Mathematics foundations
Math Notes
These notes are about the part of mathematics I care about most: understanding why the structure works instead of only memorizing what operation comes next.
One idea that comes up constantly is that mathematical objects can be represented in different ways, and those representations make different things easy to see. A useful question whenever mathematics changes shape is: what changed, and what stayed the same?
Foundations
- 0.1 Form and Value Equivalent expressions, why representation matters, and the question every algebraic transformation should answer: what does this preserve?
- 0.2 What Is a Number? Number versus numeral, the number line as a model, and how origin, direction, and unit give numbers geometric meaning.
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0.3 Addition — coming next Addition as combining quantities, translating position, and composing movement.
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0.4 Multiplication — coming later Multiplication as repeated addition, scaling, area, and the beginning of a much larger family of structures.