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Discover open online courses in calculus, geometry, statistics and more

It’s hard to overstate the shortage of STEM-educated professionals in today’s job market. The U.S. is struggling to graduate enough scientists, engineers and mathematicians from its colleges and universities to keep up with demand. One result of this problem is the rising number of alternate online education options like massive open online courses (MOOCs), seminars, apps and podcasts to educate students and professionals. This guide takes a look at the variety of online math courses available today, many of which are free of charge, to practically anyone with a high-speed internet connection.

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10 Must-Take Online Math Courses for All Levels

There are dozens of excellent math courses available from a wide variety of quality online sources, such as edX, Coursera and Alison. As a way of introduction, the following list offers a look at some of the best:

plusCalculus I

Offered by: Academy
Price: Free, optional proctored exam for $25
Length: Approx. 130 hours
Format: Text, workbook, quizzes and final exam
Eligible for college credit?: Depends on the academic institution.

This course offers a detailed introduction to functions, limits, continuity, derivatives, graphs, and the relationship between derivatives and graphs. This course is divided into five learning sections plus appendix. The course begins with a review of algebra specifically designed to prepare students for the study of calculus.

plusDifferentiation and Functions in Mathematic

Offered by: XSIQ via Alison
Price: Free
Length: Two to three hours
Format: Text and assessments
Eligible for college credit?: No

Intermediate math course that covers rules and applications of differentiation, inverse functions, graphing circular functions, the Binomial theorem, logs and indices, straight line graphs, and factors of polynomials. Students must complete all modules and score a minimum 80% in each of the course assessments to qualify for the course certificate.

plusGame Theory

Offered by: Stanford University/University of British Columbia via Coursera
Price: Free
Length: Nine weeks, five to seven hours per week
Format: Videos, slides, quizzes, online lab exercises, problem sets, final exam, screen-side chats
Eligible for college credit?: No

Game theory concerns the mathematical modeling of strategic interaction among rational and irrational agents. This course provides the basics of game theory, including topics such as: representing games and strategies; the extensive form (game trees); Bayesian games; repeated and stochastic games; and others.


Offered by: Khan Academy
Price: Free
Length: Varies, self-paced
Format: Videos and exercises
Eligible for college credit?: No

Eighth-grade-level course covering all aspects of basic geometry through a series of self-pace modules. Topics covered include: angles, parallel lines and transversals; parallel and perpendicular lines; missing angles with a transversal; parallel lines; measure of angles formed by a transversal; and equation practice with congruent angles.

plusIntro. to Statistics

Offered by: Stanford University via Udacity
Price: Free
Length: Eight weeks, six hours per week
Format: Self-paced with videos and exercises
Eligible for college credit?: No

Beginning level course offering an introduction to techniques for visualizing relationships in data and systematic techniques for understanding the relationships using mathematics. The course consists of six lessons and a final exam on topics such as: visualizing relationships in data; probability; estimation; outliers and normal distribution; inference; and regression.

plusIntroduction to Mathematical Thinking

Offered by: Stanford University via Coursera
Price: Free (additional fee required for textbook purchase)
Length: Eight or 10 weeks, eight to 10 hours per week
Format: Videos, discussion forums, quizzes, textbook
Eligible for college credit?: No

The course is offered in two versions: An eight-week-long basic course for students who want to develop or improve mathematics-based, analytic thinking for professional or general life purposes; and a ten-week-long extended course designed primarily for high school seniors or first-year college-level students considering a major in mathematics or a mathematically-dependent subject.

plusLinear Algebra – Foundations to Frontiers

Offered by: University of Texas at Austin via edX
Price: Free; optional verified certificate for $50
Length: 15 weeks, eight hours per week
Format: Videos, exercises, visualizations and programming assignments
Eligible for college credit?: No

Course covers standard topics taught in typical undergraduate linear algebra courses, including: connections between linear transformations, matrices, and systems of linear equations; partitioned matrices and characteristics of special matrices; algorithms for matrix computations and solving systems of equations; vector spaces, subspaces, and characterizations of linear independence; and orthogonality, linear least-squares, eigenvalues and eigenvectors.

plusNonlinear Differential Equations: Order and Chaos

Offered by: Boston University via edX
Price: Free; optional verified certificate for $49
Length: Five weeks, eight to 10 hours per week
Format: Video
Eligible for college credit?: Credit may be available through the Alternative Credit Project.

An introduction to the mathematical theory of ordinary differential equations. The course follows a modern dynamical systems approach. Students learn: how to apply linear systems theory to nonlinear systems near equilibrium points; how to use nullclines to simplify phase plane analysis and discuss systems with conserved quantities, dissipative systems, and gradient systems; a basic understanding of chaotic systems using the Lorenz system.

plusStatistical Learning

Offered by: Stanford Lagunita (Stanford University)
Price: Free
Length: Self-Paced
Format: Video, textbook (available in PDF at no charge)
Eligible for college credit?: No

This is an introductory-level course in supervised learning, with a focus on regression and classification methods. Topics covered include; linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods; nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; and support-vector machines.

plusTechnical Math for Industry

Offered by: Colorado Community College System
Price: Free
Length: Five weeks, four hours per week
Format: Self-paced, videos
Eligible for college credit?: No

This course reviews the fundamental processes of mathematics with an emphasis on problem-solving techniques. Students select individual math concepts or proceed through each of five self-paced learning modules. Topics include introductory algebra; rudiments of analytic geometry; elementary trigonometry; introductory statistics and basic finance. The course also contextualizes math for trades, including machining, welding, electro-mechanical, and engineering graphics.

Find the Right Online Math Course for You

The number and variety of open online courses in mathematics is growing almost daily. Math is a broad field, however, which can make finding the right online course to match a student’s particular area of interest challenging. The search tool below is designed to help prospective students locate the right math course for you. Course listings include information on price, length and required time commitment, starting date, and institution.

Types of Online Math Classes

Students taking open online courses typically do so with a clear result in mind, something most providers understand and take into account when designing their courses. Open online math courses, for example, are commonly offered with one or more of three options: for credit (usually college credit); with a certificate of completion; or simply for learning enhancement. Here’s a more detailed look at each option:

  1. 1


    Description: A common option for open online courses. Certificates provide proof of the successful completion of the course, allowing the student to verify their work on a college application or resume.

    Who takes this type of course? Individuals, often already in the workforce, seeking verification of math skills to enhance their job prospects or improve their on-the-job performance.

  2. 2


    Description: Still a relative rarity. Some courses offer the potential for college credit. Students should always confirm acceptance of credit for an online course with their intended postsecondary institution before beginning the course.

    Who takes this type of course? Students who intend to pursue a college education and want to get a head start by compiling some college credits at low or no cost..

  3. 3


    Description: Almost always an option with open online math courses, particularly those offered at no charge. Students typically work at their own pace, focusing on those parts of the course that interest them the most.

    Who takes this type of course? Almost always an option with open online math courses, particularly those offered at no charge. Students typically work at their own pace, focusing on those parts of the course that interest them the most.

Top 3 Benefits to Taking an Online Class in Math

Success in any online course depends a lot on the individual’s own motivation. There’s no instructor or fellow class member looking over your shoulder to make sure you’re keeping up with your work. If self-discipline is not a problem for you, then online math courses provide a lot of advantages. Here are three key benefits to studying math online:

  1. 1

    Learn math concepts at your own pace

    Mathematics can be a tricky subject and for some students, going over some specific areas and problems several times is essential to getting it right. Most online math courses are asynchronous, meaning that students can tackle difficult sections at their own pace. This allows students to repeat lectures as often as needed to nail down tricky math concepts.

  2. 2

    Avoid remedial math courses in college

    First-year college students must often pass an initial placement exam for core subjects like English and math at the beginning of their first term. Low scores on an entry-level math exam can mean that students need to take remedial math classes before moving on to their other classes. A great way to avoid taking remedial math courses is to brush up on one’s math skills with an open online course before heading off to college.

  3. 3

    Learn the specific concepts you want or need

    Online math courses are a great way to take on a brand new subject area, or enhance one’s skills in that area, without having to cover the stuff in a traditional math class that you’re not interested in. This offers a big advantage for those needing some specific knowledge for a particular problem or project at work, for example.

Essential Apps and Podcasts for Mathematicians


There are apps for everything today, including mathematicians and math students. Math apps can be of tremendous assistance when learning a new area of the subject or when complex calculations are called for. Students can choose from among dozens of apps designed specifically for them. Here are just a few of the most popular:

Algeo Graphing Calculator

Free ($2.99 for some in-app products)

Graphic app that allows users to draw functions, find intersections and show a table of the values of the function. Features include: symbolic differentiation; definite integrals; Taylor series calculations; and equation solutions.

Mathway – Math Problem Solver


Free (in-app products from $9.99 to $99.99)

One of the most popular math apps out there. Mathway’s problem solving engine answers a huge variety of math problems, such as basic math, algebra and linear algebra, trigonometry, calculus, statistics, finite math, and more. Additionally, the apps built-in graphing calculator provides detailed graphs to accompany solutions.

MyScript Calculator


How about this? With the MyScript Calculator app, users handwrite mathematical expressions on the screen of their device. The app then converts handwritten symbols and numbers to digital text, performs the calculations, and delivers the results in real time.

Wolfram Alpha


An encyclopedia of everything math, science, engineering, and more, right at your fingertips. It also does calculations. Math subjects covered include elementary math, plotting, algebra, matrices, calculus, geometry, trigonometry, discrete math, number theory, logic functions, definitions and more.


Podcasts are another great source of knowledge for mathematicians, math educators and math students. Many go beyond the equations to explore the meaning and importance of math in theoretical, practical and even personal terms. And some of them are just plain fun. Want to get excited and inspired by math? Check out a podcast, like one from one of these sources:

Pulse-Project Math/Maths Weekly Podcasts
Peter Rowlett and Samuel Hansen
Recent Episode to Try:
Math/Maths 120: Math Wins US Election

Described as, “a conversation about mathematics between the UK and USA,” the hosts discuss all things mathematics. There are currently over 120 podcasts that can be accessed from this site.

Mathgrad Podcasts
Christopher Frederick
Recent Episode to Try:
Show #13: We make your mind all woobely discussing infinity

This series of podcasts are meant to provide, “… an educational tool for high school and early college students, as well as people of all ages involved in IT-related occupations.” Hosted by a graduate student in the mathematics department at Colorado State University.

University of Oxford Podcasts
Recent Episode to Try:
The Irrational, the chaotic and incomplete: the mathematical limits of knowledge

If there are such things as high-brow math podcasts, this is where you’ll find them. Yet these Oxford hosts keep the discussions fun and interesting for pretty much all listeners. The site currently offers access to 60 math-related podcasts.

Math Mutation
Erik Seligman
Recent Episode to Try:
216: Bowie Meets Escher

Another great site with math-related podcasts described by the host as, “… for people of all ages, where we explore fun, interesting, or just plain weird corners of mathematics that you probably didn’t hear in school.” The 220 individual podcasts can also be accessed for free through iTunes.

Expert Interview with Mike Feerick, CEO of Alison

What is the purpose, or purposes of open online courses?

The number one thing is accessibility. We’ve been putting big price tags on education for as long as we’ve had organized education. Today, we have the technology to make engineering and math education, among everything else, much more accessible. We can also make it free. People use Google and Facebook every day and they’re extremely profitable companies and yet you get a very good product for free. The same with ALISON, with nearly eight million online, and every one of those people have studied for free.

Can you tell us about your online offering in the field of mathematics?

Many years ago, we partnered with McMillan, the UK publisher, and created about 400 videos with high school teachers going from the very basics of math, that a student would be doing at middle school, right through to college. And what we’ve done is collated these videos and put them in different orders according to the different national standards. Math education is something that is pretty standard around the world. So once these resources are created and are digital, the marginal cost of providing [them] to another person is next to zero. So if we have the opportunity worldwide to teach everybody math for free, why wouldn’t we do it? That’s why you need platforms like ALISON.

Are you seeing any resistance from people who still think that, because these open online learning resources are free, their quality is questionable?

The answer is no. There’s very little resistance today because the ordinary consumer has gotten to the stage where they expect to get very good math education resources for free online. It’s becoming so widespread and so many people are producing good quality content.

Where do you see the future of online learning heading, particularly in regard to math?

I think you are going to see the platforms like ALISON dominating online education in engineering and math. We will be signing up 300,000 people to our website this month alone. And that’s a lot of people and a lot of studying. So, the idea that you are going to charge for knowledge that is freely accessible on the web – I just don’t see the old ways of teaching math and engineering to be something that’s going to last.

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