Artificial Intelligence in Math Education of Engineers

This paper considers if Artificial Intelligence (AI) tools based on Large Language Models (LLMs) can support math education of engineers. A typical spectrum of engineering math tasks is evaluated with the help of GPT-4 which is also used as a verification tool. Suitable prompting methods compatible with the facilities of students are investigated. A proposal for a zero-shot prompt is made that uses <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{AT}_{\mathrm{E}} \mathrm{X}$</tex> for the input of mathematical formulas and demands outputs in natural language and Python code as additional output format. For verification purposes the LLM is provided with the natural language and code outputs and the offline computed Python results. A statistical evaluation shows that LLMs as GPT-4 have reached a sufficient level of maturity to be used in math education, reaching an average solution level of almost 82%. However, the quality of the LLM answers shows big variances. In the paper an itemization for different math topics is given along with an analysis of typical errors. Detailed examples (arithmetic calculus, symbolic integration, ordinary differential equation, and Fourier series of a half-wave rectifier) are provided to demonstrate typical GPT-4 solutions and errors along with the corresponding verification results. AI-based tools will replace many standard tools in engineering tasks similar to the pocket calculator decades ago. Hence there is a strong requirement that future engineers learn the handling and pitfalls of these tools. As a proposal a combined education in engineering math, AI handling, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{HT}_{\mathrm{E}} \mathrm{X}$</tex> and a programming language like Python in the first semesters could create the synergies to take the best advantage of AI tools.