Where can I find advanced math books and practice materials for self-study?

[uoydniheB]

I want to advance myself in math so for the past couple months I've been self-studying my school textbooks. So far it's been successful and I've already worked through and completed the Algebra I topics (I'm in 8th grade, shoot me) we're supposed to cover through this school year, and started some Geometry. My main problem started when I noticed that the textbooks are designed in such a way to get schoolkids to think "math is fun" and all that ****, with flashy covers and random pictures of kids blowing bubbles placed on the pages. That led me to question the actual "mathematical content" and I realized that although I could "do" the problems I never felt I got an in-depth understanding of why I was doing the problems that way. I also found this link interesting, http://www.textbookleague.org/103feyn.htm which highlighted the possible flaws in textbooks. I'm not going to debate on the validity of this argument and I'm still going to use the school textbooks but the point is I want something other...

With this in mind, I was hoping someone could help me find some higher-level supplementary material to aid my math studies. I want to ultimately gain a good understanding of geometry, Alg II, Trig, pre-calc, plus maybe something extra and then be ready for a calculus class by 10th grade. (I know this is difficult but I am serious about self-studying) The only book on my reading list so far is Basic Mathematics by Serge Lang, and I am looking of more like that.

I'm also looking for some workbooks with just a lot of problems. I'm seriously dying from the lack of practice problems I can complete in my textbooks. In my Algebra I one there's a great section called "extra practice" which is peachy and all but there aren't any answers in the back of the book! Why would I do extra practice if I can't check my work, if I make a stupid mistake I have no way of knowing... I learn by looking back at my answers and catching myself on what I did wrong. I'm seriously surprised at the lack of such books, on Amazon I've only found one called "The Humongous Book of Algebra Problems" which has the frustrating format of giving the problem and then immediately giving the answer underneath it. I know in Russian you can find a dozen of such books on every topic, problems in front, then answers at back of the book. (I can read Russian but not too well, yes I know numbers are the same but it does matter when it will give certain directions, I'd get confused on what it's asking.) Maybe I'm just looking in the wrong place?
-------------
tl;dr version

1. Math books that cover the things school textbooks do + going deeper to gain better understanding (subjects on alg I,II; geometry, trig, precalc)

2. Math practice books for the above topics with a format similar to a bunch of problems listed and then answers in the back of the book.

Also, my school textbooks are "Holt, Rinehard and Winston" around 2007 edition.

Also also, sorry if a thread with such books has been posted before, I haven't found much with the search function

 

[Ivan92]

Hey uoydniheB, Welcome to PF! :)
Are you looking to purchase your books or find free online books/lectures?

 

[uoydniheB]

Purchase, but of course if there are online resources for extra work problems (w/answers somewhere) then links would be helpful as well.

 

[micromass]

Take a look at http://hbpms.blogspot.com/2008/05/stage-1-elementary-stuff.html
The site lists some of the best math books out there. And be assured that they are books that aren't flashy or dumbed down. Additionaly, many of the books in the list are freely downloadable!

I hope that this is what you're looking for.

 

[Ivan92]

Very well. I do not know much about Geometry sources but I will point some out to you when I find some online.

As for Algebra 2, I would suggest buying a College Algebra book (College Algebra is like Algebra 2, just a bit more advanced with harder problems). I have Michael Sullivan's College Algebra 8th Edition and it is a great book with helpful examples. It can be pricey but it's worth your education. Link: https://www.amazon.com/dp/0132402866/?tag=pfamazon01-20

I came across a free open source Trigonometry book, awhile back. Its free to download but if you want a hard copy, you are going to have to pay $15 I believe. I am sure it will do the job though. Link: http://www.stitz-zeager.com/

As for Pre-Calculus, it is a review of all the math you should have learned prior to Calculus (and will go over some new material as well). I have Michael Sullivan's PreCalculus. Again great book and I highly recommend it. Link: https://www.amazon.com/dp/0132256886/?tag=pfamazon01-20

Another resource you can use is Khan's Academy. It is a site full of video lectures starting from basic math all the way up to the calculus level math along with other subjects. A great resource if you want to see video lectures. Link: http://www.khanacademy.org/

Have fun in your learning adventure and enjoy your stay here in PF :)

 

[uoydniheB]

Thanks Micromass, very useful since most of them are free and I can use them whenever. I've noticed some of the links have things like the origins of certain math topics, that's pretty interesting.

Thanks very much Ivan, Sullivan's college algebra seems to be just the kind of thing I was searching for. (one kind of stupid question, there isn't much of a difference between 8th and 9th edition, right?) I'll start by getting that one and if I like his book I'll get the precalc one.

But if a lot of precalc is review of other topics why is it that my high school requires a full year of precalc before you could take calculus? I believe it also requires algebra II and trig to be taken separately (equaling two years for both) which would put me at kind of a disadvantage unless they allow me to take a test to advance like I'm planning to for geometry...

 

[Ivan92]

Well Calculus is a very hard subject. The purpose of Pre-Calculus is to make sure that you are ready for what Calculus will bring to you by reviewing all necessary Algebra and trigonometry. Calculus requires you to be really good in Algebra.

The math itself is the same in all of College Algebra. I really cannot say what the difference is between the two texts. But any should be good to go. If you really care, you can read the reviews of what people put about the book.

 

[feuxfollets]

I would suggest you look at these, especially since you're just starting high school.

http://www.artofproblemsolving.com/Store/index.php?

The math is not as "advanced" as a college level textbook, but it makes you think much more and really understand what's going on and how to use the math.

Those books have lots of good practice problems too.

 

[EBENEZR]

Well Calculus is a very hard subject. The purpose of Pre-Calculus is to make sure that you are ready for what Calculus will bring to you by reviewing all necessary Algebra and trigonometry. Calculus requires you to be really good in Algebra.

The math itself is the same in all of College Algebra. I really cannot say what the difference is between the two texts. But any should be good to go. If you really care, you can read the reviews of what people put about the book.

What if you're not ready for precalculus? Feeling pretty stupid, I checked out precalculus to find it equally confusing.

 

[A. Bahat]

For the record, don't worry about the edition of any textbook. In fact, the earlier ones are often better.