Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
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This course includes
- 9.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 85 lessons • 9.5 hours of video
Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
85 lessons
• 9.5 hours
Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
85 lessons
• 9.5 hours
- Intro to Discrete Math - Welcome to the Course! 05:59
- Intro to Sets | Examples, Notation & Properties 07:12
- Set-Roster vs Set-Builder notation 05:15
- The Empty Set & Vacuous Truth 04:07
- Cartesian Product of Two Sets A x B 07:10
- Relations between two sets | Definition + First Examples 06:39
- The intuitive idea of a function 05:51
- Formal Definition of a Function using the Cartesian Product 05:47
- Example: Is this relation a function? 05:09
- Intro to Logical Statements 06:19
- Intro to Truth Tables | Negation, Conjunction, and Disjunction 05:53
- Truth Table Example: ~p V ~q 03:24
- Logical Equivalence of Two Statements 03:42
- Tautologies and Contradictions 03:41
- 3 Ways to Show a Logical Equivalence | Ex: DeMorgan's Laws 05:29
- Conditional Statements: if p then q 07:09
- Vacuously True Statements 02:01
- Negating a Conditional Statement 02:52
- Contrapositive of a Conditional Statement 05:00
- The converse and inverse of a conditional statement 05:05
- Biconditional Statements | "if and only if" 02:54
- Logical Arguments - Modus Ponens & Modus Tollens 08:44
- Logical Argument Forms: Generalizations, Specialization, Contradiction 03:23
- Analyzing an argument for validity 02:13
- Predicates and their Truth Sets 06:04
- Universal and Existential Quantifiers, ∀ "For All" and ∃ "There Exists" 09:32
- Negating Universal and Existential Quantifiers 08:03
- Negating Logical Statements with Multiple Quantifiers 08:35
- Universal Conditionals P(x) implies Q(x) 03:27
- Necessary and Sufficient Conditions 07:37
- Formal Definitions in Math | Ex: Even & Odd Integers 03:23
- How to Prove Math Theorems | 1st Ex: Even + Odd = Odd 08:35
- Step-By-Step Guide to Proofs | Ex: product of two evens is even 18:41
- Rational Numbers | Definition + First Proof 06:40
- Proving that divisibility is transitive 11:09
- Disproving implications with Counterexamples 08:18
- Proof by Division Into Cases 05:41
- Proof by Contradiction | Method & First Example 09:00
- Proof by Contrapositive | Method & First Example 03:38
- Quotient-Remainder Theorem and Modular Arithmetic 09:30
- Proof: There are infinitely many primes numbers 07:09
- Introduction to sequences 06:14
- The formal definition of a sequence. 03:50
- The sum and product of finite sequences 09:20
- Intro to Mathematical Induction 12:15
- Induction Proofs Involving Inequalities. 06:34
- Strong Induction // Intro and Full Example 10:09
- Recursive Sequences 07:37
- The Miraculous Fibonacci Sequence 06:23
- Prove A is a subset of B with the ELEMENT METHOD 06:36
- Proving equalities of sets using the element method 03:01
- The union of two sets 05:07
- The Intersection of Two Sets 05:47
- Universes and Complements in Set Theory 02:50
- Using the Element Method to prove a Set Containment w/ Modus Tollens 03:42
- Power Sets and the Cardinality of the Continuum 14:43
- Relations and their Inverses 02:49
- Reflexive, Symmetric, and Transitive Relations on a Set 06:54
- Equivalence Relations - Reflexive, Symmetric, and Transitive 04:36
- You need to check EVERY spot for reflexivity, symmetry, and transitivity 03:40
- Introduction to probability // Events, Sample Space, Formula, Independence 08:52
- Example: Computing Probabilities using P(E)=N(E)/N(S) 02:02
- What is the probability of guessing a 4 digit pin code? 06:22
- Counting with Triple Intersections // Example & Formula 11:07
- Permutations: How many ways to rearrange the letters in a word? 06:53
- The summation rule for disjoint unions 05:55
- Counting formula for two intersecting sets: N(A union B)=N(A)+N(B)-N(A intersect B) 07:32
- Combinations Formula: Counting the number of ways to choose r items from n items. 06:33
- How many ways are there to reorder the word MISSISSIPPI? // Choose Formula Example 07:04
- Counting and Probability Walkthrough 17:18
- Intro to Conditional Probability 06:14
- Two Conditional Probability Examples (what's the difference???) 06:16
- Conditional Probability With Tables | Chance of an Orange M&M??? 09:37
- Bayes' Theorem - The Simplest Case 05:31
- Bayes' Theorem Example: Surprising False Positives 12:37
- Bayes' Theorem - Example: A disjoint union 08:32
- IS CHESS A GAME OF CHANCE? Classical vs Frequentist vs Bayesian Probability 13:26
- Intro to Markov Chains & Transition Diagrams 11:25
- Markov Chains & Transition Matrices 06:54
- Intro to Linear Programming 14:23
- Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg 05:53
- Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph 04:03
- Degree of Vertices | Definition, Theorem & Example | Graph Theory 04:57
- Euler Paths & the 7 Bridges of Konigsberg | Graph Theory 06:24
- The End of Discrete Math - Congrats! Some final thoughts... 04:22
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