Preferences

Still remember the “advance calculus” book vs the “elementary set theory” in high school. To this day even though I got A in pure maths (count myself top 400 in 100,000 cohort) every time I heard the world “elementary” I shivered.

Any advanced thing no problem. Just do not start from the “first principle”. Please not. Please.


KasparEtter
For me, "from first principles" is not the same as "elementary". It's just about "reductionism" and answering all (or at least most) "why" questions. Let me know if you find any gaps in the explanations, which make it impossible for you to follow. While I would claim that the first five chapters of the article/"book" are fairly elementary, it's in the nature of the topic that things get more and more advanced after that. (PS: I'm the author of the blog.)
fuzzfactor
Well, I like it.

Your Contributions are highly admirable and easy to summarize as you have done, Focus, Notation, Intuition, and Completeness are major milestones on their own and I don't even experience the Interactivity on my browser.

I also agree with some of the other commenters who say the reader should already have more than just a bit of exposure to number theory beforehand, developing understanding of more introductory applications would be good and could probably be chosen to provide a particularly firm foundation for the march toward cryptography which gets quite advanced quite quickly.

Next, you might want to draft what could be considered a prerequisite text of your own for this masterpiece so the less initiated can get up to speed and get the most out of it. Also, I suppose your next two articles will be further advanced and could be easier to grasp for those who first have better understanding of what you have now.

KasparEtter
Have a look at https://explained-from-first-principles.com/number-theory/to... for the interactivity. :-)
broadwaylamb
To me, "from first principles" implies a certain presentation style that's different than what this article employs. It feels like you take it to mean "start from the axioms and build up without any gaps or unanswered whys" which is fine, but it turns into a laundry-list of topics the reader needs to get through before seeing the payoff, which in a way is no different from any other math text. I was expecting a more reverse-engineering approach where the first principles are derived from analysis of the problem / application, and we proceed from there.
hasmanean
Yup. Just buying and using a spoon is trivial, but building one from “first principles” is 1,000x harder.

This item has no comments currently.