The 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.

The 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)

Probability 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.

Fundamental 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.

Three 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.

All students in the MSc in Data-Driven Modeling program are required to take this course. Appropriate seminars and small group tutorials are scheduled to expose students to a variety of issues in data science and industry, and to enhance students' communication with industry experts and faculty. This course lasts for one year. The students are required to attend the seminars and tutorials in two regular terms. For students of MSc in Data-Driven Modeling only. Graded PP, P or F.

Data 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.

The 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.

This 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.

This course introduces deep learning methodologies, including basic concepts, programming frameworks, and practical techniques. Topics include regression neural network, convolutional neural network, generative adversarial network, variational autoencoder, normalizing flow, reinforcement learning, and sequential models. Students will learn to implement typical models in PyTorch and apply them to various datasets in many real-world applications.

Empirical 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.

This 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.

This 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 pivot tables, linear programming, network flow models, project management, support vector algorithms, kernel methods, convex sets, duality, Lagrange multipliers, 1-D optimization algorithms, unconstrained optimization, guided random search methods, and constrained optimization.

Under 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.

This course will introduce atomistic computational methods to model, understand, and predict the properties and behavior of real materials including solids, liquids, and nanostructures. Their applications to sustainable energy will be discussed. Specific topics include: density-functional theory (DFT), Kohn-Sham equations, local and semi-local density approximations and hybrid functionals, basis sets, pseudopotentials; Hartree-Fock method; ab initio molecular dynamics with interatomic interactions derived on the fly from DFT, Car-Parrinello molecular dynamics; Monte-Carlo sampling; computational spectroscopy from first principles, IR and Raman. Students will learn how to use free open-source packages to do materials simulations on a Linux computer cluster. Students should have basic knowledge of quantum mechanics. The instructor's approval is required for taking this course.