Related papers: Interactions of Computational Complexity Theory an…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Computing education widely applies general learning theories and pedagogical practices. However, computing also includes specific disciplinary knowledge and skills, e.g., programming and software development methods, for which there has…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
With the advent of high-level programming languages capable of quickly rendering three-dimensional simulations, the inclusion of computers as a learning tool in the classroom has become more prevalent. Although work has begun to study the…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
Computation is a central aspect of modern science and engineering work, and yet, computational instruction has yet to fully pervade university STEM curricula. In physics, we have begun to integrate computation into our courses in a variety…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
This paper is a survey dedicated to the analogy between the notions of {\it complexity} in theoretical computer science and {\it energy} in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested…
This paper outlines ongoing dissertation research located in the intersection of science fiction, human-computer interaction and computer science. Through an interdisciplinary perspective, drawing from fields such as human-computer…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a…
This book discusses computational curiosity, from the psychology of curiosity to the computational models of curiosity, and then showcases several interesting applications of computational curiosity. A brief overview of the book is given as…
Studying corruption presents unique challenges. Recent work in the spirit of computational social science exploits newly available data and methods to give a fresh perspective on this important topic. In this chapter we highlight some of…