# Mathematics Summer Program

High-School Program, *Institute for STEM Education, Stony Brook University*, 2019

I have been selected by David Kahn to be an instructor for the Mathematics Summer Program. Below, you can find the contents of the mini-courses that I taught, with a breakdown of the topics for each lecture.

# Summer 2019 – *An Introduction to Logic with Puzzles and Mysteries*

For this summer, I taught an introductory course on logic. This was a great addition to the existing catalog of courses offered in this program since this specific course had never been taught before!

## Day 1

An introduction to the mathematics of arguments: how can we formulate arguments mathematically? What is the difference between a sound argument and a valid argument? After exploring these notions, we dive into various methods of proof, and put our knowledge to the test with a little Sherlock Holmes mystery.

## Day 2

We go further into our discovery of logic by introducing conditionals and various rules of inference. We also introduce the Fitch format and learn how to use the rules of inference via various exercises. We conclude with a challenging logic puzzle created by Lewis Carroll.

Here is the handout for this mini-course.

# Summer 2020 – *The Calculus of Logic Gates*

For this summer, I taught an introductory course on logic gates. I tried to mix and match by incorporating some basics of mathematical logic along with a (sequent) calculus-type approach using Boolean algebra.

## Day 1

A brief introduction to mathematical logic: propositions, logical connectors, truth tables, and their formulations in terms of Boolean algebra.

## Day 2

Introduction to logic gates: NOT, AND, and OR along with their combinations. Applications of logic gates to logic circuits, and connections to Boolean algebra.