Discovery learning in an interdisciplinary course on finite fields and applications

TL;DR

This paper presents an innovative interdisciplinary course on finite fields and their applications, employing discovery learning and active engagement to enhance understanding among students with diverse backgrounds.

Contribution

It introduces a hybrid teaching approach combining lectures and active discovery-based discussions tailored for an interdisciplinary setting.

Findings

Enhanced student engagement through active learning methods

Improved intuition for abstract concepts without heavy technical details

Adapted curriculum for students with varied mathematical backgrounds

Abstract

The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom model, there are two lecture days and two discovery-based discussion days each week. Discussions center around group activities that build intuition for abstract concepts while avoiding excessive technical machinery. Teaching this course presents some unique challenges, as much of the content typically appears in a second course in abstract algebra, yet the students exhibit a wide range of mathematical preparation.