The purpose of MathVerse.org is to provide a reference for the study of mathematics at the intermediate level between the skills of the elementary level and the level of scientific research or, in other words, from the level of high school to that of university under/graduate courses. The realization of the intent depends essentially on the speed with which articles are added to the collection: in order to build a body of information that is as complete as possible in a short time, it is necessary to make use of the contribution of the largest number of international experts willing to cooperate. This enlargement of the number of authors necessarily requires the exercise of appropriate directives aimed at controlling the growth of the material, its coherence and its quality: standards of the site, described below, must be used by the creators of the articles and enforced by moderators.
Standards for the preparation of articles
Sections Mathematics and Applications
Directives relating to sections Mathematics (except for cathegory New strands) and Applications concern
- Complexity level of the argumentation
The material is classified according to three different levels of complexity:
- ★ represents an rgumentation that needs to be understandable by those who have only basic skills level, comparable to those generally acquired by students attending the first two years of High school,
- ★★ represents the next level of difficulty approachable by those who have mastered the content on the lower level, and are comparable to a student of the last years of High school,
- ★★★ corresponds to the level of detail of the content that is found in university courses.
- Titole and subtitle
The title of the article must be self-explanatory, the most synthetic possible and must not exceed the length of a line. The article could also show a subtitle of maximum length equal to two lines: it has to be placed directly under the title. Under the group title-subtitle, separated by a blank line and in a separate line, it shall be stated the level of complexity by putting the image of the gold star (Source = images/Article-Images/Star.png Dimensions = 21 × 20) once, twice or three times.
Each article is accompanied by a list of keywords to be included in the tags section. The keywords should refer to all the concepts used in the text and the subject areas (according to the classification of MathVerse.org) to which the content relates, except the name of the category in which it was included. Among the keywords it must also appear the level of difficulty marked with the abbreviation 1S which stands for ★, 2S for ★★ and 3S for ★★★.
Three blank lines below the indication of the complexity it is needed to insert an abstract presenting briefly (maximum 15 lines) the content of the article.
- Article’s body
The text of the article is separated from the abstract by means of a blank line. The text should be divided into sections progressively numbered 1., 2. ... and, if appropriate, into subsections numbered n.1, n.2, ... (where n is the section number) and it is preferable that it contains as a first section an introduction.
- Exposition of the concepts
The article content should give priority to the resolution of problems than to simple calculation rules: an article describing only calculation rules will not be accepted. All the concepts that were introduced in articles on the same subject and in the same category, but of lower complexity, must be considered well-known, thus used without the need to define and explain them, however a link to the occurrence of their definition must be added. For the new concepts that are already defined in articles of lower or equal complexity about other topics and / or in other categories, the preferable approach is to introduce them briefly, so as to make clear both the meaning and the use, and to place a link to the article that defines them. Each new concept other than those already discussed within the collections must be brought out starting from discussion of its origins — also identified in the reasons that have prompted its definition — and the benefits that may result from its use, and then elaborated by means of an argumentation which is initially informal and intuitive and then becomes gradually formalized up to the mathematical rigor. The requirement is mandatory regardless of the level of complexity the article.
- Contextualization and exemplification
The article must be uniform and complete as regards the argument that it addresses, relative to the level of complexity faced. The material must be contextualized precisely and key links to other related topics must be provided, without getting too much on the details. Both the examples necessary to introduce the concepts and those (including effective counterexamples) required to fully understand their meaning, use and possible developments must be included.
- Multimedia content
The article may contain, sparingly if they consume resources, the following multimedia contents.
- Formulae and PSPicture: they can be incorporated using LATEX language. For those unfamiliar with the language, the code — which goes placed between two symbols , as in , to enter a formula on the same line of text or between two pairs of , as in , to insert an isolated formula — can be obtained using any online editor, such as www.codecogs.com/latex/eqneditor.php. Formulae can be numbered and you can insert references to numbered formulas within articles. For examples of PSPicture you can consult Mathapedia. Since the symbol has a special meaning as an identifier of formulae, if you need to insert it you must enter instead the corresponding image taken from the site (Source = images/Article-Images/Dollar.png Dimensions = 8 × 14 Advanced→Style = vertical-align: -1px;).
- Images: must not exceed size 800px × 600px and resolution of 92 px/in. Images are uploaded to the site (up to five at a time) with the special tool provided in the menu on the creation of articles, which stores them in the folder “images/Article-Images/username”.
- Videos: can not be uploaded to the site, you need to include a reference to the resource present in other sites, such as YouTube, using the html tag iframe. As the authors are not allowed to enter html code, the correct procedure is as follows: copy the embed code ‹iframe src="/..."...›‹/iframe› and paste it replacing the angular brackets ‹ and › with square brackets [ and ]. The site administrator will enter the code correctly.
- GeoGebra documents: you can enter with the procedure used for videos, a document in the collection of GeoGebra materials on the site tube.geogebra.org. To obtain the html code you need to click Embed, select HTML, set the parameters and click Copy to Clipboard.
- References to other content
Notes should not be used — as they would make reading difficult — and, where possible, links should be placed to articles on this site that discuss or use the same technical terms. You can insert links to external sites which open up their content in another window (i.e. with Target equal to New window). At the end you have to include
- an essential bibliography, each citation must have the form [B progressive nr.] Author, Title, Journal, nr. (year), Publisher where the fields are not applicable should be omitted;
- an essential sitography, each citation must have the form [S progressive nr.] Author, Title, Web address where the fields are not applicable should be omitted;
- a clause on the license under which the article is published.
- Typographic standards
The author must use the following typographic standards.
- The color of the text should be generally black but you can assign different colors to specific terms to be highlighted.
- The font used must be Book Antiqua.
- The size of the font used for the title should be 18pt, and the title should be bold.
- The size of the font used for the subtitle should be 14pt and plane (i.e. without modifiers such as bold, ...).
- The title of sections (including the abstract) and the corresponding numbering (which is on the same line) must use a font of 14pt and must be bold.
- The title of subsections and the corresponding numbering must use a font 12pt and must be bold.
- The text of the various sections and subsections (including the abstract) must use a 12pt font, it must be separated by a blank line from the section title, while it must begin directly to the next line in the summary and in subsections.
- Only formulas that are placed on separate lines (introduced by the identifier ) and are then referred to in the article should be numbered.
- Small images (width lower than 500px) need to be aligned left and right alternately and surrounded by text (Advanced→Style = float: left; / float: right;) while larger ones must be placed at the center of a separate paragraph.
- Videos and GeoGebra documents must be at the centre of a separate paragraph and with a width of 800px: if the quality of the resolution is too low, you can insert the document by reducing it in size and aligning it according to the rules for small images.
Cathegory New strands
This category collects scientific papers at the border of mathematical research regarding innovative ideas. There may be included proposals for new lines of research related to areas generally undeveloped, with the hope that the seed will one day produce important new knowledge. For this reason, the only requirements to be publishable, besides the presence of a specific bibliography, are the originality of the proposal, its meaningfulness and the prediction of significant applications (not only mathematical).
As for the creation of articles (category Past artistic works) applies what is indicated above for the sections Mathematics and Applications: these can discuss, for example, the influences of mathematics in the artistic works of any kind in the past, the presence of implicit mathematics in works, the comparison between artistic concepts and mathematical concepts in order to identify possible similarities or analogies.
Poems, prose works, images and videos must be original and mathematics must play an essential functional role: the mere mention of mathematical concepts is not sufficient to justify the publication in the site collections. Images and videos must be accompanied by a text that contains title, author, license, any advice on the interpretation if the author wishes to provide a privileged key. Because of resource constraints
- images, which are stored on the site, must have a maximum size of 2048px × 2048px and a resolution of 92 px/in,
- we do not accept similar pictures from the point of view of the construction criteria and / or the visual impact, unless it is made explicit a different interpretative potential,
- videos must be stored in a server on the Internet, such as YouTube, from where they will be displayed.
Additional criteria for publication
The publication of articles requires fulfillment of additional criteria needed to achieve a self-sufficient collection and to reduce the use of resources.
In the sections Mathematics (with the exception of the category New strands) and Applications the publication of an article with a given complexity level (e.g. ★★★) is not authorized unless articles on the same subject and lower complexity (in the example both ★ and ★★) are not already present in the same cathegory.
For all collections the following applies.
- The publication of an article about a certain topic is not authorized in the same collection if there is already another with the same level of complexity and on the same subject, unless the new article is of significantly higher quality in terms of comprehensibility, exposure, connection with other areas. The eventual approval of the new article requires the archiving of the old one. Authors can update their articles without the need to submit the new draft to review by a moderator if the changes are small and do not alter the structure. More extensive revisions involve the writing of a new article that, once approved, will replace the old one (which will be permanently deleted from the collection).
- Italian language authors are required to write two versions of the article: one in Italian and one in English. English language authors who know Italian language will present the article in both languages. English language authors who write only the English version authorise MathVerse.org to include in the collection an Italian translation of the published article.