Classroom Resources Index – Discrete Mathematics, Combinatorics, and Probability

Classroom-Ready Resources and Teaching Suggestions

Browse index of informative background articles for discrete mathematics and combinatorics.
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Discrete Mathematics

Extending al-Karaji’s Work on Sums of Odd Powers of Integers, by Hasan Unal and Hakan Kursat Oral
The authors share their discovery of an 1867 article in a Turkish scientific journal that extends al-Karaji’s famous formula for the sum of the cubes to sums of higher odd powers, with suggested exercises.

Primary Historical Sources in the Classroom: Discrete Mathematics and Computer Science
A collection of projects designed to help students learn concepts in discrete mathematics, combinatorics, linear algebra and computer science by studying primary historical sources, with an overview of the benefits of this approach to teaching and learning. Includes the following specific projects suitable for use in Discrete Mathematics.

• An Introduction to Elementary Set Theory, by Guram Bezhanishvili and Eachan Landreth
• An Introduction to Symbolic Logic, by Guram Bezhanishvili and Wesley Fussner
• Applications of Boolean Algebra: Claude Shannon and Circuit Design, by Janet Heine Barnett
• Boolean Algebra as an Abstract Structure: Edward V. Huntington and Axiomatization, by Janet Heine Barnett
• Deduction through the Ages: A History of Truth, by Jerry Lodder
• Euclid’s Algorithm for the Greatest Common Divisor, by Jerry Lodder, David Pengelley and Desh Ranjan
• Figurate Numbers and Sums of Numerical Powers: Fermat, Pascal, Bernoulli, by David Pengelley
• Gabriel Lamé’s Counting of Triangulations, by Jerry Lodder
• Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce, by Janet Heine Barnett
• Sums of Numerical Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand, by David Pengelley

Sums of Powers of Positive Integers, by Janet Beery
A history of attempts to develop formulas expressing the sums of powers of the first n positive integers from the Pythagoreans to Jakob Bernoulli, with exercises (and their solutions) for students.

Combinatorics

Extending al-Karaji’s Work on Sums of Odd Powers of Integers, by Hasan Unal and Hakan Kursat Oral
The authors share their discovery of an 1867 article in a Turkish scientific journal that extends al-Karaji’s famous formula for the sum of the cubes to sums of higher odd powers, with suggested exercises.

Primary Historical Sources in the Classroom: Discrete Mathematics and Computer Science
A collection of projects designed to help students learn concepts in discrete mathematics, combinatorics, linear algebra and computer science by studying primary historical sources, with an overview of the benefits of this approach to teaching and learning. Includes the following specific projects suitable for use in courses on combinatorics:

• Figurate Numbers and Sums of Numerical Powers: Fermat, Pascal, Bernoulli, by David Pengelly
• Gabriel Lamé’s Counting of Triangulations, by Jerry Lodder
• Networks and Spanning Trees, by Jerry Lodder
• Sums of Numerical Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand, by David Pengelly

Sums of Powers of Positive Integers, by Janet Beery
A history of attempts to develop formulas expressing the sums of powers of the first n positive integers from the Pythagoreans to Jakob Bernoulli, with exercises (and their solutions) for students.

Probability

A Selection of Problems from A.A. Markov’s Calculus of Probabilities, by Alan Levine
Translation of excerpts from Markov's Calculus of Probabilities (1900), with suggestions for classroom use.

Informative Background Articles

Browse index of classroom-ready resources and teaching suggestions for discrete mathematics and combinatorics.
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Discrete Mathematics

Math Origins: The Logical Ideas and Math Origins: The Logical Symbols, by Erik Tou
Two articles from the Math Origins series in which the author explores how concepts, definitions, and theorems familiar to today's students of mathematics developed over time.

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