Master in Applied Mathematics and Data Science

Course Description

Basic Core Courses

MIMZ01 Mathematics Methods for Data Science (3 credits)

This course provides some topics including various basic mathematics methods commonly used in optimization. We will cover basic definitions, concepts, and results from convex analysis and convex optimization, a variety of applications of convex optimization, in areas like probability and statistics, computational geometry, and data fitting. We will describe numerical methods for solving convex optimization problems, focusing on Newton’s algorithm and interior-point methods.

MIMZ02 Numerical Linear Algebra (3 credits)

This course supplies an introduction to the basics of linear algebra. Then the course provides some common topics in numerical computation. Such as, conditioning of problems and stability of algorithms、 Gaussian Elimination and LU decomposition、 Gram-Schmidt orthonormalization、 least squares problems、 eigenvalue problems、 singular value decomposition as well as basic iterative methods. Furthermore, it describes how to implement related algorithms.

MIMZ03 Open Source Tool for Data Science (3 credits)

This course mainly introduces the basic syntax and control structure of Python language, and then introduce the commonly used modules in data analysis such as Numpy, Pandas, Mathplotlib, Sqlite3, Sklearn etc. Finally, it introduces common data analysis operations, such as crawling network data, regular expressions, storing and accessing data, regression and classification, cluster analysis, principal component analysis, time series analysis and prediction. Additionally, this cource will also introduce the use of other open source tools, including SQL, Shell, Julia, OpenCV, etc.

MIMZ04 Applied Statistics (3 credits)

This course provides fundamentals of probability and statistics for data analysis in application and research. Topics include data collection, exploratory data analysis, random variables, common discrete and continuous distributions, sampling distributions, estimation, confidence intervals, hypothesis tests, regression model, analysis of variance, and multivariate statistical analysis and Bayesian statistics et.

MIMZ05 Data Mining (3 credits)

This course introduces the latest data mining technology and its application. The object of the course is to help students understand the principles and the importance of data mining technology and mainly focus on the technical developments of data mining and its related subject such as artificial intelligence and machine learning. Topics of this course include the concepts and techniques of data science, such as statistical descriptions of data, data visualization, data preprocessing, data warehousing, frequent pattern mining and association rule analysis, classification and supervised learning, clustering and unsupervised learning, variable selection. To realize related algorithms by Python are also required.

MIMZ06 Machine Learning (3 credits)

This course will cover a wide range of concepts and techniques such as machine learning, data mining and statistical pattern recognition. More specifically, topics will include: (1) supervised learning (e.g. parametric/nonparametric algorithms, support vector machines, kernel methods and neural networks), (2) unsupervised learning (e.g. clustering, dimension reduction and recommendation systems) and (3) advanced topics in machine learning.

MIMZ07 Time Series Analysis (3 credits)

This course is intended to provide students with an introduction to the basic knowledge and methods of analyzing real data of time series analysis. It introduces time series decomposition, moving average method, exponential moving average method, as well as basic knowledge such as correlation, stationarity. In addition, the course presents traditional time series models, such as Bass model, Holt-Winters exponential smoothing model, linear model, Harmonic seasonal model, random walk, moving average process, autoregressive process, autoregressive conditional heteroskedastic model. These models will be used to fit real data to help better understand and use. R language will be used to make graphs and analyze data. These contents are helpful for time series theoretical research and interpretation of real-world data.

Elective Courses:

MIME01 Advanced Topics in Applied Mathematics (3 credits)

This course mainly introduces practical topics in applied mathematics, such as numerical methods of inverse problem in mathematical physics. The course covers Truncated Singular Value Decomposition, Tikhonov regularization method, Variation regularization, and Statistical inversion(Markov Chain Monte Carlo Sampling and Bayesian Inference). Additionally, some applications including computed tomography, convolution and image deblurring will also be included.

MIME02 Advanced Topics in Data Science (3 credits)

This course introduces the latest theories and applications in data science, such as deep learning and its application to computer vision and natural language processing. Deep learning is a branch of machine learning concerned with the development and application of modern neural networks. Deep learning algorithms extract layered high-level representations of data in a way that maximizes performance on a given task. The course will cover a range of topics from basic neural networks, convolutional and recurrent network structures, deep unsupervised and reinforcement learning, and applications to problem domains like natural language processing and computer vision.

MIME03 Programming in Data Science (3 credits)

This course aims to focus on algorithms, models, and frameworks for Deep Learning and its programming. It specifically deals with Deep Learning with PyTorch, including NumPy, Pandas, Machine Learning Theory, Test/Train/Validation Data Split, Model Evaluation, Tensors with PyTorch, Neural Network Theory (Perceptron, Network, Activation Function, Cost/Loss Function, Backpropagation, Gradient), Artificial/Deep Neural Network (ANN/DNN), Convolutional Neural Network (CNN), Recurrent Neural Network (RNN, LSTM, GRU), NLP with PyTorch, Using GPU with PyTorch, and many more.

MIME04 Digital Image Processing (3 credits)

This course will give lectures to introduce the principle, technique and application of digital image processing and pattern recognition, including digital image preprocessing, feature extracting and analysis; statistical pattern recognition and structural pattern recognition and their application in different areas. Students will be asked to select some special topics in the PRIP area based on the contents they have learnt from the course, search and read related papers, and then give a survey report on the topics selected.

MIME05 Data Visualization and Analyzation (3 credits)

This course will focus on the visualization techniques commonly used in data processing, including multi-dimension display of data with various feature distributions and popular modules in Python such as Matplotlib and Seaborn.

MIME06 Data Warehouse and Data Mining (3 credits)

This course will introduce the principle, technique and application of Data warehouse and Data Mining, including Data Warehousing and On-Line Analytical Processing (OLAP), data Preprocessing techniques (data cleaning, integration, transformation and reduction), Data Mining techniques (Data classification, prediction, correlation and clustering), their application and developing trends.

MIME07 Stochastic Processes (3 credits)

Stochastic process is to study time-varying random phenomena. This course will introduce the basic theory and applications of stochastic processes from an engineering perspective, including basic concepts of stochastic processes, Possion processes, Markov chains, queuing theory.

MIME08 Multimedia Signals and Systems (3 credits)

This subject intends to introduce students to the notion of multimedia signals and their processing techniques. There are various methods for representing a multimedia signal, e.g., time domain, frequency domain, time-frequency domain, and eigen-domain. Such representations will be used to characterize multimedia signals. Moreover, filter designs for multimedia signals will be considered. Some adaptive processing techniques, e.g., hidden Markov models, random field models, state space models will be considered for modeling multimedia signals.

MIME09 Database Systems (3 credits)

The course aims to provide a foundation in understanding of database design principles, implementation and management. Upon completion, students should be able to identify and execute the steps involved in the design of a database, implement the design via a relational database management system, maintain the goal of data sharing and consistency of database systems.