Course Notes and Supplemental Materials
Data Science and Machine Learning
Slides: Statistical Learning Theory, Generalization Errors, and Sampling Complexity Bounds: [Large Slides][PDF] [MicrosoftSlides]
Slides: Complexity Measures, Radamacher, VC-Dimension: [Large Slides] [PDF] [MicrosoftSlides]
Slides: Support Vector Machines, Kernels, Optimization Theory Basics: [Large Slides] [PDF] [MicrosoftSlides]
Slides: Regression, Kernel Methods, Regularization, LASSO, Tomography Example: [Large Slides] [PDF] [MicrosoftSlides] [Video (Part 1)] [Video (Part 2)]
Slides: Unsupervised Learning, Dimension Reduction, Manifold Learning: [Large Slides] [PDF] [MicrosoftSlides]
Slides: Neural Networks and Deep Learning Basics:
[PDF] [GoogleSlides]
Slides: Convolutional Neural Networks (CNNs) Basics:
[PDF]
[GoogleSlides]
Slides: Recurrent Neural Networks (RNNs) Basics: [Large Slides]
[PDF]
[MicrosoftSlides]
Slides: Generative Adversarial Networks (GANs): [Large Slides] [PDF] [MicrosoftSlides]
Image Classification using Convolutional Neural Networks (course exercise)
Jupyter Notebook Codes | CIFAR10 PDF | MNIST PDF | Data Folder
Facial Recognition and Feature Extraction (course exercise)
Jupyter Notebook Codes | Jupyter PDF | Data Folder | Kaggle: Facial Recognition (SVM) | Kaggle PDF
Machine Learning Exercise 1: [PDF]
Kaggle1: Linear Regression (warm-up) [Python Code]
Machine Learning Exercise 2: [PDF]
Kaggle2: [Kaggle PDF]
Digit Classification MNIST (k-NN)
Machine Learning Exercise 3: [PDF]
Kaggle3: [Kaggle PDF] Facial Recognition (SVM)
Facial Recognition Codes: [Jupyter Notebook PDF]
[Jupyter Notebook Code]
[data-folder]
Machine Learning Exercise 4: [PDF]
Machine Learning Exercise 5: [PDF]
Kaggle4: [Kaggle PDF] Image Classification: Convolutional Neural Networks (CNNs)
Neural Network Codes: [Jupyter Notebook CIFAR10 PDF] [Jupyter Notebook MNIST PDF]
[Jupyter Notebook Codes] [data-folder]
Machine Learning Take-home Final [PDF]
Machine Learning Course Link
Machine Learning: Foundations and Applications Course (MATH CS 120) [course-link]
Machine Learning: Foundations and Applications Course (MATH 260J) [course-link]
Finite Element Methods: Slides
- Introduction to FEM and Ritz-Galerkin Approximation [PDF] [GoogleSlides]
- Sobolev Spaces [PDF] [GoogleSlides]
- Finite Element 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]
Non-linear Optimization: Notes
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:
The specific parameters are ` delta=0.25, gamma=0.3, omega=1.0 `.