2. Mathematical Explanations of MIMO Technologies

Mathematical Explanations in Euler’s Königsberg

I examine Leonhard Euler’s original solution to the Königsberg bridges problem. Euler’s solution can be interpreted as both an explanation within mathematics and a scientific explanation using mathematics. At the level of pure mathematics, Euler proposes three different solutions to the Königsberg problem. The differences between these solutions can be fruitfully explicated in terms of explanat...

Principles Used to Evaluate Mathematical Explanations

Mathematics is critical for making sense of the world. Yet, little is known about how people evaluate mathematical explanations. Here, we use an explanatory reasoning task to investigate the intuitive structure of mathematics. We show that people evaluate arithmetic explanations by building mental proofs over the conceptual structure of intuitive arithmetic, evaluating those proofs using criter...

Pre-service Teachers’ Explanations of Two Mathematical Concepts

There has been growing interest in the role played in mathematics teaching by teachers’ pedagogical content knowledge. This form of teacher knowledge goes beyond mastery of the subject to incorporate how subject matter is actually used in teaching. In particular, it includes knowledge of how to explain concepts and what models can be used to facilitate students’ understanding. In this study two...

Smart Antennas, MIMO systems and Related Technologies

Key Technologies Actualizing Broadband MIMO-OFDM Hardware

Fig.1 Key technologies actualizing MIMO-OFDM hardware