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Articles 61 - 90 of 93
Full-Text Articles in Education
Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett
Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett
Analysis
No abstract provided.
A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville
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.
The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville
The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville
Topology
No abstract provided.
The Derivatives Of The Sine And Cosine Functions, Dominic Klyve
The Derivatives Of The Sine And Cosine Functions, Dominic Klyve
Calculus
No abstract provided.
Construction Of The Figurate Numbers, Jerry Lodder
Construction Of The Figurate Numbers, Jerry Lodder
Number Theory
No abstract provided.
Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett
Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett
Number Theory
No abstract provided.
Pascal's Triangle And Mathematical Induction, Jerry Lodder
Pascal's Triangle And Mathematical Induction, Jerry Lodder
Number Theory
No abstract provided.
Babylonian Numeration, Dominic Klyve
Primes, Divisibility, And Factoring, Dominic Klyve
Primes, Divisibility, And Factoring, Dominic Klyve
Number Theory
No abstract provided.
Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett
Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett
Number Theory
No abstract provided.
Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg
Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg
Linear Algebra
No abstract provided.
A Genetic Context For Understanding The Trigonometric Functions, Danny Otero
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 …
An Introduction To A Rigorous Definition Of Derivative, Dave Ruch
An Introduction To A Rigorous Definition Of Derivative, Dave Ruch
Analysis
No abstract provided.
Euler's Rediscovery Of E With Instructor Notes, Dave Ruch
Euler's Rediscovery Of E With Instructor Notes, Dave Ruch
Analysis
No abstract provided.
Bolzano On Continuity And The Intermediate Value Theorem, Dave Ruch
Bolzano On Continuity And The Intermediate Value Theorem, Dave Ruch
Analysis
No abstract provided.
The Mean Value Theorem, Dave Ruch
Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch
Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch
Analysis
No abstract provided.
Investigating Difference Equations, Dave Ruch
Investigating Difference Equations, Dave Ruch
Discrete Mathematics
No abstract provided.
All They Want To Do Is Dance: A Study Of Dance Education In K-12 Public Schools, Kelsey Jean-Baptiste
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, in …
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.
Miss Snell's Way: A Life-Affirming Organic Model Created In Sport, Robin G. Cash
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 three …
Counting Quality, John Strassburger
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
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.