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Ask HN: Which math/CS books follow a top-down approach for pedagogy?
Top-down approach:
Instead of building up from the axioms to reach a fact, first, a fact is presented, then it is shown how to use it in practice with examples. Then it is broken down to reveal how and where it comes from. Maybe a proof or something of that sort.
- bugfix-66 4y agoNumerical Recipes in C: The Art of Scientific Computing https://www.cec.uchile.cl/cinetica/pcordero/MC_libros/NumericalRecipesinC.pdf https://www.cec.uchile.cl/cinetica/pcordero/MC_libros/Numeri...
- throwaway81523 4y agoDo you have a particular CS or math topic that you want to study? Is there a book that you tried, that was too bottom-up? If it's in an applied area, like calculus or statistics, there are usually plenty of books that skip the theory and simply give you recipes to use. If it's a more theoretical area then the theory is presumably why you came, so of course they aren't going to skip it. It's also common to study application-style first, then theory later. So first you take "calculus", then "intro to analysis" which is the same topics as calculus but with the proofs done carefully, and then a more theoretical and abstract approach to analysis. If you start with an abstract textbook, you'll see a bunch of definitions and axioms at the beginning that might make the book feel self-contained like you can start from nothing, but in practice you are supposed to know the basics of the topic before you start such a book. Otherwise you will have a hard time. That might be the difficulty you've encountered.
- curious16 4y agoI am talking about a mixture of both such that both the applied and theoretical parts are well explained. But not in a theory first way. More like this: Here is a tool you can use to perform these many tasks in these many situations. Now that you have seen how it works, let us investigate why it works and where does it come from (maybe with a bit of history). Because stories are always easier to remember.
- throwaway81523 4y agoIt would still help if you could give a specific example of a topic you want to study that way. I think a book that includes a serious axiomatic approach is unlikely to include a "tool" approach, and vice versa. If you can name a specific topic, people here might be able to recommend specific books. I'd say if you want an applied approach, then just go for that. If you also want an axiomatic approach, do that afterwards, from a different book.
- __rito__ 4y agoDeep Learning for Coders by Howard, Gugger comes to mind. Absolutely top to bottom with no nonsense at all.
- curious16 4y agoI have heard about the book and the courses. What do you come out with after completing either of them? Can you read research papers and implement them and try to beat state of the art?
- bananabiscuit 4y agoI think “Who Is Fourier? A Mathematical Adventure”, would be an example of the kind of book you are looking for. Its a top-down intro to Fourier transforms that explains the derivation of the transform and why there are complex numbers involved, etc. Starts out very basic and top level, but covers all the important little details by the end.