# 辛辛那提大学离散数学-学习资料辛辛那提大学离散数课程，内容覆盖集合、命题逻辑、逆否命题、范式、谓词逻辑、贝叶斯定理、图论、树等 🏆 课程学习中心 | 🚧 CS数学基础课程合辑 | 🌍 课程主页 | 📺 中英字幕视频 | 🚀 项目代码解析
Discrete Math

University Of Cincinnati

MATH1071
⭐⭐⭐⭐⭐

## 课程介绍 Trefor Bazett 教授在 Cincinnati 大学任教时，制作了两套完整的的数学课程（微积分、离散数学），上传网络后备受欢迎！课程覆盖核心知识要点，并借助可视化的方式做了生动讲解，是基础学习和查漏补缺的优先选择。 Discrete Math是其中的离散数学课程，内容覆盖集合、命题逻辑、范式、概率空间、图论、树结构等，离散数学也是后续部分工科方向课程（例如 数据库）的基础，该课程形象的可视化与活泼的授课方式，让你更好地掌握相关的抽象数学知识。  ## 课程资料 | 下载  ShowMeAI 对课程资料进行了梳理，整理成这份完备且清晰的资料包：

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## 课程视频 | B站

🌍 B站 | 【双语字幕+资料下载】辛辛那提 MATH1071 | 离散数学(2020·完整版)

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L1 Intro to Discrete Math - Welcome to the Course!
L2 Intro to Sets - Examples, Notation & Properties
L3 Set-Roster vs Set-Builder notation
L4 The Empty Set & Vacuous Truth
L5 Cartesian Product of Two Sets A x B
L6 Relations between two sets - Definition + First Examples
L7 The intuitive idea of a function
L8 Formal Definition of a Function using the Cartesian Product
L9 Example: Is this relation a function?
L10 Intro to Logical Statements
L11 Intro to Truth Tables - Negation, Conjunction, and Disjunction
L12 Truth Table Example: ~p V ~q
L13 Logical Equivalence of Two Statements
L15 3 Ways to Show a Logical Equivalence - Ex: DeMorgan’s Laws
L16 Conditional Statements: if p then q
L17 Vacuously True Statements
L18 Negating a Conditional Statement
L19 Contrapositive of a Conditional Statement
L20 The converse and inverse of a conditional statement
L21 Biconditional Statements - “if and only if”
L22 Logical Arguments - Modus Ponens & Modus Tollens
L23 Logical Argument Forms: Generalizations, Specialization, Contradiction
L24 Analyzing an argument for validity
L25 Predicates and their Truth Sets
L26 Universal and Existential Quantifiers, ∀ “For All” and ∃ “There Exists”
L27 Negating Universal and Existential Quantifiers
L28 Negating Logical Statements with Multiple Quantifiers
L29 Universal Conditionals P(x) implies Q(x)
L30 Necessary and Sufficient Conditions
L31 Formal Definitions in Math - Ex: Even & Odd Integers
L32 How to Prove Math Theorems - 1st Ex: Even + Odd = Odd
L33 Step-By-Step Guide to Proofs - Ex: product of two evens is even
L34 Rational Numbers - Definition + First Proof
L35 Proving that divisibility is transitive
L36 Disproving implications with Counterexamples
L37 Proof by Division Into Cases
L38 Proof by Contradiction - Method & First Example
L39 Proof by Contrapositive - Method & First Example
L40 Quotient-Remainder Theorem and Modular Arithmetic
L41 Proof: There are infinitely many primes numbers
L42 Introduction to sequences
L43 The formal definition of a sequence.
L44 The sum and product of finite sequences
L45 Intro to Mathematical Induction
L46 Induction Proofs Involving Inequalities.
L47 Strong Induction
L48 Recursive Sequences
L49 The Miraculous Fibonacci Sequence
L50 Prove A is a subset of B with the ELEMENT METHOD
L51 Proving equalities of sets using the element method
L52 The union of two sets
L53 The Intersection of Two Sets
L54 Universes and Complements in Set Theory
L55 Using the Element Method to prove a Set Containment w/ Modus Tollens
L56 Relations and their Inverses
L57 Reflexive, Symmetric, and Transitive Relations on a Set
L58 Equivalence Relations - Reflexive, Symmetric, and Transitive
L59 You need to check EVERY spot for reflexivity, symmetry, and transitivity
L60 Introduction to probability // Events, Sample Space, Formula, Independence
L61 Example: Computing Probabilities using P(E)=N(E)/N(S)
L62 What is the probability of guessing a 4 digit pin code?
L63 Permutations: How many ways to rearrange the letters in a word?
L64 The summation rule for disjoint unions
L65 Counting formula for two intersecting sets: N(A union B)=N(A)+N(B)-N(A intersect B)
L66 Counting with Triple Intersections // Example & Formula
L67 Combinations Formula: Counting the number of ways to choose r items from n items.
L68 How many ways are there to reorder the word MISSISSIPPI? // Choose Formula Example
L69 Counting and Probability Walkthrough
L70 Intro to Conditional Probability
L71 Two Conditional Probability Examples (what’s the difference???)
L72 Conditional Probability With Tables - Chance of an Orange M&M???
L73 Bayes’ Theorem - The Simplest Case
L74 Bayes’ Theorem Example: Surprising False Positives
L75 Bayes’ Theorem - Example: A disjoint union
L76 Intro to Markov Chains & Transition Diagrams
L77 Markov Chains & Transition Matrices
L78 Intro to Linear Programming and the Simplex Method
L79 Intro to Graph Theory - Definitions & Ex: 7 Bridges of Konigsberg
L80 Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph
L81 Degree of Vertices - Definition, Theorem & Example - Graph Theory
L82 Euler Paths & the 7 Bridges of Konigsberg - Graph Theory
L83 The End of Discrete Math - Congrats! Some final thoughts

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