How we understand mathematics : conceptual integration in the language of mathematical description / Jacek Woźny.
Woźny, Jacek, author.
2018
QA8.4
Available Online

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Title How we understand mathematics : conceptual integration in the language of mathematical description / Jacek Woźny.
Author Woźny, Jacek, author.
ISBN 9783319776880 (electronic book)
3319776886 (electronic book)
9783319776873
3319776878
DOI https://doi.org/10.1007/978-3-319-77688-0
Published Cham, Switzerland : Springer, [2018]
Language English
Description 1 online resource.
Other Standard Identifiers 10.1007/978-3-319-77688-0 doi
Call Number QA8.4
Dewey Decimal Classification 510.1
Summary 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.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Source of Description Online resource; title from PDF title page (viewed May 02, 2018).
Series Mathematics in mind.
Available in Other Form How we understand mathematics.
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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
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