The human brain has the ability to carry out new tasks with limited experience. It utilizes prior learning experiences to adapt the solution strategy to new domains. On the other hand, deep neural networks (DNNs) generally need large amounts of data and computational resources for training. However, this requirement is not met in many settings. To address these challenges, we propose the TUTOR DNN synthesis framework. TUTOR targets tabular datasets. It synthesizes accurate DNN models with limited available data and reduced memory/computational requirements. It consists of three sequential steps. The first step involves generation, verification, and labeling of synthetic data. The synthetic data generation module targets both the categorical and continuous features. TUTOR generates the synthetic data from the same probability distribution as the real data. It then verifies the integrity of the generated synthetic data using a semantic integrity classifier module. It labels the synthetic data based on a set of rules extracted from the real dataset. Next, TUTOR uses two training schemes that combine synthetic and training data to learn the parameters of the DNN model. These two schemes focus on two different ways in which synthetic data can be used to derive a prior on the model parameters and, hence, provide a better DNN initialization for training with real data. In the third step, TUTOR employs a grow-and-prune synthesis paradigm to learn both the weights and the architecture of the DNN to reduce model size while ensuring its accuracy. We evaluate the performance of TUTOR on nine datasets of various sizes. We show that in comparison to fully connected DNNs, TUTOR, on an average, reduces the need for data by 5.9x, improves accuracy by 3.4%, and reduces the number of parameters (fFLOPs) by 4.7x (4.3x). Thus, TUTOR enables a less data-hungry, more accurate, and more compact DNN synthesis.