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Unit 3: Foundations in logic
Unit Outline:
3.1: Proof methods
Course Reader:
Introduction to Proofs (Bill Shillito):
Proof Techniques (Bill Shillito):
Quotient-Remainder Theorem and Modular Arithmetic (Trefor Bazett):
Modular Arithmetic (TheTrevTutor):
The fundamental theorem of arithmetic (Khan Academy - Brit Cruise):
Primes, Twin Primes, Triplets of Primes. How many? (TANTON Mathematics):
3.2: Quantified statements
Course Reader:
Quantificational Logic and Quantifier Negation (TheTrevTutor):
3.3: Indirect argument: contradiction and contraposition
Course Reader:
Proof by Contradiction (Spoonful of Maths):
5 Proofs that the Square Root of 2 is Irrational (Tipping Point Math):
3.4: Mathematical Induction
Course Reader:
Mathematical Induction (Spoonful of Maths):
Proof by induction (Khan Academy):
3.5: Logic
Course Reader:
Truth tables made easy (Randell Heyman):
Truth Tables for Negation, Conjunction, and Disjunction (Trefor Bazett):