Classroom Resources Index – Number Theory and Abstract Algebra

Classroom-Ready Resources and Teaching Suggestions

Browse index of informative background articles for number theory and abstract algebra.
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A Series of Mini-projects from TRIUMPHS: TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources
A collection of student-ready modules based on primary historical sources designed to teach standard topics from the curriculum of a wide range of undergraduate courses. Includes the following specific projects suitable for use in Number Theory.

• Generating Pythagorean Triples: A Mini-Primary Source Project in Number Theory for Mathematics Majors, Elementary Teachers and Others, by Janet Heine Barnett
• Lagrange’s Work on Wilson’s Theorem: Three Mini-Primary Source Projects for Number Theory Students, by Carl Lienert
• The Origin of the Prime Number Theorem: A Primary Source Project for Number Theory Students, by Dominic Klyve

Fibonacci and Square Numbers, by Patrick Headley
A discussion of aspects of Leonardo of Pisa's Book of Squares, with suggested questions for student investigation.

The Theorem that Won the War, by Jeff Suzuki
The story of the three Polish mathematicians (Marian Rejewski, Henryk Zygalski, and Jerzy Róẓycki) who first cracked the German encryption system known as Enigma, accompanied by classroom activities that address several key concepts in abstract algebra, including permutation groups, cycle notation, conjugates, and cycle decomposition.

Informative Background Articles

Browse index of classroom-ready resources and teaching suggestions for number theory and abstract algebra.
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A Modern Vision of the Work of Cardano and Ferrari on Quartics, by Harald Helfgott and Michel Helfgott
A study of the solution of quartic equations in Cardano’s Ars Magna and in the work of Euler and Descartes.

Did Euler Know Quadratic Reciprocity?: New Insights from a Forgotten Work, by Paul Bialek and Dominic W. Klyve
The authors use their newly-translated paper of Leonhard Euler to answer their title question.

Divisibility Tests: A History and User's Guide, by Eric L. McDowell
Discoveries, rediscoveries, and generalizations of these tests to pique students' interest.

Math Origins: Orders of Growth and Math Origins: The Totient Function, 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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