College Algebra
Also known as "High School Algebra"
OK. So what are you going to learn here?
You will learn about Numbers, Polynomials, Inequalities, Sequences and Sums, many types of Functions, and how to solve them.
You will also gain a deeper insight into Mathematics, get to practice using your new skills with lots of examples and questions, and generally improve your mind.
With your new skills you will be able to put together mathematical models so you can find good quality solutions to many tricky real world situations.
Near the end of most pages is a "Your Turn" section ... do these! You need to balance your reading with doing . Answering questions helps you sort things out in your mind. And don't guess the answer: use pen and paper and try your best before seeing the solution.
So what is this thing called Mathematics? And how do you go about learning it?
- Welcome to Mathematics
- Learning Mathematics
- The Language of Mathematics
- Symbols in Algebra
Next, we need to think about mathematics in terms of sets .
- Introduction to Sets
Now we know what a set is, let us look at different sets of numbers that are useful:
- The Evolution of Numbers
- Prime and Composite Numbers
- Fundamental Theorem of Arithmetic
- Whole Numbers and Integers
- Rational Numbers
- Using Rational Numbers
- Irrational Numbers
- 0.999... = 1
- Real Numbers
- Imaginary Numbers
- Complex Numbers
- Multiplying Complex Numbers
- The Complex Plane
- Common Number Sets
Inequalities
"Equal To" is nice but not always available. Maybe we only know that something is less than, or greater than. So let's learn about in equalities.
- Introduction to Inequalities
- Properties of Inequalities
- Solving Inequalities
- Solving Inequality Word Questions
We will be using exponents a lot, so let's get to know them well.
- Variables with Exponents
- Using Exponents in Algebra
- Squares and Square Roots
- Squares and Square Roots in Algebra
- Fractional Exponents
- Laws of Exponents
- Exponents of Negative Numbers
Polynomials
Polynomials were some of the first things ever studied in Algebra. They are simple, yet powerful in their ability to model real world situations.
- What is a Polynomial?
- Adding And Subtracting Polynomials
- Multiplying Polynomials
- Polynomials - Long Multiplication
- Dividing Polynomials
- Polynomials - Long Division
- Degree (of an Expression)
- Special Binomial Products
- Difference of Two Cubes
- Factoring in Algebra
- Solving Polynomials
- Roots of Polynomials: Sums and Products
- Rational Expressions
- Using Rational Expressions
- Fundamental Theorem of Algebra
- Remainder Theorem and Factor Theorem
- General Form of a Polynomial
Graphing Polynomials
- How Polynomials Behave
- Polynomials: The Rule of Signs
- Polynomials: Bounds on Zeros
And, of course, we need to know about equations ... and how to solve them.
- Equations and Formulas
- Solving Equations
- Solving Word Questions
- Zero Product Property
- Implication and Iff
- Theorems, Corollaries, Lemmas
Graphs can save us! They are a great way to see what is going on and can help us solve many things. But we need to be careful, as they sometimes don't give the full story.
- Cartesian Coordinates
- Pythagoras' Theorem
- Distance Between 2 Points
- Graph of an Equation
- Finding Intercepts From an Equation
- Symmetry in Equations
- Linear Equations
They are just equations for lines. But they come in many forms.
- Equation of a Straight Line
- Point-Slope Equation of a Line
- General Form of Equation of a Line
- Equation of a Line from 2 Points
- Midpoint of a Line Segment
- Parallel and Perpendicular Lines
A function relates an input to an output. But from that simple foundation many useful things can be built.
- What is a Function?
- Domain, Range and Codomain
- Evaluating Functions
- Increasing and Decreasing Functions
- Maxima and Minima of Functions
- Even and Odd Functions
- Set-Builder Notation
Common Functions Reference :
- Square Function
- Square Root Function
- Cube Function
- Reciprocal Function
- Absolute Value Function
- Floor and Ceiling Function
- Function Transformations
- Equation Grapher
- Operations with Functions
- Composition of Functions
- Inverse Functions
Equations of Second Degree
"Second degree" just means the variable has an exponent of 2, like x 2 . It is the next major step after linear equations (where the exponent is 1, like x).
- Quadratic Equations
- Factoring Quadratics
- Completing the Square
- Derivation of Quadratic Formula
- Graphing Quadratic Equations
- Quadratic Equations in the Real World
- Circle Equations
We already have experience in solving, but now we can learn more!
- Mathematical Models and Mathematical Models 2
- Approximate Solutions
- Intermediate Value Theorem
- Solving Radical Equations
- Change of Variables
- Algebra Mistakes
We learned about inequalities above, now let's learn how to solve them.
- Graphing Linear Inequalities
- Inequality Graphing Tool
- Solving Quadratic Inequalities
- Solving Rational Inequalities
- Absolute Value in Algebra
Exponents and Logarithms
We already know about exponents ... well logarithms just go the other way. And together they can be very powerful.
- Introduction to Logarithms
- Exponents, Roots and Logarithms
- Working with Exponents and Logarithms
- Exponential Function
- Logarithmic Function
- Exponential Growth and Decay
- Systems of Linear Equations
What happens when we have two or more linear equations that work together? They can often be solved! It isn't very hard but can take a lot of calculations.
- Types of Matrix
- How to Multiply Matrices
- Determinant of a Matrix
- Inverse of a Matrix:
- Using Elementary Row Operations (Gauss-Jordan)
- Using Minors, Cofactors and Adjugate
- Scalar, Vector, Matrix and Vectors
- Matrix Calculator
- More at Matrix Index
- Solving Systems of Linear Equations Using Matrices
- Systems of Linear and Quadratic Equations
- Probability
Is it likely? You be the judge!
- The Basic Counting Principle
- Combinations and Permutations
Sequences, Series and Partial Sums
A Sequence is a set of things (usually numbers) that are in order. We can also sum up a series, where Sigma Notation is very useful.
- Sequences - Finding A Rule
- Sigma Notation
- Partial Sums
- Arithmetic Sequences and Sums
- Geometric Sequences and Sums
These last few subjects use what we have learned above.
- Partial Fractions
- Mathematical Induction
- Pascal's Triangle
- Binomial Theorem
And that is all!
But there are many other interesting algebra topics such as:
- Euler's Formula for Complex Numbers
- Taylor Series (needs a basic understanding of derivatives )
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English teachers tell their students explicitly how to format their papers: what fonts, what page margins, what style guides, etc. Math teachers, on the other hand, frequently just complain amongst themselves in the faculty lounge about how messy their students' work is. Meanwhile, their students wonder why they've lost points on homework and tests.
Study these Guidelines , print out this " formatting " PDF, and improve your learning, retention, and test scores. Don't leave easy points on the table!
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Standardized test preparation platform at an affordable cost. Equipped with timed practice questions , video lessons , performance statistics and remote assistance . Available in both desktop and mobile.
COVERED STANDARDIZED TESTS
A non-profit, ed-tech initiative founded at Rice University, OpenStax provides free, peer-reviewed math textbooks in digital forms written by experts in the field. Printed versions of the textbooks are also available for purchase at a low cost as well.
- Pre-Algebra
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Paul's Online Math Notes
Founded by a math professor of Lamar University, Paul's Online Math Notes provides a complete set of free math notes and tutorials on specific math topics, with review questions and solutions integrated in between and other handy features such as cheat sheets and tables.
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A social learning platform dedicated to gifted students in math and science, where users learn by solving interesting problems of increasing difficulties.
FEATURED TOPICS
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A specialized, community-based wiki for mathematical proofs , housing a giant repertoire of definitions , axioms and theorems from all branches of mathematics. Also proved to be interesting is the random proof page on the site.
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A pion e ering educational company which partners with world-renowned math experts to offer 40+ online math courses , with materials presented in textual , audio and visual formats.
- Elementary Algebra
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A comprehensive platform with most of the undergraduate / graduate-level math courses offered by MIT , featuring video instructions, eTextbooks, presentation slides and other helpful materials.
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Online graphical calculator on steroids with calculus and statistics tools, plus other web applications for 3D graphing and the creation of geometrical figures . The favorite part? Graphs and figures created in GeoGebra can be exported to TikZ, thereby making drawing less time-consuming in LaTeX.
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A cloud-based LaTeX editor with real-time collaboration and rich text capabilities. It also provides an extensive database of LaTeX templates that one can choose from.
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Specialized platforms such as forums and question-and-answer platforms — where people gather and geek out about higher mathematics.
One of the most popular question-and-answer site on the Web. Since its LaTeX integration in May 2015, Quora has become a hub where higher mathematics enthusiasts around the world ask and answer ultra-specific questions related to their fields of interest.
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An educational powerhouse providing mathematical training to high-performing grade-school students all around the world.
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Are you looking for college algebra apps, tools, and resources that you can use with your students? If so, we have you covered. Check out our list below. Let us know if there are any that we missed.
Algebra tor – Algebrator is one of the leading math tutoring apps available. Using Algebrator’s step-by-step explanations of the answers to even the most difficult math problems, students can learn to solve homework problems in a way that is easy to understand. Algebrator can be used by parents, adult learners, and homeschoolers to improving their math skills.
Khan Academy – Khan Academy has more than 40,000 interactive Common Core-aligned practice questions and above 10,000 videos and explanations in economics, history, math, and more. This is the best study app and tutoring app for students of all ages who are struggling in science and other subjects. You can easily bookmark your best content to “Your List,” which can be used offline when you’re not connected to the Internet.
First In Math – The First In Math (FIM) online program offers comprehensive content in an engaging format, ranging from single-step addition to complex algebra. The game-style activities ensure that students engage in active practice needed for skill retention; they are motivated using electronic award stickers when they solve questions correctly.
GeoGebra – GeoGebra comes with an easy-to-use interface and many features that help you create, modify, and share math simulations and models. It comes with multiple platforms and dynamic math software that brings together tables, graphing, geometry, algebra, calculus, and statistics in a free easy-to-use package. The app also comes with free and open source software; it has received many educational software awards in the US and Europe.
Knowre – This is an interactive math learning app, which includes lessons on pre-algebra, algebra 1, and algebra 2. Some lessons are designed with comical introductions to improve the fun experience for the kids. There are also instructional videos and opportunities for kids to practice their skills. As kids progress, they earn a coin for correct answers; these coins can be used to unlock more lessons.
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The 12 Best Online Algebra Courses (2024 Rankings)
Last Updated: 09/16/2024
By My eLearning World
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Looking for the best online algebra courses to help you improve your math skills and boost your grades?
Algebra is one of the most important subjects in math, and it’s a required course for many high school and college students.
And while you might not realize it, algebra is used in a wide range of career fields, from engineering to medicine.
If you’re struggling with algebra, or just looking to improve your skills, there are a number of great online algebra courses available.
Online courses offer a flexible, convenient, and affordable way to learn, and many courses are self-paced so you can work at your own speed.
In this article, we’ve reviewed and ranked the best online algebra courses based on a variety of key factors, including content, price, student reviews, and instructor experience.
Disclosure: Some of the links in this article are affiliate links, meaning at no additional cost for you, we might get a commission if you click the link and purchase.
How We Chose the Best Algebra Courses Online
Algebra is an essential element of mathematics, and it’s important to have a good understanding of the subject in order to progress onto more advanced topics.
It’s all around us in things we do every day without even realizing it, and it’s also a subject we can’t escape in school
That’s why we put together this guide to help you find an algebra course that can help you get the knowledge and skills you need.
Our team of experts has reviewed dozens of mathematics courses to come up with the best ones available.
Our review process included:
- In-depth evaluations of each algebra course’s curriculum and course content by poring over the syllabus and taking lessons
- Analyzing student comments and course ratings to gain insight into experiences of real users
- Reviewing the credentials of each course’s instructor to verify they have the expertise and qualifications to teach effectively
- Looking at pricing options offered
After all of this, we came up with a list of what we truly believe are the very best algebra lessons and course programs you can take online.
We’ve presented our findings below.
What are the Best Online Algebra Classes?
Here are our top picks for algebra classes online worth trying in 2024…
1. Pre-Algebra (Brilliant)
This introductory algebra course will help you learn the basics of variables and equations.
Get access to all courses on the Brilliant platform with one of the following plans:
- Annual – $12.99/month (billed annually)
- Monthly – $24.49/month
- Groups (3+ users) – $299.88 (billed annually)
Click here to start a free 7-day trial.
The course is self-paced, with 28 interactive lessons.
If you’ve just stepped into the world of algebra, this course is a perfect way to kick-start your journey! The curriculum and topics covered will give you a brief insight into some basic algebraic concepts, along with diving into their complexities.
Once you’re done with the course, you’ll be able to solve complex algebraic equations on your own because of the in-depth dissection of the concepts.
You’ll also learn what tips and shortcuts you need to prioritize so that working with algebra becomes quick and efficient.
What You Will Learn
- How to work with Bar Models
- Understanding distributive properties and how they can be used
- How to evaluate and simplify algebraic expressions
- Polishing your skills by solving problems
- Understanding where and how letters can replace numbers
- How to create equations on your own
- How to find unknown values and order of operations
- Using prime numbers and understanding factorization
- Using circle puzzles and equations
2. Algebra I (Brilliant)
In this course, you can improve your algebra skills by learning equations, exponents, and more.
The course is self-paced, with 39 interactive lessons.
If you have some algebraic skills, it’s time to polish them.
Offered by Brilliant.org, this course curriculum focuses more on actively practicing algebraic concepts rather than just reading about them. This helps you build a stronger foundation as you progress through the course.
You’ll also be solving different types of problems so that you can apply your skills in various situations. This way, you’re better equipped to handle algebraic equations in the real world.
The fact that this course caters to people of both kinds- the ones who have extensive knowledge about the subject and the ones who are relatively new- is a plus.
- How to work with graphs of equations
- How to find answers using extensive methodologies
- Studying the concept of acceleration and velocity
- Common misconceptions in Algebra and how to get around them
- Understanding scientific notations and systems of equations
- Studying different types of equations, exponents, and factorials.
3. Algebra II (Brilliant)
In this class, you'll have the chance to play and experiment using interactive graphing apps to strengthen your foundation in algebra.
Get access to all courses on the platform with one of the following Brilliant pricing options:
Looking for a course that lets you dive into experimenting with algebra? If yes, then this course will be a perfect fit.
The instructor will take you through interactive graphing apps so you can practice algebra in an engaging way. You’ll also get to explore some methods not commonly taught in school.
The course aims to make you a pro in problem-solving so working with complex equations becomes a piece of cake. From polynomials to logarithms, get ready for a highly knowledgeable experience.
By the end of it, you’ll have a strong understanding of the subject and be able to solve complex equations with confidence.
- Unconventional and easy methods of Factoring
- Practicing model scenarios
- Studying different types of exponents and Factoring polynomials
- How to transform functions
- Understanding the dynamics of domain and range
- How to use functions for Shifts and Stretches
- Using negatives to achieve symmetry
- Getting prepared for inverse functions
- Exploring different types of power and radicals
- Projectile motion and how quadratics can affect it
4. Beginning Algebra: Building a Foundation (Udemy)
11.5 hours.
This course targets newbies and will briefly take you through the introductory concepts and make you well aware of how they can be implemented when dealing with algebraic equations.
The basic aim of this course is to act as a bridge between high-school-level algebra and college-level algebra. This means you can take up the course if you’re an eager student or if you’re a mathematician looking to revise his concepts.
The best part is that at the end of each chapter, you’re expected to undergo an assessment that will test your learning. This will help you identify your weak points so you can revise your lessons and emerge as a successful mathematician.
- Understanding the Order Of Application and its implementation
- How to perform operations on polynomial expressions
- Understanding factor polynomials and Graph Linear Equations
- How to solve Literal Equations
- How to simplify algebraic expressions
- Understanding the conversion between Scientific and Standard Notations.
5. Linear Algebra for Data Science in R (Datacamp)
$25/mo billed annually
If you know even a little bit about algebra, you’d know how important linear equations are. This course is your one-stop solution for learning everything about linearity in algebra, making it a popular pick amongst the masses.
The most unique thing is that all analysis is performed in R, a famous programming language, which simplifies the use of data science. If you’re familiar with R, there’s no course better than this to learn Linear Algebra!
- Working with Vectors and Matrices
- How to solve vector-matrix equations
- How to perform eigenvalue/eigenvector analysis
- How to do dimension reduction
- How to create Vectors in R
- What is the compatibility in matric vectors?
- An in-depth insight into WNBA data
- Understanding the properties and workings of Massey Matrix
- Understanding what is ‘Big Data’ and its importance
- What are the alternatives to Regular Matrix Inverse?
- How to solve matrix-vector equations using various methods.
6. Become an Algebra Master (Udemy)
12.5 hours of on-demand content.
Looking for a course that will make you a pro in Algebra? This course is an end to your search! Offered by Udemy, it has everything in the syllabus required to excel in the subject. From Order Of Operations to various types of graphing, it’s safe to say that the curriculum is designed to fit a wide range of topics without making it overwhelming for the students.
While the course doesn’t have any exuberant demands, you must possess a fair knowledge of arithmetic to understand the topics. Addition, subtraction, and multiplication of decimals should be a part of prior knowledge before proceeding with this course.
- Different types of equations and systems of equations
- Understanding fractions, exponents, radicals, and their properties
- How to complete the square
- Studying Like Terms and Functions
- How to work with Imaginary Numbers
- Understanding exponents and logarithmic functions
- Different types of Polynomials
- Getting the knack of Factoring
- Understanding and implementing Graphic Points
- What are the laws of logs?
7. Algebra 1 (Khan Academy)
22 hours for 241 videos.
If you’re looking for a comprehensive insight into the subject without spending a fortune, this course will be your best bet. Offered by Khan Academy, Algebra I takes you through the history of algebra and modern concepts as well. You can walk into the course without knowing anything, but it’s guaranteed that you’ll emerge as an Algebra master.
The best part is that this course is available for free, making it a popular choice among students and teachers. Each topic also has a quiz at the end, which helps you polish your analytical skills and revise all the information within a few minutes.
- A brief introduction to variables and substitution
- History of algebra
- How to evaluate expressions
- How to solve linear equations that have variables on both sides
- Understanding the dynamics of rate conversion
- Introduction to two-variable linear equations
- The importance and properties of horizontal and vertical lines
- What are systems of equations, and how to work around them
- Understanding functions and sequences
- Studying absolute value and piecewise functions
8. Algebra: Elementary to Advanced Specialization (Coursera)
Get started free
4 months (2 hours every week)
As it’s clear from the name, this course aims to enhance your expertise from beginner to expert in a couple of months. The curriculum is designed to cover both algebraic and geometrical concepts so you have a well-rounded insight.
Throughout the course, you’ll have several problems and equations to solve, which will help you polish your analytical skills. The best part is that it includes a shareable certificate at the end, which you can add to your resume or LinkedIn profile to make it stand out! You can also fit the course into your busy schedule because of its flexible timing. It’s entirely up to you if you wish to complete it within a month or take it slow over four months.
- How to solve linear, quadratic, and polynomial equations
- Understanding the properties of varieties of functions
- What are the properties of real numbers?
- Understanding the properties of graphs and domains
9. Algebra and Differential Calculus for Data Science (Coursera)
This course is a perfect choice for people who aren’t looking to dedicate weeks or months to understand the concepts of algebra. In mere eight hours, this course will take you through some of the most common algebraic topics and familiarize you with common problems faced by students.
This course is particularly famous among people who want to explore scientific fields but lack a mathematical background. If it sounds like you fit this description, head over to Coursera and register yourself for this course!
- What are logarithmic properties, and how to work around them
- Studying the core differences between continuous and non-continuous function
- How to know what a derivative is calculating.
- Dissecting derivatives and how they can be used for problem-solving
- How to create graphs of functions.
10. Linear Algebra II: Matrix Algebra (edX)
3 weeks ( 5-6 hours per week)
We know how important Linear Algebra is when it comes to studying the subject as a whole. The curriculum aims to take you through all the dynamics and properties of Linear Algebra so the foundations of your learnings are solid.
Once you’ve successfully mastered linearity, you’ll find the rest of the topics much easier to understand as opposed to diving into them without any expertise in Linear Algebra.
- How to perform algebraic operations with matrices
- Applying the Invertible Matrix Theorem
- How to solve and analyze matrix equations
- How to construct a basis for a subspace
- How to characterize matrixes
- Invertibility Theorem
- How to calculate the coordinates of a vector
11. Abstract Algebra: Group Theory with the Math Sorcerer (Udemy)
If you’re past the beginner level and looking for some advanced learning, give this course a go! Designed for college students, this course focuses on excelling in Group Theory.
The on-demand videos in this course will explain every step in detail and make the concepts easy to grasp. Once you’re proficient, you can easily solve complex Algebraic expressions!
Since this is an extensive learning course, you’ll have to make sure you stay vigilant during the lectures. Having a notepad and a pen with you is essential throughout the lesson so you’re able to jot down all tips and tricks. Your current Algebraic skill is bound to increase by ten folds if you complete this course.
- Introduction to Binary Operation
- Understanding Group and General Linear Group
- Finding the Order Of Element in a Group
- Learning how and why Functions are Subjective
- Multiplying Permutations in Array Notation
- How Equivalence Classes Partition a Set
- Learning the dynamics of Lagrange’s Theorem and proving its authenticity
- Understanding Normal Subgroups, Group Isomorphisms, and Quotient Groups
- Proving the First Isomorphism Theorem and the Second Isomorphism Theorem
12. Matrix Algebra for Engineers (Coursera)
Looking forward to making a career in engineering? This course is a must for you! Matrices always tend to drive mathematicians to their wit’s end because of their difficulty. If you also face similar issues when dealing with the topic, take this course, and you’ll be a matrice master within no time.
While the difficulty level of this course is past high school, instructors recommend it should be taken only by people who have taken a university-level single variable calculus course. You need to have good mathematical knowledge to take up this course so you don’t find any difficulty in understanding matrix Algebra.
The best part is that at the end of every lecture, you’re supposed to solve a bunch of related problems. This ensures absolute learning and helps you retain the information for a long time.
- Understanding Matrices
- What is the Determinant of the Identity Matrix
- Understanding the Systems of Linear Equations
- Performing vector addition and scalar multiplication
- Understanding Two-by-Two and Three-by-Three Determinants
- Learning the Leibniz Formula and Laplace Expansion
- How to find Eigenvalues and Eigenvectors
- Understanding how to find the Powers of a Matrix
- How to Compute Determinants Using Gaussian Elimination
What to Consider Before Signing Up for Algebra Classes Online
While our guide above is the perfect starting point for narrowing down your choices of algebra math courses, you still have to ask yourself a few questions to find the right course that best fits your needs:
- What is my current skill level? If you already consider yourself to be an advanced algebra learner, then you may want to choose a course that covers more complex topics. If you’re just starting out with the basics or are struggling with particular concepts, however, then it’s best to take it slow and start with something more basic.
- How much time can I commit to learning? Some classes might only contain a few algebra lessons designed for a quick learning experience while others might be more comprehensive and require more of a time commitment.
- What sort of support and resources are available? Does the course provide additional resources such as resource books, worksheets, or a forum where you can ask questions and receive help? These added extras can often make a world of difference when trying to master more difficult concepts.
- What’s my budget? Courses come in all shapes and sizes, so it’s important to compare and assess what’s available and decide which course best fits your budget.
- Can I take a trial version of the course? Many courses offer a free trial version so you can get a feel for the material covered before committing to purchase it. This is especially helpful if you are uncertain about a course’s suitability or if you just want to explore what’s available.
A Final Word on the Best Online Algebra Courses
No matter what your reason is for studying algebra, we hope this article has helped you find the best online algebra courses for your needs.
With so many great online course platforms out there today, there’s no shortage of options when it comes to finding the perfect algebra course for you.
And remember, many online course platforms like Brilliant have free trial periods, so you can always try out a course before you commit to it.
So what are you waiting for? Get started on your algebra education today!
Have any questions about our guide to the best online algebra courses? Let us know by commenting below.
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