Current research on Internet of Things (IoT) mainly focuses on how to enable general objects to see, hear, and smell the physical world for themselves, and make them connected to share the observations. In this paper, we argue that only connected is not enough, beyond that, general objects should have the capability to learn, think, and understand both the physical world by themselves. On the other hand, the future IoT will be highly populated by large numbers of heterogeneous networked embedded devices, which are generating massive or big data in an explosive fashion. Although there is a consensus among almost everyone on the great importance of big data analytics in IoT, to date, limited results, especially the mathematical foundations, are obtained. These practical needs impels us to propose a systematic tutorial on the development of effective algorithms for big data analytics in future IoT, which are grouped into four classes: 1) heterogeneous data processing, 2) nonlinear data processing, 3) high-dimensional data processing, and 4) distributed and parallel data processing. We envision that the presented research is offered as a mere baby step in a potentially fruitful research direction. We hope that this article, with interdisciplinary perspectives, will stimulate more interests in research and development of practical and effective algorithms for specific IoT applications, to enable smart resource allocation, automatic network operation, and intelligent service provisioning.