Books to review before entering Calculus?

[nickadams]

i'm about to enter calculus, and I'm worried I have a weak background in K-12 math.

What are some good books I could review over my month-long winter break to get ready for calculus? I could study like 6+ hours a day and since the concepts in K-12 math are not overly complicated I think I could get a lot done review-wise. Do I need to get a book for algebra 1, geometry, algebra II, and precalc like they had it structured in high school or do some books have some of those subjects combined?

 

[micromass]

Go over the book "basic mathematics" by Lang. It's all you need.

 

[nickadams]

Go over the book "basic mathematics" by Lang. It's all you need.

really, all K-12 math topics can be covered in one book? That's pretty sweet.

Since I doubt I will have time to complete every problem in the textbook in 1 month, does anyone have a syllabus for a class that assigned problems so I can take advantage of an experienced teacher's selection of problems?

 

[nickadams]

I was wondering if there are books that treat introductory math topics "rigourously"? I want to try to read Spivak's calculus after I strengthen my high school math background, so I thought it may be useful to have seen some rigourous treatment of classes like Algebra I and II, geometry, and Pre-cal...

Any suggestions? I would like to start from the beginning and work my way up to Spivak's calculus...


Edit: @ Micromass, thank you for the lang recommendation. I found out my library has that book and I will definitely use it but I still wanted to ask about how I could strengthen my high school math background enough to prepare me for spivak's calc.

 

[eumyang]

What are some good books I could review over my month-long winter break to get ready for calculus? I could study like 6+ hours a day and since the concepts in K-12 math are not overly complicated I think I could get a lot done review-wise. Do I need to get a book for algebra 1, geometry, algebra II, and precalc like they had it structured in high school or do some books have some of those subjects combined?

For Algebra I and Algebra II I would recommend Lial:
http://www.pearsonhighered.com/educator/product/Introductory-Algebra/9780321557131.page"
http://www.pearsonhighered.com/educator/product/Intermediate-Algebra/9780321574978.page"
These are college textbooks for remedial classes. The teaching is done in the text. There are plenty of exercises.

If you haven't done so, look at the "https://www.physicsforums.com/showthread.php?t=122924" (by Allendoerfer & Oakley) for a rigorous Pre-calculus course.