Master in Applied Mathematics and Data Science

Program Introduction

  • Duration of Study

    The normal duration of this program is 2 years,and the maximum duration is 3 years.

  • Teaching Approach

    Face-to-face Teaching

  • Teaching Language

    Chinese/English

  • Academic Field

    Mathematics and Data Science

  • Course Introduction

    This program is dedicated to cultivating high-level talents in applied mathematics and data science to satisfy the requirements in the business community, research institutions, and academia. Furthermore, developing the theories and applications of applied mathematics and data science required in cross-disciplinary research is the long-term goal to integrate the Big data processing in various industries, providing talents in big data analysis for Guangdong, Hong Kong and Macau Greater Bay Area.


Study Plan


Admission Requirements

 

Hold a bachelor's degree in Mathematics, Physics, Computer, Engineering, Statistics, Economics, Biology, Medicine or related fields.

(Applicants must submit proof of English proficiency)

Research Area

Under the guidance of instructors, students perform research from (but not limited to) the following fields:

Applied mathematics, Data mining, Machine learning



VI. Course Structure

Table 1: Core Courses (21 Credits)


Course Title

Type

Credit

Mathematics Methods for Data Science

Compulsory

3

Numerical Linear Algebra

Compulsory

3

Open Source Tool for Data Science

Compulsory

3

Applied Statistics

Compulsory

3

Data Mining

Compulsory

3

Machine Learning

Compulsory

3



Table 2: Elective Courses (9 Credits)


Course Title

Type

Credit

Advanced Topics in Applied Mathematics

Elective

3

Advanced Topics in Data Science

Elective

3

Programming in Data Science

Elective

3

Digital Image Processing

Elective

3

Data Visualization and Analyzation

Elective

3

Data Warehousing and Data Mining

Elective

3

Stochastic Processes

Elective

3

Multimedia Signals and Systems

Elective

3

Database Systems

Elective

3



*University has the ultimate right to cancel the course with insufficient number of students

Table 3: Other core courses (3 Credits)


Course Title

Type

Credit

Literature Survey and Thesis Proposal 

Compulsory

2

Academic Activities(At least six times of attendance)

Compulsory

1



Table 4: Thesis (6 Credits)

Course Title

Type

Credit

Thesis

Compulsory

6


Course Description

Compulsory Courses

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.


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.


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.


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.


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.


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.


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:

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.


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.


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.


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.


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.


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.


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.


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.


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.


Degree Requirements

1. Students are required to complete seven courses from Table 1 during the first two semesters to gain 21 credits. 2. Students are required to complete 3 elective courses in Table 2 during the second and third semesters to gain 9 credits. 3. After finishing each course, students will be assessed based on regulations established by the instructor and the Faculty.

Learning Time

1. The maximum study period is 36 months.1.The duration for taking all courses is 18 months and the duration for thesis writing should not be less than 6 months.The maximum study period is 36 months. 2. In general, classes will be arranged from Monday to Friday daytime.

Qualifications of Graduation

Upon approval from the Senate of the University, a Master’s Degree will be conferred on a student when he or she has: Completed and met the requirements prescribed in the study plan of his or her program within the specific study period, and achieved a cumulative GPA of 2.50 or above (excluding thesis) Abided by the regulations of the University Cleared all fees and charges and returned all University’s property and equipment borrowed If students pass all courses required in Table 1, 2, 3 above with a cumulative GPA of 2.5 or above, but fail to submit or pass the final thesis oral defense during the specified period, he/she can only get a completion certificate. Note: All curriculums and study plans are based on the newest announcement of the Boletim Oficial da Região Administrativa Especial de Macau. ※ In case of any discrepancy, the Chinese version shall prevail.