What's in Convergence? - Contents of Volume 10 - 2013 (Loci - Volume 4)

Editors:  Janet Beery, Kathleen Clark


Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection, by Janet Beery and Carol Mead

The well-known mathematician took most of these 343 photos of mathematicians from the 1950s through the 1980s. We welcome you to provide additional information about the photo subjects, including fond memories and interesting stories. This article was an expanding feature throughout 2012 and through March of 2013, with new photos added every week.

HOM SIGMAA 2013 Student Paper Contest Winner

Read "Paradigms and Mathematics: A Creative Perspective," by Hood College graduate Matthew Shives.

Maya Geometry in the Classroom, by John Diamantopoulos and Cynthia Woodburn

Classic Maya people probably used knotted ropes to form desired geometric shapes in art and architecture: here's how!

External Influences on U.S. Undergraduate Mathematics Curricula: 1950-2000, by Walter Meyer

To what extent did forces outside of mathematics influence such curricular changes as increased emphasis on applications and modeling, discrete mathematics, and calculus reform?

Robert Murphy: Mathematician and Physicist, by Anthony J. Del Latto and Salvatore J. Petrilli, Jr.

The authors show that Murphy (1806-1843) displayed “true genius” in a very short life and they provide a transcription of Murphy’s first published work in 1824.

Solving the Cubic with Cardano, by William B. Branson

The author shows how, in order to solve the cubic, Cardano relied on both classical Greek geometric and abbaco traditions. He illustrates Cardano's geometric thinking with modern manipulatives.

Primary Historical Sources in the Classroom: Discrete Mathematics and Computer Science, by Janet Barnett, Guram Bezhanishvili, Hing Leung, Jerry Lodder, David Pengelley, Inna Pivkina, Desh Ranjan, and Maria Zack

Sixteen projects designed to help students learn important concepts from discrete math, combinatorics, linear algebra, and computer science by studying original sources

1.  Deduction through the Ages: A History of Truth, by Jerry Lodder

  • Project in which discrete mathematics students learn about logic, truth tables, and implication by consulting original sources from ancient to modern times

2.  Sums of Numerical Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand, by David Pengelley

  • Project in which discrete math or calculus students learn from Archimedes’ writings how he computed the sum of the squares

3.  Euclid's Algorithm for the Greatest Common Divisor, by Jerry Lodder, David Pengelley, and Desh Ranjan

  • Project in which discrete math, computer science, or number theory students learn the Euclidean Algorithm from Euclid’s writings

4.  An Introduction to Symbolic Logic, by Guram Bezhanishvili and Wesley Fussner

  • Project in which discrete mathematics students learn the basics of symbolic logic by studying excerpts from Russell’s and Whitehead’s Principia Mathematica

5.  An Introduction to Elementary Set Theory, by Guram Bezhanishvili and Eachan Landreth

  • Project in which discrete mathematics students learn the basics of set theory by reading Dedekind’s and Cantor’s original papers on the subject 

6.  Computing the Determinant Through the Looking Glass, by Maria Zack

  • Project in which linear algebra students learn an easy way to compute determinants from a paper by mathematician Charles Dodgson (whose pen name was Lewis Carroll)

7.  Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn, and C. S. Peirce, by Janet Barnett

  • Project in which discrete mathematics students are introduced to set operations, Venn diagrams, and Boolean algebra by the masters

8.  Boolean Algebra as an Abstract Structure: Edward V. Huntington and Axiomatization, by Janet Barnett

  • Project in which discrete math or abstract algebra students develop the 'algebra of logic' along with E. V. Huntington, who built on the work of Boole

9.  Applications of Boolean Algebra: Claude Shannon and Circuit Design, by Janet Barnett

  • Project in which discrete mathematics students apply Boolean algebra to circuit design by studying Claude Shannon’s pioneering paper

10. Figurate Numbers and Sums of Numerical Powers: Fermat, Pascal, Bernoulli, by David Pengelley

  • Project in which students in upper-level discrete math or combinatorics courses learn connections between sums of powers and binomial coefficients by “reading the masters”

11. Gabriel Lamé's Counting of Triangulations, by Jerry Lodder

  • Project in which upper-level discrete mathematics or combinatorics students count triangulations with Lamé and meet the Catalan numbers along the way

12.  Networks and Spanning Trees, by Jerry Lodder 

  • Project in which students in an upper-level discrete math or combinatorics course are introduced to labeled graphs and minimal spanning trees by Cayley, Prüfer, and Boruvka

13.  Striving for Efficiency in Algorithms: Sorting, by Inna Pivkina

  • Project in which computer science students study quicksort, insertion sort, efficiency of algorithms, and stack data structure via its history

14.  Discovery of Huffman Codes, by Inna Pivkina

  • Project in which computer science students learn the fundamentals of information theory by reading the papers of Fano and Huffman

15.  Program Correctness, by Hing Leung

  • Project in which computer science students learn the fundamentals of partial correctness proof from Robert W Floyd’s original paper on the subject

16.  Regular Languages and Finite Automata, by Hing Leung

  • Project in which computer science students discover the connection between these two topics by studying the original paper of S. C. Kleene

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 2012 and 2013:


Review of Mathematical Expeditions: Exploring Word Problems across the Ages, by Frank J. Swetz. Reviewed by Kathleen M. Clark.

A collection of problems that should be of interest and use to teachers at all levels