MIT math courses have a distinct flavor. Here is what to expect in 18.090:
Exploring the sizes of infinite sets and understanding why some infinities are larger than others. Why 18.090 is Critical for Aspiring Mathematicians
REST (Restricted Elective in Science and Technology) Why Take 18.090? The Transition to Proof-Based Math
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. 18.090 introduction to mathematical reasoning mit
A mathematical proof is an act of communication. It is a persuasive essay written with symbols and logic. Your grader should not have to guess your line of reasoning. Write in complete sentences, clearly label your assumptions, and transition smoothly between logical steps. Final Thoughts
Transitioning from geometric vectors to abstract spaces satisfying specific algebraic properties. 4. Introductory Concepts in Analysis
18.090 changes how you view problems. It teaches you to question assumptions, look for edge cases, and value absolute clarity. This structural thinking is highly valued in fields outside of math, including law, quantitative finance, and data science. Tips for Success in MIT 18.090 MIT math courses have a distinct flavor
Understanding countable (countably infinite) versus uncountable sets, and Cantor's diagonal argument. 3. Topics in Algebra Permutations: Introduction to group theory concepts.
Often cited as the first "true" proof course for many majors. 18.701 (Algebra I):
Defining functions strictly as relations, and proving whether a function is injective (one-to-one), surjective (onto), or bijective (invertible). The Transition to Proof-Based Math The course syllabus
The course is taught using a variety of methods, including:
How 18.090 Compares to 18.062J (Mathematics for Computer Science)