18.090 Introduction To Mathematical Reasoning Mit

Unlike calculus, where you apply formulas, this course teaches you how to verify truth. You will learn the language of mathematics.

The primary goal is not to memorize facts, but to master the methodology of mathematics. By the end of the course, you should be able to:

Typical breakdown:

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. 18.090 introduction to mathematical reasoning mit

While specific syllabi vary by semester (and instructor, often Prof. Paul Seidel or Prof. Andrew Lin), the canonical topics of 18.090 include:

  • Relations and Functions: Injective (one-to-one), surjective (onto), bijective, and inverse functions. Equivalence relations (reflexive, symmetric, transitive) and partitions.

  • Elementary Number Theory: Divisibility, modular arithmetic, greatest common divisors (GCD), the Euclidean algorithm, and Bézout's identity. This is where you get your hands dirty with actual math. Unlike calculus, where you apply formulas, this course

  • Cardinality: The shocking discovery that not all infinities are equal. Countable sets (like integers and rationals) vs. uncountable sets (like reals). Cantor’s diagonal argument.

    • Recent offerings of 18.090 have included a unit on Lean (a proof assistant). If your semester uses this:

    Introduces the fundamental language, logic, and proof techniques essential for advanced mathematics. Emphasizes how to read, understand, and construct rigorous mathematical arguments. Topics include propositional and predicate logic, set theory, proof by contradiction, induction, and the axiomatic method. Designed for students transitioning from computational to proof-based mathematics. The primary goal is not to memorize facts,

    Confusion often arises because MIT has multiple courses that involve proofs. Here is the hierarchy:

    Verdict: If you struggled with the proof portions of 6.042 or feel lost reading a math textbook, 18.090 is your parachute.