Assuming the opposite of a statement to uncover a logical impossibility.
While MIT often cycles through different variations of this course (sometimes combined with Discrete Math), the best resource on MIT OCW is:
Intersections, unions, complements, and power sets.
Mapping out the truth values of statements to verify logical equivalences. Quantifiers: Mastering universal ( ∀for all , "for all") and existential ( ∃there exists
Pedagogical methods and assessment
Transitioning to proof-based math is difficult. Here is how to succeed:
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
MIT 18.090: The Gateway to Abstract Mathematical Reasoning MIT’s 18.090 (Introduction to Mathematical Reasoning) is a foundational course designed to transition students from computational mathematics to abstract mathematical thinking. While high school math focuses heavily on formulas and calculations, advanced mathematics demands proof, logic, and structural analysis. This course bridges that gap. It teaches students how to read, write, and think with the rigor required by the Massachusetts Institute of Technology. Core Objectives of the Course
3-0-9 (3 lecture hours, 0 lab hours, 9 preparation/homework hours per week) Spring Only Prerequisites Corequisites Calculus II (GIR) — e.g., 18.02 Requirement Fulfillments Survival Guide: How to Excel in 18.090
The course description succinctly states that 18.090 "focuses on understanding and constructing mathematical arguments". The subject matter is a broad introduction to core mathematical concepts, serving as a "transition" course. Instead of memorizing formulas, students learn to prove why those formulas work. The curriculum covers:
For anyone looking to move beyond the "formula-crunching" of early calculus and start doing "real" math, 18.090: Introduction to Mathematical Reasoning at MIT is the ultimate gateway.
): Assuming a statement is false and showing that this assumption leads to an impossible logical paradox.
: Demystifying logical statements using universal ( ∀for all ) and existential ( ∃there exists ) quantifiers.
18.090 is an undergraduate subject offered by the MIT Department of Mathematics that focuses on understanding, constructing, and critiquing mathematical arguments catalog.mit.edu. It is not simply about calculating answers; it is about proving why those answers are correct. None. Corequisites: Calculus II (GIR).
3-0-9 (3 hours of lecture, 0 hours of lab, 9 hours of outside preparation per week)
REST (Restricted Elective in Science and Technology) Why Take 18.090? The Transition to Proof-Based Math
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