The "extra quality" of the course lies in this attention to detail. Grading is not binary (right/wrong); it is nuanced. Students lose points for "hand-waving"—skipping over difficult logical steps with vague assertions. They learn to write proofs that are not only correct but elegant. This focus on clarity and precision is a skill that translates far beyond mathematics, proving invaluable in fields like computer science, law, and engineering.
3-0-9 (3 hours of lecture, 0 hours of lab, and 9 hours of outside preparation per week).
: Direct proof, contrapositive, contradiction, and mathematical induction .
Advanced mathematics does not care about computation. It cares about truth, structure, and logic. The "extra quality" of the course lies in
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The "extra quality" of 18.090 stems from its deliberate instructional design, which counters the isolation often felt in proof-heavy courses.
: Relations, functions, and the concept of cardinality (different types of infinity). They learn to write proofs that are not
It serves as a recommended prerequisite for 18.701 (Algebra I) , which is notoriously difficult for students without prior proof experience. How to Access the Course 18.0x - MIT Mathematics
Week 9:
Defining equivalence classes, partitions, and modular arithmetic—the bedrock of modern algebra and number theory. Elementary Number Theory Sample PS8 (Induction)
As a CI-M course, 18.090 ensures that students can write mathematics at a professional level.
For any mathematics student, the transition from computational calculus and algebra to rigorous, proof-based mathematics is often described as the single most challenging step in their academic journey. It's a shift from solving problems to proving truths—from asking "what's the answer?" to asking "why is this true?" MIT's serves as the official, high-quality bridge designed to carry students across this crucial divide. More than just another course number, 18.090 has rapidly become a celebrated cornerstone of the MIT mathematics curriculum, earning a reputation for exceptional quality and effectiveness.
Sample PS8 (Induction)