Recent zbMATH articles in MSC 97https://zbmath.org/atom/cc/972021-01-08T12:24:00+00:00WerkzeugResearch of mathematics learning ability for graduate students based on BP neural network and cluster analysis.https://zbmath.org/1449.970012021-01-08T12:24:00+00:00"Du, Shaohong"https://zbmath.org/authors/?q=ai:du.shaohong"Li, Wenshuo"https://zbmath.org/authors/?q=ai:li.wenshuo"Zhen, Jiangyi"https://zbmath.org/authors/?q=ai:zhen.jiangyi"Tan, Yuanshun"https://zbmath.org/authors/?q=ai:tan.yuanshunSummary: The purpose of this paper is to give some pertinent suggestions for improving postgraduates' mathematical ability through research and analysis to improve the current situation that graduate students' mathematics learning ability cannot reach the level of scientific research. This study obtains objective indicators that can comprehensively measure mathematics learning ability through BP neural network to get the math learning ability evaluation score, and uses SPSS software to test the correlation between influencing factors and the indicators, so as to get the factors that significantly affect postgraduates' mathematics learning ability. Finally, according to the different characteristics of the respondents, the graduate students are clustered, and specific suggestions are given for each type of individuals to improve their mathematics learning ability.Trigonometric functions in elementary mathematics.https://zbmath.org/1449.330012021-01-08T12:24:00+00:00"Smýkalová, Radka"https://zbmath.org/authors/?q=ai:smykalova.radkaThe book discusses various elementary aspects and applications of trigonometric functions. Most of the text is accessible to high-school students, but it will be useful to teachers as well. Despite being elementary, it contains a significant amount of advanced material, including olympiad-level problems. The contents are as follows:
Chapter 1 deals with the history of trigonometric functions, beginning with the roots or trigonometry in the ancient Greece, proceeding to the developments in the medieval India and Arabic lands, and concluding with Euler's analytical approach to trigonometric functions.
The next three chapters provide a modern and systematic treatment of high-school trigonometry and trigonometric functions. Chapter 2 begins with trigonometry in right triangles, and includes geometric derivations of the trigonometric addition formulas. It covers some slightly more advanced topics, such as the construction of a regular pentagon, or expressing the values of trigonometric functions for special angle values in terms of radicals. Chapters 3 proceeds to high-school trigonometry of general triangles, and extends the definitions of trigonometric functions to arguments from the interval \((90^\circ,180^\circ)\). It covers the well-known laws of sines and cosines, and the less familiar law of tangents and Mollweide's formula. Finally, Chapter 4 uses the unit circle to introduce trigonometric functions for an arbitrary real argument, discusses the validity of addition formulas in this more general setting, and devotes considerable space to the solution of trigonometric equations and inequalities.
Chapter 5 contains an overview of many advanced (but still elementary) identities and inequalities involving trigonometric functions. The final Chapter 6 describes some applications, such as the solution of algebraic equations using trigonometric substitutions, derivations of various identities and inequalities using the trigonometric form of complex numbers, and the appearance of trigonometric functions in cartography (with emphasis on the Mercator projection).
Reviewer: Antonín Slavík (Praha)More characterizations of cyclic quadrilaterals.https://zbmath.org/1449.510142021-01-08T12:24:00+00:00"Josefsson, Martin"https://zbmath.org/authors/?q=ai:josefsson.martinSummary: We continue the project of collecting a large number of characterizations of convex cyclic quadrilaterals with their proofs, which we started in [the author, Int. J. Geom. 8, No. 1, 5--21 (2019; Zbl 1449.51013)]. This time we prove 15 more, focusing primarily on characterizations concerning trigonometry and the diagonals.Application of hybrid teaching mode in ``Probability and statistics''.https://zbmath.org/1449.970022021-01-08T12:24:00+00:00"Sun, Yan"https://zbmath.org/authors/?q=ai:sun.yanSummary: Probability and Statistics course is widely offered in colleges and universities as a public foundation course, and it is very important to study its teaching mode. At present, thanks to the continuous development of technical means, the hybrid teaching mode is more and more integrated into the teaching activities in colleges and universities because it can combine the advantages of network teaching mode and traditional teaching mode. However, due to its wide audience and few practical links, the public foundation course in mathematics is difficult to bring out the advantages of network teaching mode. In order to mobilize the initiative of students' learning, we introduce the concept of ``flipped classroom'' into the teaching activities of Probability and Statistics course. A ``strategic progressive'' hybrid teaching design idea is proposed which is based on the ``Taiji Ring'' flipped classroom model and the characteristics of the Probability and Statistics course. From this idea, corresponding teaching modes and evaluation models for different teaching stages are developed. The idea is also tested through the teaching activities in order to provide experiences for the reform of the Probability and Statistics course in the future.Fractional-order mathematical model for calcium distribution in nerve cells.https://zbmath.org/1449.354432021-01-08T12:24:00+00:00"Joshi, Hardik"https://zbmath.org/authors/?q=ai:joshi.hardik"Jha, Brajesh Kumar"https://zbmath.org/authors/?q=ai:jha.brajesh-kumarSummary: Calcium (Ca\(^{2+})\) ions are known as a second messenger, involved in a variety of signalling process. It regulates various physiological processes like signal transduction, proliferation, etc. Calbindin-D\(_{28k}\) reacts with free Ca\(^{2+}\) ions and significantly lowers down the cytosolic free calcium concentration ([Ca\(^{2+}])\) in nerve cell. Voltage-gated calcium channel (VGCC) works as an outward source of Ca\(^{2+}\) which initiates and sustains Ca\(^{2+}\) signalling process for the smooth functioning of the cells. An alteration in Ca\(^{2+}\) signalling process leads to the early symptoms of Parkinson's disease (PD). In this piece of work two major analyses has done. First, we have developed a mathematical model in the form of a fractional reaction-diffusion equation. Second, the obtained results are interpreted with a neuronal disorder, i.e., PD. Hence the physiological role of calbindin-D\(_{28k}\) and VGCC in PD is analyze using mathematical model by incorporating all important parameters like diffusion coefficient, fluxes, etc. Appropriate initial and boundary conditions are used according to the biophysical conditions of the cell.On Pell hybrinomials.https://zbmath.org/1449.110322021-01-08T12:24:00+00:00"Liana, Mirosław"https://zbmath.org/authors/?q=ai:liana.miroslaw"Szynal-Liana, Anetta"https://zbmath.org/authors/?q=ai:szynal-liana.anetta"Włoch, Iwona"https://zbmath.org/authors/?q=ai:wloch.iwonaSummary: Hybrid numbers generalize complex, hyperbolic and dual numbers, simultaneously. Special kinds of hybrid numbers, related to numbers of Fibonacci type, among others Pell numbers, were introduced quite recently. In this paper we introduce and study polynomials, which are a generalization of Pell hybrid numbers and so called Pell hybrinomials.