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Course Notes and Supplemental Materials

Data Science and Machine Learning

Slides: Statistical Learning Theory, Generalization Errors, and Sampling Complexity Bounds:
[MicrosoftSlides] [PDF]

Slides: Complexity Measures, Radamacher, VC-Dimension:
[MicrosoftSlides] [PDF]

Slides: Support Vector Machines, Kernels, Optimization Theory Basics:
[MicrosoftSlides] [PDF]

Slides: Regression, Kernel Methods, Regularization, LASSO, Tomography Example:
[MicrosoftSlides] [PDF] [Video (Part 1)] [Video (Part 2)]

Slides: Unsupervised Learning, Dimension Reduction, Manifold Learning:
[MicrosoftSlides] [PDF]

Slides: Neural Networks and Deep Learning Basics:
[GoogleSlides] [PDF]

Slides: Convolutional Neural Networks (CNNs) Basics:
[GoogleSlides] [PDF]

Slides: Recurrent Neural Networks (RNNs) Basics:
[MicrosoftSlides] [PDF]

Slides: Generative Adversarial Networks (GANs):
[MicrosoftSlides] [PDF]

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

Partial Differential Equations (PDEs)

Supplemental Course Notes:
(please submit any typos here)
- 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]

Non-linear Optimization: Notes

Monte-Carlo Methods

Mathematical Finance

Dynamical Systems and ODEs

The specific parameters are delta=0.25, gamma=0.3, omega=1.0.

Course Webpages | Publications