What's in Convergence? - Contents of Volume 21 - 2024

Editors: Amy Ackerberg-Hastings, Daniel E. Otero

Associate Editors: Phil Blau, Eugene Boman, Ximena Catepillan, Abe Edwards, Toke Knudsen, Stacy Langton, Betty Mayfield, Adam Parker, Andrew Perry, Adrian Rice, Laura Turner

Founding Editors: Victor Katz, Frank Swetz

Articles

Pitfalls and Potential Solutions to Your Primary Source Problems, by Adam E. Parker
Suggestions for dealing with difficulties that can arise when an instructor brings primary sources into the mathematics classroom. (posted 12/18/2023)

Ongoing Series

Historical Notes for the Calculus Classroom, by V. Frederick Rickey
A series of short articles on the history of calculus, developed through the author’s experiences with historical research and teaching and written for the use of instructors.

• Series Introduction
• Fermat’s Integration of Powers

Historically Speaking, by Betty Mayfield
Selections from the short columns on historical mathematics that ran in NCTM’s Mathematics Teacher between 1953 and 1969, with new commentary placing the history and mathematics into context.

• Series Introduction
• The Quadrature of the Parabola: An Ancient Theorem in Modern Form, by Carl Boyer with commentary by William Dunham
• The Oldest American Slide Rule, by Phillip S. Jones with commentary by Peggy Aldrich Kidwell
• “Large” Roman Numerals, by Phillip S. Jones with commentary by Victor J. Katz

Quotations in Context, by Michael Molinsky
A series of columns that explores the origins and meanings of various quotations about mathematics and mathematicians.

• Series Introduction
• Albert Einstein
• Alfred North Whitehead
• Bernard Le Bovier de Fontenelle
• Bertrand Russell
• Charles Darwin
• Galileo Galilei (1)
• Galileo Galilei (2)
• Henri Poincaré
• J. Robert Oppenheimer
• James Joseph Sylvester
• John Adams
• Leo Tolstoy
• Napoleon
• Nicolaus Copernicus
• Oliver Wendell Holmes, Jr.
• Plato
• Robert Coveyou
• Voltaire

Keys to Mathematical Treasure Chests
A series that offers examples of how online databases of mathematical objects can be mined to unlock the collections that they preserve for use in research and teaching.

• Series Introduction, by Peggy Aldrich Kidwell
• 19th-century String Models, by Peggy Aldrich Kidwell
• Andean Khipus, by Manuel Medrano
• Classroom Slide Rules, by Amy Ackerberg-Hastings

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 1, 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 2 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 2 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
• Bhāskara’s Approximation to and Mādhava’s Series for Sine: A Mini-Primary Source Project for Calculus 2 Students, by Kenneth M Monks
• The Logarithm of -1: A Mini-Primary Source Project for Complex Variables Students, by Dominic Klyve
• Gaussian Guesswork: Three Mini-Primary Source Projects for Calculus 2 Students, by Janet Heine Barnett
• Fourier’s Heat Equation and the Birth of Modern Climate Science: A Mini-Primary Source Project for Differential Equations and Multivariable Calculus Students, by Kenneth M Monks
• How to Calculate \(\pi\): Buffon's Needle – A Mini-Primary Source Project on Geometric Probability for Calculus 2 Students, Pre-service Teachers and Others, by Dominic Klyve
• Solving Linear Higher Order Differential Equations with Euler and Johann Bernoulli: A Mini-Primary Source Project for Differential Equations Students, by Adam E. Parker
• Fourier’s Infinite Series Proof of the Irrationality of e: A Mini-Primary Source Project for Calculus 2 Students, by Kenneth M Monks
• Fermat’s Method for Finding Maxima and Minima: A Mini-Primary Source Project for Calculus 1 Students, by Kenneth M Monks
• The Closure Operation as the Foundation of Topology: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
• Beyond Riemann Sums: Fermat's Method of Integration – A Mini-Primary Source Project for First-Year Calculus Students, by Dominic Klyve
• Lagrange’s Work on Wilson’s Theorem: Three Mini-Primary Source Projects for Number Theory Students, by Carl Lienert
• Three Hundred Years of Helping Others: Maria Gaetana Agnesi on the Product Rule – A Mini-Primary Source Project for Calculus 1 Students, by Kenneth M Monks
• Solving First-Order Linear Differential Equations: Three Mini-Primary Source Projects for Differential Equations Students, 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 2024:

• Nasīr al-dīn al-Ṭūsī’s Tadhkirah uṣūl handasah al-ḥisāb li-Uqlīdis (Commentary on Euclid’s Elements, 1485, 13th-century original)
• Gaspar Lax’s Arithemetica speculativa (1515)
• Gaspar Lax’s Proportiones (1515)
• Johann Heinrich Alsted’s Methodus admirandorum mathematicorum: complectens novem libris matheseos universae (1613, 1623)
• Ismaël Boulliau’s Exercitationes geometricæ tres (1647)
• Grégoire de Saint-Vincent’s Opus geometricum quadraturae circuli et sectionum coni. Decem libris comprehensum (1647)
• Johann Jakob Heinlin’s Synopsis Mathematica (1653)
• Ismaël Boulliau’s De lineis spiralibus: Demonstrationes novae (1657)
• Christoph Nottnagel’s Synopsis mathematica: continens mathesin generalem, arithmeticam, geometricam, astronomiam, geographiam (1657)
• Johann Placentinus’s Geotomia, sive Terrae sectio, exhibens praecipua & difficiliora problemata (1657)
• Johann Jakob Heinlin’s Synopsis Mathematica Universalis (1663, 1653 original)
• Ismaël Boulliau’s Opus novum ad arithmeticam infinitorum (1682)
• Johann Jakob Heinlin’s Synopsis Mathematica Universalis (1679, 1653 original)
• Antoine Thomas’s Synopsis Mathematica complectens varios tractatus (1685)
• Robert Steell’s A Treatise of Conic Sections (1723)
• Emmanuel Caranza’s Phisicae Particularis Cursus (1730)
• Thomas Simpson’s Mathematical Dissertations on a Variety of Physical and Analytical Subjects (1743)
• The Analyst: or, An Introduction to the Mathematics: Containing the Doctrine of Vulgar and Decimal Fractions (1746)
• Thomas Simpson’s Trigonometry, Plane and Spherical; With the Construction and Application of Logarithms (1748)
• Francis Walkingame’s The Tutor’s Assistant (1752, 1751 original)
• Thomas Simpson’s Elements of Geometry (1760, 1747 original)
• Thomas Simpson’s Select Exercises for Young Proficients in the Mathematicks (edited by Charles Hutton, 1792, 1752 original)
• Thomas Simpson’s Trigonometry, Plane and Spherical; With the Construction and Application of Logarithms (edited by E. L., 1810, 1748 original)
• Alexander Macfarlane’s Principles of the Algebra of Logic (1879)
• Felix Klein’s Riemann'sche Flächen (1892, 1894)
• Felix Klein’s Ueber die hypergeometrische Function (1894)
• Carl David Tolmé Runge’s Graphical Methods (1912)
• Alexander Macfarlane’s Lectures on Ten British Mathematicians of the Nineteenth Century (1916)