What's in Convergence? - Contents of Volume 18 - 2021

Editors:  Amy Ackerberg-Hastings, Janet Barnett

Associate Editors:  Paul Bialek, Eugene Boman, Maureen Carroll (through 1/31/21), Ximena Catepillan, Sloan Despeaux, Joel Haack, Toke Knudsen, Stacy Langton, Betty Mayfield, Michael Molinsky, Andrew Perry, Adrian Rice, Elyn Rykken (through 1/31/21), Amy Shell-Gellasch, Gary Stoudt (through 1/31/21), Erik R. Tou, Laura Turner

Founding Editors: Victor Katz, Frank Swetz

Articles

The Evolutionary Character of Mathematics, by Richard M. Davitt and Judy Grabiner (posted 2/20/2021)
Richard Davitt’s classroom application of Judy Grabiner’s “use-discover-explore/develop-define” model for historical change in mathematics, along with commentary by Grabiner.

Ongoing Series

Teaching and Learning the Trigonometric Functions through Their Origins, by Daniel E. Otero
A series of curricular units based on primary source texts for use in teaching and learning trigonometry.

• Series Introduction
• Episode 1 – Babylonian Astronomy and Sexagesimal Numeration
• Episode 2 – Hipparchus’ Table of Chords
• Episode 3 – Ptolemy Finds High Noon in Chords of Circles
• Episode 4 – Varāhamihira and the Poetry of Sines

A Series of Mini-projects from TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources
A collection of student-ready projects for use in teaching standard topics from across the undergraduate curriculum.

• Series Introduction, by Janet Barnett, Kathy Clark, Dominic Klyve, Jerry Lodder, Daniel E. Otero, Nick Scoville, and Diana White
• The Derivatives of the Sine and Cosine Functions: A Mini-Primary Source Project for Calculus I, by Dominic Klyve
• Why be so Critical? Nineteenth Century Mathematics and the Origins of Analysis: A Mini-Primary Source Project for Introductory Analysis Students, by Janet Heine Barnett
• Connecting Connectedness: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
• Generating Pythagorean Triples: A Mini-Primary Source Project for Mathematics Majors, Elementary Teachers and Others, by Janet Heine Barnett
• Euler's Rediscovery of e: A Mini-Primary Source Project for Introductory Analysis Students, by Dave Ruch
• How to Calculate \(\pi\): Machin's Inverse Tangents, A Mini-Primary Source Project for Calculus II Students, by Dominic Klyve
• Henri Lebesgue and the Development of the Integral Concept: A Mini-Primary Source Project for Undergraduate Analysis Students, by Janet Heine Barnett
• Seeing and Understanding Data: A Mini-Primary Source Project for Students of Statistics, by Charlotte Bolch and Beverly Woods
• The Origin of the Prime Number Theorem: A Primary Source Project for Number Theory Students, by Dominic Klyve
• The Cantor Set Before Cantor: A Mini-Primary Source Project for Analysis and Topology Students, by Nicholas A. Scoville
• Euler’s Calculation of the Sum of the Reciprocals of the Squares: A Mini-Primary Source Project for Calculus II Students, by Kenneth M Monks
• Completing the Square: From the Roots of Algebra, A Mini-Primary Source Project for Students of Algebra and Their Teachers, by Daniel E. Otero
• Regression to the Mean: A Mini-Primary Source Project for Statistics Students, by Dominic Klyve
• Investigations Into d'Alembert's Definition of Limit: A Mini-Primary Source Project for Students of Real Analysis and Calculus 2, by David Ruch
• Braess’ Paradox in City Planning: A Mini-Primary Source Project for Multivariable Calculus Students, by Kenneth M Monks
• Topology from Analysis: A Mini-Primary Source Project for Topology Students, by Nick Scoville
• Babylonian Numeration: A Mini-Primary Source Project for Pre-service Teachers and Other Students, by Dominic Klyve
• Wronskians and Linear Independence: A Theorem Misunderstood by Many – A Mini-Primary Source Project for Students of Differential Equations, Linear Algebra and Others, by Adam E. Parker

Mathematical Treasures

Mathematical Treasures, by Frank J. Swetz

Index to Mathematical Treasures Collection: Images of historical texts and objects from libraries, museums, and individuals around the world for use in your classroom!

Mathematical Treasures added during 2021:

• Filippo Calandri's Trattato di arithmetica (1491)
• Johannes Widman’s Behend und hüpsch Rechnung uff [auf] allen Kauffmanschafften (1508, original 1489)
• Eukleidou Stoicheion (printed Greek-language Euclid’s Elements, 1533)
• Christoff Rudolff’s Die Coss (1553, original 1525)
• Simon Stevin’s L’Arithmetique (1558)
• Rafael Bombelli’s L’Algebra Opera (1579, original 1572)
• Peter Ramus's Arithmeticae libri duo: Geometriae septem et viginti (1580)
• Frans van Schooten’s Latin translation of François Viéte’s works, Opera mathematica (1641)
• Bonaventura Cavalieri’s Geometria indivisibilibus continuorum (1653, original 1635)
• Pierre Varignon’s Élémens de Mathématiques (1731)
• Joseph Fenn’s Instructions Given in the Drawing School (vol. 2, 1772)
• Nathan Daboll’s Schoolmaster’s Assistant (1829, original 1799)
• Benjamin Greenleaf’s Common School Arithmetic (1855)
• Warren Colburn’s First Lessons in Intellectual Arithmetic (1863, original 1821)