Teaching

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

Outline [GitHub]
• [Slides] Introduction to the course & logistics
• [Slides] Mathematical modeling & engineering problem solving
• [Slides] Introduction to Python programming: Part I
• [Slides] Introduction to Python programming: Part II
• [Slides] Modeling and errors
• [Slides] Review class (Exam 1)
• [Slides] Nonlinear equations
• [Slides] Introduction to applied linear algebra: Part I
• [Slides] Introduction to applied linear algebra: Part II
• [Slides] Linear algebraic equations
• [Slides] Ordinary differential equations
• [Slides] Optimization techniques: Part I
• Optimization techniques: Part II
• Curve fitting
Assignment
• [PDF] Schedule & progress
• [PDF] Euler's method, engineering modeling, and Python programming
• [PDF] Introduction to Python Programming
• [PDF] Modeling and errors
• [PDF] Nonlinear equations
Reading Material
• [Website] CVXPY Course at NASA
• [Website] The Matrix Cookbook
• [Website] Matrix Calculus (for Machine Learning and Beyond)
• [Website] Convex Optimization
• [Website] Randomized Linear Algebra, Optimization, and Large-Scale Learning
• [Website] Applied Numerical Computing

Matrix Computations and Optimization for Machine Learning

Matrix Computations
• [YouTube] [Slides] What Is the Orthogonal Procrustes Problem (OPP)? [LinkedIn] 600+ reactions

Optimization
• [YouTube] [Slides] Intuitive Understanding of Linear Programming

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] 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

March 2026
• [Slides] [DZ26] Sparse Gaussianized canonical correlation analysis with applications to portfolio analysis. (Creator: Ben-Zheng Li)
• [Slides] [BCM25] Tail-robust factor modelling of vector and tensor time series in high dimensions. (Creator: Ben-Zheng Li)
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) High-Dimensional Probability: An Introduction with Applications in 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
• [PDF] (2022) The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation
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