Related papers: Engaging Students Through Math Competitions
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
The purpose of this manuscript is to gather together a large amount of source material pertaining to women in mathematics, from studies of girls in elementary school through data on females winning prizes for mathematical research. Along…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural"…
This document is an exposition of an assortment of open problems arising from the exact enumeration of (perfect) matchings of finite graphs. Roughly half have been solved at the time of this writing; see the document "Twenty Open Problems…
This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of…
We describe the main features of the Research Experience for Undergraduates Program at the American Institute of Mathematics. We also present our perspective on identifying appropriate projects for students, guiding students as they begin…
In this note we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task-design that gives students the opportunity to conjecture, refute and prove. What is…
A few remarks on how mathematics quests for freedom.
Using a bit-string model similar to biological simulations, the competition between different languages is simulated both without and with spatial structure. We compare our agent-based work with differential equations and the competing…
We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.
When funding public goods, resources are often allocated via mechanisms that resemble contests, especially in the case of research grants. A common critique of these contests is that they induce ``too much'' effort from participants. This…
This paper explores middle-grade students' conceptions of median. Describes, where and why they struggle and provides learning trajectory to improve their understanding.
We study the obstacle problem associated with the American chooser option. The obstacle is given by the maximum of an American call option and an American put option, which, in turn, can be expressed as the maximum of the solutions to the…
Student-generated multiple-choice questions (MCQs) revised by the instructor were used to design an educational game and to set part of the exam in the framework of an elementary course in Photonics. An anonymous survey among the students…
Multiple teams participate in a random competition. In each round the winner receives one point. We study the times until ties occur among teams. We construct martingales and supermartingales that enable us to prove the results regarding…
The paper opens with an overview of the discussion of international comparisons (including goals) in mathematics education. Afterwards, the two most important recent international studies, the PISA Study and TIMSS-Repeat, are described.…
In voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number $k$ of new candidates will be added. We…
This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.