Ideal for students desiring additional experience with proofs before tackling advanced subjects like 18.701 (Algebra I), 18.100 (Real Analysis), or 18.901 (Introduction to Topology) catalog.mit.edu.
The course is typically taken after single-variable calculus (18.01) and before real analysis (18.100) or abstract algebra (18.700). Its credit load is 3-0-9 (3 class hours, 0 lab hours, 9 expected study hours per week), reflecting MIT’s intensive unit system.
Direct proof, contrapositive, contradiction, and induction. Foundational Topics: Logical quantifiers ( ), set theory, and relations.
By the end of the semester, students are expected to move comfortably between abstract concepts and concrete proofs. Why Take 18.090 at MIT? 18.090 introduction to mathematical reasoning mit
If you have typed "18.090 introduction to mathematical reasoning mit" into a search engine, you are probably standing at a crossroads. You have finished the computation-based math and are peering into the abstract unknown.
The curriculum introduces students to the formal language of mathematics through several pillars:
The course covers a range of topics, including: Direct proof, contrapositive, contradiction, and induction
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).
This course is notorious for being a "shock" to students who relied solely on memorization in calculus.
Students must have completed 18.01 (Single Variable Calculus) . Why Take 18
Distinguishing between countable infinities (like integers) and uncountable infinities (like real numbers).
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: A major focus is placed on writing clear, unambiguous, and elegant proofs. Key Topics Covered in the Curriculum
If you are planning on the "Pure Option" for Course 18, this is a frequently recommended starting point to build the necessary "mathematical maturity". The Student Experience