Related papers: Teaching Interactive Proofs to Mathematicians
This paper describes some strategies used in a `transition' course. Such courses help undergraduate mathematics majors move from learning procedures to learning to function as critical mathematicians in order to understand and work with…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
Elfe is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof…
The article deals with the problem of intellectual development of students in learning of physics by means of computer simulation. The main objectives of teaching computer simulation in learning of physics is the general outlook…
Verification of neural networks is currently a hot topic in automated theorem proving. Progress has been rapid and there are now a wide range of tools available that can verify properties of networks with hundreds of thousands of nodes. In…
Project-Based Learning (PBL) is a teaching technique in which authentic, real-world projects are used as the primary vehicle to drive the student's learning experience. This technique has been found to be very effective, but its overall…
This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present…
The increasing availability of digital tools for education offers significant opportunities to enhance teaching practices and student engagement. This study presents a structured categorization of online educational tools based on their…
The automation offered by modern program proof tools goes hand in hand with the capability to interact with the tool when the verification fails. The SPARK proof tool tries to help the user by providing the right information, so that the…
In Machine-Assisted Theorem Proving, a theorem proving agent searches for a sequence of expressions and tactics that can prove a conjecture in a proof assistant. In this work, we introduce several novel concepts and capabilities to address…
In this paper, we make an important step towards the black-box machine teaching by considering the cross-space machine teaching, where the teacher and the learner use different feature representations and the teacher can not fully observe…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
Quantum Computing is an exciting field that draws from information theory, computer science, mathematics, and quantum physics to process information in fundamentally new ways. There is an ongoing race to develop practical quantum computers…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such…