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Logical Argument Forms: Generalizations, Specialization, Contradiction
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Classroom Contents
Discrete Math - Sets, Logic, Proofs, Probability, Graph Theory
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- 1 Intro to Discrete Math - Welcome to the Course!
- 2 Intro to Sets | Examples, Notation & Properties
- 3 Set-Roster vs Set-Builder notation
- 4 The Empty Set & Vacuous Truth
- 5 Cartesian Product of Two Sets A x B
- 6 Relations between two sets | Definition + First Examples
- 7 The intuitive idea of a function
- 8 Formal Definition of a Function using the Cartesian Product
- 9 Example: Is this relation a function?
- 10 Intro to Logical Statements
- 11 Intro to Truth Tables | Negation, Conjunction, and Disjunction
- 12 Truth Table Example: ~p V ~q
- 13 Logical Equivalence of Two Statements
- 14 Tautologies and Contradictions
- 15 3 Ways to Show a Logical Equivalence | Ex: DeMorgan's Laws
- 16 Conditional Statements: if p then q
- 17 Vacuously True Statements
- 18 Negating a Conditional Statement
- 19 Contrapositive of a Conditional Statement
- 20 The converse and inverse of a conditional statement
- 21 Biconditional Statements | "if and only if"
- 22 Logical Arguments - Modus Ponens & Modus Tollens
- 23 Logical Argument Forms: Generalizations, Specialization, Contradiction
- 24 Analyzing an argument for validity
- 25 Predicates and their Truth Sets
- 26 Universal and Existential Quantifiers, ∀ "For All" and ∃ "There Exists"
- 27 Negating Universal and Existential Quantifiers
- 28 Negating Logical Statements with Multiple Quantifiers
- 29 Universal Conditionals P(x) implies Q(x)
- 30 Necessary and Sufficient Conditions
- 31 Formal Definitions in Math | Ex: Even & Odd Integers
- 32 How to Prove Math Theorems | 1st Ex: Even + Odd = Odd
- 33 Step-By-Step Guide to Proofs | Ex: product of two evens is even
- 34 Rational Numbers | Definition + First Proof
- 35 Proving that divisibility is transitive
- 36 Disproving implications with Counterexamples
- 37 Proof by Division Into Cases
- 38 Proof by Contradiction | Method & First Example
- 39 Proof by Contrapositive | Method & First Example
- 40 Quotient-Remainder Theorem and Modular Arithmetic
- 41 Proof: There are infinitely many primes numbers
- 42 Introduction to sequences
- 43 The formal definition of a sequence.
- 44 The sum and product of finite sequences
- 45 Intro to Mathematical Induction
- 46 Induction Proofs Involving Inequalities.
- 47 Strong Induction
- 48 Recursive Sequences
- 49 The Miraculous Fibonacci Sequence
- 50 Prove A is a subset of B with the ELEMENT METHOD
- 51 Proving equalities of sets using the element method
- 52 The union of two sets
- 53 The Intersection of Two Sets
- 54 Universes and Complements in Set Theory
- 55 Using the Element Method to prove a Set Containment w/ Modus Tollens
- 56 Relations and their Inverses
- 57 Reflexive, Symmetric, and Transitive Relations on a Set
- 58 Equivalence Relations - Reflexive, Symmetric, and Transitive
- 59 You need to check EVERY spot for reflexivity, symmetry, and transitivity
- 60 Introduction to probability // Events, Sample Space, Formula, Independence
- 61 Example: Computing Probabilities using P(E)=N(E)/N(S)
- 62 What is the probability of guessing a 4 digit pin code?
- 63 Permutations: How many ways to rearrange the letters in a word?
- 64 The summation rule for disjoint unions
- 65 Counting formula for two intersecting sets: N(A union B)=N(A)+N(B)-N(A intersect B)
- 66 Counting with Triple Intersections // Example & Formula
- 67 Combinations Formula: Counting the number of ways to choose r items from n items.
- 68 How many ways are there to reorder the word MISSISSIPPI? // Choose Formula Example
- 69 Counting and Probability Walkthrough
- 70 Intro to Conditional Probability
- 71 Two Conditional Probability Examples (what's the difference???)
- 72 Conditional Probability With Tables | Chance of an Orange M&M???
- 73 Bayes' Theorem - The Simplest Case
- 74 Bayes' Theorem Example: Surprising False Positives
- 75 Bayes' Theorem - Example: A disjoint union
- 76 Intro to Markov Chains & Transition Diagrams
- 77 Markov Chains & Transition Matrices
- 78 Intro to Linear Programming and the Simplex Method
- 79 Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg
- 80 Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph
- 81 Degree of Vertices | Definition, Theorem & Example | Graph Theory
- 82 Euler Paths & the 7 Bridges of Konigsberg | Graph Theory
- 83 The End of Discrete Math - Congrats! Some final thoughts...
