The Standards for Mathematical Practice describe varieties of expertise that mathematics educators should develop in their students including NCTM process standards (problem solving, reasoning and proof, communication, representation, and connections), NRC's report Adding It Up (adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition), and Common Core State Standards in Mathematics (ICT application) to support mathematics teaching and learning. There is a need to provide effective ways that technology can be integrated into mathematics classrooms. Mathematical methods and techniques are typically used in engineering and industrial fields. It can also become an interdisciplinary subject motivated by engineers' needs. Mathematical problems in engineering result in rigorous engineering application carried out by mathematical tools. Therefore, the solid understanding and command of mathematical knowledge is very necessary. This chapter presents the introduction of currently available ICTs and their application to create e-learning environments to prepare for the students' future engineering education.
TopBackground
Data integration techniques or information and communication technologies have been intensively used in different data mining applications such as data clustering, classification, association rules mining, sequential pattern mining, outlier detection, feature selection, and information extraction in the industrial and environmental research via air quality monitoring network. A huge increase in the number of papers and citations in the area has been observed in the previous decade, which is clear evidence of the popularity of these techniques. These have included the adoption of such kind of methodologies in the research field of polarization-difference imaging for observation through scattering media (Rowe, Pugh, Tyo, & Engheta, 1995), biologically inspired self-adaptive multi-path routing in overlay networks (Leibnitz, Wakamiya, & Murata, 2006), a biologically inspired system for action recognition (Jhuang, Serre, Wolf, & Poggio, 2007), programmable self-assembly using biologically-inspired multiagent control (Nagpal, 2002), biologically inspired growth of hydroxyapatite nanocrystals inside self-assembled collagen fibers (Roveri et al., 2003), biologically inspired cognitive radio engine model utilizing distributed genetic algorithms for secure and robust wireless communications and networking (Rieser, 2004), biomimetics of biologically inspired technologies (Bar-Cohen, 2005), biologically inspired computing (De Castro & von Zuben, 2005), and biologically inspired algorithms for financial modeling (Brabazon & O'Neill, 2006). Before we start to give the introduction of these techniques in the research field of industrial operation and environment sustainability, the brief introduction will be given for these techniques.
Artificial Neural Networks
In computer science and related fields, artificial neural networks are models are derived from animal central nervous systems (Wang & Fu, 2008). The biologically neural networks are capable of machine learning and pattern recognition. They can be regarded as systems of internally connected neurons. They can compute values from inputs by feeding information through the network (Stevens & Casillas, 2006). For example, in a neural network for image recognition, a set of input neurons may be activated by the pixels of an input image representing a shape or color. The activations of these neurons are then passed on, weighted and transformed by some function determined by the network's designer, to other neurons, etc., until finally an output neuron is activated that determines which image was recognized. Similar with other methods of machine learning, neural networks have been applied to solve a wide range of jobs which are difficult to solve using ordinary rule-based programming (Yang & Zheng, 2009).Generally, artificial neural network handles a problem with the combination of simple processing elements which have complex global behavior. A class of statistical models will be called “neural” if they have sets of adaptive weights (numerical parameters that are tuned by a learning algorithm, and are capable of approximating non-linear functions of their inputs) (Patterson, 1998).
The adaptive weights are conceptually connection strengths between neurons. They will be activated during the period of model training and prediction. Neural networks can also perform functions collectively and in parallel by the units, which are also similar to biological neural networks. The terminology of neural network usually means the model with the integration of statistics, cognitive psychology and artificial intelligence (Sarle, 1994). They are part of theoretical neuroscience and computational neuroscience. In modern software implementations of artificial neural networks, the approach inspired by biology has been largely abandoned according to statistics and signal processing (Holler, Tam, Castro, & Benson, 1989). In some of these systems, neural networks or parts of neural networks can form components in larger systems that combine both adaptive and non-adaptive elements (Cochocki & Unbehauen, 1993). The general approach of such systems is feasible for real-world problem solving while it has been different from the traditional artificial intelligence models, which adopt the principles of non-linear, distributed, parallel and local processing and adaptation.