ME - EECS 203 lyrics

Chapter 1 - Foundations: Logic and Proofs 1.1 Propositional Logic Proposition Truth Table(2^n) Connectives Negation Conjunction Disjunction Implication Converse Inverse Contrapositive(equivalent) Operator Precedence 1.2 Applications of Propositional Logic System Specifications Consistent Contradiction Solving Logic Puzzles 1.3 Logical Equivalence Tautology Contradiction Contingency De Morgan's Law Disjunctive Normal Form Boolean Logic Laws Identity Domination Idempotent Double Negation Commutative Associative Distributive De Morgan's Absorption Negation Propositional Satisfiability Satisfiable Unsatisfiable Solution Solving Satisfiability Problems(w/o truth table) 1.4 Predicates and Quantifiers Predicate Logic Predicate Propositional Function P(x) Preconditions - Valid Input Postconditions - Valid Outputs Quantifiers Quantification All, some, many, none, few Domain of Discourse Universal Quantifier(For All) Counterexample Existentital Quantifier(There exists) Uniqueness Quantifier Quantifier Precedence Binding Variables Logical Equivalence Involving Quantifiers Negating Quantified Expressions(De Morgan's) Translating from English Quantifiers in System Specifications 1.5 Nested Quantifiers Quantification as Loops Order of Quantifiers Scope Multiplicative Inverse Translating to/from English Negating Nested Quantifiers 1.6 Rules of Inference Argument Premise Valid Fallacies Conclusion Argument Forms Modus ponens(law of detachment) Modus tollens Hypothetical syllogism Disjunctive syllogism Addition Simplification Conjunction Resolution Building Arguments Common Fallacies Fallacy of affirming the conclusion Fallacy of denying the hypothesis Universal Instantiation Universal Generalization Existential Instantiation Existential Generalization Combining rules of inference for propositions and quantified statements 1.7 Introduction to Proofs Informal Proofs Proof Theorem Axioms(Postulates) Lemma Corollary Conjecture Omitting Quantifiers Methods of Proving Theorems Direct Proof Parity Proof by Contraposition Indirect Proof Proof by Contradiction Proof of Equivalence Counterexamples Common Mistakes in Proofs Vacuous and Trivial Proofs "begging the question" "circular reasoning" Definitions: Integer Even Odd Perfect square Sum of all integers less than n Rational number General Proof Strategy Readability(compa**ion) 1.8 Proof Methods and Strategy Exhaustive Proof Proof by Cases Leveraging Proof by Cases Without Loss of Generality Common Errors with Exhaustive Proofs and Proof by Cases Existence Proofs Witness Constructive Non-constructive Uniqueness Proofs Proof Strategies Forward and backward reasoning Adapting Existing Proofs Looking for Counterexamples Tiling Problems Definitions: Perfect Power Arithmetic Mean Metric Mean Fermat's Theorem Chapter 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices 2.1 2.2 2.3 2.4 2.5 2.6 Chapter 5 5.1 5.2