How We Understand Mathematics
Conceptual Integration in the Language of Mathematical Description
Authors: Woźny, Jacek
Free Preview- 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
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- About this book
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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.
- Table of contents (7 chapters)
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Introduction
Pages 1-5
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The Theoretical Framework and the Subject of Study
Pages 7-30
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Sets
Pages 31-49
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Mappings
Pages 51-59
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Groups
Pages 61-81
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- How We Understand Mathematics
- Book Subtitle
- Conceptual Integration in the Language of Mathematical Description
- Authors
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- Jacek Woźny
- Series Title
- Mathematics in Mind
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG, part of Springer Nature
- eBook ISBN
- 978-3-319-77688-0
- DOI
- 10.1007/978-3-319-77688-0
- Hardcover ISBN
- 978-3-319-77687-3
- Series ISSN
- 2522-5405
- Edition Number
- 1
- Number of Pages
- X, 118
- Number of Illustrations
- 6 b/w illustrations, 10 illustrations in colour
- Topics
