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Halomda offers comprehensive e-learning platform for math courses, including a module for trusted e-assessment. Assessment is performed by checking all the steps of the solution, enabling various types of answers: multiple-choice, open answer allowing entering algebraically equivalent expressions, etc. The platform provides both a trusted e-assessment and a highly sophisticated tool for teaching and self-learning of mathematical courses. [ABSTRACT FROM AUTHOR]

Very often, difficulties with higher mathematics courses are the reason for the dropout of a significant part of STEM students. In order to help students be more confident in their knowledge, as well as fill gaps in the study of various high math courses, we suggest interactive guided training for students through the Halomda educational platform. [ABSTRACT FROM AUTHOR]

The mode of assessment is one of the most important factors influencing learning as it affects how students organize their time and what subjects they focus on. It is well known fact that students may exhibit different abilities in different forms of assessment. In this paper, we show how e-assessment with the Halomda educational platform can enhance students' learning experiences. In addition, we present how technology-assisted math education can help students study at home and in the classroom, as well as support teachers in their routine work of checking student assignments. Results from teaching courses with Halomda demonstrate not only high student learning outcomes on the final exam, but also a good correlation between exam marks and weekly assignment marks. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate weighted time-varying causal graphs based on daily log-return and realized volatility time series of the S&P500 stocks. In order to construct causal graphs for each quarter between Q1 2005 and Q2 2020, we compute cross-correlations between series and conduct pairwise Granger Causality tests for lead-lag relationships. We take individual stocks as nodes and significant causal relationships as weighted edges. Our analysis is based on a comparison of network topology and properties for different periods, including the 2007-2010 subprime crisis, the European sovereign debt crisis, and the coronavirus pandemic, as well as tranquil periods. In addition to edge weights, our study also takes into account the estimated lag of the causal interactions and uses network level measures to identify meaningful patterns over time. We also conduct an analysis of the industrial sectors interconnectedness via smaller graphs derived from the stock-level causality graphs. The results of the work reveal that network topology changes during periods of market stress and crisis and this can be captured by using convenient network construction methods and measures. Our results also show that the patterns of network topology transformation and magnitude of spillovers transmission during the coronavirus crisis and accompanying events differs from previous crisis periods. [ABSTRACT FROM AUTHOR]

We investigate similarities and differences between stock and cryptocurrency networks obtained from log-return and volatility time series. We constructed correlation and Fast Fourier Transform based graphs and minimum spanning trees from a set of 100 highly capitalized cryptocurrencies and 100 highly capitalized NASDAQ stocks over a time window of fixed length. Our analysis is based on comparison between both economies in terms of network properties. We also examined distributions of node degrees and edge weights. Our results show that cryptocurrencies and companies with high capitalization tend to correspond to central and densely connected nodes. Network topologies for both economies and node degree distributions are rather similar. Nevertheless, the crypto-economy is more correlated and more strongly linked to important nodes, unlike the graphs of NASDAQ stocks, where we observed clusters of nodes having small dissimilarities. [ABSTRACT FROM AUTHOR]

Common opinion of educators in engineering education is the need for innovations in existing teaching and learning strategies by implementing the latest achievements of information and communication technologies (ICT) supporting teaching, learning and assessment processes. As employers’ requirements are constantly increasing, graduates need to get used to evolve and develop their skills for acquiring knowledge, independent learning, critical thinking, innovation competence, networking, creativity, effective time management. Online teaching and learning forms provide nowadays this opportunity. The TeSLA system as an innovative enhancement of virtual learning environments, provides students and teachers with the opportunity for trust-based eAssessment process with guaranteed quality, thus completing the online learning triad. Current paper shares the innovation results for teaching and assessment practices based on the experience gained by the Technical university of Sofia (TUS) when performing eAssessment in engineering courses supported by the TeSLA authentication and authorship analysis system. [ABSTRACT FROM AUTHOR]

eAssessment of students in engineering courses is specific due to the nature of the teaching, learning and examination process in technical education in general. Students need to write program codes, design electronic schemes, solve mathematical problems, analyze performance of engineering devices, describe solutions graphically, etc. Online assessment has to support the correct authentication of the examinee for guaranteeing trusted online examination process. The TeSLA eAuthentication and authorship analysis system provides a variety of biometric instruments for students’ authentication. Current paper aims to analyze the results of the application of combinations of TeSLA authentication instruments in different engineering and fundamental courses and assessment activities during the pilots of the system conducted at the Technical University of Sofia. The experience gained can be implemented for ensuring trustworthy eAssessment process for students in other engineering courses and assessment activities. [ABSTRACT FROM AUTHOR]

Computer Algebra Systems (CAS) extend the capabilities of applying and using mathematical models in the routine work of engineers, researchers, applied mathematicians, as well as in the education of students who are preparing for such specialists. Formal logic is an important part of the “Discrete Mathematics” course for students of the specialty “Applied Mathematics and Informatics” of the Technical University of Sofia. In this paper, we show our experience in teaching the rules of formal logic and its exploring and modeling with CAS Maple. [ABSTRACT FROM AUTHOR]

Some recent research has shed new light on the idempotent (additively and/or multiplicatively) semirings. In this paper we explore the consequences of this for considering different properties of additively and/or multiplicatively idempotent semirings of order two. The varieties generated by these semirings are also considered. [ABSTRACT FROM AUTHOR]