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Description: TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS) creates freely downloadable materials for use in the undergraduate mathematics classroom which teaches content based around original mathematical sources such as the writings of Poincaré, Euclid, Lobachevsky, and Hausdorff. Completed PDFs, with exercises and references, include "Richard Dedekind and the Creation of an Ideal: Early Developments in Ring Theory"; "The Derivatives of the Sine and Cosine Functions"; "Rigorous Debates over Debatable Rigor: Monster Functions in Introductory Analysis"; "Euler's Rediscovery of e With Instructor Notes"; "Investigating Difference Equations"; "The Failure of the Euclidean Parallel Postulate and Distance in Hyperbolic Geometry"; "Solving a System of Linear Equations Using Ancient Chinese Methods"; "Gaussian Integers and Dedekind's Creation of an Ideal: A Number Theory Project"; "Babylonian Numeration"; "Construction of the Figurate Numbers"; "Pascal's Triangle and Mathematical Induction"; "A Compact Introduction to a Generalized Extreme Value Theorem"; and "The Cantor Set Before Cantor." Supported in part by the National Science Foundation (NSF).

Levels: College
Languages: English
Resource Types: Lesson Plans and Activities, Problems/Puzzles, Bibliographies
Math Topics: Linear Algebra, Modern Algebra, Analysis, Calculus (Single Variable), Calculus (Multivariable), Communicating Math, Differential Equations, Euclidean Plane Geometry, History and Biography, Number Theory, Topology
Math Ed Topics: Specific Math Concepts/Techniques, Curriculum/Materials Development

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