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

Editors: Janet Beery, Kathleen Clark

Articles

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) Huffman

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 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:

Mesopotamian Accounting Tokens: Mesopotamian accounting evolved from simple clay token counters to a number-recording system that included depictions of these tokens on clay tablets.
The Best Known Old Babylonian Tablet?: YBC 7289, though written by a scribal student, contains an excellent estimate of the square root of 2 and shows how to use it to obtain the length of the hypotenuse of any isosceles right triangle.
Babylonian Scribal Exercises: From the collection of Jöran Friberg, images of four clay tablets containing geometry problems for ancient Mesopotamian scribes-in-training
Euclid Proposition on Papyrus: One of the oldest extant text fragments from Euclid's Elements is Proposition II.5, from first century Egypt.
An Egyptian Student’s Math Tablet: A wooden tablet from 5th or 6th century Egypt contains multiplication facts (doubling and halving) from ancient Egypt.
The Archimedes Palimpsest: Modern photographic techniques reveal layers of meaning in this long lost medieval manuscript.
The Peutinger Map: Road map of the ancient Roman world, compiled in 1265 from maps dating back to the time of Agrippa (c. 64-12 BCE)
Problems from the Zibaldone da Canal: Colorful images from a 14th century 'notebook' of arithmetic and other practical information
Ratdolt's Euclid's Elements: Images of the first printed edition of Euclid's Elements (1482)
Ptolemy’s Almagest: Images from Petri Liechtenstein's first complete Latin edition (1515) of Ptolemy's second century Almagest
Cuthbert Tunstall's De arte supputandi: Images from a 1529 edition of the first arithmetic book published in England
Oronce Fine's Protomathesis: Fine presented arithmetic, geometry, trigonometry, instrument-making, and astronomy in this 1532 compendium.
Peter Apian’s Cosmographia: This 1545 version, like the 1524 original, was a “description of the World ... also the Sun, Moon and Stars and of the Heavens.”
Copernicus' De revolutionibus: Images from the book in which Copernicus presented his heliocentric theory, arguing that the planets, including the Earth, rotated about the Sun
Jacques Peletier's l'Algebra: This 1554 book was popular in France for 30 years after its publication.
Sumario Compendioso: Book on arithmetic and gold and silver assaying, published in 1556 in Mexico City
Wenzel Jamnitzer's Platonic Solids: Sampling of 120 exquisitely detailed engravings of perspectives and variations on the Platonic solids
Stratioticos, by Leonard and Thomas Digges: Images from the 1579 manual (in English) on the mathematics of war
Robert Tanner's A Mirror for Mathematiques: Images from a 16th century text about the astrolabe and its uses
George Waymouth's Jewell of Artes (1604): Images from a beautifully illustrated book of practical mathematics designed to impress King James I of England
Specula mathematica of Roger Bacon: A 1614 collection of Roger Bacon's 13th century writings on applications of mathematics
Euclid in China: Two early translations of Euclid's Elements into Chinese (17th century)
John Napier's Mirifici logarithmorum: Famous 1614 publication in which Napier introduced logarithms
John Napier's Rabdologiae: Arithmetic text and how-to manual for constructing and using "Napier rods"
Arithmetica logarithmica of Henry Briggs: Images from the 1624 work in which Briggs presented his base 10 logarithms, along with many examples of their use in geometry
Japanese Temple Mathematics: Images from the Jinkō-ki, originally published in 1627, and challenge problems presented to temple-goers on wooden plaques
LeDuke's Arithmetical Questions: Images from a 17th century English arithmetic book by a French teacher, probably for English gentry
The Mariner's Magazine: 17th century British sea captain Samuel Sturmy applied mathematics to navigation and naval gunnery.
Edward Cocker's Arithmetick: Image of the title page of the second volume (1685) of the most popular arithmetic book in England from its publication in 1673 through the 18th century
Moxon's Mathematical Dictionary: Or Mathematicks Made Easie (1679), the first known English language mathematics dictionary
Traite de la Lumiere of Huygens: Treatise in which Christiaan Huygens presented his wave theory of light (1690)
l’Hospital’s Differential Calculus: Analyse des Infiniment Petits, published by the Marquis de l’Hospital in 1696, was the first calculus text for a popular audience.
Jacques Ozanam’s Récréations: Images of geometry problems from this 1698 French book of recreational mathematics and physics problems
Mary Serjant's Copybook (1688): Images from the handwritten copybook of a 15-year-old girl learning penmanship and arithmetic
Matthew Wood's Copybook (1699): Images from a handwritten copybook presenting counting and arithmetic needed by merchants
Newton's Method of Fluxions: Isaac Newton's fluxions (derivatives) and infinite series
Newton's Principia Mathematica: Isaac Newton's great work of natural philosophy
Euler's Elements of Algebra: Images from an 1828 English translation of the influential Algebra first published in 1770
Farrar's Translation of Lacroix's Algebra: Farrar first translated Lacroix's 1818 Algebra for his Harvard students in 1825.
De Morgan's Formal Logic: Images of discussion of fallacies from Formal Logic (1847) and first page of an article on learning mathematics (1831)
Playfair's Elements of Geometry: Euclid's Elements as presented by John Playfair, of Playfair's Axiom fame
Dodgson's Defense of Euclid: In Euclid and His Rivals (1879), Charles Dodgson (a.k.a. Lewis Carroll) argued for teaching classical Euclidean geometry.
Geometry of Jakob Steiner: Posthumously published lectures of "one of the greatest pure geometers"
Works of Abel and Galois: Collected articles on algebraic equations by the short lived mathematicians
Darboux on Orthogonality: Differential geometry text for circa 1900 l'Ecole Polytechnique students
Ernst Mach's Space and Geometry: The physicist and philosopher argued that geometric space differs from physiological space.
Lobachevski's New Geometries: Images from the first widely available English translation of Lobachevski's non-Euclidean geometry