Courses & Teaching Resources

The Cantor Set Activity  (grades 6-graduate)

This is an interactive Desmos activity that developed and presented at the CMC-S. It helps students make better sense of the decimal system by exploring the Cantor set. It provides an example of how graduate level mathematics can be made approachable to even grade-schoolers through intuition about mathematical ideas developed in the primary and secondary grades. It is a tiered activity so you can stop the activity when the content gets too advanced, but it is designed primarily for grades 6-12. 

Number Visualization Code

This is a link to some bash codes that take a rational number (or a truncated irrational number) and produce an image of that number by assigning a color to each decimal digit, and assigning each digit to a pixel. If you are a bit comfortable with a command line interface, this code helps illuminate the difference between rational and irrational numbers in a visual way that is very satisfying. Some examples are below. Notice the rational numbers exhibit visual patterns but the irrational numbers do not (except perhaps those induced by the pixels in your screen). You can find full size versions of the images below, and others, on my GitHub.

Can I Take Your Ordering?

This is a fun workshop I hosted at the CMC-S in 2023 related to mathematical orderings. The idea to make this workshop was sparked when I asked the question "What letter is above K?" and found that I got differing answers. It gives some survey results and then an introduction to order theory including some brief activities. The workshop covered partial orders, total orders, connections to computer science, and connections to space-filling curves and my pure math research.

COURSES

(All slides made with LaTeX)

MATH 7 - Calculus I

Here are the slides from my current Calculus I course at SMC. We use Stewart, Watson, and Clegg's Calculus - Late Transcendentals - 9th ed.  I haven't made lecture videos for this course yet, but I certainly will in the future. I include a brief discussion of the Riesz-Markov-Kakutani Representation Theorem near the end of this course in Section 5.2. This is an advanced, graduate-level mathematics theorem but, in my opinion, it motivates the study of integration. It also gives students a glimpse into the idea of functionals and the intgeral as a linear function. I refer to this theorem in Calculus II and III as well.

MATH 8 - Calculus II

Here are the slides from my current Calculus II course at SMC, and a link to the lecture videos. We use Stewart, Watson, and Clegg's Calculus - Late Transcendentals - 9th ed.  I include a (brief) lesson in logic in this series just before we get to sequences and series because there are so many subtle theorems that it is good practice to introduce students to some basics of logic. This includes things like conditional statements, converses, inverses, contrapositives, etc.

MATH 11 - Calculus III

Here are the slides from my current Calculus III course at SMC, and a link to the lecture videos. We use Stewart, Watson, and Clegg's Calculus - Late Transcendentals - 9th ed.  I incorporate many lessons in how to use Mathematica as well since every student at SMC has free access to Mathematica and WolframAlpha Pro. In class, we do about half a dozen Mathematica activities where we will graph 3D objects, and use it to solve messy systems of equations like those produced when working with Lagrange multipliers.

MTED 110 - The Real Number System for K-8 Teachers

This is a mathematics education course I taught at CSULB. I've included a link to the lecture videos and the slides. I recommend it to any math majors since, while the topics may be considered elementary, having a firm grasp of them is critical, and you may be surprised at how minimal your understanding of them is. The textbook used is Sowder's Reconceptualizing Mathematics, and the slides cover the first 11 chapters of the book. I usually mix chapters 2 and 3 together when I teach them, and I pull chapter 11 forward to lie between chapters 5 and 6 so that students (future math educators) are exposed to number theory before making sense of fractions.