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Improving algebraic understanding using history of mathematics: the case of structural reasoning in cubic equations [PDF]
Frontiers in PsychologyTeaching algebra at the senior high school level often privileges procedural fluency at the expense of deeper conceptual understanding, which has left students unable to reason about the underlying structures of algebraic objects. This study investigates
Alfred Gyasi Bannor +2 more
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Classification of cubic equations
Lietuvos Matematikos Rinkinys, 2018 Rather unexpectably all real equations of the fourth degree are solvable by real means. So we can classify all real equations of the third and fourth degree. In this article we classify real cubics. The real quartics will be classified in another article.
Juvencijus Mačys, Jurgis Sušinskas
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A generalized computation procedure for Ramanujan-type identities and cubic Shevelev sum [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 A generalized Computation procedure for construction of the Ramanujan-type from a given general cubic equation and a cosine Ramanujan-type identity is developed from detailed analyses of the properties of Ramanujan-type cubic equations.
Peter J.-S. Shiue +3 more
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Fundamental theorem of algebra
Lietuvos Matematikos Rinkinys, 2022 The purpose of the article is to familiarize teachers and students with the fundamental theorem of algebra for real polynomials and its proof. Polynomials of small degrees are considered separately.
Juozas Juvencijus Mačys
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Solving Volterra-Fredholm integral equations by natural cubic spline function [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 Using the natural cubic spline function, this paper finds the numerical solution of Volterra-Fredholm integral equations of the second kind. The proposed method is based on employing the natural cubic spline function of the unknown function at ...
S.H. Salim, K.H.F. Jwamer, R.K. Saeed
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A Complete Review of the General Quartic Equation with Real Coefficients and Multiple Roots
Mathematics, 2022 This paper presents a general analysis of all the quartic equations with real coefficients and multiple roots; this analysis revealed some unknown formulae to solve each kind of these equations and some precisions about the relation between these ones ...
Mauricio Chávez-Pichardo +4 more
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On a Cubic Equation and a Jensen-Quadratic Equation [PDF]
Abstract and Applied Analysis, 2007 We obtain the general solutions of the cubic functional equation3[g(x+y)+g(x−y)+6g(x)]=2g(2x+y)+2g(2x−y)+g(−x−y)+g(−x+y)+6g(−x)and the Jensen-quadratic functional equationf((x+y)/2,z+w)+f((x+y)/2,z−w)=f(x,z)+f(x,w)+f(y,z)+f(y,w).
Bae, Jae-Hyeong, Park, Won-Gil
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Mathematics, 2023 In order to propose a deeper analysis of the general quartic equation with real coefficients, the analytical solutions for all cubic and quartic equations were reviewed here; then, it was found that there can only be one form of the resolvent cubic that ...
Mauricio Chávez-Pichardo +4 more
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Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities [PDF]
Opuscula Mathematica, 2022 We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface.
Shunya Adachi
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A New Solution to a Cubic Diophantine Equation
Axioms, 2022 A positive integer, which can be written as the sum of two positive cubes in two different ways, is known as a “Ramanujan number”. The most famous example is 1729=103+93=123+13, which was identified by Ramanujan as the lowest such number.
John C. Butcher
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