Related papers: Learning Foundations Beneath the Stars
This theoretical paper introduces a new way to view and characterize teaching and learning astronomy. It describes a framework, based on results from empirical data, analyzed through standard qualitative research methodology, in which a…
This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems…
Foundation models for structured time series data must contend with a fundamental challenge: observations often conflate the true underlying physical phenomena with systematic distortions introduced by measurement instruments. This…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
Computer science (CS) education needs to evolve to support software and artificial intelligence (AI) systems engineering, and it needs to happen now -- precisely because the core intellectual contributions of CS have never been more…
This book provides an introduction to the field of star formation at a level suitable for graduate students or advanced undergraduates in astronomy or physics. The structure of the book is as follows. The first two chapters begin with a…
Primitive recursion is a mature, well-understood topic in the theory and practice of programming. Yet its dual, primitive corecursion, is underappreciated and still seen as exotic. We aim to put them both on equal footing by giving a…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
Momentum exists in the physics community for integrating computation into the undergraduate curriculum. One of many benefits would be preparation for computational research. Our investigation poses the question of which computational skills…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
Conceptual modeling is a strongly interdisciplinary field of research. Although numerous proposals for axiomatic foundations of the main ideas of the field exist, there is still a lack of understanding main concepts such as system, process,…
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…
Discrete mathematics and probability theory contain foundational material for computer scientists. Despite their importance, instructors often worry that students will find these courses to be too abstract and seemingly disconnected from…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Generative foundation models like Stable Diffusion comprise a diverse spectrum of knowledge in computer vision with the potential for transfer learning, e.g., via generating data to train student models for downstream tasks. This could…
These are the notes for a 5-lecture-course given at ESSLLI 2006 in Malaga, Spain. The URL of the school is http://esslli2006.lcc.uma.es/ . This version slightly differs from the one which has been distributed at the school because typos…
Two transformative waves of computing have redefined the way we approach science. The first wave came with the birth of the digital computer, which enabled scientists to numerically simulate their models and analyze massive datasets. This…