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Sets, Relations and Functions
Published in Sriraman Sridharan, R. Balakrishnan, Foundations of Discrete Mathematics with Algorithms and Programming, 2019
Sriraman Sridharan, R. Balakrishnan
A function (also called a map or mapping or a single-valued function) f:A→B $ f:\, A\rightarrow B $ from a set A to a set B is a rule by which to each a∈A $ a\in A $ , there is assigned a unique element f(a)∈B $ f(a)\in B $ . f(a) is called the image of a under f.
Overview of Cryptography
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
While this book is not a treatise on abstract mathematics, a familiarity with basic mathematical concepts will prove to be useful. One concept which is absolutely fundamental to cryptography is that of a function in the mathematical sense. A function is alternately referred to as a mapping or a transformation.
Enhancing pre-service mathematics teachers’ understanding of function ideas
Published in International Journal of Mathematical Education in Science and Technology, 2022
Hande Gülbağci Dede, Zuhal Yilmaz, Hatice Akkoç, David Tall
Studies have documented various function ideas that are essential for having a robust understanding of functions (Ayalon et al., 2017; Cooney et al., 2010; Watson et al., 2013). The first idea of mapping approaches the meaning of a function as a ‘single-valued mapping from one set-domain of the function to another-range’ (Ayalon et al., 2017, p. 8). This can be either in the form of a one-to-one or many-to-one mapping between sets (Watson et al., 2013). Vinner and Dreyfus (1989) called the same idea correspondence. They defined the function as ‘any correspondence between two sets that assigns to every element in the first set exactly one element in the second set’ (p. 359). Ayalon et al. (2017) stated that correspondence is an approach to understand functions. They asserted that a mapping and an input-output model are methods that emphasize correspondence. In this paper, we will use the term mapping instead of correspondence to distinguish mapping from an input-output idea, which is more general.
Designing for interpersonal motor synchronization
Published in Human–Computer Interaction, 2022
Michal Rinott, Noam Tractinsky
Mapping is a technical term, borrowed from mathematics, referring to the relationship between the elements of two sets of things (Norman, 2013). Whereas traditional mappings of systems rely on a good spatial model, synchronization requires temporal mapping as the main coordinating principle, or even the combination of temporal and spatial mapping together. When two or more participants act together, a relatively precise temporal and spatial mapping between their actions is necessary for synchronization. This relates to the relationship between movement and temporal patterns presented in Section 4.2: when movements are identical, the mapping is trivial; however, when the movements and temporal patterns differ, the mappings need to be readable and clear.