Mathematical foundations of computer science introduces to the students how to use mathematical models and methods to analyze problems that arise in computer science. It aims to enhance the logical and analytic abilities of the students to model and solve computational problems in a rigorous manner. The course is going to cover several important and useful topics in modern computer science, including ordering theory, combinatorics, graph theory, probabilistic methods, network etc.. At the end of each semester, some cutting-edge topics will be introduced to make the course more adaptable. This is one of the core courses for computer science major, offering them the mathematical sophistications necessary for further study.