Related papers: Teaching Divisibility and Binomials with Coq
Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye…
Quantum mechanics is a field often considered very mathematical, abstract, and unintuitive. One way some instructors are hoping to help familiarize their students with these complex topics is to have the students see quantum effects in…
In a recent report, the American Association of Physics Teachers has developed an updated set of recommendations for curriculum of undergraduate physics labs.1 This document focuses on six major themes: constructing knowledge, modeling,…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
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…
We are at the dawn of the second quantum revolution, where our ability to create and control individual quantum systems is poised to drive transformative advancements in basic science, computation, and everyday life. However, quantum theory…
We introduce a theory of finite polynomial cohomology with coefficients in this paper. We prove several basic properties and introduce an Abel-Jacobi map with coefficients. As applications, we use such a cohomology theory to study…
Quasi-set theory provides a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the quantum statistics into the scope of quasi-set theory and discuss the…
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…
The set of integer number lists with finite length, and the set of binary trees with integer labels are both countably infinite. Many inductively defined types also have countably many elements. In this paper, we formalize the syntax of…
Understanding instructor attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to…
Among the ideas to be conveyed to students in an introductory quantum course, we have the pivotal idea championed by Dirac that functions correspond to column vectors (kets) and that differential operators correspond to matrices (ket-bras)…
In this work, the authors describe efforts aimed at Indigenizing a second-year linear algebra course at a small liberal arts university in Manitoba, Canada. This is done through an assignment, part hands-on and part written work, that…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
We prove a recent conjecture of Lassalle about positivity and integrality of coefficients in some polynomial expansions. We also give a combinatorial interpretation of those numbers. Finally, we show that this question is closely related to…
The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom…
These are the notes of my lectures at the 1996 European Congress of Mathematicians. {} Polynomials appear in mathematics frequently, and we all know from experience that low degree polynomials are easier to deal with than high degree ones.…
The binomial notation (w u) represents the number of occurrences of the word u as a (scattered) subword in w. We first introduce and study possible uses of a geometrical interpretation of (w ab) and (w ba) when a and b are distinct letters.…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…