Teaching

Your contibutions to our materials would be highly appreciated.

COT-4500: Numerical Calculus (Undergraduate level, incoming Spring 2027, UCF)

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
• [Slides] Optimization techniques: Part II
• [Slides] 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

Tutorials

Our tutorial materials are publicly available for dissemination. If you are interested, feel free to subscribe our YouTube channel, which has already reached over 100 subscribers.

Matrix Computations and Optimization for Machine Learning

Matrix Computations
• [YouTube] [Slides] Orthogonal Procrustes Problem [LinkedIn] 600+ reactions
• [YouTube] [Slides] The Geometry of Quadratic Functions
• [YouTube] [Slides] Why Does Eigenvalue Decomposition Define the Shape of Multivariate Gaussian?
• [YouTube] [Slides] The Geometry of Mahalanobis Distance
• [YouTube] [Slides] Conjugate Gradient Method
Optimization
• [YouTube] [Slides] Linear Programming
• [YouTube] [Slides] Quadratic Programming
• [YouTube] [Slides] Mixed-Integer Quadratic Programming
• [YouTube] [Slides] Solvig Piecewise Linear Regression with Binary Search & Linear Programming
• [YouTube] [Slides] Solvig Unconstrained Nonlinear Optimization with Newton's Method
• [YouTube] [Slides] The Beauty of Cone in Optimization

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.

Blog Posts

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

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
Quantum Computing
• [PDF] (2026) Numerical Analysis on Quantum Computers