Taking a class at the MIT Department of Mathematics means facing a significant jump in difficulty from high school. Students often report:
Many math and computer science majors take both 18.090 and 6.042, noting that 18.090 offers a purer, theorem-proving experience. 18.090 introduction to mathematical reasoning mit
The journey begins by stripping math down to its bones. You don't start with complex equations; you start with "Statements"—sentences that are either definitively true or false. The Language of Logic: Students learn to use symbols like (for all), there exists (there exists), and (implies) to build airtight arguments. Methods of Proof: You master the "weapons" of a mathematician: Direct Proof Proof by Contradiction Taking a class at the MIT Department of
State all prerequisite definitions clearly before using them in the proof. The Theorem Statement: Use precise mathematical language. For example: "Theorem: Let be a finite set. Then the power set has cardinality You don't start with complex equations; you start
For those interested in learning more about 18.090 Introduction to Mathematical Reasoning at MIT, here are some additional resources:
Divisibility, modular arithmetic, greatest common divisors (GCD), the Euclidean algorithm, and Bézout's identity. This is where you get your hands dirty with actual math.