# Education Commons™

Articles 31 - 56 of 56

## Full-Text Articles in Education

The Derivatives Of The Sine And Cosine Functions, Dominic Klyve Jul 2017

#### The Derivatives Of The Sine And Cosine Functions, Dominic Klyve

##### Calculus

No abstract provided.

The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville Jul 2017

#### The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville

##### Topology

No abstract provided.

A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville Jul 2017

#### A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville

##### Topology

In a short paper published just one year prior to his thesis, Maurice Frechet gives a simple generalization one what we might today call the Extreme value theorem. This generalization is a simple matter of coming up with ``the right" definitions in order to make this work. In this mini PSP, we work through Frechet's entire 1.5 page paper to give an extreme value theorem in more general topological spaces, ones which, to use Frechet's newly coined term, are compact.

Mar 2017

#### A Genetic Context For Understanding The Trigonometric Functions, Danny Otero

##### Pre-calculus and Trigonometry

In this project, we explore the genesis of the trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. The goal is to provide the typical student in a pre-calculus course some context for understanding these concepts that is generally missing from standard textbook developments. Trigonometry emerged in the ancient Greek world (and, it is suspected, independently in China and India as well) from the geometrical analyses needed to solve basic astronomical problems regarding the relative positions and motions of celestial objects. While the Greeks (Hipparchus, Ptolemy) recognized the usefulness of tabulating chords of central angles in a circle as aids ...

Investigating Difference Equations, Dave Ruch Jan 2017

#### Investigating Difference Equations, Dave Ruch

##### Discrete Mathematics

No abstract provided.

#### Bolzano's Definition Of Continuity, His Bounded Set Theorem, And An Application To Continuous Functions, Dave Ruch

##### Analysis

No abstract provided.

The Mean Value Theorem, Dave Ruch Jan 2017

#### The Mean Value Theorem, Dave Ruch

##### Analysis

No abstract provided.

Jan 2017

#### Euler's Rediscovery Of E With Instructor Notes, Dave Ruch

##### Analysis

No abstract provided.

Jan 2017

#### An Introduction To A Rigorous Definition Of Derivative, Dave Ruch

##### Analysis

No abstract provided.

Jan 2017

#### Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch

##### Analysis

No abstract provided.

#### Investigations Into D'Alembert's Definition Of Limit: A Student Project With Primary Sources, Dave Ruch

##### Analysis

No abstract provided.

All They Want To Do Is Dance: A Study Of Dance Education In K-12 Public Schools, Kelsey Jean-Baptiste Jul 2016

#### All They Want To Do Is Dance: A Study Of Dance Education In K-12 Public Schools, Kelsey Jean-Baptiste

##### Dance Summer Fellows

This project involves investigating the value of dance within a student’s life. The research has included a variety of facets of dance - how it is related to brain/neuroscience research and motor skills; how it is fun and an opportunity to learn in a different way; and how it enhances academics, mental stability, and social interactions. The bulk of the study included examining past and current national studies that investigated the effects of dance education within the K-12 school setting. Also included were two on-site visits pertinent to the study: one was a visit to a Philadelphia dance classroom ...

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.

Apr 2016

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

##### Geometry

No abstract provided.

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.

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.

Jan 2002

#### Miss Snell's Way: A Life-Affirming Organic Model Created In Sport, Robin G. Cash

##### Eleanor Frost Snell Programs, Correspondence and Other Documents

This 156 page dissertation by Robin G. Cash, Ursinus College Class of 1972, was submitted to the faculty of Fielding Graduate Institute in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Human and Organizational Systems.

The dissertation explores a women’s way of coaching and being in sport that existed prior to Title IX. It considers a shift from an organic to a mechanistic coaching approach. An alternative model based on the concept of organicism and underlying principles of relational power, life-affirming actions, and inclusiveness of all beings is presented. This new model emerged from ...

Counting Quality, John Strassburger Jan 2000

#### Counting Quality, John Strassburger

##### Publications

This is the fifth in a series of occasional papers about the challenges confronting students and what Ursinus is doing to help them enter adult life.

Transforming Experiences: The Benefits Of Intellectual Risk, John Strassburger Jan 1999

#### Transforming Experiences: The Benefits Of Intellectual Risk, John Strassburger

##### Publications

This is the fourth in a series of occasional papers about the challenges confronting students and what Ursinus is doing to help them enter adult life.

Tales Out Of School: Six Secrets From Successful Teachers, John Strassburger Jan 1998

#### Tales Out Of School: Six Secrets From Successful Teachers, John Strassburger

##### Publications

This is the third in a series of occasional papers about the challenges confronting students and what Ursinus is doing to help them enter adult life.

Writing For Their Lives, John Strassburger Jan 1997

#### Writing For Their Lives, John Strassburger

##### Publications

This is the second in a series of occasional papers about the challenges confronting students and what Ursinus is doing to help them enter adult life.

Education For Self-Reliance, Responsibility And Hope, John Strassburger Jan 1996

#### Education For Self-Reliance, Responsibility And Hope, John Strassburger

##### Publications

This is the first in a series of occasional papers about the challenges confronting students and what Ursinus is doing to help them enter adult life.