Description of my Mathematical Studies

This is a description of my studies experience in Mathematics and Data science.
Click on the light blue words to view the corresponding supporting documents.

Statement of mathematics study

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Mathematical Preparation

MIT Math Boot Camp for Engineers

• Topics:
  • Single- and multivariable calculus;
  • ordinary differential equations;
  • linear algebra;
  • series;
  • probability and statistics;
• Certificate:
  • MITx Math Boot Camp for Engineers

Real Analysis

• Topics: Basic topology of metric spaces; sequences and series of functions; uniform convergence; Riemann–Stieltjes integral; Lebesgue measure; Lebesgue integral
• Certificates:
  • Real Analysis I: Basic Topology
  • Real Analysis II: Sequences and Series of Functions
  • Real Analysis III: Uniform Convergence
  • Real Analysis IV: Riemann–Stieltjes Integral
  • Real Analysis V: Lebesgue Measure
  • Real Analysis VI: Lebesgue Integral

Fourier Analysis

• Topics: Fourier series; Fourier transform; frequency domain analysis; applications to signals and functions
• Certificates:
  • Fourier Analysis

Complex Analysis

• Topics: Analytic functions; contour integration; Cauchy theorem; residues; complex integration techniques
• Certificates:
  • Complex Analysis

Abstract Algebra

• Topics: Group theory; ring theory; basic field concepts
• Certificates:
  • Group Theory
  • Ring Theory

Topology

• Topics: Open and closed sets; continuity; compactness; connectedness
• Certificates:
  • Topology

Discrete Mathematics

• Topics: Logic; combinatorics; graph theory; discrete structures
• Certificates:
  • Discrete Mathematics

Mathematical Modeling

The following are the prizes I earned in the competitions

• Asia-Pacific Mathematical Modeling Competition (contest in Chinese), International Second Prize
• Asia-Pacific Mathematical Modeling Competition (contest in English), International Third Prize
• China Undergraduate Mathematical Contest in Modelling（CUMCM）, Second Prize

Data science course in The University of Hong Kong

Program：Data Science for Beginners: Theory, Algorithms and Applications

• This is the start of my studies in data science
• Relevant courses: Neural Network; Nonlinear Programming; Genetic Algorithm

Harvards edx courses

• Project 1: Explainable EEG Network Analysis for Alzheimer’s Disease Detection: Node-Level Graph Features and XGBoost In this study, we utilized the EEG Alzheimer’s dataset provided by the UCI Machine Learning Repository to systematically analyze EEG signals associated with Alzheimer’s disease, aiming to explore the relationship between different brain regions and disease status.
  • The Rmarkdown PDF report
  • Github
• Project 2: MovieLens Recommendation System The project builds a movie recommendation system using the MovieLens 10M dataset, following the guidance of the HarvardX PH125.9 course, with the goal of accurately predicting user movie ratings.
  • The Rmarkdown PDF report
  • Github
    
    
• All of 9 Courses are completed and certificated here
• HarvardX PH125.1x Certificate R_Basics edX
• HarvardX PH125.2x Certificate Visualization_ edX
• HarvardX PH125.3x Certificate Probability_ edX
• HarvardX PH125.4x Certificate Inference and Modeling_ edX
• HarvardX PH125.5x Certificate Productivity Tools_ edX
• HarvardX PH125.6x Certificate Wrangling_ edX
• HarvardX PH125.7x Certificate Linear Regression_ edX
• HarvardX PH125.8x Certificate Machine Learning_ edX
• HarvardX PH125.9x Certificate Capstone_ edX

All finished will get:

• Professional Certificate _ edX Credentials