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Der Kurs enthält
- 9 Std. 38 Min. Video
- 85 Lektionen
- Niveau: Mittelstufe
- Sprache: English
- Wir merken uns, wo du warst
- Komplett kostenlos, ohne Karte
Lektionen
9 Abschnitte · 85 Lektionen · 9 Std. 38 Min. Gesamtlänge
Lektionen 1–1010 Lektionen · 59 Min.
- Intro to Discrete Math - Welcome to the Course!6 Min.
- Intro to Sets | Examples, Notation & Properties7 Min.
- Set-Roster vs Set-Builder notation5 Min.
- The Empty Set & Vacuous Truth4 Min.
- Cartesian Product of Two Sets A x B7 Min.
- Relations between two sets | Definition + First Examples7 Min.
- The intuitive idea of a function6 Min.
- Formal Definition of a Function using the Cartesian Product6 Min.
- Example: Is this relation a function?5 Min.
- Intro to Logical Statements6 Min.
Lektionen 11–2010 Lektionen · 44 Min.
- Intro to Truth Tables | Negation, Conjunction, and Disjunction6 Min.
- Truth Table Example: ~p V ~q3 Min.
- Logical Equivalence of Two Statements4 Min.
- Tautologies and Contradictions4 Min.
- 3 Ways to Show a Logical Equivalence | Ex: DeMorgan's Laws5 Min.
- Conditional Statements: if p then q7 Min.
- Vacuously True Statements2 Min.
- Negating a Conditional Statement3 Min.
- Contrapositive of a Conditional Statement5 Min.
- The converse and inverse of a conditional statement5 Min.
Lektionen 21–3010 Lektionen · 1 Std. 1 Min.
- Biconditional Statements | "if and only if"3 Min.
- Logical Arguments - Modus Ponens & Modus Tollens9 Min.
- Logical Argument Forms: Generalizations, Specialization, Contradiction3 Min.
- Analyzing an argument for validity2 Min.
- Predicates and their Truth Sets6 Min.
- Universal and Existential Quantifiers, ∀ "For All" and ∃ "There Exists"10 Min.
- Negating Universal and Existential Quantifiers8 Min.
- Negating Logical Statements with Multiple Quantifiers9 Min.
- Universal Conditionals P(x) implies Q(x)3 Min.
- Necessary and Sufficient Conditions8 Min.
Lektionen 31–4010 Lektionen · 1 Std. 25 Min.
- Formal Definitions in Math | Ex: Even & Odd Integers3 Min.
- How to Prove Math Theorems | 1st Ex: Even + Odd = Odd9 Min.
- Step-By-Step Guide to Proofs | Ex: product of two evens is even19 Min.
- Rational Numbers | Definition + First Proof7 Min.
- Proving that divisibility is transitive11 Min.
- Disproving implications with Counterexamples8 Min.
- Proof by Division Into Cases6 Min.
- Proof by Contradiction | Method & First Example9 Min.
- Proof by Contrapositive | Method & First Example4 Min.
- Quotient-Remainder Theorem and Modular Arithmetic10 Min.
Lektionen 41–5010 Lektionen · 1 Std. 16 Min.
- Proof: There are infinitely many primes numbers7 Min.
- Introduction to sequences6 Min.
- The formal definition of a sequence.4 Min.
- The sum and product of finite sequences9 Min.
- Intro to Mathematical Induction12 Min.
- Induction Proofs Involving Inequalities.7 Min.
- Strong Induction // Intro and Full Example10 Min.
- Recursive Sequences8 Min.
- The Miraculous Fibonacci Sequence6 Min.
- Prove A is a subset of B with the ELEMENT METHOD7 Min.
Lektionen 51–6010 Lektionen · 53 Min.
- Proving equalities of sets using the element method3 Min.
- The union of two sets5 Min.
- The Intersection of Two Sets6 Min.
- Universes and Complements in Set Theory3 Min.
- Using the Element Method to prove a Set Containment w/ Modus Tollens4 Min.
- Power Sets and the Cardinality of the Continuum15 Min.
- Relations and their Inverses3 Min.
- Reflexive, Symmetric, and Transitive Relations on a Set7 Min.
- Equivalence Relations - Reflexive, Symmetric, and Transitive5 Min.
- You need to check EVERY spot for reflexivity, symmetry, and transitivity4 Min.
Lektionen 61–7010 Lektionen · 1 Std. 20 Min.
- Introduction to probability // Events, Sample Space, Formula, Independence9 Min.
- Example: Computing Probabilities using P(E)=N(E)/N(S)2 Min.
- What is the probability of guessing a 4 digit pin code?6 Min.
- Counting with Triple Intersections // Example & Formula11 Min.
- Permutations: How many ways to rearrange the letters in a word?7 Min.
- The summation rule for disjoint unions6 Min.
- Counting formula for two intersecting sets: N(A union B)=N(A)+N(B)-N(A intersect B)8 Min.
- Combinations Formula: Counting the number of ways to choose r items from n items.7 Min.
- How many ways are there to reorder the word MISSISSIPPI? // Choose Formula Example7 Min.
- Counting and Probability Walkthrough17 Min.
Lektionen 71–8010 Lektionen · 1 Std. 35 Min.
- Intro to Conditional Probability6 Min.
- Two Conditional Probability Examples (what's the difference???)6 Min.
- Conditional Probability With Tables | Chance of an Orange M&M???10 Min.
- Bayes' Theorem - The Simplest Case6 Min.
- Bayes' Theorem Example: Surprising False Positives13 Min.
- Bayes' Theorem - Example: A disjoint union9 Min.
- IS CHESS A GAME OF CHANCE? Classical vs Frequentist vs Bayesian Probability13 Min.
- Intro to Markov Chains & Transition Diagrams11 Min.
- Markov Chains & Transition Matrices7 Min.
- Intro to Linear Programming14 Min.
Lektionen 81–855 Lektionen · 26 Min.
- Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg6 Min.
- Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph4 Min.
- Degree of Vertices | Definition, Theorem & Example | Graph Theory5 Min.
- Euler Paths & the 7 Bridges of Konigsberg | Graph Theory6 Min.
- The End of Discrete Math - Congrats! Some final thoughts...4 Min.
Was du brauchst
- Grundlagen helfen: der Kurs setzt hinter den Basics an.
Beschreibung
A one-semester course on Discrete Math taught by Dr. Trefor Bazett Covers: Logical Statements, Logical Operations, Truth Tables, Sets, Functions, Relations, Proof Methods such as Contrapositive, Contradiction and Induction, and Probability.
Für wen dieser Kurs ist
- Alle, die die Grundlagen von Wissenschaft kennen.
Diese beiden Punkte sind unsere Einschätzung aus dem Niveau. Die Beschreibung stammt vom Autor.