How to Use AOPS Books for Self-Learning: Tips and Recommendations

[member 624364]

Hi, I just acquired the art of problem solving prealgebra book.

So I would like to ask, how does one use the AOPS books, are they meant to be supplementary to a full textbook? Or are they used for introducing new concepts that you would have leant in a textbook etc.
I am hoping to use the AOPS Introduction to algebra book alongside a full textbook on algebra 1 once I am finished with prealgabra. I would like advice on how to get the most out of it, as a self learner that is.

Also, would anyone be able to recommend a complementary full algebra 1 textbook for my introduction to algebra book? I already know about open stax. I could use that one, but I am wondering if there is anything people consider better?

Thanks.

 

[Wrichik Basu]

If you have a good book from where you have already learned and understood the topics well, then it is of no use to again study the topics from another book, because that is simply waste of time. I'll advice you to first concentrate on the problems: study the solved examples before starting with the exercises. That will help you understand whether the book has anything extra that you've not studied. In such a case, you can just go through that topic from that book. This will save you time, and also help you to get in touch with advanced problem solving strategies.

Regarding the algebra 1 book, I haven't got one in hand, so let's hope someone else will help you.

 

[member 624364]

If you have a good book from where you have already learned and understood the topics well, then it is of no use to again study the topics from another book, because that is simply waste of time. I'll advice you to first concentrate on the problems: study the solved examples before starting with the exercises. That will help you understand whether the book has anything extra that you've not studied. In such a case, you can just go through that topic from that book. This will save you time, and also help you to get in touch with advanced problem solving strategies.

Regarding the algebra 1 book, I haven't got one in hand, so let's hope someone else will help you.

Thanks for the reply. I understand what you are saying for prealgebra since I pretty much already know all of it.

However, when I go on to learn algebra which I don't know all of. Is it still best to use just one book instead of 2? Would it be considered a waste of time to use 2 books even when your learning from both at the same time, and not simply using it to review everything you already know?

 

[member 624364]

As well, to anyone that knows about the Aops books, should I use them as a full textbook?
Or more as a problem solving book when learning which ever part of algebra is in the accompanying textbook I would be using?

 

[Wrichik Basu]

However, when I go on to learn algebra which I don't know all of. Is it still best to use just one book instead of 2? Would it be considered a waste of time to use 2 books even when your learning from both at the same time, and not simply using it to review everything you already know?

If you can use two books at the same time in the way you've mentioned, I'll not stop you. I cautioned you because I've seen many students wasting time in studying same topics from different books. If you can use two books properly, then you're welcome to do so. In higher classes, we need to refer to three or more books, in case neither book is self-sufficient.

 

[TurboDiesel]

Hi Novantix,

How do you like the AoPS Prealgebra book?

For anyone looking for a similar approach . .

Understanding the curriculum:
- AoPS curriculum is designed to build mathematical thinking aka problem solving ability aka 'mathematical maturity'. (You get a genuine 'feel' for how math works.) Complete the curriculum and the 'maturity' (or problem-solving skills) you gain will be formidable. This ability will be increasingly useful in upper-undergraduate level STEM courses.
- They recommend not skipping topics covered (e.g. Counting and Probability) before advancing in the curriculum.
- It is very comprehensive coverage, so you don't 'need' another textbook.

Intended use of the curriculum:
- It's targeted at top 5% (in the US) students, who would use it as a primary curriculum.
- They think it is 'accessible' to top 20% students, when used as a primary curriculum--in a class which is targeting that broader group.
- If you are a top 5% (in the US) student who's already covered the material, you could simply do the two problem solving books (more fast paced coverage, than found in the main curriculum).

I disagree with the 'top 20%' idea and would suggest anyone can do this stuff, not just 'top 20%' students. For people who have already studied through calculus, I think Jenny Olive's "Maths: A Student's Survival Guide" would probably be an excellent prequel. Or you could start with the AoPS Prealgebra book (and continue) without any prequel studies. Since AoPS books are designed to build 'maturity', it is perfectly OK--or even desirable--to work through them in subjects that you've already 'learned'.

For regular people (not 'top 20%') who haven't studied this stuff (not even prealgebra), I suggest studying from a text designed to teach everyone first. That is, first study a regular prealgebra book. And second, then start a regular algebra book--at the same time you study the AoPS Prealgebra book. Third, study a regular geometry book--at the same time you study the AoPS Intro to Algebra book. By the time you've completed the AoPS Intro to Geometry book, you might have gained enough 'maturity' to jump straight into the AoPS Counting and Probability book without first studying a 'normal' counting and probability book.

I would suggest both of these groups of people start with the AoPS Prealgebra book. AoPS guys actually have a training software (covering the first half of the AoPS curriculum) which provides excellent solutions to problems after you complete them. It's called "Alcumus." They basically have a proof approach to problems even at the prealgebra level. I would suggest emulating that approach to your best ability for every problem. So you find it easy? Great, then concentrate on the quality of your solutions (as opposed to simply getting a right answer). AoPS is about the approach, not about simply being 'right'.

Note: AoPS is targeting mathematical thinking, so plan on being challenged and actually getting some problems wrong. Perfectly normal. Starting with the Prealgebra book should ease the transition.

Regular books that might be useful as prequels:
- No idea about prealgebra.
- I've seen some people really like Harold Jacobs' "Elementary Algebra" and "Geometry" (Geometry 2nd edition is supposed to be less colorful picture oriented and more proof oriented than Geometry 3rd edition).
- Intro problem solving / love-of-math: Harold Jacobs' "Mathematics: A Human Endeavor" (Jacobs' algebra and geometry books follow a similar approach). This book 'can be used before or after algebra' and touches on algebra, geometry, combinatorics, and more.
- Chris Jeris had some interesting recommendations that might be useful, here (for a second look, at least). The Gelfand books were written for distance learning:
Gelfand/Shen "Algebra"
Gelfand/Glagoleva/Shnol "Functions and Graphs"
Gelfand/Glagoleva/Kirillov "The Method of Coordinates"
David Cohen's "Precalculus with Unit Circle Trigonometry" (note Cohen wrote several different precalculus books)
- Or, if in a rush, you could try Jenny Olive's book as a primary 'regular' text (starts with algebra and goes through basic calculus).Hope this helps!

 

[MTB]

Hi, I just acquired the art of problem solving prealgebra book.

So I would like to ask, how does one use the AOPS books, are they meant to be supplementary to a full textbook? Or are they used for introducing new concepts that you would have leant in a textbook etc.
I am hoping to use the AOPS Introduction to algebra book alongside a full textbook on algebra 1 once I am finished with prealgabra. I would like advice on how to get the most out of it, as a self learner that is.

Also, would anyone be able to recommend a complementary full algebra 1 textbook for my introduction to algebra book? I already know about open stax. I could use that one, but I am wondering if there is anything people consider better?

Thanks.

Im not using AoPS algebra book but based on my experience with its introduction to geometry I’d say the book itself can be used as a full textbook ( I looked through some other introductory geometry textbooks and the contents are quite similar, but this may be different from person to person).

Sorry can't help u with the algebra book recommendation though as I am not very familiar with the books out there regarding the field