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Department of Mathematics College of Liberal Arts and Sciences

Courses

Spring 2026:

Note to undergraduate students interested in enrolling in MAD 6406/6407:

I usually have a few undergraduates per semester take this course with me, some successfully, and some not.  Due to increased interest, here are some guidelines: Undergraduates interested in taking either course should:

  • be in at least their third year (Junior status) when taking the class
  • be comfortable with basic programming in Matlab
  • be aware that these classes have a substantial theorem/proof component, and don’t cover applications
  • have taken MAD 4401 (Introduction to numerical analysis), and possibly MAS 4115 (Linear algebra for data science)
  • have a reason for taking the class, beyond wanting to take a graduate class
  • send me a CV and tell me why you are interested in taking the class

Titles of previous final projects for MAD 6406/6407

MAD6406

  • Yield Curve Factors, Macroeconomic Conditions, and Equity Returns: An SVD–Based Analysis
  • Finding Hidden Signals in Noise: PCA for Gravitational Wave Experiments
  • Nullspace Purification of Linear Pencils
  • Singularity-Aware Guidance Algorithm using SVD-Based Projections
  • Knowledge of Particular Sensible Objects: SVDs Predicated on the Philosophy of Plato
  • Eigenvalue-Based Network Alignment: The IsoRank Algorithm
  • Non-Linear Optimization Problems and Conditioning
  • Preservation of Topological Structure of Data under Principal Component Analysis
  • Conjugate Gradient method for solving PDEs
  • Relating Singular Value Decomposition and the Principal Component Analysis
  • An Empirical Inspection into the Stability of CycleGAN and Pix2Pix
  • Singular Value Decomposition in Principal Component Analysis
  • Conjugate Gradients
  • Dynamic Factor Models and Their Application to Inflation
  • Generation of Orthogonal Random Matrices
  • Error analysis of coordinate system transformation in robot geometry
  • Diagonalization Strategies in Ab Initio Quantum Chemistry
  • Application of principal component analysis in clay-water contact angle determination
  • Mean-variance portfolio optimization using an ill-conditioned covariance matrix
  • Ridge regression and MAD6406
  • Arnoldi Iteration
  • Brief history of automated reasoning and some applications
  • Use of Matrix Decompositions in Microbiome Data Analysis
  • A conditional analysis of the least squares orbit determination problem
  • Bi-cross-validation for the selection of rank in low-rank matrix approximations, with application to single-cell genomics data
  • Scaling optimal control problems for improved convergence and increased precision
  • A closer look at algorithm of direct micromechanics method (DMM)
  • Machine learning problems with PCA and SVM
  • Numerical analysis of Jacobi’s constant in the circular restricted three-body problem
  • Floating point representation and its relevance in the field of optimal control

MAD6407

  • Implementing the Method of Sturm in MATLAB
  • Cubic splines in regression problems
  • Infinite interpolation
  • Approximating the Prime Counting Function pi(x) via Bernstein Polynomials
  • Modeling the proliferation of a virus within a host
  • Using Least-Squares Approximation and Cubic Spline for Levelset Methods based Process Simulation of IC Fabrication
  • Sensitivity to initial conditions in the Hodgkin-Huxley equation
  • Multistep methods
  • Approximate Anderson acceleration: An empirical inspection
  • Finite elements for 2D heat transfer

Previous Semesters

  • Fall, 2025
    • MAD 4401: Introduction to Numerical Analysis
    • MAD 6406: Numerical Linear Algebra (graduate)
  • Spring, 2025
    • MAD 4401 Introduction to Numerical Analysis
  • Fall, 2023
    • MAP 6375 Numerical Partial Differential Equations
  • Spring, 2023
    • MAT 4930/6932 Computational methods for ill-posed problems
  • Fall, 2022
    • MAD 4401 Introduction to Numerical Analysis (2 sections)
  • Spring, 2022
    • MAP 6376 Finite Element Method
  • Fall, 2021
    • MAD 4401 Introduction to Numerical Analysis
    • MAD 6406 Numerical Linear Algebra
  • Spring, 2021
    • MAD 6407 Numerical Analysis
  • Fall, 2020
    • MAD 6406 Numerical Linear Algebra
  • Spring, 2020
    • MAD 6407 Numerical Analysis
    • MAP 6375 Numerical Partial Differential Equations
  • Fall, 2019
    • MAD 6406 Numerical Linear Algebra
  • Spring, 2019
    • MAD 6407 Numerical Analysis
  • Fall, 2018
    • MAD 6406 Numerical Linear Algebra
    • MAP 2302 Elementary Differential Equations