Anonymous
11/25/2024 09:17
Subject: Re:AOPS Precalculus book
Anonymous wrote:Thank you. All you said sound right! We have done all intro books and the intermediate algebra book so far, and liked them. We will continue.
You should know by now that the AOPS books are in a whole different league from school math. Major League vs Little League.
School math is no more than the first example or 2 of each of a subset of the sections in the AOPS book. (And then that example is repeated 50 times on the homework and exam).
Anonymous
11/23/2024 21:28
Subject: Re:AOPS Precalculus book
Thank you. All you said sound right! We have done all intro books and the intermediate algebra book so far, and liked them. We will continue.
pettifogger
11/23/2024 21:04
Subject: Re:AOPS Precalculus book
First of all, why would you believe that kids should be able to understand any textbook 'cover to cover', nevermind this particular AoPS book?
To your questions:
- Yes, the Precalculus book is challenging and tries to go deeper into trigonometry than in a standard precalc book. That isn't necessarily a bad thing; one can take it as an opportunity to write down questions and try to resolve them by asking teachers/peers, or looking things up online and/or from other books.. basically an opportunity to learn how to learn.
- You cannot compare the Schaums series with a textbook, especially the AoPS precalc book. The Schaums series are meant for review of concepts for those who have already seen most of the material before. They're not meant to be used as first time teaching tools.
- The AoPS precalc book could be useful for some aspects of math contests, particularly ones that may contain trigonometry concepts. But that is not even remotely close to its main goal, which is to do a deep dive into 3 main topics and connect them together: trigonometry, complex numbers, and linear algebra basics (i.e vectors in 2D and 3D).
If your main goal is to have your child understand standard precalcus material (such as from the school AP precalcus course you mentioned), the AoPS book could be good for certain topics, such as the first few chapters on trigonometry. But that's likely to be a more difficult experience, due to the depth, as well as specific focus on the 3 topics I mentioned above, which may not quite match the typical precalculus curriculum found in schools.
If on the other hand, your goal is to have your child develop a deep understanding of important precalculus topics and how they are connected to each other, as well as to develop problem solving skills in the process (and even perhaps try out some problems that are either similar to, or actual from some past math contests), then the AoPS precalc book is a good choice. However, it is one of their more difficult books, so the bar is pretty high. If your child does not have any previous experience with other AoPS material, starting with the precalc book could initially feel like a very frustrating experience.
To your questions:
- Yes, the Precalculus book is challenging and tries to go deeper into trigonometry than in a standard precalc book. That isn't necessarily a bad thing; one can take it as an opportunity to write down questions and try to resolve them by asking teachers/peers, or looking things up online and/or from other books.. basically an opportunity to learn how to learn.
- You cannot compare the Schaums series with a textbook, especially the AoPS precalc book. The Schaums series are meant for review of concepts for those who have already seen most of the material before. They're not meant to be used as first time teaching tools.
- The AoPS precalc book could be useful for some aspects of math contests, particularly ones that may contain trigonometry concepts. But that is not even remotely close to its main goal, which is to do a deep dive into 3 main topics and connect them together: trigonometry, complex numbers, and linear algebra basics (i.e vectors in 2D and 3D).
If your main goal is to have your child understand standard precalcus material (such as from the school AP precalcus course you mentioned), the AoPS book could be good for certain topics, such as the first few chapters on trigonometry. But that's likely to be a more difficult experience, due to the depth, as well as specific focus on the 3 topics I mentioned above, which may not quite match the typical precalculus curriculum found in schools.
If on the other hand, your goal is to have your child develop a deep understanding of important precalculus topics and how they are connected to each other, as well as to develop problem solving skills in the process (and even perhaps try out some problems that are either similar to, or actual from some past math contests), then the AoPS precalc book is a good choice. However, it is one of their more difficult books, so the bar is pretty high. If your child does not have any previous experience with other AoPS material, starting with the precalc book could initially feel like a very frustrating experience.
Anonymous
11/23/2024 18:55
Subject: AOPS Precalculus book
We are currently working on the trigonometry chapters of AOPS Precalculus book at home. It looks getting complicated moving forward. . .
I am wondering if this book is designed for math competitions, or this is something that kids taking AP precalculus should be able to understand cover to cover with exceptions of a few very difficult topics.
By the way, Schaum's Outline of Precalculus seems popular. Is Schaum's better than the AOPS book if our purpose is just covering the AP precalculus contents.
Thank you.
I am wondering if this book is designed for math competitions, or this is something that kids taking AP precalculus should be able to understand cover to cover with exceptions of a few very difficult topics.
By the way, Schaum's Outline of Precalculus seems popular. Is Schaum's better than the AOPS book if our purpose is just covering the AP precalculus contents.
Thank you.