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  1. Last 7 days
    1. Woit does provide problems, but they are all at the back of the book. It would have been better to see them between chapters. That provides a natural break in the material and gives the student a quick check on his understanding.

      Homework problems are pedagogical devices and many (most) authors place them in the text near where they would be profitably be done. They also provide a useful break in the text to prompt more novice students to actually perform them at the end of a section.

      More advanced students, however, should have caught on eventually at the need to work out examples for themselves which are presented in a textbook, but they should also be seeking out additional problems where ever they appear in the text, not to mention seeing out any outside additional problems, making up their own, and exploring any additional questions these pose.

      In mathematics textbooks this working of problems, expanding on them and seeking out new ones is often a large part of what is lurking behind the sometimes nebulous sounding idea of "mathematical sophistication". The rest of that equation typically includes experience with the various methods and means of proofs and some basic background in logic.

  2. Jun 2020
  3. Apr 2018
    1. A red hand stencil. A series of lines that look like a ladder. A collection of red dots.

      All these are forms of art that prove some sophistication because these marks were not left randomly and there surely was a purpose and/or meaning behind them.