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Algebra

Elementary to Advanced - Equations & Inequalities

Joseph W. Cutrone, PhD

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.

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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.

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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

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Reviews summary

Solid algebra foundation for advanced study

According to learners, this course offers a strong and comprehensive foundation in algebra, covering concepts from elementary to intermediate levels with a clear progression. Many appreciate the structured modules and the way the content helps solidify computational methods and apply concepts to real-world situations. The course is frequently cited as excellent preparation for higher-level mathematics, including precalculus and calculus. While the 'advanced' portion might not delve into highly complex topics for all, the fundamental concepts are presented with clarity, making it a valuable resource for review or initial learning.

Pacing suitable for review; 'advanced' may not be deep enough for some.

"The pace was excellent for me, as I was looking to review algebra before tackling precalculus. It wasn't too fast or too slow."

"While it says 'advanced,' I found the 'advanced' parts to be more like a thorough intermediate review. It's great for what it is, but don't expect university-level advanced algebra."

"I think the course is perfect for someone brushing up or learning algebra for the first time, but it might be too elementary for those seeking truly advanced topics."

Course effectively demonstrates real-world applications of algebra.

"The examples used to show how algebra applies to real-world situations really helped connect the theory to practical use."

"I enjoyed learning how linear equations model physical situations, which made the concepts much more relevant."

"This course really brought algebra to life by showing how these mathematical tools can be used in physics and engineering."

Concepts are taught in a clear, logical, and well-organized manner.

"The instructor's explanations were incredibly clear, breaking down complex ideas into manageable pieces."

"I appreciated the logical flow of the modules; each built perfectly on the last, making the learning process smooth."

"The course structure is very well-thought-out, making it easy to follow along even if I had forgotten some basics."

Provides essential algebraic groundwork for future math courses.

"This course laid a very strong foundation for my understanding of algebra, which I know will be crucial for calculus."

"I found the topics covered to be precisely what I needed to build a solid base for college-level math."

"It really helped me solidify my understanding of algebraic concepts from elementary to advanced, making me feel ready for more."

Some learners desired more practice problems or exercises.

"I sometimes felt the need for more practice problems beyond what was provided to truly solidify my understanding."

"While the quizzes were good, I found myself searching for additional exercises online to get more hands-on practice."

"More challenging problems or a larger bank of practice questions would have made this course even better for me."

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:

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.

See salaries and explore the career path for Quantitative Analyst

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.

See salaries and explore the career path for Actuary

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.

See salaries and explore the career path for Data Scientist

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.

See salaries and explore the career path for Operations Research Analyst

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.

See salaries and explore the career path for Financial Analyst

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.

See salaries and explore the career path for Statistician

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.

See salaries and explore the career path for Economist

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.

See salaries and explore the career path for Market Researcher

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

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.

See salaries and explore the career path for High School Mathematics Teacher

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.

See salaries and explore the career path for Software Engineer

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

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.

See salaries and explore the career path for Financial Advisor

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.

See salaries and explore the career path for Insurance Agent

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.

See salaries and explore the career path for Real Estate Agent

Reading list

We've selected 13 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Algebra: Elementary to Advanced - Equations & Inequalities.

Precalculus, Global Edition

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This textbook is written in a clear and concise style and provides numerous examples and exercises. It covers all of the topics that this course covers, as well as additional topics, and it could be considered either a substitute for or supplemental to this course's material.

Algebra

Elementary to Advanced - Equations & Inequalities

Two deals to help you save

What's inside

Syllabus

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Save this course

Reviews summary

Solid algebra foundation for advanced study

Activities

Career center

Reading list

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