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Online mathematics learning resources
From Cognito
This page lists a number of online math learning resources.
Video lectures
We list here resources that contain large numbers of video lectures. Note that some of these resources offer videos in other subjects. Comments about quality may not apply to the other subjects.
Resource | Website | Topics covered in the video lectures | Duration of the lectures | Cost | Comments on quality and links to reviews | Computational/conceptual spectrum (scale of 1 to 5, 1 for very computational, 5 for very conceptual) |
---|---|---|---|---|---|---|
Center of Math (only math) | Center of Math videos | Calculus and multivariable calculus (following textbooks published by them) | 50-70 minutes | Free | The videos are very good for in-depth learning. In general, the teachers exhibit considerable conceptual depth. The videos are long, and require patience to get through | 4, maybe 5 |
Calculus: Single Variable by Robert Ghrist (University of Pennsylvania) on Coursera | coursera.org/course/calcsing | Most relevant for people taking Advanced Placement Calculus, or who have already taken Advanced Placement Calculus and want to understand calculus somewhat better | 10-20 minutes | Free, but you need to register and enroll to watch the videos | The videos are part of a course with quizzes and course materials. However, some materials may become available only at a particular time of the year because the courses run on the academic year timetable | 4 (?) |
Math Doctor Bob (only math) | Courses (toggle between different course types -- the link goes to basic algebra) | High school algebra, precalculus, calculus, and multivariable calculus, plus higher math | 5-15 minutes | Free | Reasonably good videos. | 3 (?) |
MIT OpenCourseWare (includes math and other subjects, math courses relevant for high schoolers include only calculus-related courses) | ocw.mit.edu, most relevant subset: calculus courses | Most relevant for people taking Advanced Placement Calculus (or equivalent) or more advanced courses | Since these are mostly actual lectures delivered in college classes, they are generally about 50 minutes long. | Free | Reasonably good videos. The Highlights of Calculus course should be the most accessible to high school students since it provides a big picture overview of calculus. (Add links to reviews?) | 3 (?) |
Vipul's Classroom (only math) (COI disclosure?) | YouTube channel | Calculus and multvariable calculus (covers only selected topics) | 5-20 minutes | Free | Similar to Center of Math, but shorter videos often focus on more specific topics rather than on developing an entire thread. No corresponding book, but related pages at calculus.subwiki.org | 4 or 5 |
Art of Problem Solving (only math) (COI disclosure?) | homepage for videos | Middle school math and high school algebra and precalculus. | 5-15 minutes | Free | Focused on computational methods, but considerable emphasis on understanding the computational processes and why they work. The videos are synced with the AoPS books and courses, so you can learn the most from the videos by also buying the books. You can also use the videos to get a sense of whether you would like to try the AoPS courses. | 4 or 5 relative to the grade level (i.e., not as conceptual as the other resources, but highly conceptual relative to the grade level of the audience). |
Dr. Chris Tisdell (only math) | YouTube channel | calculus (integration onward), differential equations, and more advanced math | 10-25 minutes | Free | Reasonably good videos | 3 (?) |
Thinkwell | thinkwell.com | courses in high school math and calculus | 10-25 minutes | Paid (you can pay ~$150 for a year-long subscription to their video-based course, along with many supplementary materials) | Lectures are accompanied by summaries appearing on the side, that help with effective learning. We would recommend this highly if it were not for the cost. | 3, maybe 4 |
Khan Academy (includes math and other subjects) | khanacademy.org | Entire school math curriculum plus large parts of the introductory college math curriculum | 5-15 minutes | Free | Functional but unremarkable. However, the ability to pause and review video lectures, combined with the comprehensive curriculum coverage and integration with worked examples, may make this worthwhile. See reviews here, here, and here | 2, but the conceptual explanations are sometimes misguided. |
PatrickJMT (only math) | patrickjmt.com | Large parts of high school math curriculum and beginning college curriculum, including all of calculus | 5-10 minutes | Free, but you can donate to the author | Somewhat better than Khan Academy in terms of the quality of explanation, but no integration with practice exercises. The videos are very computation-oriented and place little emphasis on conceptual understanding. (Write a separate review, link to it? Or find reviews) | 1, but conceptual explanations, when offered, are likely to be correct. |
IntegralCALC (only math) | integralcalc.pathwright.com | all of calculus | ? | Paid, free trial | Not evaluated | ? |
Our top recommendations
We recommend the following based on the kind of learner you are:
Type of learner and stage | Our top recommendation | Supplementary resources |
---|---|---|
Middle school or early high school student (grades 6-9) who is reasonably good at school math but has not explored math much beyond school and wants to learn algebra or precalculus. | Start with the Art of Problem Solving videos (free). If you like them, consider buying the AoPS books and enrolling in the courses (costs money, but not a lot). See our algebra learning recommendations for more. | Khan Academy and PatrickJMT also cover many of the topics, but less well. We would not recommend these as primary resources, but you can use them to supplement learning for topics where you are unable to find AoPS videos. ThinkWell also has videos, but these are not free. |
High school student (grades 10-12) who wants to learn calculus. | Two relatively complete course sets you can consider: (a) The Center of Math videos (free) offer a strong conceptual foundation in precalculus and calculus. It may be worth buying the textbook (~$15) to supplement the videos. (b) Coursera's "Calculus: Single Variable" course by Robert Ghrist. In addition to videos, you also have course materials that you can use to study. See our calculus learning recommendations for more. |
Three other resources to consider for videos on some subtopics are: Vipul's Classroom (for a more conceptual version), Math Doctor Bob (for a reasonable mix of concepts and computational techniques), and MIT OpenCourseWare. |
High school student (grades 10-12) who has already learned Advanced Placement (AP) Calculus or equivalent but wants to understand some of the trickier topics of single variable calculus at the level taught in top colleges. | The majority of the calculus playlists at Vipul's Classroom are specifically designed for people who have already studied calculus at the AP level (or slightly less) and now want to understand it at the level of a college course. See our calculus learning recommendations page for more. |
We also recommend watching suitable subsets of Robert Ghrist's Coursera course and the Center of Math videos. |
High school student (grades 10-12) who has already learned Advanced Placement (AP) Calculus or equivalent and wants to study multivariable calculus. | Two relatively complete course sets you can consider: (a) The Center of Math videos (free) offer a strong conceptual foundation in multivariable calculus. It may be worth buying the textbook (~$10) to supplement the videos. (b) MIT OpenCourseWare multivariable calculus course. |
Math Doctor Bob has a set of videos on multivariable calculus. Vipul's Classroom has playlists dealing with partial derivatives, gradient vectors, directional derivatives, and other select topics of multivariable calculus. |
Online practice and diagnostic assessment
Resource | Website | Topics covered for diagnosis and assessment | Cost | Dependencies between topics included? | Detailed solutions provided? | Can learners keep track of their mastery? |
---|---|---|---|---|---|---|
ALEKS | aleks.com | Most of school math and calculus | up to $20/month, but free 14-day trial | Yes, in a very detailed form using knowledge spaces | Yes | Yes |
Khan Academy | khanacademy.org | Most of school math and calculus | Free | Yes, but very preliminary | Yes, and partial hints also provided | Yes |
Brilliant | brilliant.org | Middle school and high school math and calculus, may not comprehensively cover all topics | Free | No, but they may be building it soon | Yes (?) | Yes |
IXL | ixl.com | Most of school math | about $20/month, but heavy discounts for use in classrooms, with $200/year per classroom of 30 students | ? | Yes | |
Varsity Tutors | varsitytutors.com, practice tests here | Many subjects, including mathematics | practice tests are free; there are other resources on the website |