Mathematics

This course offers a study of stochastic processes. Topics include: discrete time Markov chains; renewal theory and Poisson process; continuous time Markov chains; Brownian motion. Pre-requisite: Probability 

Through software-assisted learning, you will be able to intuitively understand fundamental mathematical concepts such as linear algebra, and delve into advanced topics like the PageRank algorithm, Analytic Hierarchy Process (AHP), function fitting, numerical integration, solution of ordinary differential equations, and machine learning methods.

This course provides in depth knowledge of fundamental results and methods in discrete dynamical systems, knowledge of the concrete dynamical systems presented during the course, and an understanding of the many and diverse appearances and applications of discrete dynamical systems. It develops skills to analyze and argue for results on discrete dynamical systems, produce proofs for theorems, and solve exercises posed during the course.

This course introduces the mathematical theory of probability, starting with the definition of probability spaces to the fundamental limit theorems, namely the law of large numbers and the central limit theorem. The following concepts are covered: measurement theory, probability spaces; conditional probability and independence; random variables, discrete random variables; density random variables; discrete random vectors; density random vectors; notions of convergence for sequences of random variables; limit theorems; Gaussian vectors. 

This course examines examples of statistical data and the use of graphical means to summarize the data. It covers basic distributions arising in the natural and behavioral sciences; the logical meaning of a test of significance and a confidence interval; and tests of significance and confidence intervals in the one and two sample setting (means, variances and proportions).

This course examines basic properties of metric spaces; openness; closedness; interior; closure; derived set; boundary; compactness; completeness; continuity; connectedness; pathwise connectedness; uniform continuity; uniform convergence; and Banach's fixed point theorem.

This course will focus on basic mathematical models and methods in financial calculation analysis. Specifically, it includes basic problems in financial mathematics: basic concepts and methods of interest calculation, calculation of annuity cash flow model, basic method of calculating general investment return rate, principal and interest decomposition process of cash flow, fixed income securities, interest risk analysis, financial income in random situations.

Mathematical logic is a fundation of mathematics and computer science, and foundation course for the students of mathematics and computer science. The content of this course includes propositional logic, first-order (predicate) logic and basic mathematical systems.

Probability is to describe the measure of the likelihood of random events. Probability theory is to make research through simple random events and gradually into complex random events. Probability theory is an efficient method and tool to study complex random phenomena. It is also the base to learn statistics.