Algebra: Elementary to Advanced - Equations & Inequalities from Coursera

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Syllabus

Module 1: The Structure of Numbers

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.

Module 2: Linear Equations

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.

Module 3: Solving Inequalities

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

Module 4: Systems of Equations

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.

Final Exam: Equations with Inequalities and Real Numbers

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!

Good to know

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Develops algebraic skills, which are necessary to succeed in Calculus, Probability, and Statistics

Teaches concepts that are foundational for many areas of mathematics, both pure and applied

Provides a comprehensive review of algebraic formulas and properties

Covers a range of topics relevant to precalculus, including linear equations, inequalities, and functions

Recommended for students who need a solid foundation in algebra before taking more advanced mathematics courses

Reviews summary

Algebra: basics refresher and review

Learners say this algebra course is a well-structured refresher for elementary algebra concepts. Lectures are clear and helpful, and the practice problems and quizzes cement concepts. The instructor, Joseph W. Cutrone, is praised for his clear explanations and engaging delivery. Overall, this course is a highly recommended resource for those looking to strengthen their algebra foundation.

Practice problems and quizzes are challenging and helpful.

"Great way to refresh myself from all the topics. Thanks a lot."

"The quizzes and final exam were well done. They really cemented the learning objectives."

"This course was incredibly taught. I did well at math in high school but I don't think I ever had the level of understanding that I gained from taking this course. Thank you!"

Course is great for refreshing algebra knowledge.

"Excellent refresher for those of us that have been out of a math class for a while."

"It's fast but a great refresher and the Instructor is excellent."

Lectures are clear and easy to understand.

"The course was very good. I learned a lot from it."

"This course had a wealth of material that was very easy to navigate. The instructor included videos, notes, and examples to help master the material."

"Really enjoyed this class. Lectures are very clear and develop your intuition."

Excellent instructor with clear explanations.

"Joseph W. Cutrone is a great explainer."

"The lecturer gave very clear explanations, this made it easy to follow the material."

"Excellent explanations with challenging sample problems. Well worth the time invested! Thank you. "

Quizzes have wrong answers with no explanations

"A few times I had to look up concepts on Google to get a deeper understanding."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Algebra: Elementary to Advanced - Equations & Inequalities with these activities:

Find online tutorials on simplifying radicals

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Supplement your understanding of simplifying radicals by exploring well-explained tutorials.

Browse courses on Radicals

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Search for online tutorials on simplifying radicals.
Select a tutorial that is clear and provides step-by-step instructions.
Follow the tutorial and work through the examples to grasp the process.

Develop a cheat sheet on algebraic formulas

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Create a concise and helpful reference guide that summarizes important algebraic formulas.

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Gather all the relevant algebraic formulas.
Organize the formulas into logical categories or topics.
Design a visually appealing and easy-to-read cheat sheet.

Practice solving algebraic equations

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Enhance your problem-solving skills by practicing with various types of algebraic equations.

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Find practice problems or worksheets online or in textbooks.
Solve the equations step-by-step, showing all your work.
Check your answers to identify any areas where you need improvement and focus on those topics in your practice.

Six other activities

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Polynomial Long Division Practice

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Practice long division to strengthen understanding of polynomial operations.

Browse courses on Algebra

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Review the steps for polynomial long division.
Find a polynomial divisor and dividend.
Perform the long division process.
Check the answer by multiplying the quotient by the divisor and adding the remainder.

Solve quadratic equations by factoring

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Master the technique of factoring to solve quadratic equations effectively.

Browse courses on Quadratic Equations

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Review the steps of factoring quadratic equations.
Practice factoring quadratic equations of varying complexity.
Check your solutions and identify any patterns or common mistakes.

Solve inequalities and graph solutions on a number line

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Strengthen your ability to solve and represent inequalities graphically.

Browse courses on Inequalities

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Review the concepts of inequalities and number lines.
Practice solving various types of inequalities.
Graph the solutions of the inequalities on a number line.

Create a visual representation of a linear equation

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Deepen your understanding of linear equations by creating a visual representation that illustrates the relationship between variables.

Browse courses on Linear Equations

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Choose a linear equation and identify the slope and y-intercept.
Use a graphing tool or software to plot the line using the slope and y-intercept you found.
Label the axes and the line with the equation it represents.
Optionally, explore different values for the variables to see how they affect the graph.

Organize and review course notes, assignments, and practice problems

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Enhance your understanding by organizing and reviewing the materials you have gathered throughout the course.

Browse courses on Note taking

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Gather all your notes, assignments, and practice problems.
Create a system for organizing these materials, such as using folders or a digital note-taking app.
Review the materials regularly to reinforce your learning.

Apply algebraic concepts to solve a real-world problem

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Challenge yourself by applying algebraic concepts to a practical problem and finding a solution.

Browse courses on Problem Solving

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Identify a real-world problem that can be solved using algebraic equations.
Formulate the problem into an algebraic equation or set of equations.
Solve the equation(s) to find the solution to the problem.
Validate your solution by checking it in the context of the original problem.

Career center

Learners who complete Algebra: Elementary to Advanced - Equations & Inequalities will develop knowledge and skills that may be useful to these careers:

Actuary

Actuaries use mathematical and statistical skills to assess risk and uncertainty in a variety of industries. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and apply actuarial models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Quantitative Analyst

Quantitative Analysts bridge the gap between finance and computer science, using statistical models to identify investment opportunities and manage risk. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and develop these models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Statistician

Statisticians use mathematical and statistical skills to collect, analyze, and interpret data. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and apply statistical models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Financial Analyst

Financial Analysts use mathematical and statistical skills to analyze financial data and make investment recommendations. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and apply financial models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Data Scientist

Data Scientists use mathematical and statistical skills to analyze data and draw insights from it. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and apply data science models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve problems in business and industry. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and apply operations research models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Economist

Economists use mathematical and statistical skills to study the economy and make policy recommendations. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and apply economic models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Market Researcher

Market Researchers use mathematical and statistical skills to study consumer behavior and make marketing recommendations. Algebra: Elementary to Advanced - Equations & Inequalities can help build a foundation for success in this role by providing the necessary mathematical skills to understand and apply market research models. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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High School Mathematics Teacher

High School Mathematics Teachers teach mathematics to high school students. Algebra: Elementary to Advanced - Equations & Inequalities may be useful for preparing to teach the subject of algebra at the high school level. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Professor of Mathematics

Professors of Mathematics teach and research mathematics at colleges and universities. Algebra: Elementary to Advanced - Equations & Inequalities may be useful for preparing to teach the subject of algebra at the college level. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

See salaries and explore the career path for Professor of Mathematics

Computer Programmer

Computer Programmers write and maintain computer programs. Algebra: Elementary to Advanced - Equations & Inequalities may be useful for preparing to work on computer programs that require mathematical or algebraic skills. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

See salaries and explore the career path for Computer Programmer

Software Engineer

Software Engineers design, develop, and maintain software systems. Algebra: Elementary to Advanced - Equations & Inequalities may be useful for preparing to work on software systems that require mathematical or algebraic skills. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Insurance Agent

Insurance Agents sell insurance policies to individuals and businesses. Algebra: Elementary to Advanced - Equations & Inequalities may be useful for preparing to work with clients who need help with mathematical or algebraic concepts related to their insurance policies. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Financial Advisor

Financial Advisors help clients plan and manage their finances. Algebra: Elementary to Advanced - Equations & Inequalities may be useful for preparing to work with clients who need help with mathematical or algebraic concepts related to their finances. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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Real Estate Agent

Real Estate Agents help clients buy and sell real estate. Algebra: Elementary to Advanced - Equations & Inequalities may be useful for preparing to work with clients who need help with mathematical or algebraic concepts related to their real estate transactions. Topics covered in the course, such as solving equations and inequalities, understanding systems of equations, and working with polynomials, will provide the computational methods and algebraic formulas needed for success in this role.

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