Teaching

Higher Algebra I (高等代数 I, Undergraduate level, Fall 2026, CCNU)

  • Outline
    • [Slides] Course positioning and introduction
    • [Slides] Chapter 3: Determinants (行列式)
    • [Slides] Chapter 4: Matrices and vectors (矩阵与向量)
    • [Slides] Chapter 5: Polynomials (多项式)
    • [Slides] Chapter 6: Eigenstructure and similarity diagonalization of matrices (矩阵的特征系与相似对角化)

Teaching Samples


○ Homogeneous linear equations and its solutions. [Slides(Chinese)]

○ Lagrange’s Mean Value Theorem and its applications. [Slides(Chinese)]


Reading Notes


○ Sparse Gaussianized Canonical Correlation Analysis with Applications to Portfolio Analysis, JASA(2026). [Slides]

○ Partial Quantile Tensor Regression, JASA(2025). [Slides]

○ Matrix Completion and Decomposition in Phase‑Bounded Cones, SIMAX(2025). [Slides]

○ Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees, arXiv(2025). [Slides]

○ Tail-robust factor modelling of vector and tensor time series in high dimensions, Biometrika(2025). [Slides]

○ Functional Tensor Regression, arXiv(2025). [Slides]

○ Fast and Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems, SIMAX(2024). [Slides]

○ Dynamic Matrix Recovery, JASA(2024). [Slides]

○ Spectral Change Point Estimation via Sparse Tensor Decomposition, arXiv(2024). [Slides]

○ Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems, SISC(2023). [Slides]

○ High-Dimensional Portfolio Selection with Cardinality Constraints, JASA(2023). [Slides]

○ ISLET: Fast and Optimal Low-Rank Tensor Regression via Importance Sketching, SIMODS(2020). [Slides]

○ Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions, The Annals of Statistics(2020). [Slides]

○ Quantum Natural Gradient, NIPS(2019). [Slides]

○ High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition, JASA(2019). [Slides(Chinese)]

○ Robust Sample Average Approximation, MP(2018). [Slides]


Reading Hub


♫ Enveloped Huber Regression, JASA(2024). [Slides](Creator: Sheng Liu)

♫ A scalable algorithm for sparse portfolio selection, INFORMS Journal on Computing(2022). [Slides](Creator: Sheng Liu)

♫ Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding, arXiv(2025). [Slides](Creator: Zhi-Long Han)

♫ High-Dimensional Low-Rank Tensor Autoregressive Time Series Modeling(2021). [Slides](Creator: Zhi-Long Han)


Favorite Books/Textbooks


○ (2025) Optimization Bootcamp with Applications in Machine Learning, Control, and Inverse Problems [PDF]

○ Simon J.D. Prince (2023). Understanding Deep Learning. The MIT Press. [PDF]

○ Jayakrishnan Nair, Adam Wierman, Bert Zwart (2022). The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation. Cambridge Series in Statistical and Probabilistic Mathematics. [PDF]

○ Bernard Zygelman (2025). A First Introduction to Quantum Computing and Information. Springer. [PDF]

○ Grey Ballard, Tamara G. Kolda (2025). Tensor Decompositions for Data Science. Cambridge University Press. [PDF]

○ Cristina Garcia-Cardona, Harlin Lee (2023). Advances in Data Science. Springer. [PDF]

○ Jörg Liesen , Volker Mehrmann (2015). Linear Algebra. Springer. [PDF]

○ Per Christian Hansen, James G. Nagy, and Dianne P. O'Leary (2006). Deblurring images: Matrices, spectra, and filtering. SIAM. [Book website]

○ Francis Bach (2023). Learning Theory from First Principles. Draft. [PDF]

○ M. Elad (2010), Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer. [Book website]