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所在平台: Udemy |
课程主页: https://www.udemy.com/course/relations-and-functions-class-12-important-questions/
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**课程名称：** 机器学习中的关系与函数 **课程概述：** 本课程通过一个生动的故事，以烘焙师 Alan 和园艺师 Betty 的友谊为主线，深入浅出地讲解了机器学习领域中至关重要的“关系”与“函数”概念。课程从基本概念“集合”和“关系”入手，解释了何为两个集合的笛卡尔积的子集。随后，课程将详细阐述不同类型的关系，特别是“等价关系”这一核心概念。 接着，课程将函数定义为一种特殊的关系，重点介绍函数的“定义域”和“值域”。通过 Alan 烘焙的糕点和 Betty 种植的花朵之间的对应关系，直观地展示了一对一、满射、多对一等概念，并引申出函数的构成、反函数和恒等函数等重要知识点。 此外，课程还将涵盖单射函数、满射函数以及双射函数，并教授如何计算双射函数的反函数。学习过程中，您还将接触到“二元运算”这一在高等数学（如群论）中广泛应用的概念。 **课程亮点：** * **故事化教学：** 通过 Alan 和 Betty 的故事，让抽象的数学概念变得生动有趣，易于理解。 * **全面覆盖：** 涵盖了关系与函数的基础知识、关键类型以及在机器学习中的应用。 * **实践导向：** 讲解如何计算函数的定义域、值域以及反三角函数的定义域、值域和主值。 * **拓展性强：** 课程内容对准备 SAT 和 GRE 量化考试也大有裨益。 * **额外福利：** 提供课程中所有公式的汇总，以及一套考察性的多项选择题，以激发您的思考。 * **自主学习：** 允许您按照自己的节奏，轻松学习。 **讲师介绍：** Suman Mathews，拥有数学双硕士学位，拥有三十多年的高中和大学数学教学经验。 **总结：** 本课程旨在揭示关系与函数在我们日常生活中的美妙之处，并帮助您理解它们在微积分等领域的重要性，为深入学习机器学习打下坚实的基础。 **建议：** 鼓励您的朋友和同事一起报名学习！
Once upon a time, in a beautiful village called Mathville, there lived two best friends Alan and Betty. Alan was a dedicated baker and Betty, an enthusiastic gardener. Each time Alan would bake a delicious pastry, Betty would plant a beautiful flower.Each pastry that Alan baked corresponded to a particular flower that Betty planted thus establishing a relation. Thus different types of relations such as one to one, onto and many to one could be explained by the relation between the pastries and flowers. The concept of functions was also introduced by associating each pastry with exactly one flower.The story progresses to explaining domain and range where the domain consisted of all the pastries which Alan could bake and the range comprising all the flowers which Betty could plant. The story continues to unfold by illustrating concepts such as composite functions, invertibility and the identity function.In short, understanding Relations and functions is a mutual exchange of talents. This course illustrates the beauty of Relations and Functions in our everyday lives..You have been introduced to Calculus and you realise the importance of Functions in Calculus. That is precisely what this course teaches you.I am Suman Mathews. I have a double Master's in Mathematics and I have taught and helped students of high school and college for the past three decades. The course unfolds with the basic concept of Sets and a Relation as a subset of the cross product of two sets. You learn the different types of Relations and a very important concept, namely, what is an equivalence Relation.Next, you'll be introduced to a function as a type of Relation. You'll understand what is meant by Domain and Range of a function. As you progress through the course, you'll learn about injective and surjective functions and consequently bijective functions.You'll learn how to calculate the inverse of a bijective function. You'll glide to Binary Operations, a very important concept used in Group Theory in Higher Mathematics.You'll receive all the formulas learnt in this course as a gift. There's also a set of Multiple choice questions at the end of the course. This will inspire you to think out of the box.On a side note, the concepts taught here will also help you to answer SAT and GRE QUANT examinations.I hope you'll find this course helpful. Encourage your friends and acquaintances to also enrol for the course and learn hassle free at your own pace. Bonus-Learn how to find the domain and range of Inverse Trigonometric Functions. Also learn simple techniques to find the principal values of Inverse Trigonometric functions.
