# Postgraduate Courses

- MSDM 5001Introduction to Computational and Modeling Tools[3-0-0:3]DescriptionThe basics about CPU, GPU and their applications in high performance computing; introduction of the operating systems; introduction of the parallel program design, implementation and applications in physics and other areas; basics about quantum computation: the concept, algorithm and future hardware.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Identify hardware requirement for high performance computing.
- 2.Explain the basic structure of CPU and GPU.
- 3.Use basic algorithms for some of the numerical problems.
- 4.Explain the basics about parallel computing.
- 5.Explain the main ideas about quantum computation.

- MSDM 5002Scientific Programming and Visualization[3-0-0:3]DescriptionThe Python programming language and its application to scientiﬁc programming (packages such as Scipy, Numpy, Matplotlib); introduction to Matlab, Mathematica, Excel and R; visualization techniques for data from scientiﬁc computing, everyday life, social media, business, medical imaging, etc. (stock price, housing price, highway traffic data, weather data, fluid dynamics data) (3 hours lecture in computer lab)Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Use Python to write computer programs.
- 2.Apply Matlab, Mathematica, Excel and R to write programs.
- 3.Select suitable figures to represent data clearly.
- 4.Create animation to show the evolution of data.
- 5.Solve simple scientific problems and show the results clearly.

- MSDM 5003Stochastic Processes and Applications[3-0-0:3]BackgroundWorking knowledge in at least one computer language, and basic training in calculus and linear algebra.DescriptionProbability theory; maximum likelihood; Bayesian techniques; principal component analysis, data transformation and filtering; Brownian motion and stochastic processes; cross-correlations; power laws; log-normal distribution and extreme value distributions; Maxwell-Boltzmann distribution; Monte Carlo methods; agent-based models; evolutionary games; Black-Scholes equation.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Use appropriate mathematical tools to reveal the statistical parameters of data sets.
- 2.Process data sets to extract their salient features.
- 3.Formulate mathematical equations for stochastic processes.
- 4.Summarize the behaviors of data sets using typical statistical laws and distributions where applicable.
- 5.Relate stochastic process equations to the macroscopic properties of many-component systems in real-life based on their microscopic behaviors.
- 6.Apply stochastic process techniques to make predictions in real-life problems.

- MSDM 5004Numerical Methods and Modeling in Science[3-0-0:3]Exclusion(s)PHYS 5410BackgroundThe basic knowledge of multivariable calculus and linear algebra is required.DescriptionFundamental numerical techniques: error, speed and stability, integrals, derivatives, interpolation and extrapolation, least squares ﬁtting, solution of linear algebraic equations, mathematical optimization, ordinary differential equations, partial differential equations; Fourier and spectral applications, random processes, Monte Carlo simulations, simulated annealing.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply numerical methods for derivatives and integrals and explain their errors.
- 2.Apply numerical methods for interpolation, extrapolation, and least squares fitting.
- 3.Apply numerical methods to solve linear algebraic equations.
- 4.Apply numerical methods to solve ordinary differential equations and partial differential equations.
- 5.Apply mathematical optimization.
- 6.Explain Fourier and spectral methods.
- 7.Apply Monte Carlo simulations.

- MSDM 5005Innovation in Practice[2-1-0:3]DescriptionThree topics will be selected each term. For each topic, specialists from the industry will be invited to introduce the industrial landscape and related issues. Students will then form groups to explore methodology of collecting useful data and propose innovative solutions related to the topics based on real data. This course enables students to apply mathematical theories to real context and gives students hands-on experience on data science.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain the use of data science as a platform to impact the society and business decisions.
- 2.Identify and describe the common themes and topics in data science in modern business and society.
- 3.Conduct experiential workshops using data from industries under real life or simulated situation.
- 4.Apply data analytics model, coding in real life situations.
- 5.Apply Web scraping, Web robots, and other Ai automation tools.

- MSDM 5051Algorithm and Object-Oriented Programming for Modeling[2-1-0:3]DescriptionData structures (such as list, queue, stack), algorithms (such as recursion, sorting and searching), concepts and design patterns of object-oriented programming are introduced. Students are expected to understand and use these techniques to handle data.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Define and use data structures in solving programming problems.
- 2.Describe and implement recursion, searching and sorting algorithms.
- 3.Explain and apply object-orientated programming.
- 4.Explain and apply design patterns in modeling.

- MSDM 5053Quantitative Analysis of Time Series[3-0-0:3]Exclusion(s)MSBD 5006, MAFS 5130BackgroundStatistics courses at the UG level (e.g. MATH 2411) are desirable.DescriptionThe course introduces some fundamental concepts of time series, including strict stationarity and weak stationarity, and series correlation. Students will study some classical time series models, including autoregressive model, moving averages model and ARMA model, seasonal ARIMA models, multivariate time series models, and some new financial time series models, including ARCH and GARCH models. Students will also learn the forecasting techniques based on those time series models and build up time series models for real time series data in natural science, engineering and economics.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Check if a data set is from white noise/series correlation.
- 2.Identify relevant models of time series.
- 3.Perform estimation and model selection.
- 4.Make forecasts based on time series.
- 5.Model volatilities.

- MSDM 5054Statistical Machine Learning[2-1-0:3]Exclusion(s)MATH 5470, MFIT 5010BackgroundBasic knowledge in probability, statistics and computer science.DescriptionThis course introduces modern methodologies in machine learning, including tools in both supervised learning and unsupervised learning. Examples include linear regression and classification, tree-based methods, kernel methods and principal component analysis. Students will practice R or Python, and apply them to real data analysis.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Recognize and use appropriately important concepts in machines learning.
- 2.Describe the methods in machines learning and apply them in concise form.
- 3.Apply machine learning tools in real data analysis.
- 4.Explain and use software such as R or Python.

- MSDM 5056Network Modeling[2-1-0:3]BackgroundStudents are required to have working knowledge in at least one computer language, and basic training in calculus and linear algebra.DescriptionEmpirical study of networks in social science, economics, ﬁnance, biology and technology, network models: random networks, small world networks, scale free networks, spatial and hierarchical networks, evolving networks, methods to generate them with a computer, dynamical processes on complex networks: network search, epidemic spreading, rumor and information spreading, community detection algorithms, applications of network theory.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Analyze real world networks empirically.
- 2.Apply fundamentals of graph theory and techniques to calculate various properties of complex networks.
- 3.Predict the outcomes of dynamical processes that evolve on networks.
- 4.Apply network theory to trace the factors determining the properties of real world complex (social, financial, biological, technological) systems.
- 5.Develop computational algorithms for calculating network properties and analyzing large scale networks.

- MSDM 5058Information Science[3-0-0:3]BackgroundGood performance in undergraduate mathematicsDescriptionThis course will cover: (1) decision theory and its applications to ﬁnance; options and payoff diagrams, binomial trees; (2) portfolio management of financial time series using mean variance analysis; (3) evolutionary computation for optimization, with applications in ﬁnding good prediction rules in finance; (4) measure of information, various information entropies, and methods of maximum entropy; (5) game theory and its applications in competitive situations; (6) multi-agent systems modelling and applications to social networks and financial systems.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain the concept information measure, mutual information, and various types of information entropy.
- 2.Describe and explain the method of Bayesian decision criterion and other common tools in decision theory.
- 3.Explain association rule in prediction using decision theory and data pre-procession.
- 4.Define options with examples in payoff diagrams and binomial tree.
- 5.Explain the method of mean variance analysis in portfolio management.
- 6.Assess the financial time series database to form new tools of FinTech.
- 7.Describe and explain the method of evolutionary computation (genetic algorithm) and its application.
- 8.Explain and apply the game theory (zero sum non zero sum game, Nash equilibrium and Pareto optimum).

- MSDM 5059Numerical Optimization and Applications[2-1-0:3]BackgroundWorking knowledge in at least one computer language, and basic training in calculus and linear algebra.DescriptionThis course will introduce the concepts and techniques of optimization and modeling in systems and applications with many variables and constraints. Topics to be discussed include Linear programming, network flow models, project management, convex sets, duality, Lagrange multipliers, 1-D optimization algorithms, unconstrained optimization, guided random search methods, and constrained optimization.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain the underlying principles of optimization techniques and algorithms.
- 2.Assess the differences and pros and cons of different optimization techniques and algorithms.
- 3.Select the appropriate optimization methods for solving various optimization problems.
- 4.Apply software tools to solve optimization problems.
- 5.Formulate real-world problems in terms of models and solve them.
- 6.Assess whether optimization techniques used in applications are used effectively.

- MSDM 6980Computational Modeling and Simulation Project[3 credits]DescriptionUnder the supervision of a faculty member, students will carry out an independent research project on computational modeling and simulation. At the end of the course, students need to summarize their results in the form of short theses and give oral presentations. Enrollment in the course requires approval by the course coordinator and supervisor.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Initiate new research areas, identify goals of significant importance, search relevant literature, and collect new data.
- 2.Construct data-driven models, test hypothesis, write simulation programs, and interpret simulation results.
- 3.Draw meaningful conclusions, write convincing reports, and propose further directions.