Related papers: Mathematical Proof
This article presents the findings of a case study which introduced online quizzes as a form of assessment in pure mathematics. Rather than being designed as an assessment of learning, these quizzes were designed to be an assessment for…
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.
Proof scores can be regarded as outlines of the formal verification of system properties. They have been historically used by the OBJ family of specification languages. The main advantage of proof scores is that they follow the same syntax…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
In this work, we develop statistical tools to understand core courses at the university level. Traditionally, professors and administrators label courses as "core" when the courses contain foundational material. Such courses are often…
We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
The connection method has earned good reputation in the area of automated theorem proving, due to its simplicity, efficiency and rational use of memory. This method has been applied recently in automatic provers that reason over ontologies…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…
In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.