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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/polynomials-roots
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课程名称：代数：初级到高级 - 多项式与根 课程概述：该课程是三部分代数课程的最后一部分，学生将在本课程中扩展对更高级函数的知识，并应用和建模这些函数，使用代数和几何技术。此课程使学生能够进行逻辑推理，并得出合理的结论。这种技能在当今世界至关重要。分析定量信息以便进行决策、判断和预测的能力对于理解许多重要的社会和政治问题至关重要。定量技能与推理提供了评估基于定量论证所需的技能。该课程的重要性在于其所处理的数学思想、数学语言及其符号操作，对于希望继续学习微积分、统计或数据科学的学生来说都是必不可少的。 课程大纲： 1. 模块1：指数函数 描述：指数函数在纯数学和应用数学中普遍存在，被认为是"数学中最重要的函数"。在应用中，指数函数建模独立变量的恒定变化与依赖变量的同等比例变化之间的关系，广泛应用于自然和社会科学等多个领域。 2. 模块2：多项式 描述：多项式是一个包含变量（也称为不确定量）和系数的表达式，仅涉及加、减、乘和非负整数指数化操作。多项式是线性函数和二次函数的推广，应用于多个数学和科学领域，广泛用于解决从简单问题到复杂科学问题的多项式方程。 3. 模块3：根 描述：本模块将学习实数的根，自然作为多项式方程 x^n - a = 0 的解决方案而出现。平方根在解决二次多项式中非常重要，并广泛应用于概率论和统计中的标准差等重要概念。 4. 模块4：应用 描述：此模块将探讨代数概念在现实世界中的应用。 5. 期末考试 描述：祝贺您到达期末考试！本次评估将覆盖课程的所有内容。请利用此次考试作为学习工具，识别自己的知识盲点和需要改进的地方。考试后，请复习任何错误的答案以查找失误。祝您好运！
Name:Module 1: Exponentials
Description:The ubiquitous occurrence of the exponential function in pure and applied mathematics has led mathematician W. Rudin to opine that the exponential function is "the most important function in mathematics". In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (i.e., percentage increase or decrease) in the dependent variable. This occurs widely in the natural and social sciences, as in a self-reproducing population, a fund accruing compound interest, or a growing body of manufacturing expertise. Thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics.
Name:Module 2: Polynomials
Description:In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Polynomials generalize our linear and quadratic functions that we have studied so far. An example of a polynomial is x^2 − 4x + 7. Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions.
Name:Module 3: Roots
Description:In this module, we will learn about roots of real numbers. Roots arise naturally as solutions to the polynomial equation x^n - a = 0. Square roots help to solve quadratic polynomials. The square root of a nonnegative number is used in the definition of Euclidean distance, as well as in generalizations such as Hilbert spaces. It defines an important concept of standard deviation used in probability theory and statistics. It has a major use in the formula for roots of a quadratic equation; quadratic fields and rings of quadratic integers, which are based on square roots, are important in algebra and have uses in geometry. Square roots frequently appear in mathematical formulas elsewhere, as well as in many physical laws. Generalizing square roots lead to n-th roots, their properties, and applications.
Name:Module 4: Applications
Description:
Name:Final Exam
Description:Congratulations on reaching the final exam! This final assessment will be cumulative in nature, covering all aspects of the course. Use this final as a teaching tool: justify what you know and identify areas for improvement. Use scrap paper as you take this final. Try to use any formula sheets or outside resources as a tool and not a crutch. Check your answers before you submit. After the test, review any incorrect answers to find your mistakes. Try to separate "silly" mistakes from the more substantial mistakes in understanding. Good luck!
This course is the final course in a three part algebra sequence, In this course, students extend their knowledge of more advanced functions, and apply and model them using both algebraic and geometric techniques. This course enables students to make logical deductions and arrive at reasonable conclusions. Such skills are crucial in today's world. Knowing how to analyze quantitative information for the purpose of making decisions, judgments, and predictions is essential for understanding many important social and political issues. Quantitative Skills and Reasoning provides students the skills needed for evaluating such quantitatively-based arguments. This class is important as the mathematical ideas it treats and the mathematical language and symbolic manipulation it uses to express those ideas are essential for students who will progress to calculus, statistics, or data science.
