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Articles 1 - 8 of 8

Full-Text Articles in Education

The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder Jul 2016

The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder

Geometry

No abstract provided.


Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett Jul 2016

Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett

Analysis

No abstract provided.


Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett Jul 2016

Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett

Abstract Algebra

No abstract provided.


Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett Jul 2016

Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett

Analysis

No abstract provided.


The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder Apr 2016

The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder

Geometry

No abstract provided.


Topology From Analysis, Nicholas A. Scoville Apr 2016

Topology From Analysis, Nicholas A. Scoville

Topology

Topology is often described as having no notion of distance, but a notion of nearness. How can such a thing be possible? Isn't this just a distinction without a difference? In this project, we will discover the notion of nearness without distance by studying the work of Georg Cantor and a problem he was investigating involving Fourier series. We will see that it is the relationship of points to each other, and not their distances per se, that is a proper view. We will see the roots of topology organically springing from analysis.


The Cantor Set Before Cantor, Nicholas A. Scoville Apr 2016

The Cantor Set Before Cantor, Nicholas A. Scoville

Topology

A special construction used in both analysis and topology today is known as the Cantor set. Cantor used this set in a paper in the 1880s. Yet it appeared as early as 1875 in a paper by the Irish mathematician Henry John Stephen Smith (1826 - 1883). Smith, who is best known for the Smith normal form of a matrix, was a professor at Oxford who made great contributions in matrix theory and number theory. In this project, we will explore parts of a paper he wrote titled On the Integration of Discontinuous Functions.


Connecting Connectedness, Nicholas A. Scoville Apr 2016

Connecting Connectedness, Nicholas A. Scoville

Topology

No abstract provided.