Wolfram Computation Meets Knowledge

Learn Algebra from the Ground Up with Wolfram Language

Learn Algebra from the Ground Up with Wolfram Language

Algebra is an essential course for understanding nearly all mathematics at the high-school level and beyond. Whether you plan to calculate profits at a business, balance a chemical equation, write efficient computer code or even just figure out which weights to put on the bar at the gym, algebra is completely indispensable. It’s no wonder that elementary algebra is a required field of study regardless of your eventual career or academic goals.

I am pleased to announce that we are launching a free interactive course, Introduction to Elementary Algebra, which aims to help students learn algebra entirely from the ground up. Whether you are a beginner wanting to learn algebra for the first time, someone looking for a refresher or are curious about how to use Wolfram Language to learn and visualize algebraic concepts, this course is made for you. This course introduces students to basic algebraic terminology and rules, then uses these ideas to explore everything from linear equations to systems of inequalities to quadratic equations. Along the way, powerful Wolfram Language functions are used to verify, simplify and visualize all subjects of discussion.

Clicking the following will take you directly to the course, where you can immediately begin to explore the world of algebra.

Go to free course

Motivation from History

The roots of algebra can be traced all the way back to the ancient Babylonians, who had developed a comparatively advanced arithmetical system with which they were able to do calculations using algorithms, or steps, for problem solving. In fact, we get the English word algorithm from a corruption of “al-Khwārizmī,” a Persian mathematician who lived roughly 12 hundred years ago and who is widely credited as being one of the fathers of algebra as a whole. Algebra even comes from al-Jabr, an abbreviation of the title of a book al-Khwārizmī wrote about how to balance and solve equations systematically. Many of the methods he discussed—updated with the notation introduced by the ancient Greek mathematician Diophantus—are still in use today.

Despite its ancient origins, algebra remains a relevant foundation to nearly every part of society. There are many questions in the real world that you might want to answer without knowing every single detail, and algebra equips you with the power to find those answers yourself.


The course begins with a full introduction to the basic terminology, notation and ideas of elementary algebra. Students will then learn how to write, solve and graph linear equations before moving on to linear inequalities and systems of linear equations. The lessons conclude with an introduction to polynomials, which are then used to introduce and understand quadratic functions and equations.

Here is a bit of a sneak peak of the lessons that comprise this course:

Course topics

This course has 28 primary lessons and one bonus lesson. I have made sure to pace the early lessons in particular very comfortably so as to ensure that the ideas have time to breathe and settle appropriately for even the newest student of algebra. My expectation is that you can finish watching all of the videos and complete the six short quizzes in roughly 10 hours.

Students taking this course need to know nothing other than the basics of arithmetic—addition, subtraction, multiplication and division—in order to dive in.

The rest of this blog post will discuss the different pieces of this course in more detail.


This course is built around a collection of 28 lessons that aim to build the student’s problem-solving abilities and give them a solid sense of mathematical intuition. The first lesson of this collection asks the question “What is algebra?” and explains how algebra is distinct from arithmetic and why that distinction matters. The lesson continues by giving a brief history of the origins of algebra and a quick but in-depth look at where algebra is useful in the modern world, then outlines and summarizes the course as a whole.

Lesson 1 of Introduction to Elementary Algebra

The lessons in this course all contain examples that are worked out in real time in the corresponding videos. A full lesson notebook with detailed solutions is also included for each lesson. Wolfram Language usage is explained in careful detail, and students can use the code contained in the notebooks as a template for finding their own solutions, performing their own simplifications and generating their own graphs. Any code in these notebooks can be copied with a simple click, and that code can be pasted into (and edited within) the scratch notebook area at the bottom of the screen.

Videos for each lesson are roughly 16 minutes in length, but may be shorter or longer depending on the requirements of the material—the video on simplification, for example, is by far the longest video given the prime importance of that skill in the study of elementary algebra.


Each lesson includes many worked examples to demonstrate the solution processes for all of the subject matter in the course, and additionally includes a separate set of exercises that are not featured in the accompanying video. Because this course is intended to facilitate independent study, these exercises also have solutions included.

Exercise 1


Each of this course’s six sections ends with a 10-question multiple-choice quiz. The questions in these quizzes are intended to be of comparable difficulty to the exercises and general material from the relevant sections, and I expect that anybody who reviews the material beforehand will be able to pass the quizzes without difficulty.

Quiz 1

Students receive instant feedback upon submitting their responses to the quiz questions, and can use any method they think is reasonable to arrive at the correct answer.

Course Certificate

Students who wish to take advantage of everything this course has to offer will, by the time they complete it, have watched all 28 lessons and passed the six quizzes. At this point, students can—and should!—request a certificate of completion showing that they have achieved proficiency in the field of elementary algebra. This certificate can easily be added to your resume or social media profile too!

Course certificate

This course also has an optional final exam that you can take after completing all of the material. This final exam has more questions and a slightly higher difficulty than the quizzes, and passing it will net you a more advanced Level 1 Certification.

A Building Block for Success

I’ve said it many times, but it bears repeating: elementary algebra is absolutely fundamental to society, and no matter what your academic or career path might look like, learning algebra will help you along that path. Scientists of all stripes, businesspeople, programmers and developers, and just people who do things like watch sports or go grocery shopping or lift weights all benefit from having a working knowledge of algebra and some of the mathematical intuition that comes with that. It is my hope that this Introduction to Elementary Algebra course will provide you with that knowledge and intuition and set you up for success in whatever field you choose to pursue.


This course is the result of the work of many people. I would like to thank Alejandra Ortiz Duran, Devendra Kapadia, Amruta Behera, Cassidy Hinkle, Joyce Tracewell, Veronica Mullen, Bob Owens, Matt Coleman, Mariah Laugesen, Laura Crawford and Anisha Basil for all the work they put into getting this course up and running.

Want more help? Register for one of Wolfram U’s Daily Study Groups.


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