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Articles 1 - 23 of 23
Full-Text Articles in Education
The Roots Of Early Group Theory In The Works Of Lagrange, Janet Heine Barnett
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 Knudsen, Keith Jones
The Pell Equation In India, Toke Knudsen, Keith Jones
Number Theory
No abstract provided.
Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett
Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett
Number Theory
No abstract provided.
Quantifying Certainty: The P-Value, Dominic Klyve
Quantifying Certainty: The P-Value, Dominic Klyve
Statistics and Probability
No abstract provided.
The Definite Integrals Of Cauchy And Riemann, Dave Ruch
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.
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.