Discussion Overview
The discussion revolves around recommendations for advanced and serious books on Number Theory and Set Theory, following the completion of a basic course in Number Theory. Participants share their suggestions and opinions on various texts.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant suggests looking for advanced Number Theory books after finding their previous course easy.
- Another participant recommends textbooks by Kunen, Jech, and Hrbacek for Set Theory.
- For Number Theory, a suggestion is made for Ireland and Rosen's book, assuming some knowledge of abstract algebra.
- Burton's book is mentioned as a more accessible option for those seeking an easier text.
- Trygve Nagell's book is noted as impressive by one participant.
- Hardy & Wright's text is highlighted as a highly-rated option that covers a wide range of topics without being too trivial or obscure.
- Apostol's and Landau's books are also recommended for Number Theory, with a note that there are multiple authors named Landau.
- One participant argues that Hardy & Wright is superior due to its larger size compared to Apostol's and Landau's books combined.
Areas of Agreement / Disagreement
Participants present multiple competing views on the best texts for Number Theory and Set Theory, with no consensus reached on a single recommended book.
Contextual Notes
Some recommendations depend on prior knowledge, such as familiarity with abstract algebra, and the discussion does not resolve which book is definitively better.