Understanding mappings, injections, surjections, and equivalence relations. Cardinality: Exploring the different "sizes" of infinity. Why it Matters
The curriculum of 18.090 is centered on several core pillars of mathematical thought: 1. Formal Logic and Set Theory 18.090 introduction to mathematical reasoning mit
Students apply these proof techniques to foundational topics such as: Formal Logic and Set Theory Students apply these
A powerful tool for proving statements about integers. Before you can build a proof, you must
Assuming the opposite of what you want to prove and showing it leads to a logical impossibility.
Properties of integers, divisibility, and prime numbers.
Before you can build a proof, you must understand the building blocks. Students learn about sentential logic (and, or, implies), quantifiers (for all, there exists), and the basic properties of sets. This provides the syntax needed to write clear, unambiguous mathematical statements. 2. Proof Techniques