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Full-Text Articles in Education

How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve Apr 2019

How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve

Pre-calculus and Trigonometry

No abstract provided.


An Introduction To The Algebra Of Complex Numbers And The Geometry In The Complex Plane, Nicholas A. Scoville, Diana White Apr 2019

An Introduction To The Algebra Of Complex Numbers And The Geometry In The Complex Plane, Nicholas A. Scoville, Diana White

Complex Numbers

No abstract provided.


Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg Apr 2019

Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

Number Theory

No abstract provided.


Connectedness- Its Evolution And Applications, Nicholas A. Scoville Apr 2019

Connectedness- Its Evolution And Applications, Nicholas A. Scoville

Topology

No abstract provided.


Dual Perspectives On Desargues' Theorem, Carl Lienert Oct 2018

Dual Perspectives On Desargues' Theorem, Carl Lienert

Geometry

No abstract provided.


The Logarithm Of -1, Dominic Klyve Oct 2018

The Logarithm Of -1, Dominic Klyve

Complex Numbers

No abstract provided.


Seeing And Understanding Data, Beverly Wood, Charlotte Bolch Oct 2018

Seeing And Understanding Data, Beverly Wood, Charlotte Bolch

Statistics and Probability

No abstract provided.


The Origin Of The Prime Number Theorem, Dominic Klyve Oct 2018

The Origin Of The Prime Number Theorem, Dominic Klyve

Number Theory

No abstract provided.


Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett Oct 2018

Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett

Abstract Algebra

No abstract provided.


Yeast: The Gateway To Redefining And Improving Biology Labs, Connor Loomis Jul 2018

Yeast: The Gateway To Redefining And Improving Biology Labs, Connor Loomis

Biology Summer Fellows

Building off of collegiate research performed during the summer of 2018, this lesson plan outlines a lab for secondary students using yeast. Yeast is an affordable and convenient organism to introduce to secondary education, and students can learn a lot about biology through it. Essentially, the goal of the lab is for students to explore the effects of certain substances on the growth of yeast. While content is emphasized, this lesson plan also looks to build students’ understanding of science in general as well as proper laboratory skills and technique. In addition, it pushes students in their thinking as they ...


From Sets To Metric Spaces To Topological Spaces, Nicholas A. Scoville Jul 2018

From Sets To Metric Spaces To Topological Spaces, Nicholas A. Scoville

Topology

No abstract provided.


Determining The Determinant, Danny Otero Jul 2018

Determining The Determinant, Danny Otero

Linear Algebra

No abstract provided.


Nearness Without Distance, Nicholas A. Scoville Jul 2018

Nearness Without Distance, Nicholas A. Scoville

Topology

No abstract provided.


The Roots Of Early Group Theory In The Works Of Lagrange, Janet Heine Barnett Oct 2017

The Roots Of Early Group Theory In The Works Of Lagrange, Janet Heine Barnett

Abstract Algebra

No abstract provided.


The Pell Equation In India, Toke Knudson, Keith Jones Oct 2017

The Pell Equation In India, Toke Knudson, Keith Jones

Number Theory

No abstract provided.


Quantifying Certainty: The P-Value, Dominic Klyve Oct 2017

Quantifying Certainty: The P-Value, Dominic Klyve

Statistics and Probability

No abstract provided.


Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett Oct 2017

Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett

Number Theory

No abstract provided.


Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett Jul 2017

Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett

Number Theory

No abstract provided.


Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett Jul 2017

Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett

Analysis

No abstract provided.


The Definite Integrals Of Cauchy And Riemann, Dave Ruch Jul 2017

The Definite Integrals Of Cauchy And Riemann, Dave Ruch

Analysis

Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.


Pascal's Triangle And Mathematical Induction, Jerry Lodder Jul 2017

Pascal's Triangle And Mathematical Induction, Jerry Lodder

Number Theory

No abstract provided.


Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett Jul 2017

Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett

Number Theory

No abstract provided.


Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg Jul 2017

Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg

Linear Algebra

No abstract provided.


Primes, Divisibility, And Factoring, Dominic Klyve Jul 2017

Primes, Divisibility, And Factoring, Dominic Klyve

Number Theory

No abstract provided.


Babylonian Numeration, Dominic Klyve Jul 2017

Babylonian Numeration, Dominic Klyve

Number Theory

No abstract provided.


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.


Construction Of The Figurate Numbers, Jerry Lodder Jul 2017

Construction Of The Figurate Numbers, Jerry Lodder

Number Theory

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.


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