How We Understand Mathematics

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Beschreibung

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.



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



Inhalt
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.

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Produktinformationen

Titel
How We Understand Mathematics
Untertitel
Conceptual Integration in the Language of Mathematical Description
Autor
EAN
9783319776873
ISBN
978-3-319-77687-3
Format
Fester Einband
Herausgeber
Springer, Berlin
Genre
Mathematik
Anzahl Seiten
118
Gewicht
350g
Größe
H14mm x B242mm x T157mm
Jahr
2018
Untertitel
Englisch
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