The curriculum of 18.090 is centered on several core pillars of mathematical thought: 1. Formal Logic and Set Theory
18.090 is an undergraduate course designed to teach students the fundamental language of mathematics: . While most high school and early college math focuses on what the answer is, 18.090 focuses on why a statement is true and how to communicate that truth with absolute certainty.
Would you like a shorter version (e.g., for a course catalog) or a LaTeX-ready syllabus with grading breakdown and weekly schedule? 18.090 introduction to mathematical reasoning mit
is a specialized undergraduate course offered by the MIT Department of Mathematics designed to bridge the gap between computational calculus and high-level abstract mathematical proofs. While high school and early university math focus heavily on executing algorithms, solving equations, and finding numerical answers, advanced university mathematics requires an entirely different mindset: constructing rigorous, logical arguments.
Pedagogical methods and assessment
Though a newer addition, 18.090 has a distinguished origin and is now a permanent part of the curriculum. It was created by professors , all of whom are renowned researchers and dedicated teachers.
Try a proof by contradiction.
Rigorous definitions of injections (one-to-one), surjections (onto), and bijections (invertible functions).
Injective (one-to-one), surjective (onto), bijective, and inverse functions. Equivalence relations (reflexive, symmetric, transitive) and partitions. The curriculum of 18
Students apply these proof techniques to foundational topics such as: