Overview
- 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
Part of the book series: Mathematics in Mind (MATHMIN)
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Table of contents (7 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: How We Understand Mathematics
Book Subtitle: Conceptual Integration in the Language of Mathematical Description
Authors: Jacek Woźny
Series Title: Mathematics in Mind
DOI: https://doi.org/10.1007/978-3-319-77688-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-77687-3Published: 07 May 2018
Softcover ISBN: 978-3-030-08513-1Published: 30 January 2019
eBook ISBN: 978-3-319-77688-0Published: 25 April 2018
Series ISSN: 2522-5405
Series E-ISSN: 2522-5413
Edition Number: 1
Number of Pages: X, 118
Number of Illustrations: 6 b/w illustrations, 10 illustrations in colour
Topics: Combinatorics, Cognitive Linguistics, Group Theory and Generalizations