During the last decades, the interest displayed in neurocognitive and brain science research is relatively high. In this chapter, the cognitive neuroscience field approach focuses in the aspect of the way that cognitive functions are produced by neural circuits in the brain. Within this frame, the effects of impairment to the brain and subsequent changes in the thought processes due to changes ...

We describe aspects of computational thinking as covered in the course Codes and Ciphers (CSC 233). 1 Cryptology and Computational Thinking Cryptology consists of cryptography and cryptanalysis, or, in other words, the making and the breaking of ciphers. History suggests that one cannot successfully do one without the other: too many ciphers were designed by enthusiasts without any knowledge of...

Andrei Nikolaevich Kolmogorov was the foremost contributor to the mathematical and philosophical foundations of probability in the twentieth century, and his thinking on the topic is still potent today. In this article we first review the three stages of Kolmogorov’s work on the foundations of probability: (1) his formulation of measure-theoretic probability, 1933, (2) his frequentist theory of...

The computer can be used as a tool to complement advanced mathematical thinking in a variety of ways. In research it has been used to provide data to suggest possible theorems, to seek counter-examples and to carry out onerous computations to prove theorems involving only a finite number of algorithmic cases. In education it can be used for the same objectives, and for one other major purpose: ...

Mathematical chemistry is often thought to be a 20-century subdiscipline of chemistry, but in this paper we discuss several early chemical ideas and some landmarks of chemistry as instances of the mathematical way of thinking; many of them before 1900. By the mathematical way of thinking, we follow Weyl’s description of it in terms of functional thinking, i.e. setting up variables, symbolizing ...

Over the past two decades, I have been working on problems at the intersection of Algorithm Design, Optimization, Algorithmic Game and Economics Theories, Scientific Computation, and Parallel Processing. I am a theoretican who cares a lot about the practical impact of mathematical and algorithmic work and who appreciates interdisciplinary research. My main research interests include Smoothed An...

This study examines the use of counterexamples for supporting development students’ algorithmic thinking. Working from premise that some are more effective than others generalized algorithms, proposes distinctions between in relation to iterative refinement student-invented algorithms. Furthermore, identifies factors may influence differences among counterexamples. Using task-based interviews, ...