My interest in education started when I worked as a teaching assistant and tutor in college.
It seems reasonable for each generation to try to help the next generation, as it was helped by the previous generation.
Introduction to a University Mathematics Course in Real Analysis
The project is primarily amed at college students in the second or third year of a mathematics major.
High school students considering a mathematics major may also find it interesting as a preview of what is to come.
The focus is a course in Analysis of Functions of a Real Variable (Real Analysis, for short. Sometimes also called Advanced Calculus).
Taking this course is a significant step on the path of mathematics, much like the step from arithmetic to Algebra or the step from Algebra to Calculus.
The linked page has a short discussion that is intended to ease the transition into this course.
A Cross-Disciplinary Project for High School Students Who Have Taken Calculus
This project was partially motivated by a desire to give my nephews a summer project that could function as a summer internship (minus the income). By the summer before their senior year, they had all taken chemistry and Calculus, and had been exposed to computer programming. In high school, and much of college, courses can focus on a single academic discipline. So I wanted to give them an real world example that combined multiple disciplines.
The tricky part was finding a real problem that they could actually solve with high school coursework (and maybe minimal additions). In this case, I picked a problem in medical diagnostics: analyzing data from Polymerase Chain Reaction, PCR. Many people will recognize PCR as the technology used in one of the covid tests. Solving this problem combines chemistry, mathematics and sofware development.
[This project was field tested in the summer of 2022. I am still working on organizing my notes.]