18.090 Introduction To Mathematical Reasoning Mit -

Course Report: MIT 18.090 Introduction to Mathematical Reasoning

Core Curriculum: The Four Pillars of Logic

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.

Schedule: Lectures are generally held twice a week (e.g., Tuesdays/Thursdays) with additional recitation sessions. Paul Seidel - MIT Mathematics 18.090 introduction to mathematical reasoning mit

Relations and Functions

The Long-Term Value: Beyond the Grade

Students often ask: "Will I ever prove that the square root of 2 is irrational again in real life?" Probably not. But here is what you will use: Course Report: MIT 18

exists," this course provides the necessary logic and set theory foundations .

• 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

Author: [Your Name / Institutional Affiliation]
Date: [Current Date] Direct proof Proof by contrapositive Proof by contradiction

: Understand definitions for domain, codomain, range, and types of functions (injective, surjective, and bijective). Department of Mathematics | University of Washington Essential Proof Techniques