5 ms·

Thanks for the references, I'll have a look. I can tell you what I don't want: books that throw theorems one after the other without any context, like Baby Rudi

Thanks for the references, I'll have a look. I can tell you what I don't want: books that throw theorems one after the other without any context, like Baby Rudin [1] for instance. I tried once to read Terence Tao's Analysis I [2], it's really good but my main problem was that I wasn't able to know if my proofs are correct when I do an exercise. So maybe the solution is to get a teacher. [1]: https://en.wikipedia.org/wiki/Principles_of_Mathematical_Analysis https://en.wikipedia.org/wiki/Principles_of_Mathematical_Ana... [2]: https://terrytao.wordpress.com/books/analysis-i/ https://terrytao.wordpress.com/books/analysis-i/

rramadass 3mo ago
AI is a godsend here. One can use the Socratic (aka Maieutic) method with AI to both explain and verify one's understanding. For some references see https://news.ycombinator.com/item?id=48342887 https://news.ycombinator.com/item?id=48342887 I have used Google's "AI Overview" and "AI Mode" profitably to have it explain new concepts to me in simple terms and also have had it verify my own understanding of something. The reason i prefer it is because it is a search-driven reasoning engine and thus gives references (in tooltips) directly to the latest sources/articles on the web from which it synthesized its answers.
- nathan_compton 3mo ago
  I've got a PhD in Physics (undergraduate in Math, fair amount of self study) and I have to caution against taking what the AI's say seriously.
  - rramadass 2mo ago
    One has to know what one is doing and think before doing it. As an example, there can be "AI Librarian" and "AI Reasoner" personas which set boundaries for what each should do. The former is for organization of data with citations and synthesizing answers objectively with simple explanations while the latter is for more detailed deep dives with logical analysis and thinking. Note however, that persona's must be distinct in terms of data usage and not role-playing which is largely ineffective.
BeetleB 3mo ago
I'll second the suggestion to use a good LLM. I haven't tried it with analysis, but I did for linear algebra. It would quickly spot flaws in my proof.

rramadass 3mo ago

AI is a godsend here. One can use the Socratic (aka Maieutic) method with AI to both explain and verify one's understanding. For some references see https://news.ycombinator.com/item?id=48342887 https://news.ycombinator.com/item?id=48342887 I have used Google's "AI Overview" and "AI Mode" profitably to have it explain new concepts to me in simple terms and also have had it verify my own understanding of something. The reason i prefer it is because it is a search-driven reasoning engine and thus gives references (in tooltips) directly to the latest sources/articles on the web from which it synthesized its answers.

nathan_compton 3mo ago
I've got a PhD in Physics (undergraduate in Math, fair amount of self study) and I have to caution against taking what the AI's say seriously.
- rramadass 2mo ago
  One has to know what one is doing and think before doing it. As an example, there can be "AI Librarian" and "AI Reasoner" personas which set boundaries for what each should do. The former is for organization of data with citations and synthesizing answers objectively with simple explanations while the latter is for more detailed deep dives with logical analysis and thinking. Note however, that persona's must be distinct in terms of data usage and not role-playing which is largely ineffective.

BeetleB 3mo ago

I'll second the suggestion to use a good LLM. I haven't tried it with analysis, but I did for linear algebra. It would quickly spot flaws in my proof.