Can mathematical cognition formulate consciousness?

Mind is a compound information handling and processing mechanism and consciousness - (the processed information) is the core component of mind. The spirit of consciousness is definite correspondence between substance with some rules or laws. Information processed in the mind approaching from both the outer world (physical world) and the inner world (mind). The information can be represented in many ways. Everything which embodies information is a model and the process is known as modeling. This paper will present that how can we formulate consciousness and discussion about two cognitive mathematical models. Firstly, a hierarchal model of human consciousness will be discussed, Secondly, the application of `homomorphism of a group' to the model of transformation from physical structures to the psychological structure. The proposed model is a robust combination of the above mentioned models and provides the mathematical representation of each hierarchal module in terms of homomorphism. This paper will try to provide a sound justification for subjectivity of human experience, in term of proposed model. Furthermore, the capacity of this model is evaluated by putting some examples before this model to formulate them. And finally the paper concludes that consciousness exists when: (a) the units of system certainly map the entities outside the system; (b) the system operates by some rules; and (c) the rules definitely map some laws or relations in the entities.