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How We Understand Mathematics: Conceptual Integration in the Language of Mathematical Description: Mathematics in Mind

Autor Jacek Woźny
en Limba Engleză Hardback – 7 mai 2018
This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. 
This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well. 
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Specificații

ISBN-13: 9783319776873
ISBN-10: 3319776878
Pagini: 144
Ilustrații: X, 118 p. 16 illus., 10 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.36 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Mathematics in Mind

Locul publicării:Cham, Switzerland

Cuprins

1. Introduction.- 2. The Theoretical Framework and the Subject of Study.- 3. Sets.- 4. Mappings.- 5. Groups.- 6. Rings, Fields, and Vector Spaces.- 7. Summary and Conclusion.- Sources. 

Textul de pe ultima copertă

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. 
​This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well. 

Caracteristici

Analyzes the language of pure mathematics in various advanced-level sources Systemically covers the whole course of advanced, academic-level algebra Presents topics in the order usually taught to students, allowing for a close scrutiny of the development of the multilayered and intricate structure of mathematical concepts