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513
ActiveMath: A Generic and Adaptive WebBased Learning Environment
 International Journal of Artificial Intelligence in Education
, 2001
"... ActiveMath is a generic webbased learning system that dynamically generates interactive (mathematical) courses adapted to the students goals, preferences, capabilities, and knowledge. The content is represented in an semantic xmlbased format. For each user, the appropriate content is retrieved fr ..."
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Cited by 92 (28 self)
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ActiveMath is a generic webbased learning system that dynamically generates interactive (mathematical) courses adapted to the students goals, preferences, capabilities, and knowledge. The content is represented in an semantic xmlbased format. For each user, the appropriate content is retrieved from a knowledge base and the course is generated individually according to pedagogical rules. Then the course is presented to the user via a standard webbrowser. One of the exceptional features of ActiveMath is its integration of standalone mathematical service systems. This offers the means for exploratory learning, realistically complex exercises as well as for learning proof methods. The article provides a comprehensive account of the current version of ActiveMath.
ΩMEGA: Towards a Mathematical Assistant
, 1997
"... Ωmega is a mixedinitiative system with the ultimate purpose of supporting theorem proving in mainstream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof presentati ..."
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Cited by 69 (30 self)
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Ωmega is a mixedinitiative system with the ultimate purpose of supporting theorem proving in mainstream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof presentation.
DOI: 10.1159/000095454
"... Leitlinie) empfehlen eine rein symptomorientierte Nachsorge, die hinsichtlich der apparativen Diagnostik allein durch eine regelmäßige Mammographie erweitert wird. Allerdings stößt diese Praxis, die in randomisierten Untersuchungen einer intensivierten Nachsorge gleichwertig war, bei den Betroffen ..."
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Leitlinie) empfehlen eine rein symptomorientierte Nachsorge, die hinsichtlich der apparativen Diagnostik allein durch eine regelmäßige Mammographie erweitert wird. Allerdings stößt diese Praxis, die in randomisierten Untersuchungen einer intensivierten Nachsorge gleichwertig war, bei den
ΩANTS  An open approach at combining Interactive and Automated Theorem Proving
 IN PROC. OF CALCULEMUS2000. AK PETERS
, 2000
"... We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integ ..."
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Cited by 44 (28 self)
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We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integration of external reasoning systems. We also introduce some notions that need to be considered to check completeness and soundness of such a system with respect to an underlying calculus.
Integrating computer algebra into proof planning
 Journal of Automated Reasoning
, 1998
"... Abstract. Mechanised reasoning systems and computer algebra systems have different objectives. Their integration is highly desirable, since formal proofs often involve both of the two di erent tasks, proving and calculating. Even more importantly, proof and computation are often interwoven and not e ..."
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Cited by 41 (24 self)
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Abstract. Mechanised reasoning systems and computer algebra systems have different objectives. Their integration is highly desirable, since formal proofs often involve both of the two di erent tasks, proving and calculating. Even more importantly, proof and computation are often interwoven and not easily separable. In this contribution we advocate an integration of computer algebra into mechanised reasoning systems at the proof plan level. This approach allows to view the computer algebra algorithms as methods, that is, declarative representations of the problem solving knowledge speci c to a certain mathematical domain. Automation can be achieved in many cases bysearching for a hierarchic proof plan at the methodlevel using suitable domainspeci c control knowledge about the mathematical algorithms. In other words, the uniform framework of proof planning allows to solve a large class of problems that are not automatically solvable by separate systems. Our approach also gives an answer to the correctness problems inherent insuch an integration. We advocate an approach where the computer algebra system produces highlevel protocol information that can be processed by aninterface to derive proof plans. Such a proof plan in turn can be expanded to proofs at di erent levels of abstraction, so the approach iswellsuited for producing a highlevel verbalised explication as well as for a lowlevel machine checkable calculuslevel proof. We present an implementation of our ideas and exemplify them using an automatically solved example. Changes in the criterion of `rigour of the proof ' engender major revolutions in mathematics.
References In LaTeX file Let $n $ be an odd prime.
"... • The correct semantic interpretation of mathematical formulae that recognised in documents is very important. • Improving the precision of systems that translate documents indirectly into speech or to other formats. • Improve the accessibility of maths documents. • Improve precision of existing ..."
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• The correct semantic interpretation of mathematical formulae that recognised in documents is very important. • Improving the precision of systems that translate documents indirectly into speech or to other formats. • Improve the accessibility of maths documents. • Improve precision of existing maths search systems. Our aim is to develop an approach which determines the semantics of mathematical formulae by analysing both mathematical formulae and their context. A ground truth of number of representative documents will be built, so the getting result can be compared to it.
mega: Towards a mathematical assistant
 Proceedings of the 14th Conference on Automated Deduction, number 1249 in LNAI
, 1997
"... Abstract. mega is a mixedinitiative system with the ultimate purpose of supporting theorem proving in mainstream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof pres ..."
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Cited by 29 (18 self)
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Abstract. mega is a mixedinitiative system with the ultimate purpose of supporting theorem proving in mainstream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof presentation. 1
PDS  A ThreeDimensional Data Structure for Proof Plans
 PROC. OF ACIDCA'2000
, 2000
"... We present a new data structure that enables to store threedimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only differe ..."
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Cited by 35 (9 self)
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We present a new data structure that enables to store threedimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only different means of the proof development environment (e.g., rule and tacticbased theorem proving, or proof planning) to act directly on the same proof object but it also allows for easy presentation of proofs on different levels of abstraction. However, the threedimensional structure requires adjustment of the regular techniques for addition and deletion of proof lines and backtracking of the proof planner.
Automatic generation of classification theorems for finite algebras
 In Proc. of IJCAR 2004, volume 3097 of LNAI
, 2004
"... Classifying finite algebraic structures has been a major motivation behind much research in pure mathematics. Automated techniques have aided this process, but this has largely been at a quantitative level, e.g., to prove that there are no quasigroups of a given type for a given size, or to count th ..."
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Cited by 22 (15 self)
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Classifying finite algebraic structures has been a major motivation behind much research in pure mathematics. Automated techniques have aided this process, but this has largely been at a quantitative level, e.g., to prove that there are no quasigroups of a given type for a given size, or to count the number of groups of a particular order. Classification theorems of a more qualitative nature are often more interesting. For example, Kronecker's classification of finite Abelian groups [1] states that every Abelian group, G, of size n can be expressed as a direct product of cyclic groups, G = C s1 \Theta \Delta \Delta \Delta \Theta C sm, where n = s
Comparing approaches to the exploration of the domain of residue classes
 ARTICLE SUBMITTED TO JOURNAL OF SYMBOLIC COMPUTATION
, 2002
"... We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using different proof techniques, which are implemented as strategies in a multistrategy ..."
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Cited by 25 (13 self)
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We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using different proof techniques, which are implemented as strategies in a multistrategy proof planner. The search space of the proof planner can be drastically reduced by employing computations of two computer algebra systems during the planning process. To test the eectiveness of our approach we carried out a large number of experiments and also compared it with some alternative approaches. In particular, we experimented with substituting computer algebra by model generation and by proving theorems with a first order equational theorem prover instead of a proof planner.
Results 1  10
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