: The study of geometric properties that are preserved through continuous deformations.
For more information on other math courses at MIT, you can visit the MIT Department of Mathematics website.
What makes 18.090 particularly special is its recent, meticulous design. It was not a course that existed in perpetuity; it was developed with high standards from the ground up. In 2022, the MIT Department of Mathematics partnered with the Undergraduate Mathematics Association and a talented math major, Paige Dote, to create a student-led IAP (Independent Activities Period) class aimed at easing the transition to proof-based classes. : The study of geometric properties that are
: Counting structures, permutations, and combinations using strict logical constraints.
By mastering these fundamentals, you aren't just preparing for a test—you are building the cognitive foundation required to tackle the most complex problems in science and technology. It was not a course that existed in
At its core, 18.090 acts as a "stepping stone" for students who want to build confidence in constructing and understanding mathematical arguments before diving into more rigorous subjects like , 18.701 (Algebra I) , or 18.901 (Introduction to Topology) . While many undergraduate math students are comfortable solving for
These are the texts that either form the basis of the course or are perfect for supplementary study. By mastering these fundamentals, you aren't just preparing
Physically split your notebook page. On the left: "Given / Assumptions." On the right: "Goal / Derived Steps." This mimics Fitch-style natural deduction and forces linear clarity.
: Success in this course depends on active problem-solving . As noted in student discussions, you cannot learn mathematical reasoning passively; you must "learn to write proofs by writing proofs".
Start by defining the shift in perspective. Most early math is about "finding the answer" through algorithms. In 18.090, the goal shifts to —proving why an answer must be true using logical principles. Mention that this course is particularly suitable for students before they tackle high-level proof-heavy subjects like 18.100 (Real Analysis) or 18.701 (Algebra I) . 2. The Core Pillars of Reasoning Discuss the specific technical toolkit the course provides: Logic and Quantifiers : Understanding how to use "for all" ( ∀for all ) and "there exists" ( ∃there exists ) to define mathematical statements precisely.
that answer must be true. It transforms math from a set of rules you follow into a logical structure you build from the ground up. Proof as a Tool