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## Full-Text Articles in Education

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

#### 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

#### 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

#### 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

#### 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

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

*Geometry*

No abstract provided.

Topology From Analysis, Nicholas A. Scoville

#### 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

#### 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