The course syllabus typically covers foundational tools of logic and set theory, alongside specific concepts from algebra and analysis used to practice these tools: Methods of proof (Direct, Contradiction, Induction). Logical quantifiers ( ∀for all ∃there exists ) and conditional statements (Converse, Contrapositive). Set Theory: Operations on sets and properties of infinite sets. Functions, relations, and cardinality. Algebraic Concepts: Permutations and group-like structures. Introduction to vector spaces and fields. Analysis Concepts: Properties of sequences of real numbers. Introductory epsilon-delta arguments used in limits. Course Logistics Prerequisites: None, though Calculus II is a co-requisite.
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According to the MIT Math Major Roadmaps , 18.090 serves as a "Stage 1" building block for advanced domains like Number Theory, alongside foundational algebra and linear algebra sequences. Core Pillars of the 18.090 Curriculum The course syllabus typically covers foundational tools of