黎曼猜想分层级的模块化教学设计

Hierarchical Modular Teaching Design of Riemann Hypothesis

黎曼猜想(或称黎曼假设),是关于黎曼ζ函数ζ(s)的零点分布的猜想。黎曼猜想于1959年提出,但依然在技术高速发展的当今社会发挥着重要作用,广泛应用于素数定理、延拓图像、广义相对论、量子力学等领域,当今数学文献中已有超过一千条数学命题以黎曼猜想(或其推广形式)的成立为前提。针对现有黎曼猜想教学专业性过强、学生难以把握相关内容的现状,本文旨在提出黎曼猜想与其相关知识的分层级模块化教学设计,提供一份针对不同学习阶段、应用各教学模块的黎曼猜想教学设计。黎曼猜想涉及到多方面的知识,如初等数论、解析领域、代数领域及遍历论等,缺乏相关知识铺垫会使黎曼猜想不容易为学生所理解,故我们从各个角度进行分层级的知识铺垫、分析讲解,并辅以实践环节等模块,让学生更好地把握黎曼猜想的具体内容、了解黎曼猜想的重要性及其应用的广泛性。

The Riemann hypothesis asserts the distribution of the zero points of the Riemann zeta func-tion(s),which is proposed in 1959 and still plays an important role in current society with the rapid development of technology,extensively applied to the fields of prime number theorem,extension image,general relativity,quantum mechanics,etc.Validity of the Riemann hypothesis(or extended form)is the precondition for more than 1000 mathematical propositions in mathematical literatures.To address the issue that currently the Riemann hypothesis teaching is too specialized to grasp for the students,a hierarchical modularized instructional design for the Riemann Hypothesis and related knowledge is proposed in this paper,providing instructional design which is suitable for various learning stages and utilizes multiple teaching modules.Riemann Hypothesis involves contents from various branches including elementary number theory,analytic field,algebraic field and ergodic theory,lacking which will make the Riemann Hypothesis difficult for students to understand.Thus,relevant basic knowledge is presented and analysis and explanation are performed hierarchically from various angles in the instructional design,coupled with the module of practice.With the instructional design,students will better grasp the detailed contents of the Riemann Hypothesis and its significance and promising application.