Fundamental influences related to language-based difficulties in financial mathematics

Motivated in part by a sustained amount of research in South Africa and principally guided by techniques of problem-solving suggested by Polya as well as error analysis by Newman, the current research examines fundamental influencers (underlying factors) relating errors due to language difficulties in financial mathematics concerning the language of instruction. The current research was accomplished using a case study design. The sample size was 105 out of a population of 186, with assumption of confidence and precision levels at 95 per cent and 0.5 respectively. The aim of the study was addressed by using both sets of structured-interview and document analysis for collecting data. Analysis of data was conducted by both content analysis as well as correlation analysis, wherein, the analysis revealed that errors committed by learners in financial mathematics were due to language difficulties. In contrast, misinterpretation of the mathematical semantics was not as a result of not indicating answers as expected, not following instructions, and not understanding instructions.

A Two-Part Defense of Intuitionistic Mathematics

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.

A Two-Part Defense of Intuitionistic Mathematics

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.

Implementing QVT-R via semantic interpretation in UML-RSDS

The QVT-Relations (QVT-R) model transformation language is an OMG standard notation for model transformation specification. It is highly declarative and supports (in principle) bidirectional (bx) transformation specification. However, there are many unclear or unsatisfactory aspects to its semantics, which is not precisely defined in the standard. UML-RSDS is an executable subset of UML and OCL. It has a precise mathematical semantics and criteria for ensuring correctness of applications (including model transformations) by construction. There is extensive tool support for verification and for production of 3GL code in multiple languages (Java, C#, C++, C, Swift and Python). In this paper, we define a translation from QVT-R into UML-RSDS, which provides a logically oriented semantics for QVT-R, aligned with the RelToCore mapping semantics in the QVT standard. The translation includes variation points to enable specialised semantics to be selected in particular transformation cases. The translation provides a basis for verification and static analysis of QVT-R specifications and also enables the production of efficient code implementations of QVT-R specifications. We evaluate the approach by applying it to solve benchmark examples of bx.

Semantics and Pragmatics in Mathematical Events

The current chapter throws light on mathematical semantics and pragmatics. Believing that the mathematics has its own language and hence linguistics principles, the chapter tries to have an in-depth insight on how learner makes a meaning from an even simple event, while it takes place, and how these finally are assimilated by the learner. As learning is also experiential in nature, the contextual values, relationship, rapport, trust, confidence, in addition to simple interaction and plain interaction between learners and facilitators, play a vital and significant role in conceptual semantics and pragmatics of events and understanding of underlying mathematics. Context and situation are capable enough of changing perception-based mathematical meaning and meaning-making process, based on linguistics, associated with even the similar simple events. Hence, the context and situations must be created, associated and exploited up to the optimum level for enhanced conceptual teaching and learning of mathematics at par the daily life experiences for a better meaning-making process.

Outer Set Operations of Table Algebra of Infinite Tables

Table algebra of infinite tables is considered. The signature of table algebra of infinite tables is filled up with outer set operations. A formal mathematical semantics of these operations is defined.

Semantics and Pragmatics in Mathematical Events

The current chapter throws light on mathematical semantics and pragmatics. Believing that the mathematics has its own language and hence linguistics principles, the chapter tries to have an in-depth insight on how learner makes a meaning from an even simple event, while it takes place, and how these finally are assimilated by the learner. As learning is also experiential in nature, the contextual values, relationship, rapport, trust, confidence, in addition to simple interaction and plain interaction between learners and facilitators, play a vital and significant role in conceptual semantics and pragmatics of events and understanding of underlying mathematics. Context and situation are capable enough of changing perception-based mathematical meaning and meaning-making process, based on linguistics, associated with even the similar simple events. Hence, the context and situations must be created, associated and exploited up to the optimum level for enhanced conceptual teaching and learning of mathematics at par the daily life experiences for a better meaning-making process.

Vicious Circle Principle and Logic Programs with Aggregates

The paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of $\mathcal{A}log$, an algorithm for computing its answer sets, and comparison with other approaches.