## 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 **

- 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]

** 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 **

- 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.