# Education Commons™

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Ursinus College

Science and Mathematics Education

Articles 31 - 48 of 48

## Full-Text Articles in Education

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.

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.

#### Characteristics Of Stem Success: A Survival Analysis Model Of Factors Influencing Time To Graduation Among Undergraduate Stem Majors, Riley K. Acton

##### Business and Economics Honors Papers

Producing more graduates in Science, Technology, Engineering, and Mathematics (STEM), as well as ensuring students complete college in a timely manner are both areas of national public policy interest. In order to improve these two outcomes, it is imperative to understand what factors lead undergraduate students to persist in, and ultimately graduate with STEM degrees. This paper uses data from the Beginning Postsecondary Students Longitudinal Study, provided by The National Center of Education Statistics, to model the time to baccalaureate degree among STEM majors using a Cox proportional hazard model.