[justinmeiners]

Author here.

I would say that modeling the computational process in math is not typically helpful (you already have a formal programming language) you should model the real-world (or at least computer world) problem you are trying to solve.

Carefully define operations and constraints, introduce abstractions for solving them, etc.

Do you have an example of an I/O problem you have thought about that you would like me to talk more about?

[dr0wsy]

Thanks for the article and discussion that sprang up around it!

The question I'm trying to ask is how I should express (part of) programs on paper using math when I don't see how they are related to math.

Example: How could I easily express a function that takes a string as input and outputs the string capitalized using math notation?

I understand that the problem you solve in the post should probably be put on paper first before you began writing any code.

My problem is to express programs in math when "calculate" isn't part of the problem description, like it is in the example in the blog post.

Edit: Changed example question.

[justinmeiners]

This is a great question. What I really tried to emphasize in the article is that math is not a formal language. Since its just you and coworkers, write out the parts you need as you need them, and ignore details. After all, its an exercise to help you think.

If I needed uppercase I would just say:

  `up(s)` is a function that maps a string s to its uppercase string

Writing that down, you and I already have a pretty good idea of how it works, or its included in our libraries, and we can figure out the details when writing the code.

This is of course assuming `uppercase` is a minor part of another algorithm. If it was the subject of discussion I might describe it like this:

  Let `u(c)` be a function that maps a characters to its uppercase character. In ASCII `u(c) = c + K` where K is some offset.

  To capitalize an entire string we need to apply that function to each character.

  Let `up(s)` = (u(c_1), u(c_2), ... u(c_n))
  where the string s = (c_1, c_2, ... c_n)

Perhaps that helps, but I don't think it addresses your question directly. I think you need some experience reading math to know how to describe problems, but I don't think you need to know fancy math. A knowledge of functions, sets, tuples, logic, summations, etc, will get most of what you need.

I highly recommend that book I linked in the article: "Introduction to Graph Theory" By: Trudeau

[dr0wsy]

Thanks for the explanation! An example to check if I understood you correctly.

  `func1(r, s)` is a function that sends a request `r` to a given server `s`. It returns a status code from the server.

How does that sound? It feels more like a spec than "doing math".

> I highly recommend that book I linked in the article: "Introduction to Graph Theory" By: Trudeau

I'll check it out! Does the book cover all the relevant parts you mentioned before?

Btw, it seems you don't link the book in the article. At least I couldn't find it when looked now.

[justinmeiners]

Sort of. That would absolutely be "allowed". Now whether that is useful to write out, depends on what problem you are trying to solve.

Here is another example

https://gist.github.com/justinmeiners/0aff3d98a66b4d5f109656...

> Does the book cover all the relevant parts

No, it isn't quite so comprehensive, but it will absolutely help you get started and help you decide if you want to learn more.

https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathe...