This course is about discrete mathematics. This course will elaborate on 1 Mathematical logics; 2 Combinational Analysis; 3 Multiple Discrete Structures; 4 Modeling and Actual Background. Through the study of this course, students should be able to establish solid foundation of the corresponding knowledge, methodology and ability to apply them in their study and research in financial engineering and financial mathematics.This course is of interest to those contemplating careers in fin-tech, financial engineering and financial mathematics. The course will be in the form of lectures, discussions, exercises, and will involve course projects. By the end of the course, students should be able to master the basic theory and methodology of the following subjects: (1) Propositional Logic, Proof Basics, Propositional Logics, Predicate logic, Rules of Inference, Proof Methods and Strategy;(2) Algebra and number theory, Groups, Rings, Fields and extentions; (3) Graphs, Euler and Hamilton Paths, Trees, Tree Traversal; (4) Permutations and Combinations, Recursive and Structural Induction.