Well rounded list of books for starting a home mathematics library.

[drummerguy198]

I have taken all maths through Calculus I in high school, which was back in 2008. I am back in college again, this time with a renewed interest in math and philosophy. Without going into too much detail, I think it safe to say that the last thing on my mind in high school was school, which I very much regret, however well I actually did (3.85 GPA, National Honors Society). I retained much of what I learned and found it all relatively easy (with the exception of vectors). However, I didn't have quite the passion for math that I have now. I want to restudy all of what I learned, but in greater detail. Also, I have found that I am very much fascinated by classical math literature and the history of how different topics of math evolved over time.

The only worry I have about buying books without the advise of others is studying for a long period of time only to find that there are gaps in my knowledge or whole topics/concepts that I have skipped.

 

[BloodyFrozen]

I want to restudy all of what I learned, but in greater detail.

If you want more rigor in math, try Spivak's Calculus (eventhough cliche)
Good Luck

 

[fourier jr]

I want to restudy all of what I learned, but in greater detail. Also, I have found that I am very much fascinated by classical math literature and the history of how different topics of math evolved over time.

for calculus this is the book for you:

it was never intended to be a textbook or a history book, but in illustration of the main ideas of calculus through the issues that came up for the people studying it.

I guess "more detailed" could also mean intro analysis (like little Rudin), & there are about a dozen good books on that stuff.

 

[Anonymous217]

How about more advanced topics? Try checking out a list of mathematical topics (on arXiV or Wikipedia) and see which one jumps out at you the most. A field you've been dying to learn about, or even a field that just "sounds cool." Then go to a library (probably a uni's) and check out some books on the topic to see if you like it.
This way, you'll get a pretty broad understanding of what's out there and you can focus on the stuff you like and not what we recommend.