Browsing by Author "Alghamdi, Nouf"

Now showing 1 - 2 of 2

Restricted
Bounded linear operators in Banach and Hilbert spaces
(Swnsea University, 2023-12-15) Alghamdi, Nouf; Lytvynov, Eugene
The initial and foundational category of spaces examined in functional analysis is that of complete normed spaces over real or complex numbers, known as Banach spaces. A notable example is a Hilbert space, in which the norm is derived from an inner product. These spaces are pivotal in diverse fields, such as the mathematical representation of quantum mechanics, machine learning, partial differential equations, and Fourier analysis. This dissertation extensively investigates continuous linear operators de- fined on Banach and Hilbert spaces. It delves into crucial theorems and properties of bounded linear operators, including the Hilbert-adjoint operators. Consequently, the Hilbert-adjoint operator is used to define three essential classes of bounded linear operators on a Hilbert space. The study concludes by examining the spectral properties of bounded self-adjoint linear operators. Key Words: Normed spaces, Banach spaces, Hilbert spaces, Bounded linear operators, Spectral theory.
16 0
Restricted
Investigating Saudi Arabia University Teachers’ Level of Self-Efficacy in The Components of The Tpack Model
(2023-06-23) Alghamdi, Nouf; Serenka, Jo Franny
This study aims to investigate the level of self-efficacy among instructors regarding the various components of the TPACK model in their teaching within Saudi Arabia. TPACK represents a viable nexus between technology and educational content, creating successful educational technology integration. Existing research demonstrates a need to study TPACK further in the context of instructors’ level of self-efficacy in the components of the TPACK model (Lee and Kim, 2017). However, this dissertation will investigate instructors’ level of self-efficacy towards utilizing technology in their classrooms. In doing so, the study will adopt a quantitative approach using a survey to gain insights into instructors’ self-efficacy. This study is significant because TPACK is a critical part of the Saudi Arabian education system. Instructor’s level of self-efficacy is essential as they shape not only the future of educational delivery, but also the future of each learner. Moreover, the growing implementation of TPACK in universities in KSA is exclusively dependent upon the instructors’ performance with this model. The findings revealed that instructors demonstrated high levels of self-efficacy across all components of TPACK. They also exhibited confidence in using technology to enrich content, support student inquiry, and organize teaching and student learning. However, there were some areas where participants indicated a lack of self-efficacy or uncertainty. The research recommends that educational institutions support instructors through mentoring programs, collaborative learning communities, and peer observations (Marx, 2005).
46 0