18090 Introduction — To Mathematical Reasoning Mit Extra Quality __full__

18.090 Introduction to Mathematical Reasoning is a foundational course at MIT Mathematics designed to bridge the gap between calculation-heavy calculus and the abstract, proof-based thinking required for high-level math. It is particularly valued by students who want to build confidence in constructing mathematical arguments before tackling rigorous subjects like Real Analysis or Abstract Algebra. Course Overview & Core Content

• Write a clear proof of a known theorem (e.g., infinitude of primes in arithmetic progression has a simple special case). Extended (3–4 weeks):
• Explore countability of algebraic numbers, produce a written report with proofs.
• Small combinatorics project: bijective proofs of identities and generating functions introduction.

• Why: It is specifically designed for this "transition" phase. It includes detailed examples and "preview activities" to test understanding before you start the heavy proofs.

• Be careful with the hypothesis. If the problem says "If $n$ is prime," you cannot assume $n$ is odd (because $n=2$ is prime and even).