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Methods of Relevance Ranking and Hitcontent Generation in Math Search
, 2007
"... To be effective and useful, math search systems must not only maximize precision and recall, but also present the query hits in a form that makes it easy for the user to identify quickly the truly relevant hits. To meet that requirement, the search system must sort the hits according to domainappro ..."
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To be effective and useful, math search systems must not only maximize precision and recall, but also present the query hits in a form that makes it easy for the user to identify quickly the truly relevant hits. To meet that requirement, the search system must sort the hits according to domainappropriate relevance criteria, and provide with each hit a queryrelevant summary of the hit target.
Roles of Math Search in Mathematics
 in Mathematical Knowledge Management, Proceedings of the 5th International Conference on Mathematical Knowledge Management, Lecture
"... Abstract. Mathaware finegrain search is expected to be widely available. A key question is what roles it can play in mathematics. It will be argued that, besides finding information, math search can help advance and manage mathematical knowledge. This paper will present the shortterm goals and st ..."
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Abstract. Mathaware finegrain search is expected to be widely available. A key question is what roles it can play in mathematics. It will be argued that, besides finding information, math search can help advance and manage mathematical knowledge. This paper will present the shortterm goals and state of the art of mathaware finegrain search. Afterwards, it will focus on how math search can help advance and manage mathematical knowledge, and discuss what needs to be done to fulfill those roles, emphasizing two key components. The first is similarity search, and how it applies to (1) discovering and drawing upon connections between different fields, and (2) proof development. The second is math metadata, which math search will surely encourage and benefit from, and which will be pivotal to mathematical knowledge management. 1
MATH GO! PROTOTYPE OF A CONTENT BASED MATHEMATICAL FORMULA SEARCH ENGINE
"... In recent years, mathematical content has started appearing on the web. As with other types of information, search capabilities must be provided to users to retrieve their required information. Conventional textbased search engines fall short of providing mathaware fine grain search. Several effor ..."
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In recent years, mathematical content has started appearing on the web. As with other types of information, search capabilities must be provided to users to retrieve their required information. Conventional textbased search engines fall short of providing mathaware fine grain search. Several efforts have been made in the recent past to develop webaccessible mathematical and scientific search systems. We identify major issues in developing math search systems and present techniques for addressing them. The issues involved in developing such a system include query format, representation of mathematical content, as well as their comparison for matching purposes. The results generated by the formula search system must strive to maximize the standard measures of precision, recall. It should also sort the query hits according to some domain specific measure and provide the hits to the user as a ranked list. This paper presents our efforts in developing a mathematical search engine for mathematical content retrieval. We present the Math GO! System to search and present the mathematical information encoded in mathematical expressions. Our approach uses the concept of template based math block identification, vector representation, searching from mathematical topic based clusters and relevance ranking. The search system interacts with the user through a simple query mechanism and provides ranked listing of results. The system is comprised of a modular architecture to organize, query, compare and presentation of math results to the user. We compare our approach with existing approaches and present the results. We have achieved encouraging results with the system.
Crossing Cultural Boundaries with Long Term Interactive Geometry Resources
"... Abstract. This paper describes I2Geo, the platform of the Intergeo project enabling math educators to share Interactive Geometry content across Europe. This webbased platform makes each resource, be it a construction, a scenario of use, or a complete course, referenceable, editable, and reviewable ..."
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Abstract. This paper describes I2Geo, the platform of the Intergeo project enabling math educators to share Interactive Geometry content across Europe. This webbased platform makes each resource, be it a construction, a scenario of use, or a complete course, referenceable, editable, and reviewable. I2Geo follows the patterns of open educational resources (OER), where anyone may participate and contribute, either by commenting, by adding constructions, or by reviewing the quality of a resource stored in a central place. The platform is based on a fine grained ontology of mathematical concepts and skills, together with a description of educational pathways in Europe. Together these two ingredients allow for crosscultural searches. We describe the current platform’s facilities and its technical foundation that are used as well as the challenges they address. These challenges are common to the other digital libraries of open educational content.
A Digital Ecosystembased Framework for Math Search Systems
"... Abstract—Textbased search engines fall short in retrieving structured information. When searching for x(y+z) using those search engines, for example Google, it retrieves documents that contain xyz, x+y=z, (x+y+z) =xyz or any other document that contain x, y, and/or z but not x(y+z) as a standalone ..."
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Abstract—Textbased search engines fall short in retrieving structured information. When searching for x(y+z) using those search engines, for example Google, it retrieves documents that contain xyz, x+y=z, (x+y+z) =xyz or any other document that contain x, y, and/or z but not x(y+z) as a standalone math expression. The reason behind this shortage; is that the textbased search engines ignore the structure of the mathematical expressions. Several issues are associated with designing and implementing mathbased search systems. Those systems must be able to differentiate between a user query that contains a mathematical expression, and any other query that contains only a text term. A reliable indexing approach, along with a flexible and efficient representation technique are highly required. Eventually, textbased search systems must be able to process mathematical expressions that are wellstructured and have properties that make them different from other forms of text. Here, in this context we take advantage from the concept of digital ecosystems to refine the text search process so it becomes applicable in searching for a mathematical expression. In this research, a framework that contains the basic building blocks of a mathbased search system is designed. Keywordscomponent; digital ecosystem; math search; information retrieval; textbased search engines; structured information; indexing approach; representation technique. I.
Expanded Grammar for Detecting Equivalence in Math Expressions
"... huge amount of different types of information are being posted on the web on a daily basis; therefore, searching capabilities should be provided to help users in finding their requested information. Locating a specific type of information within large repositories of disparate data becomes difficult ..."
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huge amount of different types of information are being posted on the web on a daily basis; therefore, searching capabilities should be provided to help users in finding their requested information. Locating a specific type of information within large repositories of disparate data becomes difficult, if not impossible, without specialized information retrieval systems. Traditional or textbased search engines do not achieve the level of success that users seek in retrieving structured information (e.g. mathematical information). For example, when a user searches for x(y+z) using Google, Google retrieves documents that contain xyz, x+y=z, (x+y+z) =xyz or any other document that contains x, y, and/or z, but not x(y+z) as a standalone expression. The reason behind this is that Google uses the textbased search capabilities / Algorithms that depend, mostly, on techniques for matching and probabilities of occurrences of x, y, and z. The major obstacle of math search in current text search systems is that those systems do not differentiate between a user query that contains a mathematical expression, and any other query that contains text terms. Therefore, those textbased search systems process mathematical expressions as other texts, regardless of its nature whether being wellstructured or not. Here in this context, the text search process will be refined to be applicable in searching for a mathematical expression by implementing a system that is responsible for detecting equivalent math expressions. In fact, more algorithms will be added to the Information Retrieval System in order to make it suitable to do search for a mathematical expression as well as other forms of text.