Artificial neural networks (ANN) have been employed successfully because of their high modeling capability. Many versions of the ANN have been proposed to increase the modeling ability. Since ANN based on the biological neural network system, the only mathematical operation is summation or subtraction (while the coefficients are negative). This research was done to investigate the application of other mathematical operations, which are multiplication, division, logarithm, and exponential, in nodes. Based on this fact, a novel a single hidden layer feed-forward artificial neural network (SLFN) model, which was called was algebraic learning machine (ALM), was proposed. The proposed ALM was evaluated and validated with 60 different benchmark datasets. Obtained results were compared with results obtained by each of the extreme learning machine (ELM), randomized artificial neural network, and random vector functional link, and back-propagation trained SLFN methods. Achieved results show that the proposed method is successful enough to be employed in classification and regression.