To supplement my classes, I have been putting together a series of educational interactives in javascript. You are welcome to use them for educational purposes. I've put *s next to my favorites if you're not sure where to get started.
Interactives have been tested in Google Chrome and most have been tested in Firefox, and they may not work or appear correctly in other browsers, particularly Internet Explorer, or on devices with small screens such as phones.
I also make educational videos about logic, teaching, and general mathematics.
Calc 1
The Calculus Carnival Game Explore Approximation and Uncertainty by trying to hit a targebt while moving
*Velocity Interactive worksheet to work towards a formula for Instantaneous Velocity
*Acceleration and Riemann Sums Interactive worksheet to work out the formulas for motion under constant acceleration and constant jerk using Riemann Sums
Limit Visualizer Visualize narrowing in a range of inputs to a function. If the range of outputs also narrows around a value, that's the limit!
Plugging-in-really-close-values Simulator Lecture aid that uses progressively closer upper and lower approximations on a number to approximate plugging it into a function to suggest the ideas of limits
Projectile Motion and Sensitivity Interactive worksheet to explore how changing launch angle affects landing position in projectile motion
Plugging-in-larger-and-larger-numbers Simulator Lecture aid that plugs in large powers of 10 to a fraction to develop intuitions for Limits of Rational Functions as x approaches plus or minus infinity
*Symbolic Differentiation Tool for step-by-step applying the rules of differentiation to demonstrate to students how to Show Intermediate Work for Multi-step Derivative Problems.
Chain Rule Visualizer Lecture aid for visualizing plugging in ranges of values to compositions of functions. This allows one to visualize limits and derivatives of compositions.
Polynomial Division One of my earliest interactives, a widget where one has to guess the quotient and remainder of polynomial division, with hopes of developing the algorithm on one's own.
Sliderules Visualizer for linear, zany, and circular slide rules.
*Transforming Functions Has a visualizer for exploring function transformations, a visualizer for developing an intuition for the relationship between stretching, squashing, and reflecting, and a guessing game interactive for testing one's understanding.
Completing The Square Widget where one has to guess the completing the square form of various quadratic polynomials, with hopes of developing the algorithm on one's own. Also visualizes the guessed function graph.
*The Quadratic Formula Interactive explainer for Using the Quadratic Formula to solve equations and factor polynomials. Generates random examples and has practice problems, and as a bonus walks the user through the algebra for deriving the quadratic formula in the first place.
Lines Practice Practice problem generator for various problems involving lines: Intersections, Reading Graphs, Estimating Slopes, Finding Equations. Shows answers but no walkthroughs.
Logarithm Equivalences Widget Rewriting Logarithms as Exponents, also contains a calculating logarithms problem generator.
Factoring Practice Practice problem generator for Factoring Quadratics. Does not have walkthroughs.
Interval Notation Visualizer for Interval Notation as ranges on a number line.
Parse Trees Parses math formula, allows the user to see their parts.
*Functions, Graphs, and Tables Practice problem generator for Plugging Numbers into Functions by Reading Graphs, Reading Tables, and using Formulas. Also can create basic and complex Composition Problems that evaluate to numbers.
Reading Graphs Quiz Practice problem generator for plugging numbers into functions and solving when f(x) is a particular value given a graph. Has a walkthrough.
Points and Coordinates Small fun widget for practicing finding the Coordinates of Points in the Plane.
*Intersections Between Lines and Conics Practice problem generator for Intersection problems between lines and lines, parabolas, or circles, and solving quadratic equation problems. Has a detailed, step by step, branching walkthrough.
Composing Functions Practice problem generator for Composition problems involving plugging in formulas with an interactive walkthrough.
Reading Graphs Visualizer for plugging in values, and Finding Domains and Ranges of graphs.
Linear Algebra
*Linear Transformations Visualizer for 2x2 matrix transformations, their compositions, determinants and eigenvalues.
Row Reduction Interactive row reduction calculator. Enter or generate a matrix/linear system/matrix to invert, then choose which row reduction operations to apply at each step. Has a walkthrough.
Linear and Affine Span in 3D Visualizer for linear and affine combinations, linear and affine spans, and cross products.
Blending Images Visualizer for linear combinations of images treated as vectors of pixels.
Matrix Powers Visualizer for applying successive powers of a 2x2 matrix to a starting vector.
RREF calculator Calculates Row Reduced Echelon Form and nothing more. User enters a matrix, possibly with fractions.
Linear Regression Widget for generating random data and calculating linear regression lines.
Sample Means Simulation of random sampling from a population.
Lagrange Polynomials Interactive for finding Lagrange Polynomials, walks a user through how to create their own.
Regular Languages and Model Theory
*Ehrenfeucht-Fraïssé Game on Finite Graphs Has an optimal AI to play against. Discovering winning strategies in this game is equivalent to exploring the expressivity of the first order logic of graphs.
What is Model Theory? Landing page for talk given at the Hudson River Undergraduate Mathematics Conference in Spring 2021. See the video here.
Ehrenfeucht-Fraïssé Games on Läuchli-Leonard Linear Orderings No AI. Discovering winning strategies in this game is equivalent to exploring the expressivity of the first order logic of linear orderings. Also has an infinite linear ordering creation and visualization system. These sorts of games originally got me into Model Theory (a branch of logic).
Polynomials: Enterprise Edition A programming game meant to help people get started thinking about Diophantine equations as a programming language, as in the negative solution to Hilbert's Tenth Problem. Created during the Game Maker's Toolkit Jam 2018. See what people had to say about it.
Associativity and Commutativity Computation assistant interactive for exploring the relationship between binary associativity/commutativity and general associativity/commutativity.
Complex "Unit Circle" Visualizer for cross sections of complex solutions to x^2+y^2=1
Platonic Solid Visualizer Visualizes the platonic solids with coordinates of their vertices labeled.
Cartesian and Polar Plots Overlap Visualizer and optimizer looking for approximations to functions whose graphs in Cartesian and polar coordinates overlap.
Libraries
Some interactives make use of the following libraries:
Sage Math Cell (Modified BSD license). Information about calling SageMathCell servers directly can be found here (replace http:// with https:// to avoid a CORS error).