# Functional analysis

This is translation Work in Progress based on the german Functional Analysis course as pilot of Wiki2Reveal translation of a lecture into another language. At the same time the Wikibook about Functional Analysis provides already contain from the mathematical domain. The challenge is to combine the concept of template based generation of content in Wikibooks and Wiki2Reveal-slide in a joined concept or workflow, so that a mathematical theory (e.g. Lemma of Zorn) can (but non compulsory) be maintained at a single place in a MediaWiki and any update or correction of the content (e.g. of an mathematical expression) is visible in the WikiBook and in Wikiversity with an dynamic generation of slides Wiki2Reveal. With Wiki2Reveal the RevealJS slides and the corresponding Wikiversity learning resource are already in sync, due to the underlying maintenance of the learning resource in Wikiversity. If an article in Wikiversity is updated (e.g. by correcting a typo) then the Wiki2Reveal slides show the corrected Wikiversity content in the next preview in the browser. In mathematical expressions are often language agnostic, which means that the mathematical expression might be used in multiple languages without any need of translation or modification, i.e. the following formula looks the same in the english, german, italian and french learning resources.
    $\sum _{k=1}^{n}={\frac {n\cdot (n+1)}{2}}$
The reference might require to use an ID in the math-tags for the mathematical expression and mathematical expressions are handled similar to images in multilingual way. It would be kind to keep the section "Wiki2Reveal - Versions" for provided alternative previews of the mathematical content and the regular chapter structure as usable for a real application in lecture setting simular to Wiki2Reveal-pilot in the german Wikiversity course for Functional Analysis.

## Chapter 0 - Preliminaries

* Set theory - (Wiki2Reveal slides)
* Complex Numbers - (Wiki2Reveal slides)
* Vector spaces - (Wiki2Reveal slides)
* Linear map - (Wiki2Reveal slides)

## Chapter 1 - Introduction

* Norms, metrics, topology - (Wiki2Reveal slides)
* Topological Algebra - (Wiki2Reveal slides)

## Use of materials for lectures

The lecture is provided in a PanDoc slide format (PanDocElectron-SLIDE) in Wikiversity, which can be transferred into annotatable slides using the Wiki2Reveal tool or using PanDocElectron to load the Wikiversity source available online and convert it into presentation slides that can be used offline. You can also use Wiki2Reveal to create a RevealJS or DZSlides presentation directly from Wikiversity articles.

## Origin of materials

In the spirit of OER (Open Educational Resources), the lecture content should be made freely available. Initially, the slides created from the customizable wiki content were made available in a GitHib repository to facilitate download and use. However, maintaining and updating the content in a repository is very costly. Therefore, Wiki2Reveal was developed for the lecture slides, which allows to generate lecture slides directly from the wiki content and to annotate this online as well. The articles are usually annotated with as little text as possible, so that the generation of the slides also does not exceed the space on a slide. All slide pages in Wikiversity therefore have a note PanDocElectron-SLIDE at the bottom of the pages and are assigned to the Wiki2Reveal category. When editing these pages, please be careful not to overfill the slides. More detailed text about the slides is usually created in separate articles. If the explanation pages explicitly refer to a slide, the explanation page gets a marker PanDocElectron-TEXT and SLIDE or TEXT version refer to each other reciprocally.