Teaching

I enjoy writing some stories and posts for explaining mathematics and machine learning. We would like to highlight the importance of some principles such as "温故而知新，可以为师矣" and "三人行，必有我师焉." Your contibutions to our materials would be highly appreciated.

CGN-3405: Applied Numerical Methods for Civil Engineering (Undergraduate level, Spring 2026, UCF)

  • Outline
    • [Slides] Introduction to the course & logistics
    • [Slides] Mathematical modeling & engineering problem solving
    • [Slides] Introduction to Python programming: Part I
    • Introduction to Python programming: Part II
    • Modeling and errors: Part I
    • Modeling and errors: Part II
    • Nonlinear equations
    • Introduction to applied linear algebra: Part I
    • Introduction to applied linear algebra: Part II
    • Linear algebraic equations
    • Ordinary differential equations
    • Optimization techniques: Part I
    • Optimization techniques: Part II
    • Curve fitting

  • Reading Material
    • CVXPY Course at NASA (Philipp Schiele, Steven Diamond, Parth Nobel, Akshay Agrawal)
    • The Matrix Cookbook (Kaare Brandt Petersen, Michael Syskind Pedersen)
    • Matrix Calculus (for Machine Learning and Beyond) (Paige Bright, Alan Edelman, Steven G. Johnson)
    • Convex Optimization (Stephen Boyd, Lieven Vandenberghe)
    • Randomized Linear Algebra, Optimization, and Large-Scale Learning (Michael Mahoney)


Teaching Samples

♫ [Slides] Definition, properties, and derivatives of matrix traces. [Video]
♫ [Slides] The relevance of t-statistics for small sample sizes.
♫ [Slides] Three rates of convergence on a sequence. [Reference material]
♫ [Slides] Fibonacci sequence & dynamic programming. [Reference material]
♫ [Slides] But what is the Orthogonal Procrustes Problem (OPP)? [LinkedIn] 600+ reactions
♫ [Slides] Interpretable time series autoregression.
♫ [Slides] Intuitive understanding of tensor factorization formula.
♫ [Slides] Essential idea of sparse autoregression & periodicity quantification.

Tutorials

♫ Time series convolution (e.g., circular convolution, convolution matrix, circulant matrix, discrete Fourier transform, and sparse regression). [Website]


Reading Hub

December 2025

♫ [Slides] [BP20] Sparse high-dimensional regression: Exact scalable algorithms and phase transitions. (Creator: Ben-Zheng Li)
♫ [Slides] [DGW23] High-dimensional portfolio selection with cardinality constraints. (Creator: Ben-Zheng Li)
♫ [Slides] [SPQ+25] Partial quantile tensor regression. (Creator: Ben-Zheng Li)
♫ [Slides] [OGS+25] Deep FlexQP: Accelerated nonlinear programming via deep unfolding. (Creator: Zhi-Long Han)
♫ [Slides] [OBG+25] Conformal mixed-integer constraint learning with feasibility guarantees. (Creator: Ben-Zheng Li)
♫ [Slides] [WZL24] High-dimensional low-rank tensor autoregressive time series modeling. (Creator: Zhi-Long Han)


Favoriate Books

  • Applied Linear Algebra
    • [PDF] (2018) Introduction to Applied Linear Algebra

  • Computer Vision
    • [PDF] (2022) Computer Vision: Algorithms and Applications

  • Machine Learning
    • [PDF] (2006) Gaussian Processes for Machine Learning
    • [PDF] (2014) Understanding Machine Learning: From Theory to Algorithms
    • [PDF] (2018) Foundations of Machine Learning
    • [PDF] (2020) Linear Algebra and Optimization for Machine Learning
    • [PDF] (2020) Mathematics for Machine Learning
    • [PDF] (2022) Algebra, Topology, Differential Calculus, and Optimization Theory for Computer Science and Machine Learning
    • [PDF] (2022) Machine Learning: A First Course for Engineers and Scientists
    • [PDF] (2024) Learning Theory from First Principles
    • [PDF] (2024) Interpretable Machine Learning: A Guide for Making Black Box Models Explainable
    • [PDF] (2025) Probabilistic Artificial Intelligence
    • [PDF] (2025) Tensor Decompositions for Data Science

  • Algorithm
    • [PDF] (2019) Algorithms
    • [PDF] (2020) Algorithms for Decision Making
    • [PDF] (2023) Mathematical Analysis of Machine Learning Algorithms

  • Deep Learning
    • [PDF] (2021) The Principles of Deep Learning Theory
    • [PDF] (2021) Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
    • [PDF] (2023) Understanding Deep Learning
    • [PDF] (2023) Equivariant and Coordinate Independent Convolutional Networks: A Guide Field Theory of Neural Networks
    • [PDF] (2024) Deep Learning: Foundations and Concepts
    • [PDF] (2024) Mathematical Theory of Deep Learning
    • [PDF] (2025) The Principles of Diffusion Models: From Origins to Advances

  • Data Science
    • [PDF] (2019) Data Science: Concepts and Practice
    • [PDF] (2020) Advanced Data Science and Analytics with Python
    • [PDF] (2022) Data Science and Machine Learning: Mathematical and Statistical Methods

  • Optimization
    • [PDF] (2004) Convex Optimization
    • [PDF] (2006) Numerical Optimization
    • [PDF] (2014) A Gentle Introduction to Optimization
    • [PDF] (2025) Optimization Bootcamp with Applications in Machine Learning, Control, and Inverse Problems [Notes]

  • Control Theory
    • [PDF] (1994) Linear Matrix Inequalities in System and Control Theory
    • [PDF] (2025) Data-Based Linear Systems and Control Theory

  • Information Theory
    • [PDF] (2022) Information Theory: From Coding to Learning

  • Signal Processing
    • [PDF] (2020) The Discrete Algebra of the Fourier Transform