FORMATION OF COGNITIVE UUD IN MATHEMATICS LESSONS IN ELEMENTARY SCHOOL

The article deals with a modern mathematics lesson in elementary school, which includes the formation of students’ UUD. An important factor in teaching younger schoolchildren is not only the knowledge gained in the lesson, but also the acquired cognitive skills.

Research on HPM Teaching Supported by Hawgent Dynamic Mathematics Software: Take “The Recognition of Circle” as an Example

History and Pedagogy of Mathematics (HPM) is one of the important research fields in mathematics education, which has received widespread attention from the mathematics education community because of its educational value. Modern mathematics education technology plays an important auxiliary role in mathematics teaching. Hawgent is a dynamic mathematics software that can present abstract mathematical knowledge visually and static mathematical knowledge dynamically. In view of this, this research takes “the recognition of circle” as an example to conduct a research on HPM teaching supported by Hawgent Dynamic Mathematics Software in three aspects: analyze the contents and uncover the history of mathematics, make the products and show the history of mathematics, design the teaching and integrate the history of Mathematics.

ROLE AND IMPORTANCE OF STHIRA BINDU (FIXED POINT) IN YOGA PHILOSOPHY

It is true that all living things and all the mechanisms of entire universe are guided by mathematical relations and results. The theory of fixed point is one of the most leading gears of modern mathematics and its results are the most generally useful in mathematics which gives the solution of non-linear problems of various fields of modern subjects [9]. Also, the human brain can perform the intellectual courses that still have not been performed by digital computers. It may therefore be seen that quantum mechanics is very much associated with the consciousness of mankind [21]. Yoga is one of the few ways to understand the eventual reality mentioned in Vedanta, quantum physics and mathematics as well [19]. This paper investigates the role and importance of fixed point in eastern philosophies especially with yoga along with meditation focusing that mathematics plays a significant role in yoga philosophy.

Archimedes of Syracuse and Sir Isaac Newton: On the Quadrature of a Parabola

Good mathematics stands the test of time. As culture changes, we often ask different questions, bringing new perspectives, but modern mathematics stands on ancient discoveries. Isaac Newton’s discovery of calculus (along with Leibniz) may seem old but is predated by Archimedes’ findings. Current mathematics students should be familiar with parabolas and simple curves; in our introductory calculus courses, we teach them to compute the areas under such curves. Our modern approach derives its roots from Newton’s work; however, we have filled in many of the gaps in the pursuit of mathematical rigor. What many students may not know is that Archimedes solved the area problem for parabolas long before the use of algebraic expressions became mainstream. Archimedes used the geometry of the ancient Greeks, which gave him a vastly different perspective. In this paper we provide both Archimedes’ and Newton’s proofs involving the quadrature of the parabola, trying to remain true to their original texts as much as feasible.

A new approach towards solving the Riemann hypothesis

In this paper, I attempt to solve one of the most difficult problems in modern mathematics-'The Riemann Hypothesis'. I redefine the gamma function and use that modified form along with some identities from Fourier analysis and concepts from complex analysis to show that all the non-trivial zeros of the Riemann zeta function must lie on the critical line and then by recalling Hardy's theorem I prove the Riemann hypothesis.

Perkembangan Matematika dan Pendidikan Matematika Di Indonesia

This study aims to determine the development of mathematics education in Indonesia. The research method used is descriptive method, by presenting a description, clarification of a phenomenon and facts in mathematics. As well as library research (library research). By collecting several books, articles and opinions from experts regarding the development of mathematics and mathematics education which are then developed with various existing findings. The results showed that the development of mathematics was based on philosophy, because philosophy is the root of all human knowledge, both scientific knowledge and non-scientific knowledge. The historical development of mathematics, Babiliona mathematics refers to all mathematics developed by the Mesopotamians since the beginning of Hellenism. At that time the development of mathematics expanded to several countries such as Egypt, Greece, Arabia and India. The development of Mathematics Education in Indonesia is never separated from the history of the curriculum. The importance of mathematics in life is not surprising if mathematics learning has developed and adapted to the needs of the times. The development of mathematics learning in Indonesia is as traditional mathematics, modern mathematics, and modern mathematics.

EQUIVALENCE OF THE HUNTER-SAXON EQUATION AND THE GENERALIZED HEISENBERG FERROMAGNET EQUATION

Integrable systems play an important role in modern mathematics, theoretical and mathematical physics. The display of integrable equations with exact solutions and some special solutions can provide important guarantees for the analysis of its various properties. The Hunter-Saxton equation belongs to the family of integrable systems. The extensive and interesting mathematical theory, underlying the Hunter-Saxton equation, creates active mathematical and physical research. The Hunter-Saxton equation (HSE) is a high-frequency limit of the famous Camassa-Holm equation. The physical interpretation of HSE is the propagation of weakly nonlinear orientation waves in a massive nematic liquid crystal director field. In this paper, we propose a matrix form of the Lax representation for HSE in 𝑠𝑢ሺ𝑛 ൅ 1ሻ/𝑠ሺ𝑢ሺ1ሻ ⊕ 𝑢ሺ𝑛ሻሻ - symmetric space for the case 𝑛 ൌ 2. Lax pairs, introduced in 1968 by Peter Lax, are a tool for finding conserved quantities of integrable evolutionary differential equations. The Lax representation expands the possibilities of the equation we are considering. For example, in this paper, we will use the matrix Lax representation for the HSE to establish the gauge equivalence of this equation with the generalized Heisenberg ferromagnet equation (GHFE). The famous Heisenberg Ferromagnet Equation (HFE) is one of the classical equations integrable through the inverse scattering transform. In this paper, we will consider its generalization. Andalso the connection between the decisions of the HSE and the GHFE will be presented.