18.090 Introduction To Mathematical Reasoning Mit [work] Jun 2026

The course assumes only high school algebra and a willingness to be confused. It rejects the "cookbook" approach to math (identify the problem type, apply the algorithm, get the answer) and replaces it with the "detective" approach (observe the hypothesis, construct a logical chain, defend every link).

For MIT students, it’s a requirement. For anyone else reading this guide, it’s a blueprint. And 18.090 is the workshop where you learn the trade. 18.090 introduction to mathematical reasoning mit

In the words of a former 18.090 TA: "This course takes the veil off mathematics. After 18.090, you realize that all of calculus, all of linear algebra—it's just arguments. And arguments can be examined, challenged, and created. You become a participant in math, not just a consumer." The course assumes only high school algebra and

While specific syllabi vary by semester (and instructor, often Prof. Paul Seidel or Prof. Andrew Lin), the canonical topics of 18.090 include: For anyone else reading this guide, it’s a blueprint

A distinctive MIT feature is the use of LaTeX for final projects. Students write a short paper (3–5 pages) proving a non-trivial theorem of their choice, from Cantor’s diagonal argument to the infinitude of primes in arithmetic progressions (special case).