Purpose of chapter 0
This chapter aligns notation and proof habits before heavy computational topics. You should read this as a methods chapter: how we write claims, track domains, and justify each algebraic transformation.
Symbol discipline
Definition
Well-formed mathematical statement
A statement should clearly specify:
- variable domain,
- operation legality,
- conclusion target.
A common source of error is transforming expressions without checking domain conditions (e.g. dividing by quantities that may be zero).
Baseline transformation rules
- Equality-preserving operations: adding/subtracting same term both sides, multiplying by nonzero constants, substituting equivalent expressions.
- Domain-sensitive steps: square roots, logarithms, division, inverse trigonometric functions.
Quick checks
Quick check
Why must x != 0 be stated before dividing an equation by x?
Think about equivalence of solution sets.
Solution