Classroom Resources Index – Real Analysis

Classroom-Ready Resources and Teaching Suggestions

Browse index of informative background articles for real analysis, topology, and complex variables.
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Real Analysis

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 Introductory Real Analysis.

• Euler's Rediscovery of e: A Mini-Primary Source Project for Introductory Analysis Students, by Dave Ruch
• Investigations Into d'Alembert's Definition of Limit: A Mini-Primary Source Project for Students of Real Analysis and Calculus 2, by Dave Ruch
• Henri Lebesgue and the Development of the Integral Concept: A Mini-Primary Source Project for Undergraduate Analysis Students, by Janet Heine Barnett
• The Cantor Set Before Cantor: A Mini-Primary Source Project for Analysis and Topology Students, by Nicholas A. Scoville
• Why be so Critical? Nineteenth-Century Mathematics and the Origins of Analysis: A Mini-Primary Source Project for Introductory Analysis Students, by Janet Heine Barnett

An Analysis of the First Proofs of the Heine-Borel Theorem, by Nicole Andre, Susannah Engdahl, and Adam Parker
A comparison of five circa-1900 proofs of the famous theorem with a view toward improving student understanding of compactness.

François-Joseph Servois: Priest, Artillery Officer, and Professor of Mathematics, by Salvatore J. Petrilli, Jr.
An analysis and English translation of the argument by a little-known 19th-century French mathematician that calculus should be based on series rather than on infinitesimals, with suggestions for using Sevois’ paper with students.

Servois’ 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation, by Robert E. Bradley and Salvatore J. Petrilli, Jr.
A study and English translation of Servois’ attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange, with suggestions for using Sevois’ paper with students.

Topology

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 Introductory Real Analysis.

• A Compact Introduction to a Generalized Extreme Value Theorem: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
• Connecting Connectedness: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
• The Cantor Set Before Cantor: A Mini-Primary Source Project for Analysis and Topology Students, by Nicholas A. Scoville
• Topology from Analysis: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville

Complex Variables

The Logarithm of −1: A Mini-Primary Source Project for Complex Variables Students, by Dominic Klyve
One of a collection of student-ready modules based on primary historical sources presented in the article A Series of Mini-projects from TRIUMPHS: TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources.

Informative Background Articles

Browse index of classroom-ready resources and teaching suggestions for real analysis, topology and complex variables.
Return to master index.

Georg Cantor at the Dawn of Point Set Topology, by Nicholas A. Scoville
How the history of analysis, and in particular that of Fourier series, can be used to motivate the study of point-set topology.