This article explains multiple ways to calculate AUC mathematically along with step by step implementation guide in Python, SAS and R.
The Area Under an ROC Curve
ROC Curves & AUC: What Are ROC Curves
AUC - Insider's Guide to the Theory and Applications – Sin-Yi Chou – Data Science Enthusiast
The Complete Guide to AUC and Average Precision: Simulations and Visualizations – Glass Box
ROC Curve explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification tutorial, by Serafeim Loukas, PhD
Methods to determine area under curve
Calculating AUC: the area under a ROC Curve (Revolutions)
AUC-ROC curves and their usage for classification in Python.
AUC - Insider's Guide to the Theory and Applications – Sin-Yi Chou – Data Science Enthusiast
python - How to calculate a partial Area Under the Curve (AUC) - Stack Overflow
Partial area under ROC curve