For more details of each project, see Details of Available Projects.

• F1: A Genetic Context for Understanding the Trigonometric Functions
  Author: Danny Otero
  


• F2: Determining the Determinant
  Author: Danny Otero
  


• F3: Solving a System of Linear Equations Using Ancient Chinese Methods
  Author: Mary Flagg
  


• F4: Investigating Difference Equations.
  Author: Dave Ruch
  


• F5: Quantifying certainty: the p-value
  Author: Dominic Klyve
  


• F6: The Exigency of the Parallel Postulate.
  Author: Jerry Lodder
  


• F7: The Failure of the Parallel Postulate.
  Author: Jerry Lodder
  


• F8: Richard Dedekind and the Creation of an Ideal: Early Developments in Ring Theory
  Author: Janet Barnett
  


• F9: Primes, divisibility, and factoring
  Author: Dominic Klyve
  


• F10: The Pell Equation in India
  Author: Keith Jones and Toke Knudsen
  


• F11: Greatest Common Divisor: Algorithm and Proof
  Author: Mary Flagg
  


• F12: The Mobius Inversion Formula
  Author: Carl Lienert
  


• F13: Bolzano on Continuity and the Intermediate Value Theorem
  Author: Dave Ruch
  


• F14: Rigorous Debates over Debatable Rigor: Monster Functions in Introductory Analysis
  Author: Janet Barnett
  


• F15: An Introduction to the Algebra of Complex Numbers and the Geometry in the Complex Plane
  Author: Diana White and Nicholas Scoville
  


• F16: Nearness without distance
  Author: Nicholas Scoville
  


• F17: Connectedness-- its evolution and applications
  Author: Nicholas Scoville
  


• F18: Construction of the Figurate Numbers.
  Author: Jerry Lodder
  


• F19: Pascal's Triangle and Mathematical Induction.
  Author: Jerry Lodder
  


• F20: The French Connection: Borda, Condorcet and the Mathematics of Voting Theory.
  Author: Janet Barnett
  


• F21: An Introduction to a Rigorous Definition of Derivative.
  Author: Dave Ruch
  


• F22: Investigations into Bolzano’s Bounded Set Theorem
  Author: Dave Ruch
  


• F23: The Mean Value Theorem
  Author: Dave Ruch
  


• F24: Abel and Cauchy on a Rigorous Approach to Infinite Series
  Author: Dave Ruch
  


• F25: The Definite Integrals of Cauchy and Riemann
  Author: Dave Ruch
  


• F26: Gaussian Integers and Dedekind's Creation of an Ideal: A Number Theory Project
  Author: Janet Barnett
  


• F27: Otto Holder's Formal Christening of the Quotient Group Concept
  Author: Janet Barnett
  


• F28: The Roots of Early Group Theory in the Works of Lagrange
  Author: Janet Barnett
  


• F29: The Radius of Curvature According to Christiaan Huygens
  Author: Jerry Lodder
  


• F30: Why square root of 2 is a Friendlier Number than e: Irrational Adventures with Aristotle, Fourier, and Liouville
  Author: Kenneth M Monks
  


• F31: Cross Cultural Comparisons: The Art of Computing the Greatest Common Divisor
  Author: Mary Flagg
  


• F32: A Look at Desargues' Theorem from Dual Perspectives
  Author: Carl Lienert
  


• F33: Completing the Square: From the Beginnings of Algebra
  Author: Danny Otero
  


• F34: Argand's Development of the Complex Plane
  Author: Diana White and Nick Scoville
  


• F35: Riemann's Development of the Cauchy-Riemann Equations
  Author: Dave Ruch
  


• F36: Gauss and Cauchy on Complex Integration
  Author: Dave Ruch
  


• F37: Representing and Interpreting Data from Playfair
  Author: Diana White, River Bond, Joshua Eastes, and Negar Janani
  


• F38: Runge-Kutta 4 (and Other Numerical Methods for ODEs)
  Author: Adam Parker
  


• F39: Stitching Dedekind Cuts to Construct the Real Numbers
  Author: Michael P. Saclolo
  


• F40: The Fermat-Torricelli Point and Cauchy's Method of Gradient Descent
  Author: Kenneth M Monks
  


• F41: Stained Glass and Windmills: An Exploration of Green's Theorems
  Author: Abe Edwards
  


• F42.1: Jakob Bernoulli’s Method for Finding Exact Sums of Infinite Series (Calculus Version)
  Author: Danny Otero and James A. Sellers
  


• F42.2: Jakob Bernoulli’s Method for Finding Exact Sums of Infinite Series (Capstone Version)
  Author: Danny Otero and James A. Sellers
  


• F43: Lagrange’s Study of Wilson’s Theorem
  Author: Carl Lienert
  


• F44: Fourier's Heat Equation and the Birth of Fourier Series
  Author: Kenneth M Monks
  


• F45: Gauss and the First ``Rigorous'' Proof of the Fundamental Theorem of Algebra
  Author: Sarah Hagen and Alan Kappler
  


• F46: Three Hundred Years of Helping Others: Maria Gaetana Agnesi on Precalculus
  Author: Kenneth M Monks
  


• F47: Understanding Compactness Through Primary Sources: Early Work Uniform Continuity to the Heine-Borel Theorem
  Author: Naveen Somasunderam
  



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• M1: Babylonian numeration
  Author: Dominic Klyve
  


• M2: L'Hopital's rule
  Author: Danny Otero
  


• M3: The Derivatives of the Sine and Cosine Functions
  Author: Dominic Klyve
  


• M4: Beyond Riemann Sums
  Author: Dominic Klyve
  


• M5: Fermat's Method for Finding Maxima and Minima
  Author: Ken Monks
  


• M6: Euler's Calculation of the Sum of the Reciprocals of the Squares
  Author: Kenneth M Monks
  


• M7: Braess' Paradox in City Planning: An Application of Multivariable Optimization
  Author: Ken Monks
  


• M8: The Origin of the Prime Number Theorem


• M9: How to Calculate pi: Machin's Inverse Tangents
  Author: Dominic Klyve
  


• M10: How to calculate pi - Buffon
  Author: Dominic Klyve
  

  M10.1: How to calculate pi - Buffon's Needle (Non-Calculus Version)


M10.2: How to calculate pi - Buffon's Needle (Calculus Version)


• M11: Bhaskara's Approximation and Madhava's Infinite Series for Sine
  Author: Kenneth M Monks
  


• M12: Fourier's Proof of the Irrationality of e
  Author: Kenneth M Monks
  


• M13-15: Gaussian Guesswork
  Author: Janet Barnett
  
  M13: Gaussian Guesswork: Elliptic Integrals and Integration by Substitution
  M14: Gaussian Guesswork: Polar Coordinates, Arc Length and the Lemniscate Curve
  M15: Infinite Sequences and the Arithmetic-Geometric Mean



• M16: The logarithm of -1.
  Author: Dominic Klyve
  


• M17: Why be so Critical? Nineteenth Century Mathematics and the Origins of Analysis
  Author: Janet Barnett
  


• M18: Topology from Analysis: Making the Connection.
  Author: Nick Scoville
  


• M19: Connecting Connectedness.
  Author: Nick Scoville
  


• M20: The Cantor Set before Cantor
  Author: Nick Scoville
  


• M21: A compact introduction to a generalized extreme value theorem
  Author: Nick Scoville
  


• M22: From sets to metric spaces to topological spaces
  Author: Nick Scoville
  


• M23: The closure operation as the foundation of topology.
  Author: Nick Scoville
  


• M24: Euler's Rediscovery of e.
  Author: Dave Ruch
  


• M25: Henri Lebesgue and the Development of the Integral Concept
  Author: Janet Barnett
  


• M26: Generating Pythagorean Triples via Gnomons: available in two versions.
  Author: Janet Barnett
  

  M26.1: Generating Pythagorean Triples via Gnomons: The Methods of Pythagoras and of Plato via Gnomons
  M26.2: Generating Pythagorean Triples via Gnomons: A Gnomonic Exploration



• M27: Seeing and Understanding Data
  Author: Beverly Wood and Charlotte Bolch
  


• M28: Completing the Square: From the Roots of Algebra
  Author: Danny Otero
  


• M29: Euler's Square Root Laws for Negative Numbers
  Author: Dave Ruch
  


• M30: Investigations Into d'Alembert's Definition of Limit
  Author: Dave Ruch
  

  M30.1: Investigations Into d'Alembert's Definition of Limit - Calculus Version
  M30.2: Investigations Into d'Alembert's Definition of Limit - Real Analysis Version



• M31: Playfair's Introduction of Bar Graphs and Pie Charts to Represent Data
  Authors: Diana White, River Bond, Joshua Eastes, and Negar Janani
  


• M32: Playfair's Introduction of Time Series to Represent Data
  Author: Diana White, River Bond, Joshua Eastes, and Negar Janani
  


• M33: Playfair's Novel Visual Displays of Data
  Author: Diana White, River Bond, Joshua Eastes, and Negar Janani
  


• M34: Regression to the mean
  Author: Dominic Klyve
  


• M35-37: Solving Linear First Order Differential Equations
  Author: Adam E. Parker
  


• M35: Solving First-Order Linear Differential Equations: Gottfried Leibniz' "Intuition and Check" Method
  
• M36: Solving Linear First Order Differential Equations: Johann Bernoulli’s Variation of Parameters
  
• M37: Solving Linear First Order Differential Equations: Leonard Euler’s Integrating Factor
  

• M38: Wronskians and Linear Independence: A Theorem Misunderstood by Many
  Author: Adam E. Parker
  


• M39: Leonhard Euler and Johann Bernoulli on Solving Higher Order Linear Differential Equations with Constant Coefficients
  Author: Adam Parker
  


• M40: Fourier's Heat Equation
  Author: Kenneth M Monks
  


• M41: The Trigonometric Functions Through Their Origins: Babylonian Astronomy and Sexagesimal Numeration
  Author: Danny Otero
  


• M42: The Trigonometric Functions Through Their Origins: Hipparchus' Table of Chords
  Author: Danny Otero
  


• M43: The Trigonometric Functions Through Their Origins: Ptolemy Finds High Noon in Chords of Circles
  Author: Danny Otero
  


• M44: The Trigonometric Functions Through Their Origins: Varahamihira and the Poetry of Sines
  Author: Danny Otero
  


• M45: The Trigonometric Functions Through Their Origins: al-Biruni Does Trigonometry in the Shadows
  Author: Danny Otero
  


• M46: The Trigonometric Functions Through Their Origins: Regiomontanus and the Beginnings of Modern Trigonometry
  Author: Danny Otero
  


• M47: Lagrange’s Proof of Wilson’s Theorem—and More!
  Author: Carl Lienert
  


• M48: Lagrange's Proof of the Converse of Wilson's Theorem
  Author: Carl Lienert
  


• M49: Lagrange’s Alternate Proof of Wilson’s Theorem
  Author: Carl Lienert
  


• M50: Three Hundred Years of Helping Others: Maria Gaetana Agnesi on Exponents
  Author: Kenneth M Monks
  


• M51: Three Hundred Years of Helping Others: Maria Gaetana Agnesi on Rational Root Theorem
  Author: Kenneth M Monks
  


• M52: Three Hundred Years of Helping Others: Maria Gaetana Agnesi on Radicals
  Author: Kenneth M Monks
  


• M53: Three Hundred Years of Helping Others: Maria Gaetana Agnesi on the Product Rule
  Author: Kenneth M Monks
  

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