نشریه ریاضی و جامعه
سال هشتم شماره 2 (تابستان 1402)

As Almighty God has promised to protect the Quran from alteration, corruption or distortion. Historically, the scripture of the Quran has been subjected to various intense mathematically-based studies to reveal the protection mechanisms embedded in the composition of the Quran and to provide evidence of its credibility, authenticity and divinity. Indeed, this study has discovered a mathematical framework in the Quran based on gematria (Abjad numerals) that provides substantial evidence of Quran’s divine authorship and its perfect protection from human tampering. Essentially, this study has proposed a new research direction in numerological studies of the Quran. This study is textually based on the text delivered to Prophet Muhammad and drawn using the primary 28 alphabets of the Arabic language (Uthmanic manuscript), the 112 un-numbered Basmalahs and the names of the Quran chapters. A numerical value (70.44911244) which is referred to in this study as the Quran Constant (QC) was derived to represent the mathematical design of the Quran. The Quran Constant has been found to be fundamental to the current study, whereby the Quran Constant manifests in all derived mathematical equations. The ratio of the total number of chapters in the Quran (114) which represents the physical design of the Quran divided by the Quran Constant (70.44911244) which represents the mathematical design of the Quran gives 1.6181893; it is amazingly almost equal to the golden ratio. This study has also discovered that Almighty God embedded mathematical equations in the composition of the Quran that can easily lead to determination of the Quran’s primary statistics (words, verses and chapters). This study has admirably discovered three elegant mathematical equations that determine the total number of words, verses and chapters with great accuracy. More importantly, letters/word ratio calculated in this study can be practically seen as a validation criterion of both the total number of letters and the total number of words in the Quran. Finally, what does this proof? It proves that the Quran’s miraculous athematical structure discovered in this study provides unequivocal mathematical proof that the Quran was divinely authored and has been perfectly preserved from the day it was revealed. Indeed, we are witnessing a mathematical phenomenon of earth-shattering proportions~ a miracle beyond earthly justification and human comprehension.

Let D be an integral domain and I be an ideal of the upper trangular matrix ring Tn(D). In this paper, we study the equalizing ideal qI = {A ∈ Tn(D)|f(A) − f(0) ∈ I, ∀f ∈ Int(Tn(D))}. of the integer-valued polynomials over Tn(D).

The role of Alexander Yakovlevich Khintchine in mathematics and especially in probability theory is undeniable. His approaches to teaching mathematics, especially in the secondary school, are still a perfect model for mathematics teachers. On the other hand, his role in the theory of infinitely divisible distributions,, distribution of the sum of independent random variables, stable distributions and the domain of attraction of the Gauss law is fundamental and influential. The purpose of this article is to introduce educational approaches and key research achievements in the 30s in mathematics.

Understanding the social interactions between individuals and social groups whose decisions and the way they achieve their goals are interdependent, has been the basis for the formation of game theory. By expanding its scope of application from economics to general sciences, mathematics and then political science, game theory is a suitable platform for determining social balances in such a way that it has created the adoption of optimal strategies in cultural and social interactions. By analyzing comprehensive cognitive, economic and environmental issues in determining the policies of the macro-nations, this theory is of interest to experts and policymakers. Therefore, by localizing this theory, it is possible to take advantage of its capacities in the field of holistic analysis, examining different scenarios, providing possible solutions and forecasts in determining the macro-strategic policies of the country. In this regard, in this article, the necessity of using game theory in solving comprehensive cognitive problems with regard to the ecology of Shirvan city is investigated. For this purpose, the game theory will be investigated with a comprehensive cognitive approach, and then the famous patterns of game theory that are effective in analyzing people’s daily behavior by considering local and regional conditions will be studied and various examples will be presented in this field. Finally, the interaction of passengers and drivers in the intra-city transportation system of Shirvan city as an example of social behavior which has be analyzed according to the game theory is investigated.

This note considers the speed of growth of the geometry and topology community of the country in the 5-year period of $2018-2022$. According the published statistics, there is no growth in human resources, and expecting growth in the number of publications or significant scientific achievements does not seem so logical. Indeed, a logical outcome of such an observation, together with the announcement of officials regarding growth in science and publications is that this growth is related to other branches of science and not basic sciences. Basic sciences have actually experienced a negative growth in human resources. The descending number of academic member of staff at some of top rank universities in the country, is an example of such a saddening phenomenon.

Mathematics and especially problem solving, has a major role in the growth of awareness and the emergence of potential human capabilities, and therefore it causes the development of human resources, which is the main goal of educational activities in every country. In this regard, sometimes a problem without algebraic reasoning or with boring algebraic reasoning, with the help of a geometric similarity and analogy, which is a kind of visualization, can be made so simple and beautiful that all aspects of the problem can be seen almost at a glance. If a student can show his thoughts in the form of pictures instead of thinking in words, then solving some abstract and distant problems will be easier and more pleasant for him. Therefore, illustration, explanation and intuition are important for teaching mathematics. Mathematics is the language of science and intuitive thinking of mathematics is the way to develop mathematics, and is accompanied by intuitive explanations and images in the primary course, and intuitive thinking is used in the goals of school mathematics education for thematic communication and connection. In this article, we will criticize and examine intuitive thinking by presenting some examples from textbooks.