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!
