Teaching and learning with primary source projects : real analysis, topology, and complex variables
 Responsibility
 Janet Heine Barnett, David K. Ruch, Nicholas A. Scoville, editors.
 Publication
 Providence : American Mathematical Society, 2023.
 Copyright notice
 ©2023
 Physical description
 1 online resource (xiv, 441 pages) : charts.
 Series
 Classroom resource materials ; v. 71.
Online
More options
Description
Creators/Contributors
 Contributor
 Barnett, Janet Heine, 1961 editor.
 Ruch, David K., 1959 editor.
 Scoville, Nicholas A., editor.
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 Intro
 Title Page
 Copyright
 Contents
 Preface
 Acknowledgments
 Part 1: Introduction
 Chapter 1: Teaching and Learning with Primary Sources Projects
 Chapter 2: PSP Summaries: The Collection at a Glance
 Chapter 3: Historical Overview
 Part 2: Real Analysis
 Chapter 4: Why Be So Critical? NineteenthCentury Mathematics and the Origins of Analysis
 Chapter 5: Investigations into Bolzano's Bounded Set Theorem
 Chapter 6: Stitching Dedekind Cuts to Construct the Real Numbers
 Chapter 7: Investigations into d'Alembert's Definition of Limit
 Chapter 8: Bolzano on Continuity and the Intermediate Value Theorem
 Chapter 9: Understanding Compactness: Early Work, Uniform Continuity to the HeineBorel Theorem
 Chapter 10: An Introduction to a Rigorous Definition of Derivative
 Chapter 11: Rigorous Debates over Debatable Rigor: Monster Functions in Introductory Analysis
 Chapter 12: The Mean Value Theorem
 Chapter 13: Euler's Rediscovery of e
 Chapter 14: Abel and Cauchy on a Rigorous Approach to Infinite Series
 Chapter 15: The Definite Integrals of Cauchy and Riemann
 Chapter 16: Lebesgue on the Development of the Integral Concept
 Part 3: Topology
 Chapter 17: The Cantor Set before Cantor
 Chapter 18: Topology from Analysis
 Chapter 19: Nearness without Distance
 Chapter 20: Connectedness: Its Evolution and Applications
 Chapter 21: Connecting Connectedness
 Chapter 22: From Sets to Metric Spaces to Topological Spaces
 Chapter 23: The Closure Operation as the Foundation of Topology
 Chapter 24: A Compact Introduction to a Generalized Extreme Value Theorem
 Part 4: Complex Variables
 Chapter 25: The Logarithm of 1
 Chapter 26: Riemann's Development of the CauchyRiemann Equations
 Chapter 27: Gauss and Cauchy on Complex Integration
 Summary
 ""It appears to me that if one wants to make progress in mathematics one should study the masters and not the pupils.""Niels Henrik AbelRecent pedagogical research has supported Abel's claim of the effectiveness of reading the masters. Students exposed to historically based pedagogy see mathematics not as a monolithic assemblage of facts but as a collection of mental processes and an evolving cultural construct built to solve actual problems.
Subjects
 Subjects
 Mathematics > Study and teaching (Higher) > United States.
 Project method in teaching.
 Mathematics > History > Sources.
 Enseignement > Méthode des projets.
 Mathématiques > Histoire > Sources.
 Mathematics
 Mathematics > Study and teaching (Higher)
 Project method in teaching
 United States
 Genre
 History
 Sources
Bibliographic information
 Publication date
 2023
 Copyright date
 2023
 Series
 Classroom resource materials, 15575918 ; Volume 71
 ISBN
 1470475219 (electronic bk.)
 9781470475215 (electronic bk.)
 9781470469894 (paperback)
 1470469898 (paperback)