Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Derived set (2)
- Limit point (2)
- Topology (2)
- Algebra (1)
- Analysis (1)
-
- Axioms (1)
- Cantor set (1)
- Civics (1)
- Connectedness (1)
- Continuity (1)
- Curriculum (1)
- Delta-epsilon (1)
- Democracy (1)
- Disenfranchisement (1)
- Education (1)
- Elements (1)
- Euclid (1)
- Geometry (1)
- High School (1)
- Ideals (1)
- Integration (1)
- Lebesgue integral (1)
- Limit (1)
- Parallel postulate; hyperbolic geometry (1)
- Pythagorean Theorem (1)
- Rings (1)
- Separation (1)
- Understanding by Design (1)
Articles 1 - 9 of 9
Full-Text Articles in Education
Literacy And Citizenship: Helping Students Learn The Importance Of Being An Informed And Educated Citizen, Luke H. Schlegel
Literacy And Citizenship: Helping Students Learn The Importance Of Being An Informed And Educated Citizen, Luke H. Schlegel
English Summer Fellows
My project utilizes the concept of Understanding by Design, as outlined by education experts Jay McTighe and Grant Wiggins, to craft a 12-week curriculum for high school junior and senior English students. McTighe and Wiggins use backwards planning to create long-term learning goals for students. Rather than superficially trying to cover a wide range of material in class, which results in short-term acquisition of knowledge mostly forgotten in the long run, McTighe and Wiggins focus on “big ideas,” that generate conceptual understanding. Ultimately, students will be able to transfer this knowledge to settings outside of the classroom. To help them …
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.
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.
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.
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.
Connecting Connectedness, Nicholas A. Scoville
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.
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 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.