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首页> 外文期刊>PRIMUS: problems, resources, and issues in mathematics undergraduate studies >Binomial Coefficients Modulo a Prime—A Visualization Approach to Undergraduate Research
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Binomial Coefficients Modulo a Prime—A Visualization Approach to Undergraduate Research

机译：二项式系数模为素数—本科生研究的可视化方法

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摘要

In this article we present, as a case study, results of undergraduate research involving binomial coefficients modulo a prime p. We will discuss how undergraduates were involved in the project, even with a minimal mathematical background beforehand. There are two main avenues of exploration described to discover these binomial identities. The first uses a p-adic approach. The second, and more modern, utilizes the self-similarity, i.e., fractal nature, of Pascal’s triangle modulo a prime. We will also discuss strategies for involving mathematics students in undergraduate research and provide some ideas which can be incorporated in several of the standard courses in the undergraduate mathematics curriculum. In particular, the identities and techniques discussed can serve as a bridge between classroom activities and future undergraduate research projects.
机译：在本文中，我们以案例研究的形式给出了涉及二项式系数模为质数p的本科生研究结果。我们将讨论本科生如何参与该项目，即使事先没有最低的数学背景。描述了发现这些二项式身份的两种主要探索途径。第一种使用p-adic方法。第二种，也是更现代的，利用了Pascal三角模的素数的自相似性，即分形性质。我们还将讨论使数学学生参与本科生研究的策略，并提供一些想法，这些想法可以纳入本科数学课程的若干标准课程中。特别是，所讨论的身份和技术可以充当课堂活动和未来的本科生研究项目之间的桥梁。

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