: Dragana Martinovic.- Learning Arithmetic.- Learning Geometry.- Learning Set Theory.- Learning Advanced Mathematics.- Role of Symbolism in Learning.- VII. APPLICATIONS: Robert Logan.- Problem-Solving.- Proofs.- Fractal Geometry.- Probability Theory.- Mathematics and Science.- VIII. INTERFACES: Gila Hanna.- Knowledge Representation.- Development of Algorithms.- Natural Language Processing and Mathematics.- Automated Proofs and Cognitive Theory.- Technology and Mathematics

O autorze

Marcel Danesi is Professor Emeritus of Anthropology at the University of Toronto. He has written extensively on the relation between mathematics and symbol systems, including how puzzles and problems in mathematics are part of a more general dialectic frame of mind for grasping the nature of reality. Among his works in the field are Language and Mathematics (2018) and Ahmes’ Legacy (2020). He also founded the CogSci Network at the Fields Institute for Research in Mathematical Sciences, which consists of internationally0renowned researchers in the field of cognitive mathematics.