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Ignacio Cao

High School Vice Principal, Math Teacher

Ignacio graduated from Renmin University of China with a bachelor's degree in Finance and a master's degree in Probability Theory and Mathematical Statistics. He served as a former Project Director at PEER, an educational non-profit organization in China.

As a mathematics teacher, Ignacio primarily teaches the Linear Algebra course and has also taught Integrated Math 1: Analysis and Integrated Math 2: Analysis. As the Vice Principal of the high school, he is mainly responsible for learner development.

He is passionate about exploring topics related to the history and culture of mathematics and is continually reflecting on new forms and focal points of mathematics education in the AI era. He is particularly interested in how procedural knowledge, structured knowledge, and application-oriented knowledge centered on mathematical modeling can be presented more holistically in AI-supported classrooms.

Curriculums1

MATH6002: Linear Algebra

This course is for learners who demonstrate a solid foundation in basic algebra as well as sufficient interest in those majors in college, like AI algorithms, social networks, and graph theory, or advanced microeconomics and macroeconomics, which heavily rely on mathematical concepts. This course will enrich learners' abstract understanding by triggering their thoughts on big ideas including "linear" and "space". The main contents for this course are vector space, matrix, the solutions of linear equations, determinant, eigenvalue and eigenvector, and linear transformation. Learners will also learn to apply the knowledge by basic Python coding on linear algebra computation and modeling analysis.

Projects1

Principal Components Analysis: Theory and Application

Disciplines/Subjects: Mathematics, Linear Algebra, Statistics, Machine Learning Key Themes: Matrix Decomposition, Dimensionality Reduction, Statistical Modeling, Real-World Applications This project explores the application of Principal Components Analysis (PCA) as a statistical tool for dimensionality reduction in real-world datasets. Starting with the foundational theory, learners learn the relationship between Singular Value Decomposition (SVD) and PCA, and how PCA can address common statistical dilemmas such as high dimensionality in data. Using Python, learners apply PCA to the "Prostate Cancer" dataset, exploring how the method extracts the most important components for predicting prostate-specific antigen (PSA) levels from various clinical measurements. Through this process, learners identify and analyze the principal components, evaluate the results, and compare the PCA-derived model with traditional linear regression models. The project emphasizes both the mathematical theory behind PCA and its practical application in data science. In addition, learners write their own PCA code from scratch using SVD, reflecting on the underlying algorithm and comparing their implementation to established Python instructions.

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