N. Karjanto

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender, specialization and final high school score in mathematics are collected. The number of valid returned questionnaires is 108. There are 55 males, 53 females, 73

To respond to global issues positively, education systems in higher education institutions play a significant role in empowering learners as well as promoting sustainable development goals. By implementing curricula that cultivate cross-cutting and transversal key competencies for sustainability, such as critical thinking, problem-solving, and collaboration, we prepare our pupils to become sustainability citizens, who not only sustain learning throughout their lives in various circumstances and

We discuss the flipped classroom implementation for a Single Variable Calculus (SVC) course in a Confucian Heritage Culture (CHC) environment. A theoretical framework is composed of Bloom's taxonomy, English-medium instruction (EMI) and technology adaptation. Four different types of instructions were designed, three were flipped and one acts as a control. We investigate both quantitative and qualitative aspects of the pedagogy. Quantitative analysis indicates a statistically significant differen

This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger equation. These breathers belong to the family of solitons on a non-vanishing and constant background, where the continuous-wave envelope serves as a pedestal. The rational Peregrine soliton acts as a limiting behavior of the other two breather solitons, i.e., the Kuznetsov-Ma breather and Akhmediev soliton. Albeit with a phase shift, the latter becomes a nonlinear extension of the homoclinic o

The nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surface gravity waves to the captivating realm of Bose–Einstein condensates. This article delves into the dual facets of the NLS equation: its capacity for modeling wave packet dynamics and its remarkable breadth of applications. We illuminate the derivation of

The level of test anxiety in mathematics subjects among early undergraduate students at the University of Nottingham Malaysia Campus is studied in this article. The sample consists of 206 students taking several mathematics modules who completed the questionnaires on test anxiety just before they entered the venue for midterm examinations. The sample data include the differences in the context of academic levels, gender groups and nationality backgrounds. The level of test anxiety in mathematics

A number of qualitative comparisons of experimental results on unidirectional freak wave generation in a hydrodynamic laboratory are presented in this paper. A nonlinear dispersive type of wave equation, the nonlinear Schr\"{o}dinger equation, is chosen as the theoretical model. A family of exact solutions of this equation the so-called Soliton on Finite Background describing modulational instability phenomenon is implemented in the experiments. It is observed that all experimental results show

The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev–Petviashvili (enKP) model through a systematic analysis of explicit solutions. Using a superposed bilinearization approach, we obtained a bilinear form of the enKP equation and constructed soliton solutions. Our findings show that the nature of the resulting solitons, such as the amplitude, width, localization, and velocity,

This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into classrooms to enhance students’ understanding of Calculus concepts. For many mathematics educators who have been using CAS, this material is of great interest, particularly for secondary teachers and university instructors who plan to introduce an alternative CAS i

This thesis deals with some theoretical aspects of deterministic freak wave generation in the wave basin of a hydrodynamic laboratory. We adopt the spatial nonlinear Schrödinger equation as a mathematical model to describe the deformation of the wave packet envelope while propagating downstream. We study extensively a family of exact solutions describing modulational instability, known as the Akhmediev-Eleonski\uı-Kulagin breather. Together with the Kuznetsov-Ma breather and Peregrine solution,

Breather solutions of the nonlinear Schrödinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a background is used as has been proposed by van Groesen et. al. (2006). Requiring the displaced phase to be temporally independent, has as consequence that the dynamics at each position is described by the motion of a nonlinear autonomous oscillator in a potential

The Nonlinear Schr\\"odinger (NLS) equation is used to model surface waves in\nwave tanks of hydrodynamic laboratories. Analysis of the linearized NLS\nequation shows that its harmonic solutions with a small amplitude modulation\nhave a tendency to grow exponentially due to the so-called Benjamin-Feir\ninstability. To investigate this growth in detail, we relate the linearized\nsolution of the NLS equation to a fully nonlinear, exact solution, called\nsoliton on finite background. As a result, w