Related papers: Learning Foundations Beneath the Stars
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
Italian master's thesis in Computer Science. It is an overview of the standard tecniques developed in the field of Proof Theory, ending with some results in the new field of Deep Inference, plus an original contribution trying to relate…
Younger generations are growing up in a world increasingly shaped by intelligent technologies, making early AI literacy crucial for developing the skills to critically understand and navigate them. However, education in this field often…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
Evidence-based education has become a central concept in science education, with meta-analyses often regarded as the gold standard for informing practice. This emphasis raises critical questions concerning the applicability,…
General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might…
The unprecedented growth in the availability of data of all types and qualities and the emergence of the field of data science has provided an impetus to finally realizing the implementation of the full breadth of the Nolan and Temple Lang…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
We present a scientific reasoning foundation model that aligns natural language with heterogeneous scientific representations. The model is pretrained on a 206B-token corpus spanning scientific text, pure sequences, and sequence-text pairs,…
Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…
This pedagogical article elucidates the fundamentals of trapped-ion quantum computing, which is one of the potential platforms for constructing a scalable quantum computer. The evaluation of a trapped-ion system's viability for quantum…
Writing and argumentation are critical to both professional physics and physics education. However, the skill of making an extended argument in writing is often overlooked in physics classrooms, apart from certain practices like lab…
The current conventional approach in teaching STEM seems inadequate; it is failing both the students and the work-force demands in several aspects. Perhaps it is succeeding in equipping students with information and facts but surely falls…
I present a new approach to teaching a graduate-level programming languages course focused on using systems programming ideas and languages like WebAssembly and Rust to motivate PL theory. Drawing on students' prior experience with…
In this paper we describe our experience in developing curriculum courses aimed at graduate students in emerging computational fields, including biology and medical science. We focus primarily on computational data analysis and statistical…
We demonstrate that the Weihrauch lattice can be used to classify the uniform computational content of computability-theoretic properties as well as the computational content of theorems in one common setting. The properties that we study…
The foundations of mathematics have long been considered settled by the Zermelo-Fraenkel-Choice axioms. But set theory abounds in models with different truths and even classical questions such as the measurability of projective sets can…
Computational modeling is a critical tool for understanding consciousness, but is it enough on its own? This paper discusses the necessity for an ontological basis of consciousness, and introduces a formal framework for grounding…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
The basics of set theory are usually copied, directly or indirectly, by computer scientists from introductions to mathematical texts. Often mathematicians are content with special cases when the general case is of no mathematical interest.…