That are required to understand vs that are necessary for the next chapters

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Looking on the internet deeply has found these results:

that are required to understand is the most popular phrase on the web. 

that are necessary for the next chapters

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that are required to understand

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Some examples and use cases from the internet:

Some examples and use cases from the internet:

  • It doesn't look like this phrase is very popular! The search could not find any examples on the internet.
  • If you are going to present a new idea or technique, find the three or four important concepts that are required to understand the new idea, and review those ...
  • Which websites will help me learn mathematics that are required to understand quantum physics? Nuclear Physics: What distinguishes ...
  • It is important to remember, however, that the basic mathematical concepts that are required to understand introductory statistics are not prohibitive for any ...
  • USMLE Step 3 examination tests on general topics that are required to understand and practice concepts of general medicine/ family medicine. The following ...

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