Beta-thalassaemia is a common disease in peoples of the Northern and Northeastern regions of Thailand. The general causes of the disease are mutations in the beta-globin gene. In this paper we discuss methods based on finite-state automata theory, regular expressions, and partially ordered sets that can be used for detecting and classifying mutations in genes. The methods are applied to three main problems. The first problem is the reliable detection in a given beta-globin gene of mutations that are known to cause beta-thalassaemia. It is shown that for most known mutations in Thailand a 5-base pattern is an optimal size search pattern for reliably detecting if that mutation is or is not present in a given beta-globin gene. The second problem is to find all differences between a standard normal beta-globin gene and a suspected abnormal gene, to identify any differences as point mutations or frameshift mutations, and to list important biochemical effects of the mutations. The third problem is to list the types of bases in a given gene pattern as purines or pyrimidines and the types of codons as weak (4 hydrogen bonds), mixed (5 hydrogen bonds), or strong (6 hydrogen bonds). Fast and easy-to-use Matlab programs have been developed for each of these three problems. The programs could be useful when large commercial packages are not available.