Research in History and Philosophy of Mathematics: The CSHPM 2019-2020 Volume (Annals of the Canadian Society for History and Philosophy of ... et de philosophie des mathématiques)

Preface
Editorial Board
Contents
Contributors
The Most Obscure and Inconvenient Tables Ever Constructed?
	1 Introduction
	2 Overview of Torporley\'s Astrology
	3 All Circles Great and Small
		3.1 Coordinate Systems
	4 The Law of Tangents
		4.1 Spherical Trigonometry
	5 Torporley\'s Miter and Menelaus\'s Figure
		5.1 Considering MT I
		5.2 Considering MT II
	6 The Spherical Right Triangle
	7 The Quadrans or Right Gateway
	8 The Quincunx or Left Gateway
	9 Conclusion
	References
Commercializing Arithmetic: The Case of Edward Hatton
	1 Introduction
	2 Edward Hatton and his Publishers
	3 A Textbook: The Merchant\'s Magazine
		3.1 Commercial Arithmetic
		3.2 Merchant\'s Accompts
		3.3 Book-Keeping
		3.4 Later Editions
	4 Ready Reckoners: Comes Commercii
	5 Ready Reckoners: Index to Interest
	6 Posters
	7 Other Works
	Appendix: A Summary Hatton Bibliography
	References
Leading to Poncelet: A Story of Collinear Points
	1 Introduction
	2 Pappus
	3 Desargues
	4 Monge
	5 Carnot
	6 Brianchon
	7 Poncelet
	References
Cauchy, Le Verrier et Jacobi sur le problème algébrique des valeurs propres et les inégalités séculaires des mouvementsdes planètes
	1 Introduction
	2 L\'inégalité séculaire des planètes
	3 Cauchy et le problème des valeurs propres en 1829
	4 Le Verrier (1840) : Trouver les coefficients du polynôme caractéristique
	5 Trouver les racines d\'un polynôme
	6 La méthode de Jacobi (1846)
		6.1 La partie théorique
		6.2 La partie pratique
	7 Conclusion
	Références
Mathematics in Astronomy at Harvard College Before 1839 as a Case Study for Teaching Historical Writing in Mathematics Courses
	1 Introduction
	2 John Winthrop
	3 Samuel Williams
	4 John Farrar
	5 Conclusion
	References
`Lectures for Women\' and the Founding of Newnham College, Cambridge
	1 Prologue
	2 Lectures for Women
	3 Newnham College
	4 Conclusion
	References
Are Euclid\'s Diagrams `Representations\'? On an Argument by Ken Manders
	1 Introduction
	2 Reductio Proofs and the `Classical View\' of Diagrams
	3 A Partial Version of the Classical View
	4 A Semantics for Diagrams
	5 By Way of Conclusion: What Is a Semantics Good for?
	References
Abstraction by Embedding and Constraint-Based Design
	1 Introduction
	2 Stick-Figure Abstraction
	3 Abstraction by Embedding
	4 Abstraction by Constraint-Based Design
		4.1 Fourier Analysis and a Challenge It Posed
		4.2 How to Define the Real Numbers
			4.2.1 Heine
			4.2.2 Cantor
			4.2.3 Dedekind
		4.3 Discussion
		4.4 Epistemic Practices
			4.4.1 Constraint-Based Design
			4.4.2 Abstraction
			4.4.3 Beyond Abstraction
			4.4.4 Summary
	5 Concluding Remarks
	References
The Birth of Undergraduate Modern Algebra in the United States
	1 Introduction
	2 What Is Modern Algebra
	3 Algebra in the Nineteenth Century: Examples of a Successful Start
	4 Modern Algebra in the American Undergraduate Curriculum
		4.1 About Cajori Two
		4.2 About Table 1
		4.3 About Table 2
	5 The Story in a Nutshell and a Caution
	6 The Environment Concerning Modern Algebra Courses
		6.1 Doubts About Abstraction and Applications
			6.1.1 The Double Mindset: Abstraction Versus Concrete Mathematics
			6.1.2 Applications of Modern Algebra Did Not Seem Compelling
		6.2 Lack of a Suitable Modern Algebra Textbook
		6.3 The “Marginal Interest” and Interrupted Pace of Research
		6.4 Polarizing Anxieties Related to Research
	7 The Fading of Reasons to Hesitate
		7.1 Advances in Research in Algebra
			7.1.1 The Arrival of Emmy Noether and Abstract Ring Theory
			7.1.2 The Development of Abstract Field Theory
			7.1.3 The Use of Group Theory in Quantum Mechanics
		7.2 The Appearance of Textbooks
			7.2.1 The Appearance of Bartel van der Waerden\'s Moderne Algebra
			7.2.2 The Appearance of Birkhoff and Mac Lane\'s A Survey of Modern Algebra
		7.3 “Marginal and Interrupted” Give Way to a Plenitude of Research in Four Important Journals
		7.4 The Fading of the Polarizing Anxieties Related to Research
		7.5 Leadership from the Top
		7.6 Conclusion
	8 Related Wider Issues
	References
History as a Source of Mathematical Narrative in Developing Students\' Interpretations of Mathematics
	1 Introduction
	2 A Brief Account of What History Is
		2.1 History as Literature
		2.2 History as Science/Social Science
		2.3 History as a Narrative
	3 Mathematics and Narrative
		3.1 History as a Source of Mathematical Narrative
		3.2 The Context of Two History of Mathematics Courses
		3.3 Changes in Students\' Views
	4 Conclusion
	References
Thoughts on Using the History of Mathematics to Teach the Foundations of Mathematical Analysis
	1 The Problem
	2 Mathematics as Reasoning
	3 Why Is There a Problem About Calculus?
	4 Proofs as Sequences of Statements
	5 Bridge Course: Mathematical Theories
	6 Bridge Course: Set Theory and Logic
	7 Analysis: Limits
	8 The Real Numbers
	9 Conclusion
	References