Need Book Suggestion for self-teaching algebra and formal mathematics

[generic_]

Well I like math, but the problem is I've found this out recently. I knew I would have to learn math to I picked up "algebra demystified" but it is basically a work book with VERY little explaining. But I made it through most of the work was straight forward and it opened my eyes a little, and I realized I REALLY like math. I picked up the sequel to it you could say, called "college algebra". I can say that it has the same amount of explaining which is worse because the concepts are not as simple any more. Got up to graphing non-linear inequalities, but the sections are so short its moving to fast. But I've also be messing getting bit's and pieces of help else where, but its not good enough I need explaining. This can be a problem because most algebra books I've seen are written to an audience who doesn't care how it works they just want to get through it. (high-schoolers I guess : / ). I met someone online who was surprised at how much I liked math and thought I might have potential to go somewhere if I learn the important stuff right. He said I should look at Calculus by Micheal Spivak. Needless to say it was too much for me, but the first chapter was very interesting and proving some of the simplest mathematical concepts was more involved than I thought. But I really enjoyed it. From what I hear this is formal mathematics. I want to grasp the inner working of algebra not learn the "tricks". I want to be able to make my own method when the need arises! Now this is my learning situation, I've had pretty much no background of mathematics except what I've taught myself. The end of September will be 3 months now. I'm only 17. I don't have a teacher, I'm not in a classroom and can't afford a tutor. I'm teaching myself on my own. For reasons I would rather not discuss I will probably never be able to get to go to college. (probably is being generous) But I'm determined, I want to learn a lot more than algebra, but only after I understand it. Also If there is some book that helps ease you into to formal math that would be great too, but I'm more concerned about algebra. Thanks for reading this far.

 

[lurflurf]

I would think at this level you would want less explanations not more. What is important is to develope an ability to phrase problems in symbols, manipulate symbols, and understand the meaning of symbols.
Have a look at http://www.thiel.edu/mathproject/ATPS/PDF/default.htm a free online book and see what you think.

I would also recommend Serge Langs high school level books
Basic Mathematics by Serge Lang
Geometry by Serge Lang and Gene Murrow
and even more basic
Algebra 1: Structure and method by Mary Dolciani

 

[generic_]

Thank you for linking me to those books I appreciate it. Though as far as problems the algebra demystified includes some 300+ problems. I have also worked through a siezable amount of another free excellent book called http://cnx.org/content/col10614/latest/" The table of contents looks interesting. Any other suggestions? Since I'm teaching my self I try to use as many resources as possible instead of just one.

 

[Gear300]

If you've already covered Calculus (at least up to basic analysis of series, inclusive of Taylor's) and if you're intending to enter abstract algebra, I can recommend you two books. The field helps as a basic grounding before advancing into other mathematical fields.

1. "Abstract Algebra" by Richard Solomon -- the Sally Series
2. "Modern Algebra An Introduction," Fifth Addition by John R. Durbin

Both are good introductions...starting off, I would recommend you the 2nd one (be sure to read appendices A, B, and C after finishing Section 1). After finishing Chapter 3, you could start the 1st one while continuing with the 2nd (the analysis in the 2nd is actually more rigorous than the 1st, but some of the starting principles are better introduced in the 2nd than the 1st).

 

[generic_]

Thank you, I do actually intend to enter abstract algebra. But I have not covered calculus, I covered only the first chapter of the calculus book I mentioned. Thank you for the suggestions though, I will remember those when I cross that bridge.