Combining logical and algebraic techniques for natural style proving in elementary analysis

Vajda, Róbert; Jebelean, Tudor; Buchberger, Bruno

doi:10.1016/j.matcom.2008.11.002

Cited by 7 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Combined methods like the PCS method introduced by Buchberger [10], [16] or the S-Decomposition strategy with extended quantifier elimination [17], [29] supports the investigation of proving problems in the CreaComp elementary analysis units. Extended quantifier elimination over reals enables to solve quantified parametric polynomial constraints, i.e., for finding witness terms for existentially quantified variables in the goal.…”

Section: Reasoning Toolsmentioning

confidence: 99%

An e-learning environment for elementary analysis: combining computer algebra, graphics and automated reasoning

Vajda¹

2009

TMCS

View full text Add to dashboard Cite

CreaComp is a project at the University of Linz, which aims at producing computer-supported interactive learning units for several mathematical topics at introductory university level. The units are available as Mathematica notebooks. For student experimentation we provide computational, graphical and reasoning tools as well. This paper focuses on the elementary analysis units. The computational and graphical tools of the CreaComp learning environment facilitate the exploration of new mathematical objects and their properties (e.g., boundedness, continuity, limits of real valued functions). Using the provided tools students should be able to collect empirical data systematically and come up with conjectures. A CreaComp component allows the formulation of precise conjectures and the investigatation of their validity. The Theorema system, which has been integrated into the CreaComp learning environment, provides full predicate logic with a user-friendly twodimensional syntax and a couple of automated reasoners that produce proofs in an easy-to-read and natural presentation. We demonstrate the learning situations and the provided tools through several examples.

show abstract

Section: Reasoning Toolsmentioning

confidence: 99%

An e-learning environment for elementary analysis: combining computer algebra, graphics and automated reasoning

Vajda¹

2009

TMCS

View full text Add to dashboard Cite

show abstract

“…Both contain proofs, but they look very different. Such variety is a significant challenge in general, although it is certainly possible to assess proof in particular constrained areas of mathematics using specially-designed tools (e.g., Gruttmann et al, 2008;Vajda, 2009;Vajda et al, 2009).…”

mentioning

confidence: 99%

A Collaboratively-Derived Research Agenda for E-assessment in Undergraduate Mathematics

Kinnear

Jones

Sangwin

et al. 2022

Int. J. Res. Undergrad. Math. Ed.

View full text Add to dashboard Cite

This paper describes the collaborative development of an agenda for research on e-assessment in undergraduate mathematics. We built on an established approach to develop the agenda from the contributions of 22 mathematics education researchers, university teachers and learning technologists interested in this topic. The resulting set of 55 research questions are grouped into 5 broad themes: errors and feedback, student interactions with e-assessment, design and implementation choices, affordances offered by e-assessment tools, and mathematical skills. This agenda gives a framework for a programme of research aligned with practical concerns that will contribute to both theoretical and practical development.

show abstract

“…In the future we will also consider problems involving satisfiability tests for formulae with (alternations) of quantifiers. We would like to analyze the possible links between our approach and the method for automated reasoning in analysis described in [12].…”

Section: Discussionmentioning

confidence: 99%

Efficient Hierarchical Reasoning about Functions over Numerical Domains

Sofronie-Stokkermans

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We show that many properties studied in mathematical analysis (monotonicity, boundedness, inverse, Lipschitz properties possibly combined with continuity, derivability) are expressible by formulae in a class for which sound and complete hierarchical proof methods for testing satisfiability of sets of ground clauses exist. The results are useful for automated reasoning in analysis and in the verification of hybrid systems. 1

show abstract

Combining logical and algebraic techniques for natural style proving in elementary analysis

Cited by 7 publications

References 7 publications

An e-learning environment for elementary analysis: combining computer algebra, graphics and automated reasoning

An e-learning environment for elementary analysis: combining computer algebra, graphics and automated reasoning

A Collaboratively-Derived Research Agenda for E-assessment in Undergraduate Mathematics

Efficient Hierarchical Reasoning about Functions over Numerical Domains

Contact Info

Product

Resources

About