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

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Discussion Overview

The discussion revolves around recommendations for building a personal mathematics library, particularly for someone looking to revisit and deepen their understanding of mathematics after a significant gap. The scope includes suggestions for textbooks, classical literature, and advanced topics in mathematics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses a desire to restudy mathematics in greater detail, emphasizing a newfound passion for the subject and an interest in its historical development.
  • Another participant suggests Spivak's Calculus as a rigorous option for studying calculus, despite acknowledging its commonality in recommendations.
  • A different participant mentions that a book illustrating the main ideas of calculus through historical context could be beneficial, indicating that "more detailed" could also refer to introductory analysis texts like "little Rudin."
  • One participant proposes exploring advanced topics by reviewing lists of mathematical subjects and selecting areas of interest, encouraging a library visit to sample books before committing to a purchase.

Areas of Agreement / Disagreement

Participants present various recommendations and approaches without a clear consensus on specific books or methods for studying mathematics. Multiple competing views on how to build a mathematics library remain evident.

Contextual Notes

Participants express concerns about potential gaps in knowledge and the importance of selecting appropriate resources, but specific limitations or assumptions regarding the recommendations are not fully explored.

Who May Find This Useful

This discussion may be useful for individuals looking to enhance their mathematics knowledge, particularly those interested in revisiting foundational concepts or exploring advanced topics in a structured manner.

drummerguy198
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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.
 
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drummerguy198 said:
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:smile:
 
drummerguy198 said:
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:

books?id=189kAkcrpYQC&pg=PP1&img=1&zoom=3&hl=en&sig=ACfU3U1KVSYCnrjQzU20PhZOK1Sh809d9w&w=575.jpg


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.
 
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.
 

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