|
所在平台: Coursera |
课程主页: https://www.coursera.org/learn/algebra-i
课程评论：没有评论
课程名称：代数：从基础到高级 - 方程与不等式
课程概述：本课程旨在为学生构建坚实的代数基础，使其能够掌握基本的数学概念，并为后续学习更高级的数学课程（如前导微积分、微积分、概率和统计）打下基础。课程将帮助学生巩固计算方法，复习代数公式和性质，并将这些概念应用于现实世界情境中。适合未来将使用代数技能的学生。课程涵盖的主题包括：实数、等式、不等式、多项式、有理表达式和方程、图形、关系和函数、根号和指数、以及二次方程等。
课程大纲：
1. 模块1：数字的结构
描述：本模块介绍了数学家乔治·康托尔正式化了集合论的概念，这一概念对研究和教学产生了深远影响。通过集合及其之间的关系作为基础，讲解实数的结构，从自然数、整数、有理数到实数的概念及其运算，形式化并应用实数的性质。
2. 模块2：线性方程
描述：两个变量之间的线性关系发生在一个变量相对于另一个变量的常量增减。线性方程具有性质，即自变量任何变化都会导致因变量的成比例变化。许多物理情境可以用线性关系建模。在散点图中，我们通常对最佳拟合线或回归线感兴趣。线性方程在所有数学和物理、工程应用中频繁出现，因为非线性系统通常可以被线性方程很好地近似。
3. 模块3：解不等式
描述：在坐标线上，两个点的相对位置用于定义实数集上的不等式关系。当实数a位于实数b的左侧时，我们说a小于b（a Name:Module 1: The Structure of Numbers Description:Georg Cantor was a famous mathematician who formalized the notion of set theory, which had a profound impact on research and teaching. Sets and the relations between them for a basis for teaching the concept of the structure of Real numbers. Starting with the concept of a natural number, {1,2,3,...} the whole numbers, integers, rationals, and real numbers are developed, as well as operations defined on them. Properties of the real numbers are formalized and applied as well. Name:Module 2: Linear Equations Description:A linear relationship between two variables occurs when there is a constant increase or constant decrease in one variable with respect to the other. Linear equations have the property that any change in the independent variable results in a proportional change in the dependent variable. Many physical situations can be modelled using a linear relationship. When data is visualized on a scatterplot, we often are interested in the line of best fit or the regression line. Linear equations occur frequently in all mathematics and their applications in physics and engineering, partly because non-linear systems are often well approximated by linear equations. Name:Module 3: Solving Inequalities Description:The relative position of two points on a coordinate line is used to define an inequality relationship on the set of real numbers. We say that a is less than b, written a Name:Module 4: Systems of Equations Description:Recall that a single linear equation in two variables is an equation of the form Ax + By = C, where A and B are both nonzero real constants. There are infinitely may ordered pairs that satisfy a single linear equation. In applications however, we are often interested in finding a single ordered pair that satisfies a pair of linear equations. In this section, we discuss several methods for solving this problem. Name:Final Exam: Equations with Inequalities and Real Numbers 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!课程大纲
课程评论(0条)
This course is intended for students looking to create a solid algebraic foundation of fundamental mathematical concepts from which to take more advanced courses that use concepts from precalculus, calculus, probability, and statistics. This course will help solidify your computational methods, review algebraic formulas and properties, and apply these concepts model real world situations. This course is for any student who will use algebraic skills in future mathematics courses. Topics include: the real numbers, equalities, inequalities, polynomials, rational expressions and equations, graphs, relations and functions, radicals and exponents, and quadratic equations.
