Digital Repository of Mathematical Formulae

The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of working mathematicians, physicists and engineers: providing a platform for publication and interaction with OPSF formulae on the web. Using MediaWiki extensions and other existing technology (such as software and macro collections developed for the NIST Digital Library of Mathematical Functions), the DRMF acts as an interactive web domain for OPSF formulae. Whereas Wikipedia and other web authoring tools manifest notions or descriptions as first class objects, the DRMF does that with mathematical formulae. See http://gw32.iu.xsede.org/index.php/Main_Page

Linking Mathematical Software in Web Archives

The Web is our primary source of all kinds of information today. This includes information about software as well as associated materials, like source code, documentation, related publications and change logs. Such data is of particular importance in research in order to conduct, comprehend and reconstruct scientific experiments that involve software. swMATH, a mathematical software directory, attempts to identify software mentions in scientific articles and provides additional information as well as links to the Web. However, just like software itself, the Web is dynamic and most likely the information on the Web has changed since it was referenced in a scientific publication. Therefore, it is crucial to preserve the resources of a software on the Web to capture its states over time. We found that around 40% of the websites in swMATH are already included in an existing Web archive. Out of these, 60% of contain some kind of documentation and around 45% even provide downloads of software artifacts. Hence, already today links can be established based on the publication dates of corresponding articles. The contained data enable enriching existing information with a temporal dimension. In the future, specialized infrastructure will improve the coverage of software resources and allow explicit references in scientific publications.Comment: ICMS 2016, Berlin, German

Examining the effectiveness of a GeoGebra-assisted open-ended approach on students’ mathematical creative thinking ability

Researchers use open-ended as a learning method to help students improve their math skills. Each open investigation of mathematical knowledge produces mixed results for components of mathematical ability, each school level, and the content taught. There are more and more studies on open-ended questions nowadays. This study tested the effectiveness of the open-ended approach assisted by GeoGebra on students' mathematical creative thinking abilities. The use of meta-analysis techniques is to analyze the effect (effect size) of a preliminary study. The instruments used were coding protocol sheets and coding sheets/Comprehensive Meta-Analysis (CMA) programs to analyze data. The resulting findings are that there are differences in the research method with the most significant effect size in the quasi-experimental research method, the research year with the most significant effect size in the 2012-2022 research year, indexing journals with the most significant effect size on web indexing scientific journals; the type of publication that has the most critical influence on the kind of thesis publication. Furthermore, the GeoGebra-assisted open-ended approach to creative thinking ability has no significant effect when viewed from the research characteristics of the sample size and level of education

Web Publication of Three-Dimensional Animation Materials for Business Mathematics : 10 Graphics for Economics Mathematics Part 2

The　paper　reports　our　web　publication　of　visual　teaching　materials　for　business　mathematics． The　objective　of　the　web　site　is　to　familiarize　students　with　our　visual　approach　for　business mathematics　at　early　stage，　The　significant　advantage　of　visualization　is　that　seeing　the　materials leads　to　better　understanding　of　the　mathematical　process．　Even　if　the　students　cannot understand　the　algebraic　calculation　process，　they　can　intuitively　understand　the　essence，　only seeing　the　visual　materials．　The　feature　of　our　developed　teaching　materials　is　utilization　of three－dimensional　graphics　and　its　animations．　Just　watching　the　animation，　students　can　see　the points，　even　if　they　have　no　idea　about　operations　on　the　web．　In　the　paper，　we　will　illustrate three　typical　economics　problems　using　three－dimensional　animation　which　are　a　national　income determination　problem，　an　IS－LM　analysis，　and　a　Marshallian　demand　function

The Price equation program: simple invariances unify population dynamics, thermodynamics, probability, information and inference

The fundamental equations of various disciplines often seem to share the same basic structure. Natural selection increases information in the same way that Bayesian updating increases information. Thermodynamics and the forms of common probability distributions express maximum increase in entropy, which appears mathematically as loss of information. Physical mechanics follows paths of change that maximize Fisher information. The information expressions typically have analogous interpretations as the Newtonian balance between force and acceleration, representing a partition between direct causes of change and opposing changes in the frame of reference. This web of vague analogies hints at a deeper common mathematical structure. I suggest that the Price equation expresses that underlying universal structure. The abstract Price equation describes dynamics as the change between two sets. One component of dynamics expresses the change in the frequency of things, holding constant the values associated with things. The other component of dynamics expresses the change in the values of things, holding constant the frequency of things. The separation of frequency from value generalizes Shannon's separation of the frequency of symbols from the meaning of symbols in information theory. The Price equation's generalized separation of frequency and value reveals a few simple invariances that define universal geometric aspects of change. For example, the conservation of total frequency, although a trivial invariance by itself, creates a powerful constraint on the geometry of change. That constraint plus a few others seem to explain the common structural forms of the equations in different disciplines. From that abstract perspective, interpretations such as selection, information, entropy, force, acceleration, and physical work arise from the same underlying geometry expressed by the Price equation.Comment: Version 3: added figure illustrating geometry; added table of symbols and two tables summarizing mathematical relations; this version accepted for publication in Entrop

Impacts of an Interdisciplinary Research Center on Participant Publication and Collaboration Activities

Interdisciplinary research centers are typically presented as a means for exploiting opportunities in science where the complexity of the research problem calls for sustained interaction among multiple disciplines. This study analyzed the effects of an interdisciplinary research center (NIMBioS) on the publication and collaboration behaviors of faculty affiliated with the center. The study also sought to determine what factors contributed to these effects for participants whose publication and collaboration behaviors were changed the most after affiliation. The study employed a mixed-method case study approach, using quantitative bibliometric data along with qualitative data collected from interviews. Publication data for each participant in the study was collected from Web of Science (WOS) and analyzed by year against several demographic control variables to understand what effect affiliation with NIMBioS had on publication behaviors of participants. In addition to bibliometrics, a selection of study participants who demonstrated the most change in publication and collaboration behaviors since their affiliation with NIMBioS were interviewed to determine (a) what benefits (if any) participants felt they achieved as a result of participating in their working group, and (b) what factors (if any) participants felt may have contributed to the impact of NIMBioS affiliation on their publication and collaboration behavior. Results of the study indicate that affiliation with a NIMBioS working group has a significant positive effect on participant collaboration activities (i.e. number of co-authors, number of international co-authors, number of cross-institutional co-authors), and a moderate effect on publication activities (i.e. publishing in new fields). Qualitative analysis of interdisciplinarity showed a shift in publication WOS subject categories (SCs) toward mathematical fields. Factors contributing to success cited by interviewees included organized leadership, a positive atmosphere, breaking into sub-groups, and the ability to collaborate with researchers with whom they would not have interacted outside of the group

AMM Historical Database

The Mathematical Association of America (MAA) is a leading scholarly organization for mathematics in North America. Their primary publication, the American Mathematical Monthly (AMM), comprises over 130 published volumes dating back to 1894. The sheer volume of text in the journal has made it difficult for those interested in the history of mathematics and the organization to locate information. Adding to this challenge, there is no central search tool for the AMM corpus consisting of over 30,000 individual documents. The project team was tasked with creating a website that provides enhanced search tools for the AMM repository. Working with a historian from the MAA and using an agile development process with regular feedback, the team identified ways to improve the search process for relevant data while navigating through the technical and legal challenges associated with the handling and presenting of the corpus. The tool suite will provide a centralized search function specific to this repository with filters that make it faster to find information. This full-stack solution relies on HTML/CSS, Python, Django, SQL, and an Apache Web Server presented to the user through a web browser. Ultimately, the project provides an e-reader and search tool for region-specific documents from participating MAA historians, simplifying the challenge of working with the large AMM corpus

WYSIWYG editor for MathML

katedra: MTI; přílohy: CD; rozsah: 81V současnosti je většina matematiky na webu zachycena pomocí obrázků, které jsou ale těžko modifikovatelné a zpracovatelné aplikacemi, jenž manipulují s HTML. Proto World Wide Web Consortium, později W3C Math working group, vytvořilo MathML pro usnadnění práce s matematikou v prostředí WWW. MathML je tedy XML aplikace pro publikaci matematických vzorců na Webu. Tato diplomová práce se zabývá úkolem návrhu a implementace WYSIWYG editoru pro tento matematický značkovací jazyk. Editor bude jak samostatnou aplikací, tak i apletem, který bude možné vystavit na web a komunikovat s ním. K vytvoření aplikace byl použit programovací jazyk Java a to především jeho knihovna Swing pro tvorbu grafického uživatelského rozhraní a Java API for XML Processing, tedy rozhraní pro zpracování dokumentů v jazyce XML.In present are almost mathematical terms on web captured through the images which are for the applications working with HTML hard to modified and hard to elaborate. That is why World Wide Web Consortium, later W3C Math working group, developed MathML to help with work with mathematical terms on WWW. MathML is thus XML application for publication the mathematical terms on web. This work deals with proposal and implementation WYSIWYG editor for mentioned mathematical marking language. Editor will be both independent application and applet, which will be able to run on web and communicate with it. For creating this editor was used the programming language Java, mainly its library Swing for creating graphical user interface and Java API for XML Processing for elaboration documents in XML language