18.090 Introduction To Mathematical Reasoning Mit [hot] May 2026

18.090 (Introduction to Mathematical Reasoning) at MIT is widely known as the "bridge" course for students transitioning from the computational math of high school to the abstract, proof-based world of a math major. It focuses on the fundamental shift from calculating an answer to why it must be true. The Story of 18.090: From Calculation to Certainty

• Sequences and limits (informal usage to illustrate proofs)
• Polynomials and basic algebraic identities used in proofs
• Examples that motivate abstraction: vector spaces, groups (introductory examples only)

Recommended Textbooks for Self-Study:

Proof techniques

This course is the bridge from computational calculus to rigorous proof-based mathematics. It covers logic, sets, functions, proof techniques (induction, contradiction), and basic number theory/analysis. 18.090 introduction to mathematical reasoning mit

Representative theorems/problems (short list)

• Prove that √2 is irrational.
• Show there are infinitely many primes.
• Prove that if a function f has a left and right inverse then they are equal and f is bijective.
• Use induction to prove formulas for sums (e.g., sum of first n integers, sum of squares).
• Prove basic properties of divisibility and gcd using Euclidean algorithm.
• Prove that every equivalence relation partitions its set, and conversely.

Number theory basics

2 raised to the the absolute value of cap S end-absolute-value power The Proof: This is the core of your paper. State the method (e.g., "We proceed by induction on Show every step of the reasoning without "gaps." Conclusion/Reflection: Sequences and limits (informal usage to illustrate proofs)