Algebra: Elementary to Advanced - Equations & Inequalities from Coursera

What's inside

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!

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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."

Career center

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

Actuary

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Quantitative Analyst

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Statistician

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Financial Analyst

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Data Scientist

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Operations Research Analyst

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Economist

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Market Researcher

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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.

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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.

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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

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