A Mathematical Approach to Turing Machines

Students are getting confused and losing interest in theoretical computer science because most instructors are doing a poor job in teaching the subject matter. Instructors are doing a poor job in teaching because they do not have a well-organized theory to explain the concepts and they are unwilling to spend the time to write up better lecture notes for the class. This paper presents a rigorous mathematical approach to the theory of Turing Machine which doesn’t currently exist in the literature of theoretical computer science. Basic definitions are developed in mathematical terms and used as the foundation for constructing mathematical proofs for theorems. It provides a model for instructors to write better lecture notes and authors to write better textbooks for educational purpose. It also corrects some critical errors and erroneous arguments that can be found in many textbooks widely used for the education of theoretical computer science.Students can use this paper for supplemental reading.