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.

 

[rezeew]

I can understand your desire to have a well-rounded mathematics library to further your studies and explore your passion for the subject. It is commendable that you are taking the initiative to restudy the topics you learned in high school in greater detail, as well as delving into classical math literature and the history of mathematics.

In selecting books for your home mathematics library, it is important to have a balance between depth and breadth of coverage. It would be beneficial to have a mix of textbooks that cover the core topics in mathematics, as well as books that focus on specific areas of interest. Some suggestions for textbooks that cover a wide range of topics in mathematics would be "Calculus" by James Stewart, "Linear Algebra" by David Lay, and "Introduction to Number Theory" by Richard A. Mollin.

In addition to textbooks, it would also be beneficial to have books that explore the history of mathematics and its evolution over time. Some suggestions for these types of books would be "A History of Mathematics" by Carl B. Boyer and "The Mathematical Experience" by Philip J. Davis and Reuben Hersh.

It is also important to have resources that can help you identify any gaps in your knowledge or areas that you may have skipped. One suggestion would be to use online resources such as Khan Academy or OpenCourseWare to supplement your studies and ensure that you have a thorough understanding of the topics.

Lastly, I would recommend seeking advice from your professors or other experts in the field of mathematics to get their recommendations for books that align with your interests and goals. With a well-rounded selection of books, you can continue to deepen your understanding and passion for mathematics.