Dependency before popularity
Fractions and ratios come before probability; functions come before calculus; equations and coordinates come before linear algebra. The order makes hidden prerequisites visible.
Learn mathematics in the order the ideas depend on one another.
Begin with number meaning, not symbol tricks. Each course explains definitions, derives methods, solves complete examples, names common boundaries, and asks you to reconstruct the reasoning.
Begin with Mathematical Foundations →01 / CURRICULUM
A fifteen-course mathematician’s path, published one complete course at a time.
Stages indicate prerequisite order, not intelligence or prestige. A course becomes available only after both languages, proofs, examples, practice, and usability checks are complete.
02 / WHY THESE TOPICS
The sequence follows dependencies, representations, and proof.
The curriculum is not a list of fashionable subjects. A topic earns a place when it supplies a reusable idea needed by several later courses or a reasoning method needed to verify claims.
One idea, several representations
A learner should connect words, symbols, tables, graphs, diagrams, and units. Translation between representations is treated as knowledge, not decoration.
Methods must be derived
Rules are explained from definitions and invariants. Worked examples show why each step preserves meaning, when the rule applies, and how to check the result.
Boundaries are part of the concept
Division by zero, extraneous roots, dependent events, noninvertible matrices, divergent series, and confounding are taught where the ordinary method is introduced.
Understand one knowledge point before collecting another.
- Read the explanation and restate the definition in your own words.
- Cover the solution, work the example, and justify each transformation.
- Answer the checkpoint without looking, then repair only the first missing relationship.
- Complete the mixed practice and check the answer’s sign, size, units, and domain.