Proving that if the conclusion is false, the hypothesis must also be false. 3. Basic Structures
Learning to eliminate ambiguity and structure arguments clearly.
Understanding that finding a proof requires exploration, trial, and error. Fundamental Topics Covered
Moving from high school mathematics to university-level mathematics is often a shock for students. In early schooling, math focuses heavily on computation, formulas, and algorithms. You are given an equation, and your job is to find the correct number. 18.090 introduction to mathematical reasoning mit
18.090 Introduction to Mathematical Reasoning is MIT's purpose-built bridge to higher mathematics. It systematically introduces the language and logic of proof, providing the essential toolkit required for any student wishing to move beyond calculation and into the creative, rigorous world of mathematical discovery. For anyone planning to major in mathematics, physics, or computer science—or who simply wants to understand what a proof truly is—18.090 is a logical and highly valuable first step.
According to the MIT Pure Mathematics Major Roadmap, 18.090 acts as an intermediate training ground. It allows students to make mistakes, learn typesetting math in LaTeX, and develop mathematical maturity in a lower-stakes environment before tackling intense upper-level seminars.
Which advanced math branches () interest you most? Share public link Proving that if the conclusion is false, the
Your paper should explore a concept that allows for rigorous proof construction. Common topics in the 18.090 syllabus include: Infinite Sets:
Mastering the syntax of mathematical statements, quantifiers, and logical connectives.
Defining one-to-one and onto functions.
The goal of 18.090 is "understanding and constructing mathematical arguments". A simple proof that is perfectly executed is better than a complex one that is logically muddy. 4. Example Theorem Construction
The course is highly recommended for students who found 18.01 or 18.02 challenging in terms of rigor, or who simply want to gain a stronger footing in pure mathematics. Core Topics Covered