The course often explores "Infinite Sets," teaching students that not all infinities are the same size—a concept that usually feels like "we aren't in Kansas anymore" for first-year students. Key Topics in the 18.090 Journey

: When studying mathematical definitions, always look for objects that fail to meet the definition. Understanding why a sequence fails to converge or why a set is not a field provides a sharper cognitive grasp than only looking at examples that work.

: Demystifying logical statements using universal ( ∀for all ) and existential ( ∃there exists ) quantifiers.

Exploring the sizes of infinite sets and understanding why some infinities are larger than others. Why 18.090 is Critical for Aspiring Mathematicians

This is the toolbox you will use for the rest of your math career.

: Review elementary properties of integers, including divisibility, prime numbers, and the distinction between even and odd integers. Functions & Relations