18.090: Introduction to Mathematical Reasoning at MIT is a foundational bridging course designed to transition students from computational "plug-and-chug" math to the rigorous, proof-oriented thinking required for upper-level mathematics. Course Overview
Number Theory: Properties of integers, divisibility, and prime numbers.
: A first look at permutations, fields, and sequences of real numbers. Student Perspective 18.090 introduction to mathematical reasoning mit
Many MIT students find that transitioning to 18.090 is where they actually start "loving" math because they stop memorizing formulas and start understanding the underlying structures. It's often the class that helps students decide if they want to double-major in Course 18 (Mathematics) 18.0x - MIT Mathematics
Foundations: Infinite sets, quantifiers, and various methods of proof . Algebra: Permutations, vector spaces, and fields . Analysis: Sequences of real numbers . Logistics: Typically offered in the Spring semester . Why Take It? Analysis: Sequences of real numbers
18.090 Introduction to Mathematical Reasoning at MIT is a proof-focused undergraduate course designed to help students bridge the gap between computational calculus and advanced, rigorous mathematics. It is especially recommended for students planning to take proof-heavy subjects like 18.100 (Real Analysis) or 18.701 (Algebra I). Course Objectives
| If you want... | Get this... | | :--- | :--- | | One book to own | Velleman – How to Prove It | | A free, online reference | Hammack – Book of Proof (people.vcu.edu/~rhammack/BookOfProof/) | | To pass the problem sets | The 18.090 OCW problem set solutions (check your work) | | To understand the logic rules | Solow – How to Read and Do Proofs (Chapter 2–4) | the focus is entirely on reasoning.
Exams are a mix of multiple-choice logic questions (e.g., “Which statement is the negation of …”) and free-response proofs. No calculators are needed; the focus is entirely on reasoning.
Analysis: Introduction to sequences of real numbers, which serves as a gateway to 18.100 (Real Analysis). Who Should Take It?