: Infinite sets, set operations, and set-builder notation.
: This text focuses directly on the transition to higher mathematics, covering number systems, combinatorics, and foundational set theory.
The Euclidean Algorithm and Bezout’s Identity.
Consider the difference between these two statements: (True: every number has an additive inverse). : Infinite sets, set operations, and set-builder notation
Beyond technical knowledge, 18.090 places a massive emphasis on mathematical writing—learning how to articulate complex logical steps in a clear, concise, and rigorous manner. Core Topics Covered in 18.090
Are you planning to take this course as a , or are you looking for online self-study resources to learn proof-writing? 18.0x - MIT Mathematics
, staring at the white space on his paper. He tried to list them. 2, 3, 5, 7... but they never ended. How do you talk about 'never ending' without getting lost in the void? Then, he remembered a line from the course description Consider the difference between these two statements: (True:
The Fundamental Theorem of Arithmetic (unique factorization).
To truly absorb the material at an MIT level, follow these three tips:
18.090 is not an isolated island. It serves as a recognized prerequisite and recommended intermediate step for MIT's most demanding proof-based courses. The department explicitly recommends taking 18.090 before attempting or 18.701 Algebra I . The official math roadmap for the Pure Option lists 18.090 alongside 18.06 (Linear Algebra) and 18.700 (Advanced Linear Algebra) as ideal preparation for the core analysis and algebra sequence. This strategic positioning means taking 18.090 directly improves your chances of success in the most challenging mathematics courses at MIT. 18.0x - MIT Mathematics
. If proving a statement directly is too difficult, you instead assume the conclusion is false and prove that the hypothesis must also be false. Example: Proving that if n2n squared is even, then 3. Proof by Contradiction (Reductio ad Absurdum)
Moving from computational mathematics to rigorous proofs is one of the biggest challenges for STEM students. At the Massachusetts Institute of Technology (MIT), serves as the bridge. This course transforms how students view mathematics. It shifts the focus from solving equations to constructing flawless logical arguments.