Sum list coloring
- Survey of sum list coloring — This is a slightly updated version of a survey article I wrote for Graph Theory Notes of New York in 2006.
- Sum choice numbers of some graphs — Introduction to sum list coloring and some techniques. Published in Discrete Mathematics, 309 (2009), 2166-2173.
- The sum choice number of P3 □ Pn — It introduces some techniques and uses them to compute the sum choice number of the Cartesian product P3 □ Pn. Published in Discrete Applied Mathematics, 160 (2012), 1126–1136.
- My dissertation — This is my 2006 dissertation on sum list coloring.
Presentations given at MathFest
- Probability Questions from the Game Pickomino — Using the game Pickomino for teaching probability, along with some interesting questions for projects based on the game.
- Using Python in a Numerical Methods Course — A few ways I've used Python in Numerical Methods, including class demos, homework, and project ideas.
- Surprises from iterating discontinuous functions — Unusual images created by iterating discontinuous functions in the complex plane.
- Some different applications of logarithms Some of the applications of logs I've been collecting that are different from the ones usually covered in textbooks.
- Patterns and number theory — Given a function fdefined on the integers and an integer n, we examine plots of all the points (x,y) for which n divides f(x,y). The plots are visually interesting and have connections to topics in number theory, such as Fermat's Theorem about sums of squares.
- A 200-Question, Campus-wide Math Contest — About a math contest we ran in 2008.
Presentations given at sectional MAA meetings
- Using standards-based grading in all classes — Some of the details of a standards-based approach to grading that I've used.
- Fun with L(2,1)-labeling — An intro to L(2,1)-labeling, a little about what's known about it, how I've used it in classes, and an app to play it as a puzzle.
- Some unusual mathematical images and the math behind them — Saturday morning lecture given on how I generate fractal images, along with a gallery of some fun ones.
- Some Original Estimation/Fermi Problems — Some estimation problems I've developed over the years for use in my department's core math class.
- Exercises for a Numerical Methods Class — A variety of exercises for a Numerical Methods class that are different from what is typically found in textbooks.
- Probability Questions from the Game Pickomino — Using the game Pickomino for teaching probability, along with some interesting questions for projects based on the game.
- Automatic differentiation — An alternative to numerical differentiation that is not as well known as it should be. Here is the Python code from the presentation.
- Creative approaches to Discrete Mathematics — A collection of interesting problems that I've used in my Discrete Math classes.
- Some different applications of logarithms — Some of the applications of logs I've been collecting that are different from the ones usually covered in textbooks.
- Some bizarre mathematical images — Some of the more unusual images I've created by iterating functions in the complex plane, with a particular focus on the floor function.
- Iterating the complex logarithm — Interesting images from iterating f(z)=c·log(z)
- Iterating a discontinuous function — Images created from iterating a pretty simple discontinuous function in the complex plane.
- Patterns and number theory — Given a function fdefined on the integers and an integer n, we examine plots of all the points (x,y) for which n divides f(x,y). The plots are visually interesting and have connections to topics in number theory, such as Fermat's Theorem about sums of squares.
- Hidden patterns in functions — Given a function f(x,y) and real numbers a and b, we examine plots of f(x,y) mod 2 for (x,y) from the lattice {(ja,kb) : j, k are integers}.
- Patterns and fractals from a generalized bitwise and — About a way to generalize the bitwise AND function to produce some fractal relatives of the Sierpinski triangle.
- A 200-question, campus-wide math contest — About a math contest we ran in 2008.
Colloquium Talks
- Beautiful images from some simple formulas — Various interesting images of contour maps and different kinds of fractals, along a little about the math used to generate them.
- e — All about Euler's constant e.
Smalltalks
- Asking for too much — A talk about things that are impossible, including Arrow's Impossibility Theorem, the Halting Problem, and Gödel's First Incompleteness Theorem.
- Conway's Game of Life — An introduction to the game and how complex phenomena can arise from simple rules. Here is the program used for demonstrations and here is a text file of some of the patterns explored in the talk.
- The Birthday Problem — A famous problem about how many people there need to be in a room for two of them to share a birthday, and its connections to computer security.
- The Poincaré Conjecture — An down-to-earth explanation of the conjecture and the story of its solution.
- Newton's Method, Chaos, and Fractals — How Newton's Method works and some surprises arising from it, including chaos and fractals.
- Dates — The math and history behind leap years, leap seconds, and dates.
- The Mathematics of Bitcoin — A little about the math that makes bitcoin work.
- The Hardest Problem — About the P=NP problem.
- Questions of Prime Importance — Various solved and unsolved problems involving prime numbers.
- Functions of two variables from an artistic perspective, slideshow — Interesting images made from plots of functions of two variables.
- The Mandelbrot Set — Presentation on the Mandelbrot set. (mandelbrot.py, mandelbrot.java)
- Is it all in your imagination? — Presentation on imaginary numbers.
- e — Presentation on Euler's constant, e.
- Rubik's Cubes — The mathematics of the Rubik's Cube and how to solve it.
- A Million Dollar Question — About the Birch Swinnerton-Dyer conjecture.