Proving properties of greatest common divisors (GCDs).
The course begins by defining what constitutes a mathematical statement—a sentence that is definitively true or false. Students learn to manipulate complex logical operations without ambiguity:
According to the MIT Course Catalog, 18.090 emphasizes active participation and developing skill in constructing arguments 3.2.2.
For a deeper look at the foundational concepts of set theory and proof methods covered in the early stages of this course: Lecture 1: Sets, Set Operations and Mathematical Induction MIT OpenCourseWare YouTube• Jun 21, 2022 18.090 introduction to mathematical reasoning mit
Unlike 18.01 or 18.02, where you might learn an algorithm and repeat it, 18.090 requires reading additional sources and collaborating with peers on complex problem sets (Psets).
Translating colloquial statements into strict logical framework and finding exact logical negations.
For many second-year undergraduates at MIT, the transition from problem sets involving derivatives and integrals to proving theorems about limits or number theory can be jarring. 18.090 – Introduction to Mathematical Reasoning is explicitly designed to ease this transition. Unlike standard “transition to proof” courses elsewhere, 18.090 leverages MIT’s problem-solving culture while emphasizing clarity, rigor, and creativity in logical argumentation. Proving properties of greatest common divisors (GCDs)
While the exact syllabus evolves, a representative semester includes:
Recent offerings of 18.090 have included a unit on (a proof assistant). If your semester uses this:
If you are planning to take this course or want to prepare for it, let me know: For a deeper look at the foundational concepts
, 18.090 is classified as an intermediate subject. It is not always a mandatory requirement for the Pure Math major, but it is highly recommended for those who find the jump to 18.100 Real Analysis
Unlike calculus, which often focuses on finding a numerical answer, this course focuses on why a statement is true and how to construct a logical argument to support it 0.5.1 . Why Take 18.090?
Often offered in a condensed format, the course is intense but highly rewarding.