Problem

The subject of general topology is often taught rather late in undergraduate mathematics courses, despite its extreme usefulness in the study of virtually every other field in mathematics. In fact, being such a fundamental part of modern mathematics, many topological principles are often used by individuals in other scientific fields or even engineering without their realizing. Thus, it is not surprising that even students from such fields might have some interest in learning the fundamentals of topology.

We consider it important to provide tools that may aid professors endeavoring to teach this fundamental part of mathematics to undergraduate mathematics students and students from other fields alike.

Solution

In order to help professors trying to teach the subject of general topology to groups of students consisting of potentially a mix of early math students and students from other fields, most of which are likely have little to no familiarity with highly abstract mathematical concepts, we've generated via AI tools a number of resources. These include:

A lesson plan for an introductory class on the subject of general topology, created with ChatGPT, which may be viewed via the following link: https://www.overleaf.com/read/znxfnkfgcxwq#ae80c8
An exercise list for students to consolidate their understanding of the materials, created with ChatGPT, which may be viewed via the following link: https://www.overleaf.com/read/bpjdsywvffvq#0043dd
A slide presentation to be used alongside a blackboard and explanations giver by a lecturer for an introductory class on basic concepts in general topology, created with Gamma App, which can be viewed via the link: https://gamma.app/docs/Introduction-to-General-Topology-07hz2idhb6pc1oz
A short booklet cataloguing a series of important definitions in general topology that students may easily consult during self-study, created with Gamma App, which can be viewed via the link: https://gamma.app/docs/General-Topology-Core-Definitions-7o9dgkg3wztc5uy

Impact

After testing and evaluation by the members of the team, we've concluded that the various tools generated via AI are likely to be of significant use for a professor trying to teach the subject of general topology to students. Although most of the resources shown here are specific to an introductory class, the same prompts that generated them can be adapted to generate similar resources for subsequent classes as well, with only minor alterations necessary.

Team

Leonardo Domingues do Amaral - Prompt Design
- Developed the various resources listed above
Caio Diniz Santana, Matheus Felipe Santos da Penha - Testing
- Provided testing and feedback

AI-generated Teaching Resources