Proof Writing - Introduction to Mathematical Proofs and Set Theory

Learn the fundamental principles and techniques of mathematical proof writing through this comprehensive 7-hour video series. Master essential concepts starting with set theory basics including Cartesian products, set operations, and indexed sets, then progress through mathematical statements, logic operations, conditional statements, and quantifiers. Develop counting skills using inclusion-exclusion principles and explore the hierarchy of mathematical results through direct proof methods. Practice various proof techniques including case-by-case analysis, contrapositive proofs, proof by contradiction, and mathematical induction (both basic and strong induction). Apply these skills to set theory proofs, learn to disprove false statements, and advance to more complex topics including relations on sets, equivalence relations and partitions, modular arithmetic properties, function theory, the pigeonhole principle via functions, function composition with injectivity and surjectivity, and inverse functions.