相关论文: PIGTIKAL (puzzles in geometry that I know and love…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
Knowledge distillation is the procedure of transferring "knowledge" from a large model (the teacher) to a more compact one (the student), often being used in the context of model compression. When both models have the same architecture,…
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…
A rep-tile is a polygon that can be dissected into smaller copies (of the same size) of the original polygon. A polyomino is a polygon that is formed by joining one or more unit squares edge to edge. These two notions were first introduced…
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The understanding of probability can be difficult for a few young scientists. Consequently, this new mathematical symbol, related to binomial coefficients and simplicial polytopic numbers, could be helpful to science education. Moreover,…
The cover of the SIAM Journal on Applied Algebra and Geometry shows seven pictures. We describe these pictures and discuss the topics they represent. About the Author: Anna Seigal is a graduate student at UC Berkeley working in applied…
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
Sudoku is a popular combinatorial puzzle. A new method of solving Sudoku is presented, which involves formulating a puzzle as a special type of transportation problem. This model allows one to solve puzzles with more than one solution,…
We propose to address the problem of how to know students' knowledge in an entirely new approach called ?epistemography? which is, roughly, an attempt to describe the structure of this knowledge. We claim that what is to be known is made of…
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…
Esoteric programming languages are challenging to learn, but their unusual features and constraints may serve to improve programming ability. From languages designed to be intentionally obtuse (e.g. INTERCAL) to others targeting artistic…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
Parsons problems (PPs) have shown promise in structured problem solving by providing scaffolding that decomposes the problem and requires learners to reconstruct the solution. However, some students face difficulties when first learning…
We introduce bindings that enable the convenient, efficient, and reliable use of software modules of CGAL (Computational Geometry Algorithm Library), which are written in C++, from within code written in Python. There are different tools…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the…
The problem of accurately measuring the similarity between graphs is at the core of many applications in a variety of disciplines. Graph kernels have recently emerged as a promising approach to this problem. There are now many kernels, each…
We do not present any original or new material. This is a tutorial addressed to students who need to study the microscopic derivation of the quantum-mechanical master equation encountered in many practical physical situations.