Related papers: Mathematical Proof
This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are: propositional logic axioms of ZFC wellorderings and…
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…
This paper describes some strategies used in a `transition' course. Such courses help undergraduate mathematics majors move from learning procedures to learning to function as critical mathematicians in order to understand and work with…
These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of…
We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
This material is a rewriting and expansion of notes for beginning graduate students in seminars in combinatorics (Department of Mathematics, University of California San Diego). Solid skills in linear and multilinear algebra were required…
Presented, in this monograph, are the results of the U. S. Naval Academy Mathematical Logic Course Project. The propositional and predicate calculus is presented in a unique manner. All aspects are rigorously established using the the…
The study of propositional logic -- fundamental to the theory of computing -- is a cornerstone of the undergraduate computer science curriculum. Learning to solve logical proofs requires repeated guided practice, but undergraduate students…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
These are notes for the course CS-172 I first taught in the Fall 1986 at UC Berkeley and subsequently at Boston University. The goal was to introduce the undergraduates to basic concepts of Theory of Computation and to provoke their…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…
This note shows that the three theorems presented in J. Math. Anal. Appl. 556 (2026), 130199, whose proofs, in their present formulation, are purely formal, follow from elementary calculus.