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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) |
---|---|---|---|---|---|---|

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 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. |

MIT OpenCourseWare (includes math and other subjects, math courses relevant for high schoolers include only calculus-related courses) | [http:/ocw.mit.edu 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 (?) |

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 |

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 (?) |

Dr. Chris Tisdell (only math) | YouTube channel | calculus (integration onward), differential equations, and more advanced math | 10-25 minutes | Free | Reasonably good videos | 3 (?) |

IntegralCALC (only math) | integralcalc.pathwright.com | all of calculus | ? | Paid, free trial | Not evaluated | ? |

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 |

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, maybe 5 |

## 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 |