This is the heart of the course. Students learn several distinct strategies to prove mathematical theorems:
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
: Working with integers, divisors, and mathematical induction. Abstract Structures
Designed specifically for students who want to transition from computational math to abstract, theoretical thinking, this course lays the groundwork for advanced mathematical analysis, algebra, and topology. What is MIT 18.090? 18.090 introduction to mathematical reasoning mit
Without the foundation provided by 18.090, the jump to analysis or abstract algebra can feel like hititng a wall. This course provides the "training wheels" for the rigorous logical rigor required in professional mathematics and theoretical computer science. The MIT Experience
Students must have completed 18.01 (Single Variable Calculus) .
Study of real number sequences and limits to prepare for advanced calculus. Academic Pathway This is the heart of the course
Representative learning artifacts (what students produce)
Briefly discuss the implications or potential generalizations of your result. 3. Adhere to Academic Standards
A powerful technique used to prove statements that apply to all natural numbers. 3. Elementary Number Theory The Language of Logic: Students learn to use
A formal paper in this domain should follow a clear, logical progression: Introduction/Motivation:
Search for "MIT 18.090 problem sets" (many are available via the MIT Math Department's course archive or student repos). Attempt the 2015–2019 p-sets. They are legendary for their difficulty.