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The TSR^2 (Talented Scholars Resource Room) is a unique, student-founded study space that provides peer-led academic assistance. This is an often overlooked "extra quality" resource, offering collaborative problem-solving and mentorship from older students who have excelled in 18.090.
Learning objectives
: Direct proof, contrapositive, contradiction, and mathematical induction. Number Theory Basics : Properties of integers, divisibility, and prime numbers. Department of Mathematics | University of Washington Recommended Resources & "Extra Quality" Content The TSR^2 (Talented Scholars Resource Room) is a
: When the negation of the conclusion provides a more concrete mathematical structure to work with than the original hypothesis. Proof by Contradiction (Reductio ad Absurdum) You assume the theorem is false ( ), which means is true and
This is where most novices stumble. The order of quantifiers changes everything. Number Theory Basics : Properties of integers, divisibility,
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(A∪B)c=Ac∩Bcopen paren cap A union cap B close paren to the c-th power equals cap A to the c-th power intersection cap B to the c-th power Functions and Mappings The order of quantifiers changes everything
What gives the MIT curriculum its "extra quality" is its focus on . Unlike a standard lecture where you passively record theorems, 18.090 encourages students to "scratch out" proofs.
MIT's mathematics curriculum is world-renowned for its depth. However, core subjects like 18.100 (Real Analysis), 18.701 (Algebra I), and 18.901 (Introduction to Topology) are built on a language of proofs and abstract logic that students typically aren't exposed to in introductory calculus (18.01/18.02).
Week 5:
Understanding 18.090: Introduction to Mathematical Reasoning at MIT
