The present article focuses on the role that the artificial teaching and learning of mathematics could play for education in the forthcoming era of a new industrial revolution that will be characterized by the development of an advanced Internet of things and energy, and by the cyber-physical systems controlled through it. Starting with a brief review of the traditional learning theories and methods of teaching mathematics, the article continues by studying the use of computers and of applications of artificial intelligence (AI) in mathematics education. The advantages and disadvantages of artificial with respect to traditional learning in the classroom are also discussed, and the article closes with the general conclusions and a few comments on the perspectives of future research on the subject.

Fuzzy logic, which is based on fuzzy sets theory introduced by Zadeh in 1965, provides a rich and meaningful addition to standard logic. The applications which may be generated from or adapted to fuzzy logic are wide-ranging and provide the opportunity for modeling under conditions which are imprecisely defined. In this article we develop a fuzzy model for assessing student groups’ knowledge and skills. In this model the students’ characteristics under assessment (knowledge of the subject matter, problem solving skills and analogical reasoning abilities) are represented as fuzzy subsets of a set of linguistic labels characterizing their performance, and the possibilities of all student profiles are calculated. In this way, a detailed quantitative/qualitative study of the students’ group performance is obtained. The centroid method and the group’s total possibilistic uncertainty are used as defuzzification methods in converting our fuzzy outputs to a crisp number. According to the centroid method, the coordinates of the center of gravity of the graph of the membership function involved provide a measure of the students’ performance. Techniques of assessing the individual students’ abilities are also studied and examples are presented to illustrate the use of our results in practice.

The assessment of a system’s performance is a very important task, enabling its designer/user to correct its weaknesses and make it more effective. Frequently, in practice, a system’s assessment is performed under fuzzy conditions, e.g., using qualitative instead of numerical grades, incomplete information about its function, etc. The present review summarizes the author’s research on building assessment models for use in a fuzzy environment. Those models include the measurement of a fuzzy system’s uncertainty, the application of the center of gravity defuzzification technique, the use of triangular fuzzy or grey numbers as assessment tools, and the application of the fuzzy relation equations. Examples are provided of assessing human (students and athletes) and machine (case-based reasoning systems in computers) capacities, illustrating our results. The outcomes of those examples are compared to the outcomes of the traditional methods of calculating the mean value of scores assigned to the system’s components (system’s mean performance) and of the grade point average index (quality performance) and useful conclusions are obtained concerning their advantages and disadvantages. The present review forms a new basis for further research on systems’ assessment in a fuzzy environment.

Post-translational glycosylation and glycation are common types of protein post-translational modifications (PTMs) in which glycan binds to protein enzymatically or nonenzymatically, respectively. They are associated with various diseases such as coronavirus, Alzheimer’s, cancer, and diabetes diseases. Identifying glycosylation and glycation sites is significant to understanding their biological mechanisms. However, utilizing experimental laboratory tools to identify PTM sites is time-consuming and costly. In contrast, computational methods based on machine learning are becoming increasingly essential for PTM site prediction due to their higher performance and lower cost. In recent years, advances in Transformer-based Language Models based on deep learning have been transferred from Natural Language Processing (NLP) into the proteomics field by developing language models for protein sequence representation known as Protein Language Models (PLMs). In this work, we proposed a novel method, PTG-PLM, for improving the performance of PTM glycosylation and glycation site prediction. PTG-PLM is based on convolutional neural networks (CNNs) and embedding extracted from six recent PLMs including ProtBert-BFD, ProtBert, ProtAlbert, ProtXlnet, ESM-1b, and TAPE. The model is trained and evaluated on two public datasets for glycosylation and glycation site prediction. The results show that PTG-PLM based on ESM-1b and ProtBert-BFD has better performance than PTG-PLM based on the other PLMs. Comparison results with the existing tools and representative supervised learning methods show that PTG-PLM surpasses the other models for glycosylation and glycation site prediction. The outstanding performance results of PTG-PLM indicate that it can be used to predict the sites of the other types of PTMs.

According to the views of social constructivism, learning takes place when individuals engage socially to talk about and act on shared problems or interests. In recent years, this approach has been very popular for the teaching and learning of mathematics in primary and secondary education. On the contrary, in tertiary education, it seems that most teachers still prefer the traditional way of delivering explicit mathematics instruction, sometimes combined with challenging questions and mathematical discourse with the students to promote conceptual understanding and critical analysis of the mathematical context. The paper at hand presents a classroom experiment comparing those two teaching methods at university level. The outcomes of the experiment were assessed and compared with the help of the Grade Point Average index to evaluate the student quality performance and by using grey numbers to evaluate their mean performance. Further empirical research is needed to obtain definitive results on the effectiveness of those two methods for teaching mathematics at university level.

A Grey Linear Programming problem differs from an ordinary one to the fact that the coefficients of its objective function and / or the technological coefficients and constants of its constraints are grey instead of real numbers. In this work a new method is developed for solving such kind of problems by the whitenization of the grey numbers involved and the solution of the obtained in this way ordinary Linear Programming problem with a standard method. The values of the decision variables in the optimal solution may then be converted to grey numbers to facilitate a vague expression of it, but this must be strictly checked to avoid non creditable such expressions. Examples are also presented to illustrate the applicability of our method in real life applications.