Textbook
1. Introduction
2. Algebra
3. Geometry
4. Number theory
5. Probability
6. Combinatorics
7. What's next?
7.1 What to do after your first pass
7.2 Learning new material
7.3 I'm done! What's next?
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7.2 Learning new material
Achievable AMC 10/12
7. What's next?

Learning new material

I’m ready to learn new material.

Great! Either you’ve achieved a high Memory Strength on the topics already in your deck, or else you have some extra time that you’d like to spend learning new material. Either way, you’re in the right place.

Your next move is to skim through the book and find a topic that looks interesting that you haven’t already “completed.” (I.e. a topic whose quiz cards are not yet in your deck.) If none of them jump out at you as especially interesting at this time. just pick the first one that isn’t already complete.

As I’ve mentioned, the point of this course isn’t actually to increase your understanding of this material very much. Not quite, anyway. Instead, the point is to bring your recall of key facts and techniques to such a high level that thinking about any topic immediately and effortlessly brings relevant formulas and techniques directly to mind. Actually learning new material is mostly your job. But of course I’ll do everything I can to help!

So, now that it’s time to learn some new material, I recommend this sequence:

  • Read through the topic as presented here, and if there are any examples, work through them as well.
  • If there are any specific links in the book to other resources, follow those links.
  • If you feel you need even more information and examples in order to feel comfortable, search for more information and examples (e.g. through Google). In most cases, that’ll give you everything you need.
  • If you’re still having trouble, please email me and I’ll do my best to get you unstuck.

Once you’ve done that, you should understand the new material pretty well, so you’re ready to start quizzing.

Continue to come back here as needed until there is nothing left in the course for you to learn.

Summary: what to do next

  • Learn one of the topics in the book that you don’t already know.
  • Use the book as a starting point, but use other resources as well.
  • You’re finished when you’ve gone through all the chapters, and your Memory Strength is high.