Working Through Class Material

Suggested Order

We've found that the material in our courses is the most manageable for students when they work through it in this order.

  1. Complete any pre-class reading.
    If the class has a required textbook, then you'll have weekly assigned readings. Those readings are noted on the Overview tab of the course homepage. Other classes have a specific Handouts tab where short handouts are provided with a brief prerequisite material about the week's topic. Before class, read the assigned sections of the book for that week or the handout.
    • If the weekly readings come from a textbook, we encourage you to also look over the How To Use The Books guide below.
  2. Attend class, if possible, or read the transcript.
    During class, we encourage you to actively participate, and ask questions if anything is unclear.
    • If you cannot attend class, review the transcript as soon as possible and post any questions you have on the course message board.
  3. Work through the homework for the week.
    • If you have Alcumus assignments, work on passing those topics first. Alcumus problems help you to gain a better understanding of the material through problem solving and prepare you for the more difficult Challenge Problems you will encounter on the Homework tab. Refer back to the class transcript and/or textbook if you're having trouble with particular problems or topics.
    • After passing the assigned Alcumus topics, then attempt the short-answer Challenge Problems on the Homework tab of the course homepage. Continue to to refer back to the class transcript and/or textbook if you are having trouble with particular problems. You can visit the course Message Board to look for helpful discussions about a problem you are stuck on. You can also create a new post asking for assistance if needed.
    • Finally, if the course has Writing Problems, try to tackle any Writing Problems after you've had time to work through Alcumus and the Challenge Problems. Doing so will make the Writing Problems much less daunting. As with all other problem types, your class transcripts, textbook, and message board may also be useful sources of help.

Some courses also have brief videos, available on the "Videos" tab of the course homepage. We recommend inserting those as fun additions wherever you're interested.

Because the majority of your learning will come from actively engaging with the material and wrestling with problems yourself, rather than watching someone else solve a problem, we consider these videos supplementary to the rest of the available resources. However, the videos can provide a nice change of pace and break from homework, especially if you're feeling a bit stuck.

Be sure to also look over the following pages for some additional tools for success in an AoPS course: It Will Be Hard and When You Get Stuck.

Read The Solutions!

When working through problems in each of the steps above, be sure to read the solutions!

Whether you have solved a problem correctly or not, we encourage you to carefully read over the solution provided. Solutions to textbook exercises can be found in the corresponding Solutions Manual.

For questions that you didn't answer correctly, read about how you could have solved the problem. For questions that you did answer correctly, read over the solution to ensure that you understand it— you may learn something, such as a new method to solve the problem. Also, the solutions provided are great examples of well-written solutions, which you can to refer to when you are asked to write your own.

How to Use the Books

Try the problems given at the beginning of the section before reading the section. If you can't solve some of the problems, it's OK. Those problems will all be fully solved as you read the section. Even if you can solve all of the problems, it is still important to read the section and all solutions. This allows you to check for understanding, and you may find that the book's solution is even simpler or easier to understand than your own.

For the weekly textbook readings, you do not need to work through all of the Exercises at the end of each section. However, you are welcome to use these problems whenever you want additional practice. The problems you will see in your homework will be different problems.

A Note To Parents and Guardians

We believe that students learn best when they are challenge with hard problems that at first they may not know how to do. That is motivating philosophy behind each Art of Problem Solving textbook.

Rather than first introducing new material, and then giving students exercises, we present problems at the start of each section that students should try to solve before the new material is presented. We start with examples that are used to explore the new topic or technique, followed by a formal presentation of the material and solutions to the example problems. The goal is for students to discover the new material on your own. Often, complicated problems are broken into smaller parts, so that they can discover new techniques one piece at a time. Then, the new material is formally presented in the text, and full solutions to each problem are explained, along with problem-solving strategies. Each section and chapter is further completed with new exercises that ask students to practice that they have recently learned.

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