18.090 Introduction To Mathematical Reasoning Mit Jun 2026

In high school and introductory college math, success is often measured by a student's ability to apply algorithms to solve equations. 18.090 dismantles this approach. The course teaches students to view mathematics as a formal language governed by strict rules of logic. The primary goals of the course are:

A solid grasp of calculus (18.01/18.02) helps, though the focus is not on computation.

While 18.100A/B (Real Analysis) teaches proof in the context of calculus, 18.090 is a gentler, standalone bridge course focusing on proof as a skill before applying it to analysis, algebra, or topology. Ideal for Course 6-14, 18, or any student seeking mathematical maturity. 18.090 introduction to mathematical reasoning mit

Builds familiarity with fields, vector spaces, and abstract mappings. (Introduction to Mathematical Logic) Formal Logic Systems

MIT 18.090: Introduction to Mathematical Reasoning For many students arriving at MIT, mathematics has been a journey of calculation—solving for In high school and introductory college math, success

Other texts occasionally referenced include:

, computing integrals, and applying formulas. However, represents the pivot point where math shifts from a tool for calculation to a language for rigorous logic. The primary goals of the course are: A

A typical 18.090 problem:

18.090 acts as a buffer. It provides a lower-stakes environment to make mistakes, learn the formatting expectations of mathematical writing, and build the mental stamina required for abstract thinking. Strategies for Success in the Course

Modern computer science—especially cryptography, algorithm design, and formal verification—relies heavily on discrete math and logic.

To give you a taste, here is a typical 18.090 homework problem (slightly simplified):