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所在平台: Udemy |
课程主页: https://www.udemy.com/course/introduction-to-mathematical-logic-college-mathematics/
课程评论：没有评论
**课程名称：** 数学逻辑基础 **课程概览：** 本课程由数学教育家 Suman Mathews 教授，旨在帮助学习者深入理解数学逻辑，这是离散数学中一项既基础又具挑战性的内容，同时也是大学数学的重要组成部分。课程将复杂的概念分解为易于理解的短小讲座，以帮助学习者掌握大学数学。 数学逻辑在计算机科学领域有着广泛的应用。本课程将引导您熟悉逻辑学的基本术语，包括否定、合取、析取、蕴含、双条件，并学习如何为它们计算真值表。 您将学习逻辑定律，理解重言式（tautology）和矛盾式（contradiction）的区别，并认识到逻辑定律在解决问题中的重要性。课程还将介绍对偶律（laws of Duality）以及 NAND 和 NOR 概念，并解释它们为何互为反例。 课程还会讲解推理定律（laws of inference），如合取简化（Conjunctive Simplification）、析取放大（Disjunctive Amplification）、假言三段论（Syllogism）、肯定前件（Modus Pones）、否定后件（Modus Tollens）等。您将学习运用这些定律来检验陈述的有效性。 此外，课程还将引入量词（quantifiers）、开放语句（open statements），以及如何计算开放语句的真值。您将了解连接全称量词和存在量词的逻辑规则，并学习量化语句（Quantified statements）及其否定形式。课程将提供一个简单的技巧，帮助您练习和掌握对其量化语句的否定。 您还将学习如何通过“找出异类”（Odd Man Out）和三段论问题来掌握逻辑谜题。课程最后会介绍在人工智能领域有应用的决策变量（Decision Variables）以及合取范式（Conjunctive Normal Form）和析取范式（Disjunctive Normal Form）。 **课程目标：** * 掌握逻辑学的基本术语和运算，并能计算真值表。 * 理解逻辑定律，辨别重言式和矛盾式，并认识其在问题解决中的作用。 * 熟悉对偶律、NAND 和 NOR 的概念。 * 掌握常见的推理定律，并能用它们来检验陈述的有效性。 * 理解量词和开放语句，并能计算其真值。 * 学习量化语句的否定形式，并掌握书写技巧。 * 通过实践掌握逻辑谜题的解题方法。 * 了解决策变量、合取范式和析取范式的概念及其在人工智能中的应用。 **谁应该参加：** * 对数学逻辑感兴趣的学习者。 * 需要理解数学逻辑的计算机科学专业的学生。 * 希望提升逻辑思维和问题解决能力的学习者。 **讲师：** Suman Mathews
Hi, I am Suman Mathews, math educator. I hope to help you understand Mathematical Logic, which is an easy, yet ,tricky part of Discrete Mathematics which is also part of College Mathematics. I can help you understand College Mathematics by breaking down complex topics into bite sized lectures.Mathematical Logic is extensively used in Computer Science. The course introduces you to basic terminology of Logic. You'll learn about negation, conjunction, disjunction, implication, bi conditional and how to calculate the truth tables for each.Learn about the laws of Logic next. You'll also come to understand the difference between a tautology and a contradiction. Realise how important the laws of logic are when it comes to problem solving.You'll be introduced to the laws of Duality and the concept of NAND and NOR. How NAND and NOR are inverses of each other is also explained. The course proceeds to explain the laws of inference. Understand the termsConjunctive SimplificationDisjunctive AmplificationSyllogismModus PonesModus Tollens and more.Use these and more, to test the validity of a statement. You'll also be introduced to quantifiers, open statements and how to calculate the truth value of an open statement. You are introduced to the rules of Logic which connect universal and existential quantifiers. Learn about Quantified statements and how to calculate their negation. Practice writing the negations of Quantified statements with a simple trick.Master Logical Puzzles: Identify the Odd Man Out and Syllogism problems. Learn about Decision Variables and Conjunctive and Disjunctive Normal Form. These are used in AI.I hope this course helps you. Would you care to help any of your fellow students who need help in Logic, by sharing details of this course. Once again, thank you and hoping to see you in the course.Looking forward to hearing from you!
