Self-learners, incoming MIT freshmen, or math competition veterans looking to solidify their transition from computational calculus to rigorous proof-writing.
: Widely considered the gold standard for learning how to construct mathematical proofs. It breaks down logical operators into clear, algorithmic blueprints.
): Assuming the negation of your desired conclusion is true, and showing that this assumption leads to a logical impossibility. ): Assuming the negation of your desired conclusion
For students aiming to transition from high school calculus to upper-level pure mathematics or advanced computer science, mastering this course's core principles is an essential step. The Paradigm Shift: Calculation vs. Reasoning
Once a week, take a theorem from 18.090 and try to prove its opposite . This is not skepticism; it is stress-testing logic. Reasoning Once a week, take a theorem from 18
A direct logical progression from axioms to the conclusion. Contrapositive: Proving by showing
The curriculum is built to establish a solid foundation in the "language" of mathematics. Description Reasoning Once a week
Sample PS8 (Induction)