Independence of the Continuum Hypothesis: an Intuitive Introduction

The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the main workhorse of set theory; and it has broad implications on mathematical foundations and on the role of syntax versus semantics. Despite its broad impact, it is not broadly taught. A main reason is the lack of accessible expositions for nonspecialists, because the mathematical structures and techniques employed in the proof are unfamiliar outside of set theory. This manuscript aims to take a step in addressing this gap by providing an exposition at a level accessible to advanced undergraduate mathematicians and theoretical computer scientists, while covering all the technically challenging parts of the proof.Comment: - Edited the example in the Reflection definition. - Changed fonts for rank() and nr() - Changed fonts for CH to \mathrm{CH} - Corrected a few spurious typo

Choosing grammars to support language processing courses

Teaching Language Processing courses is a hard task. The level of abstraction inherent to some of the basic concepts in the area and the technical skills required to implement efficient processors are responsible for the number of students that do not learn the subject and do not succeed to finish the course. In this paper we intend to list the main concepts involved in Language Processing subject, and identify the skills required to learn them. In this context, it is feasible to identify the difficulties that lead students to fail. This enables us to suggest some pragmatic ways to overcome those troubles. We will focus on the grammars suitable to motivate students and help them to learn easily the basic concepts. After identifying the characteristics of such grammars, some examples are presented to make concrete and clear our proposal. The contribution of this paper is the systematic way we approach the process of teaching Language Processing courses towards a successful learning activity.(undefined