User:Bocardodarapti/Comments

Some comments on the remarks above.

I guess I have to explain how I work and what the reasons are for doing so.

1) First of all, it would be nice if no move are taken which result in pages like Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I/Lecture 7, where a large section is now missing. This is all part of the course Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I which is taught at the university of Osnabrueck by me as a professor of mathematics. There is a German and an English version, as there is a certain amount of international students who use the English version. If you really think that Wikiversity is no space to write and present the material of a mathematical course taught at a university, please tell me, though I would be surprised.

2) I do not produce here any nonsense, to the best of my knowledge. In the German wikiversity, I have done about 26 (just counted) mathematical courses over 15 years, all given at my university. See Hauptseite for a list.

3) The material is not original research, my original research I submit to journals (see arxive or Zentralblatt). The material is quite standard for a university beginners class, trivial or not. (it is the first time I hear people saying that a mathematic course is trivial)

4) The approach for the number  as the double of the first zero of cosine goes back to  Landau and is well established since 100 years. In this approach, the sine and cosine are defined by their power series and the relation to the circle is developed later.

5) I agree that I did not make any systematic effort here (on the English wikiversity) to explain the way I am working. Let me try to do this in the following.

6) Modular approach (small bits). If you look in any mathematical book you will see that it consists of quite small and well differentiated items: Definitions, facts, proofs, examples, remarks, exercises, usually with a consisting numbering to find them quickly. Along these mathematical textforms I organize the material, in order then to be used in a course (by transclusion, see again the course).

This has many advantages.

a) The material can be used in several courses just by transclusion. A theorem like Polynomial ring/Field/Zero/Linear factor/Fact is used in an analysis course, in linear algebra, for applied mathematics, in Galois theory. Exercises can be used on an exercise sheet and on an exam. A fact can be transcluded with one proof or another. Learning lists can be made like List of definitions.

b) One can always link to the relevant definitions, when the term is used.

c) One can link in a proof to the relevant facts (or exercises) which are used. d) the material can be categorized in a systematic and detailed way (this I have not done here, as I want to transclude it from Wikidata).

7) The naming of the pages: I basically list the relevant items used, like Real numbers/Sequence/Limit and convergence/Definition. It is a definition which describes for a sequence within the real numbers what it means to be convergent. That I use here "/" has the mentioned effect that it is formally a subpage of Real numbers. For convergence in another ordered field or complex numbers or a metric space I (would) use a similar naming. In practical terms, I do not see any problem. An alternative would be to use - instead of /.

8) MDLD (mathematical definition link deviation): these are pages which help to make links to definitions. Basically everywhere I want that a term used somewhere is linked to its definition. In order to avoid always writing the link to the definitions, these deviations do the job. See e.g. what links to Real numbers/Sequence/Limit and convergence/Definition. How it is used, you can basically look everywhere in the course, like Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I/Lecture 15.

Bocardodarapti (discuss • contribs) 16:12, 30 December 2023 (UTC)