Phase 1
Mathematical Language & Proof
Phase 1 of the Quant Academy curriculum.
1.1Full Lesson
Sets, Functions, and Relations
The objects every later definition is built from: how to speak precisely about collections, mappings, and the relationsh
1.2Full Lesson
Logic, Quantifiers, and Necessary vs Sufficient Conditions
How to read and write mathematical statements without ambiguity: connectives, quantifier order, and the difference betwe
1.3Full Lesson
Proof Techniques: Direct, Contrapositive, and Contradiction
The three workhorse proof strategies, when each is the right tool, and how to structure an argument a reader can verify.
1.4Full Lesson
Mathematical Induction and Recursion
Proving infinitely many statements with two steps, and the recursive definitions that induction is built to reason about
1.5Full Lesson
Sequences, Limits, and Reading & Writing Proofs
The epsilon-N definition of a limit - your first genuinely rigorous definition - and habits for reading and