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Center of Math

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Center of Math (website centerofmath.org) is a research and teaching center that offers textbooks and corresponding video lectures related to many topics of mathematics. Their textbooks cost about $10/book in digital PDF format and about $30-40/book in print format. Their video lectures are closely synchronized with their textbook, and can be viewed for free online if your Internet connection supports playing YouTube videos.

Their books (available here) include:

  • Worldwide Differential Calculus by David B. Massey
  • Worldwide Integral Calculus by David B. Massey
  • Worldwide Multivariable Calculus by David B. Massey
  • Worldwide AP Calculus by David B. Massey: This combines the Differential and Integral Calculus texts and presents the material in a format suitable for students taking Advanced Placement Calculus.
  • Worldwide Differential Equations with Linear Algebra by Robert McOwen
  • Worldwide Pre-Calculus by Kenneth Kutler

Advantages

  • The books and videos are synchronized with each other. This means that if you are willing to buy the books (the digital editions are reasonably priced, and the print versions are also priced much cheaper than most calculus textbooks), you can get an integrated course experience with both lectures and a textbook.
  • Unlike some other resources such as Khan Academy, the authors of the books are knowledgeable about the subject at a deep level, and this is reflected in their choice of topics and mode of exposition.

Aspects that might be advantages or disadvantages depending on what you want

  • The videos are about 50-60 minutes long each, and are intended to mimic college lectures in length. This can be an advantage in that it allows the instructor to develop a topic in considerable depth. It can be a disadvantage because students may not have the attention span needed for such a long lecture.
  • The videos emphasize conceptual understanding over computational proficiency. The instructors often make parenthetical remarks about subtleties. This can be an advantage or a disadvantage depending on what you are looking for.
  • The lectures use the standard format of a lecturer at a chalkboard. This can be an advantage or disadvantage depending on the video format that you prefer.

Reviews

Kristin Lie wrote the following review of the service in a Quora answer:

Having only watched videos in Chapter 2 of the multivariable calculus section, my experience is rather limited, but I assume all the videos are fairly similar.

Pros:

  • Both more-concrete and more-conceptual explanations are provided.
  • The example problems are fairly straightforward and progress from easier to more difficult.
  • The teacher makes verbal or written mistakes very rarely, and corrects them before they can cause confusion.
  • The videos themselves follow a logical progression and are clearly named, so it's easy to see what you've studied before and what is new to you.
  • All the videos are freely available on CoM - Videos and YouTube.


Cons:

  • The videos are all about an hour long, and if you don't have time to watch the whole thing, it's hard to restart where you left off.
  • Most high schoolers would likely become bored and stop paying attention well before the end. Obviously, this isn't a problem for people who look up calculus videos on the internet for fun!
  • I would like to see more applications of the concepts.
  • Occasionally there are references to the textbook, which isn't a problem in itself but slightly annoying when one is too cheap to purchase the textbook.
Overall, I think it's very good as a free resource; I'd probably be willing to pay for it, but not exceptionally much.