: Relations, functions, and the concept of cardinality (different types of infinity).
The chapter on truth tables (20+ pages with 50 exercises) is excessive for anyone who has done basic logic. Conversely, the section on infinite sets (countability) rushes through — you’ll need external YouTube videos to truly grasp diagonalization.
: Unlike introductory calculus which focuses on computation, 18.090 centers entirely on understanding and constructing mathematical arguments .
The primary objective is to teach students how to read, write, and analyze mathematical proofs. It strips away the comfort of plug-and-play formulas and replaces them with formal logic, set theory, and abstract structures. Core Pillars of the Curriculum : Relations, functions, and the concept of cardinality
The course builds structural logic from scratch, providing the toolkit necessary for higher-level courses like Real Analysis (18.100) or Algebra I (18.701).
If you are diving into these materials, keep these tips in mind to extract the highest quality learning experience:
: Distinguishing between one-to-one, onto, and invertible mappings. 3. Core Proof Methodologies : Unlike introductory calculus which focuses on computation,
As the student types, the linter checks for:
Proving "If not B, then not A" to establish that "If A, then B." 3. Why MIT's 18.090 Stands Out
: It explores selected concepts from Algebra (permutations, vector spaces) and Analysis (sequences of real numbers) to prepare students for the 18.100 or 18.701 series. Core Pillars of the Curriculum The course builds
Accompanied by specific, actionable comments (not just a score).
Never mix your scratch-pad brainstorming with your final proof presentation. Clean up your logical path before submission. 🚀 Beyond 18.090: Where Does This Lead?
: ⚠️ Line 3: The converse (“if x² is even then x is even”) is not yet proved. Your assumption only gives one direction. Consider proof by contrapositive.