{"id":8,"date":"2012-09-05T11:20:01","date_gmt":"2012-09-05T15:20:01","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=8"},"modified":"2026-05-29T10:45:43","modified_gmt":"2026-05-29T14:45:43","slug":"courses","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/spollock\/courses\/","title":{"rendered":"Courses"},"content":{"rendered":"\n
\n

Courses<\/h1>\n\n\n\n

Fall 2026:<\/h3>\n\n\n\n
    \n
  • MAD 6406: Numerical Linear Algebra (Graduate)<\/li>\n\n\n\n
  • MAP 6375: Numerical Partial Differential Equations (Graduate)<\/li>\n<\/ul>\n\n\n\n

    Note to undergraduate students interested in enrolling in MAD 6406\/6407:<\/h3>\n\n\n\n

    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:<\/p>\n\n\n\n

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

      Titles of previous final projects for MAD 6406\/6407<\/h3>\n\n\n\n

      MAD6406<\/h4>\n\n\n\n
        \n
      • Yield Curve Factors, Macroeconomic Conditions, and Equity Returns: An SVD\u2013Based Analysis<\/li>\n\n\n\n
      • Finding Hidden Signals in Noise: PCA for Gravitational Wave Experiments<\/li>\n\n\n\n
      • Nullspace Purification of Linear Pencils<\/li>\n\n\n\n
      • Singularity-Aware Guidance Algorithm using SVD-Based Projections<\/li>\n\n\n\n
      • Knowledge of Particular Sensible Objects: SVDs Predicated on the Philosophy of Plato<\/li>\n\n\n\n
      • Eigenvalue-Based Network Alignment: The IsoRank Algorithm<\/li>\n\n\n\n
      • Non-Linear Optimization Problems and Conditioning<\/li>\n\n\n\n
      • Preservation of Topological Structure of Data under Principal Component Analysis<\/li>\n\n\n\n
      • Conjugate Gradient method for solving PDEs<\/li>\n\n\n\n
      • Relating Singular Value Decomposition and the Principal Component Analysis<\/li>\n\n\n\n
      • An Empirical Inspection into the Stability of CycleGAN and Pix2Pix<\/li>\n\n\n\n
      • Singular Value Decomposition in Principal Component Analysis<\/li>\n\n\n\n
      • Conjugate Gradients<\/li>\n\n\n\n
      • Dynamic Factor Models and Their Application to Inflation<\/li>\n\n\n\n
      • Generation of Orthogonal Random Matrices<\/li>\n\n\n\n
      • Error analysis of coordinate system transformation in robot geometry<\/li>\n\n\n\n
      • Diagonalization Strategies in Ab Initio Quantum Chemistry<\/li>\n\n\n\n
      • Application of principal component analysis in clay-water contact angle determination<\/li>\n\n\n\n
      • Mean-variance portfolio optimization using an ill-conditioned covariance matrix<\/li>\n\n\n\n
      • Ridge regression and MAD6406<\/li>\n\n\n\n
      • Arnoldi Iteration<\/li>\n\n\n\n
      • Brief history of automated reasoning and some applications<\/li>\n\n\n\n
      • Use of Matrix Decompositions in Microbiome Data Analysis<\/li>\n\n\n\n
      • A conditional analysis of the least squares orbit determination problem<\/li>\n\n\n\n
      • Bi-cross-validation for the selection of rank in low-rank matrix approximations, with application to single-cell genomics data<\/li>\n\n\n\n
      • Scaling optimal control problems for improved convergence and increased precision<\/li>\n\n\n\n
      • A closer look at algorithm of direct micromechanics method (DMM)<\/li>\n\n\n\n
      • Machine learning problems with PCA and SVM<\/li>\n\n\n\n
      • Numerical analysis of Jacobi’s constant in the circular restricted three-body problem<\/li>\n\n\n\n
      • Floating point representation and its relevance in the field of optimal control<\/li>\n<\/ul>\n\n\n\n

        MAD6407<\/h4>\n\n\n\n
          \n
        • Sputtering yield surface reconstruction via polynomial interpolation: Application to Hall yhruster erosion modeling<\/li>\n\n\n\n
        • Numerical analysis of implicit superposition for a two-droplet interaction benchmark<\/li>\n\n\n\n
        • The auspicious fount from which all sets of orthogonal polynomials flow<\/li>\n\n\n\n
        • It was the best of approximations, it was the worst of approximations<\/li>\n\n\n\n
        • Integral equations<\/li>\n\n\n\n
        • Chebyshev and Faber polynomials: Real and complex behavior beyond [-1,1]<\/li>\n\n\n\n
        • Numerical differentiation and spline-based noise mitigation in bio-kinematic data<\/li>\n\n\n\n
        • From classical approximation to Gaussian process surrogates: a comparative study<\/li>\n\n\n\n
        • Chebyshev nodes: Optimality and stability in polynomial interpolation<\/li>\n\n\n\n
        • High-dimensional Chebyshev surrogate modeling for Heston option pricing and dynamic delta hedging<\/li>\n\n\n\n
        • Error estimate for linear multistep method + Anderson acceleration<\/li>\n\n\n\n
        • Implementing the Method of Sturm in MATLAB<\/li>\n\n\n\n
        • Cubic splines in regression problems<\/li>\n\n\n\n
        • Infinite interpolation<\/li>\n\n\n\n
        • Approximating the prime counting function pi(x) via Bernstein Polynomials<\/li>\n\n\n\n
        • Modeling the proliferation of a virus within a host<\/li>\n\n\n\n
        • Using least-squares approximation and cubic spline for levelset methods based process simulation of IC fabrication<\/li>\n\n\n\n
        • Sensitivity to initial conditions in the Hodgkin-Huxley equation<\/li>\n\n\n\n
        • Multistep methods<\/li>\n\n\n\n
        • Approximate Anderson acceleration: An empirical inspection<\/li>\n\n\n\n
        • Finite elements for 2D heat transfer<\/li>\n<\/ul>\n\n\n\n

          Previous Semesters<\/h3>\n\n\n\n
            \n
          • Spring, 2026\n
              \n
            • MAD 6407 Numerical Analysis<\/li>\n<\/ul>\n<\/li>\n\n\n\n
            • Fall, 2025\n
                \n
              • MAD 6406 Numerical Linear Algebra<\/li>\n\n\n\n
              • MAD 4401 Introduction to Numerical Analysis<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Spring, 2025\n
                  \n
                • MAD 4401 Introduction to Numerical Analysis<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                • Fall, 2023\n
                    \n
                  • MAP 6375 Numerical Partial Differential Equations<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                      \n
                    • Spring, 2023\n
                        \n
                      • MAT 4930\/6932 Computational methods for ill-posed problems<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                      • Fall, 2022\n
                          \n
                        • MAD 4401 Introduction to Numerical Analysis (2 sections)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                        • Spring, 2022\n
                            \n
                          • MAP 6376 Finite Element Method<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                          • Fall, 2021\n
                              \n
                            • MAD 4401 Introduction to Numerical Analysis<\/li>\n\n\n\n
                            • MAD 6406 Numerical Linear Algebra<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                            • Spring, 2021\n
                                \n
                              • MAD 6407 Numerical Analysis<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                              • Fall, 2020\n
                                  \n
                                • MAD 6406 Numerical Linear Algebra<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                • Spring, 2020\n
                                    \n
                                  • MAD 6407 Numerical Analysis<\/li>\n\n\n\n
                                  • MAP 6375 Numerical Partial Differential Equations<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                  • Fall, 2019\n
                                      \n
                                    • MAD 6406 Numerical Linear Algebra<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                    • Spring, 2019\n
                                        \n
                                      • MAD 6407 Numerical Analysis<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                      • Fall, 2018\n
                                          \n
                                        • MAD 6406 Numerical Linear Algebra<\/li>\n\n\n\n
                                        • MAP 2302 Elementary Differential Equations<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":922,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-8","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/pages\/8","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/users\/922"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/pages\/8\/revisions"}],"predecessor-version":[{"id":1236,"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/pages\/8\/revisions\/1236"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/spollock\/wp-json\/wp\/v2\/media?parent=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}