When I was taught math, the focus was mostly on the “how”:
- How to multiply numbers.
- How to work with fractions.
- How to use calculus.
- etc..
But even more useful is to know the when:
- When to multiply numbers.
- When to work with fractions.
- When to use calculus.
- etc..
Knowing how to do something is useful, but it’s just knowledge of one tool.
For example, take a hammer. It’s nice to know how to bang in a nail without sending yourself to the hospital, but not all situations require a hammer. To select the best tool for the job, we need to know “when” each tool should (or shouldn’t) be used.
Especially nowadays, where computers can solve so many mathematical problems for us, knowing “when” allows us to navigate choice, and select between multiple tools. Once we select the right tool, then it’s easy to find the resources to teach us the “how” part.
Math catalog
I ran a bunch of Google searches for “when should I use x?”, and collected them into a list:
Addition
Joining multiple items together.
Subtraction
Removing items from a set.
Multiplication
Repeating a set of items.
Division
Breaking a set of items into parts.
Fractions
Working with partial units.
Exponents
Abbreviating large numbers.
Equation & Formulas
Describing how multiple variables relate to each other.
Geometry
Visualizing math with drawings.
Logarithms
Scaling numbers.
Linear algebra
Working with sets of equations.
Logic
A language for reasoning.
Combinatorics
Finding all possible outcomes.
Number theory
Discovering relationships between numbers.
Calculus
Finding aproximate solutions to equations.
Statistics
Gathering, reviewing, analyzing, and drawing conclusions from data.
Machine learning
Extracting algorithms from data.