To Mathematical Reasoning Mit __full__ — 18.090 Introduction
For anyone looking to move beyond the "formula-crunching" of early calculus and start doing "real" math, 18.090: Introduction to Mathematical Reasoning at MIT is the ultimate gateway.
Not everyone at MIT takes 18.090. Some arrive with AP credit in BC Calculus and a strong background in math competitions (IMO, USAMO). For those students, 18.090 might be redundant. However, for the following archetypes, 18.090 is non-negotiable: 18.090 introduction to mathematical reasoning mit
While the syllabus evolves slightly depending on the instructor (notable past instructors include Dr. Paul Bamberg and Prof. Haynes Miller), the core of 18.090 revolves around four fundamental pillars. Let’s explore each in detail. For anyone looking to move beyond the "formula-crunching"
Typical syllabus structure (concept progression) Direct proof Proof by contrapositive Proof by contradiction
4. Cardinality (Infinite Sets)
Common Misconceptions (And Why 18.090 Destroys Them)
- Direct proof
- Proof by contrapositive
- Proof by contradiction
- Proof by cases
- Proof by exhaustion
- Existence proofs (constructive vs nonconstructive)
- Uniqueness proofs
- Mathematical induction (basic, strong/complete induction)
- Well-ordering principle and its equivalence with induction
: Familiarize yourself with basic set operations (union, intersection, complement), subsets, and power sets. Integer Properties