18090 Introduction To Mathematical Reasoning Mit Extra Quality -

Students select a proof type (direct, contrapositive, contradiction, induction, cases) and the tool provides a structured template with placeholders for assumptions, chain of implications, and conclusion.

3.1. “Proof Metacognition” Sidebar

3.2. Error Diagnosis Engine

3.3. Weekly “Challenge Proof” with Rubric

3.4. Real-MIT Recitation Videos (Extra Quality) 3.3. Weekly “Challenge Proof” with Rubric

10–15 intentionally broken proofs with common student errors. Students click to reveal error categories (e.g., quantifier swap, missing case). The linter then highlights the exact lines where reasoning fails.

Even though the proofs must be rigorous text, you should draw diagrams to understand what is happening. 3.2. Error Diagnosis Engine

1.1. Thematic Units with Proof Layering

1.2. MIT-Level Problem Sets (Extra Quality) Students select a proof type (direct

This course builds your toolkit for rigorous proof construction.

One of the most mind-expanding sections of 18.090. You learn that the set of natural numbers ( \mathbbN ) and the set of integers ( \mathbbZ ) have the same cardinality (they are countable), but the real numbers ( \mathbbR ) are uncountable (Cantor's diagonal argument).