普林斯顿数学分析读本

• 沐澜

  2024-01-06
  Real analysis is typically the first course in a pure math curriculum, because it introduces you to the important ideas and methodologies of pure math in the context of material you are already familiar with.
• 沐澜

  2024-01-06
  Real analysis is hard. This topic is probably your introduction to proof-based mathmatics, which makes it even harder. But I very much believe that anyone can learn anything, as long as it is expained clearly enough.
• 任平生

  2020-01-29
  In the future, whenever you encounter a problem that uses a new definition, you should first try to fully internalize the definition before applying it to the problem. Write out what it means in both words and symbols, play with some basic examples, understand how it works in R or R^k , and draw pictures.
• 任平生

  2020-01-27
  My hope is that you learned more from this book than just how to prove that a sequence converges (you did learn that, right?). You learned how to think rigorously;you learned how to deal with infinity, in cases where your intuition wouldn’t help (for example, with countability or series). Most of all, I hope you learned that going slowlyand understanding the definitions first can make all the difference.
• 任平生

  2020-01-27
  remember that it all comes back to the basics. Everything relies on real numbers, topology, and sequences. If you can master those topics, the rest will be a breeze! Really.
• 任平生

  2020-01-26
  We’ll skip over these simple proofs, because time is money, and money can buy you a blank notebook to try writing these proofs yourself.