Course Notes and Supplemental Materials
Data Science and Machine Learning
| Supplemental Course Slides: (please submit any typos here) | |||
| - | Statistical Learning Theory, Complexity and Generalization | [MicrosoftSlides] [PDF] | |
| - | Complexity Measures, Radamacher, VC-Dimension | [MicrosoftSlides] [PDF] | |
| - | Support Vector Machines, Kernels, Optimization Theory Basics | [MicrosoftSlides] [PDF] | |
| - | Regression, Kernel Methods, LASSO, Regularization, Tomography Example | [MicrosoftSlides] [PDF] [Video (Part 1)] [Video (Part 2)] | |
| - | Unsupervised Learning, Dimension Reduction, Manifold Learning | [MicrosoftSlides] [PDF] | |
| - | Neural Networks and Deep Learning Multilayer Perceptrons (MLPs), Optimization | [GoogleSlides] [PDF] [PyTorch Tutorial] | |
| - | Convolutional Neural Networks (CNNs) Image Processing, Classification | [GoogleSlides] [PDF] [PyTorch Tutorial] | |
| - | Recurrent Neural Networks (RNNs), NLP, Inference on Sequential Data | [MicrosoftSlides] [PDF] [PyTorch Tutorial] | |
| - | Transformer Architectures, Seq2Seq, ViTs, Examples | [GoogleSlides] [PDF] | |
| - | Generative Adversarial Networks (GANs) Learning Implicit Generative Models | [MicrosoftSlides] | |
| - | Diffusion Methods, Image and Video Generation, Sampling Algorithms | [GoogleSlides] [PDF] | |
| - | PyTorch Tutorial, Tensors, Optimization, Custom Neural Networks | [github codes] | |
| Training Codes, Examples, Other Materials: | |||
| - | CNNs: Image Classification using Convolutional Neural Networks (course exercise) | [Jupyter notebook] | CIFAR10 PDF | MNIST PDF | Data Folder | |
| - | Facial Recognition and Feature Extraction (course exercise) | [Jupyter notebook] | Jupyter PDF | Data Folder | Kaggle: Facial Recognition (SVM) | Kaggle PDF | |
| - | Machine Learning Exercise 1 | [PDF] | |
| Kaggle1: Linear Regression (warm-up) | [Kaggle] [Python Code] | ||
| - | Machine Learning Exercise 2 | [PDF] | |
| Kaggle2: Digit Classification (k-NN) | [Kaggle PDF] [Kaggle] | ||
| - | Machine Learning Exercise 3 | [PDF] | |
| Kaggle3: | [Kaggle PDF] [Kaggle] | ||
| Facial Recognition (SVM) | [Jupyter PDF] [Jupyter notebook] | ||
| - | Machine Learning Exercise 4 | [PDF] | |
| - | Machine Learning Exercise 5 | [PDF] | |
| Kaggle4: | [Kaggle PDF] | ||
| Image Classification with CNNs | [Kaggle] | ||
| - | Neural Network Codes: | [Jupyter CIFAR10 PDF] [Jupyter MNIST PDF] | |
| Image Classification CIFAR10/MNIST | [Jupyter notebook] [data-folder] | ||
| - | Machine Learning Take-home Final | [PDF] | |
| Machine Learning Course Links | |||
| - | Machine Learning: Foundations and Applications Course (MATH CS 120) | [course-link] | |
| - | Machine Learning: Foundations and Applications Course (MATH 260J) | [course-link] | |
PyTorch Tutorial: Machine Learning Methods
(please submit any typos here)
| - Introduction [link] | |||
| - Tensors and Operations [link] | |||
| - Broadcast Rules for Tensors [link] | |||
| - Neural Networks and Custom Architectures [link] | |||
| - Optimization Methods and Schedulers [link] | |||
| - Training Protocols and MLP Regression Example [link] | |||
Finite Element Methods: Slides
(please submit any typos here)
| - Introduction to FEM and Ritz-Galerkin Approximation [PDF] [GoogleSlides] | ||
| - Finite Element Spaces [PDF] [GoogleSlides] | ||
| - Software for Finite Element Analysis (FEA) [PDF] [GoogleSlides] | ||
| - Sobolev Spaces [PDF] [GoogleSlides] | ||
| - Finite Element Approximation Properties and Convergence [PDF] [GoogleSlides] | ||
| - Variational Formulation of Elliptic PDEs [PDF] [GoogleSlides] | ||
| - Elasticity Theory [PDF] [GoogleSlides] | ||
| - Finite Element Mixed Methods [PDF] [GoogleSlides] | ||
| - Elasticity Theory: Numerical Example [PDF] [GoogleSlides] | ||
Partial Differential Equations (PDEs)
(please submit any typos here)
| Supplemental Course Notes: | |||
| - Method of Characteristics, Solving First-Order PDEs | [PDF] | ||
| - Classifying Second-Order PDEs and Canonical Forms | [PDF] | ||
| - Wave Equation and Solution Techniques | [PDF] | ||
| - Diffusion Equation and Solution Techniques | [PDF] | ||
| - Separation of Variables | [PDF] | ||
| - Fourier Methods, Solving Parabolic, and Hyperbolic PDEs | [PDF] | ||
| - Elliptic PDEs and Fourier Approaches | [PDF] | ||
| - Discrete Fourier Transforms (DFTs) and Approximate Solutions of PDEs | [PDF] | ||
| - Finite Difference Methods and von Neumann Analysis | [PDF] | ||
| Codes: Numerical Examples | |||
| - Wave Equation | [Jupyter notebook] [PDF] | ||
| - Diffusion Equation | [Jupyter notebook] [PDF] | ||
| - Fourier Series Examples | [Jupyter notebook] [PDF] | ||
| - Discrete Fourier Transform (DFT) | [Jupyter notebook] [PDF] | ||
Optimization Methods and Theory
(please submit any typos here)
| Supplemental Notes and Materials: | ||
| - Introduction to Nonlinear Optimization | [PDF] | |
| - An Introduction to Duality Theory | [PDF] | |
| - Linear Programming and Simplex Method | [PDF] | |
| - Linear Programming Slides | [PDF] | |
| - Simplex Method Implementation | [PDF] [python code] | |
| - Integer Linear Programming Slides | [PDF] |
Monte-Carlo Methods
Mathematical Finance
- An Introduction to Portfolio Theory [PDF]
- The Black-Scholes-Merton Approach to Pricing Options [PDF]
- Contingent Claims and the Arbitrage Theorem [PDF]
- A Brief Introduction to Stochastic Volatility Modeling [PDF]
Dynamical Systems and ODEs
- Poincare Sections of the Duffing Oscillator: [link to video].
The specific parameters are
delta=0.25, gamma=0.3, omega=1.0.
Course Webpages | Publications
Please submit any typos here.