Counting things is hard! The following rules are shortcuts that allow us to count certain collections of things rapidly.… Read More
Categorical vs quantitative variables
Quantitative variables are any variables where the data represent amounts.
Categorical variables are any variables where the data represent groups.… Read More
Probability is a measure that is associated with how certain we are of the outcomes of a particular experiment or activity. An experiment is a planned operation carried out under … Read More
The final exam will be cumulative, covering material from the entire course, with a focus on revisiting secondary school mathematics from new perspectives, especially as a coherent system of related … Read More
Why do we care so much about triangles? Why don’t we have something like “trigonometric functions” for other shapes, like rectangles, pentagons, etc?
Furthermore, why does trigonometry focus on right … Read More
Complex numbers are an area where algebraic and geometric perspectives provide very different strengths and intuitions. Having a firm grasp of both perspectives and being able to switch from one … Read More
The idea of inverse functions is very natural when thought about in the context of functions. Although your students may not have experience with the definition of an … Read More
What does it mean to raise a number to a power?
What if the power is whole number? An integer? A rational number? A real number?
For a specific example, … Read More
The idea of rational functions
“Just like polynomials but division is allowed”
Rational functions are the (smallest) collection of functions satisfying:
- The constant functions and the identity function
Polynomials and their roots
Group activity: Give a definition of polynomial.… Read More