The hardest part of 18.090 to replicate is the blackboard defense. Find a study partner. You write a proof. They try to break it. Do not accept your own proof until your partner has failed to find a loophole.
Intersections, unions, complements, and power sets.
The syllabus covers three main pillars: logic/foundations, algebra, and analysis. Key Topics Covered
It is a "transition" subject for students who want experience with proofs before moving on to higher-level Course 18 (Mathematics) requirements. 18.090 introduction to mathematical reasoning mit
Lectures are often supplemented by weekly problem sessions where students discuss exercises assigned during class.
According to the MIT Math Major Roadmaps , 18.090 is classified as a "Stage 1" foundational course. It is highly recommended for:
| Week | Topic | |------|-------| | 1 | Logical connectives, truth tables, tautologies | | 2 | Quantifiers, negations, converse/inverse | | 3 | Proof techniques: direct, contrapositive, contradiction | | 4 | Mathematical induction (ordinary and strong) | | 5 | Sets: union, intersection, power sets, Cartesian products | | 6 | Functions: injective, surjective, bijective, inverses | | 7 | Relations: equivalence relations, partitions | | 8 | Midterm review & exam | | 9 | Number theory: divisibility, primes, GCD, Euclidean algorithm | | 10 | Modular arithmetic and proofs | | 11 | Real numbers: least upper bound property, sequences | | 12 | Countability: finite, countably infinite, uncountable sets | | 13 | Introduction to combinatorial proofs | | 14 | Final review and project presentations | The hardest part of 18
Translating colloquial statements into strict logical framework and finding exact logical negations.
This ritual is terrifying but transformative. It destroys the illusion that mathematics is about getting the right answer. It reveals that mathematics is about justification .
If you are preparing for this course, I can help you preview specific concepts. Let me know if you would like to explore a , see a classic proof by contradiction , or look at recommended textbooks and open-source resources for self-study. Share public link They try to break it
The syllabus generally follows a progression from logic to specific mathematical structures.
If you are interested in browsing materials, you can check for similar foundational math courses on MIT OpenCourseWare .
The heart of 18.090 is learning how to choose and execute the correct proof strategy for a given mathematical claim. Students practice multiple techniques, including:
To understand the logical structures taught in 18.090, students must master set operations. The following diagram visualizes basic set relationships commonly discussed in the first weeks of the course. Mathematics (Course 18) | MIT Course Catalog