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所在平台: Udemy |
课程主页: https://www.udemy.com/course/pure-mathematics-for-pre-beginners/
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**课程名称：** 纯粹数学预备班 (Pure Mathematics for Pre-Beginners) **课程概述：** 本课程是为准备开始学习更高级数学但尚未准备好进行证明写作的学生设计的。它涵盖了逻辑学、集合论、抽象代数、数论、实分析、拓扑学、复分析和线性代数这八个主题的基础知识，共包含八个单元。 **目标受众：** * 希望开始学习高级数学但尚未准备好进行证明写作的学生。 * 希望向学生介绍高级数学思想但不想深入数学严谨性的高中教师。 * 希望向非STEM专业学生介绍高等数学的教授。 **课程内容：** * **八个学科领域的入门课程：** 逻辑学、集合论、抽象代数、数论、实分析、拓扑学、复分析、线性代数。 * **丰富的例子和练习：** 每节课都包含示例和练习，以帮助理解。 * **分难度级别的练习题：** 每节课后都提供按难度级别排列的练习题集。 **课程特点：** * **无先修要求：** 内容完全自给自足。 * **提升数学成熟度：** 课程旨在自然地提高学生的“数学成熟度”，即分析、理解和交流数学的能力。 * **难度适应性：** 数学成熟度高的学生可能觉得课程简单，可以快速学习；成熟度较低的学生可能会觉得更具挑战性，但回报丰厚。 **课程单元（精选目录）：** * 第一课 - 逻辑 * 第二课 - 集合论 * 第三课 - 抽象代数 * 第四课 - 数论 * 第五课 - 实分析 * 第六课 - 拓扑学 * 第七课 - 复分析 * 第八课 - 线性代数
Pure Mathematics for Pre-Beginners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra. The 8 lessons in this course cover elementary material from each of these 8 topics. A "pre-beginner" is a math student that is ready to start learning some more advanced mathematics, but is not quite ready to dive into proofwriting. Pure Mathematics for Pre-Beginners is perfect forstudents wishing to begin learning advanced mathematics, but that are not quite ready to start writing proofs.high school teachers that want to expose their students to the ideas of advanced mathematics without getting into mathematical rigor.professors that wish to introduce higher mathematics to non-stem majors.The material in this math course includes:8 lessons in 8 subject areas.Examples and exercises throughout each lesson.A problem set after each lesson arranged by difficulty level.There are no prerequisites for this course. The content is completely self-contained. Furthermore, this course will naturally increase a student's level of "mathematical maturity." Although there is no single agreed upon definition of mathematical maturity, one reasonable way to define it is as "one's ability to analyze, understand, and communicate mathematics." A student with a very high level of mathematical maturity may find this course very easy-this student may want to go through the course quickly and then move on to Pure Mathematics for Beginners. A student with a lower level of mathematical maturity will probably find this book more challenging. However, the reward will certainly be more than worth the effort.Pure Math Pre-Beginner Book Table Of Contents (Selected) Here's a selection from the table of contents:Lesson 1 - LogicLesson 2 - Set TheoryLesson 3 - Abstract AlgebraLesson 4 - Number TheoryLesson 5 - Real AnalysisLesson 6 - TopologyLesson 7 - Complex AnalysisLesson 8 - Linear Algebra
