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UC Irvine Math 10: Introduction to Programming for Data Science

Math 10 is the first dedicated programming class in the Data Science specialization designed mainly for Math majors at University of California Irvine. Some of current de facto algorithms will be featured, and some theorems in Mathematics behind in data science/machine learning are to be verified using Python, and the format can be adapted to other popular languages like R and Julia.

(Update Sep 2020): As I am not affiliated with UCI anymore, please refer to the UCI math website for the latest syllabi for Math 10.

Prerequisites:

MATH 2D Multivariate Calculus

MATH 3A Linear Algebra(can be taken concurrently)

MATH 9 Introduction to Programming for Numerical Analysis

Recommended:

MATH 130A Probabilty I

ICS 31 Introduction to Programming

Lecture notes (Jupyter notebooks) are available in the Lectures folder.

Lecture Contents
Lecture 1 Intro to Jupyter notebooks, expressions, operations, variables
Lecture 2 Defining your own functions, types (float, bool, int), Lists, IF-ELSE
Lecture 3 Numpy arrays I, tuples, slicing
Lecture 4 Numpy arrays II, WHILE and FOR loops vs vectorization
Lecture 5 Numpy arrays III, advanced slicing; Matplotlib I, pyplot
Lecture 6 Numpy arrays IV, Linear algebra routines
Lecture 7 Matplotlib II, histograms
Lecture 8 Randomness I; Matplotlib III, scatter plot
Lecture 9 Randomness II, descriptive statistics, sampling data
Lecture 10 Randomness III, random walks, Law of large numbers
Lecture 11 Introduction to class and methods, object-oriented programming
Lecture 12 Optimization I: Optimizing functions, gradient descent
Lecture 13 Fitting data I: Linear model, regression, least-square
Lecture 14 Optimization II: Solving linear regression by gradient descent
Lecture 15 Fitting data II: Overfitting, interpolation, multivariate linear regression
Lecture 16 Classification I: Bayesian classification, supervised learning models
Lecture 17 Classification II: Logistic regression, binary classifier
Lecture 18 Classification III: Softmax regression, multiclass classifier
Lecture 19 Optimization III: Stochastic gradient descent
Lecture 20 Classification IV: K-nearest neighbor
Lecture 21 Dimension reduction: Singular Value Decomposition (SVD), Principal Component Analysis (PCA)
Lecture 22 Feedforward Neural Networks I: models, activation functions, regularizations
Lecture 23 Feedforward Neural Networks II: backpropagation
Lecture 24 KFold, PyTorch, Autograd, and other tools to look at

Labs and Homeworks

There are two Labs per week. One is a Lab exercise, aiming to review and sharpen your programming skills. The other is a graded Lab assignment, which is like a collaborative programming quiz. Homework is assigned on a weekly basis, the later ones may look a mini project. Lab assignments' and Homeworks' solutions are available on Canvas.

Textbook

No official textbook but we will use the following as references: Scientific Computation: Python Hacking for Math Junkies. Version3, With iPython (Math 9 reference book)

Python Data Science Handbook. Online version

Software

Python 3 and Jupyter notebook (iPython). Please install Anaconda. To start Jupyter notebook, you can either use the Anaconda Navigator GUI, or start Terminal on Mac OS/Linux, Anaconda prompt on Windows: in the directory of .ipynb file, run the command jupyter notebook to start a notebook in your browser (Chrome recommended). If Jupyter complains that a specific package is missing when you run your notebook, then return to the command line, execute conda install <name of package>, and re-run the notebook cell.

Final Project

There is one final project using Kaggle in-class competition. A standard classification problem similar to the Kaggle famous starter competition Digit Recognizer based on MNIST dataset will be featured. You will use the techniques learned in class and not in class (e.g., random forest, gradient boosting, etc) to classify objects.

Acknowledgements

A major portion of the first half of the course is adapted from Umut Isik's Math 9 in Winter 2017 with much more emphases on vectorization, and instead the materials are presented using classic toy examples in data science (Iris, wine quality, Boston housing prices, MNIST, etc). Part of the second half of this course (regressions, classifications, multi-layer neural net, PCA) is adapted from Stanford Deep Learning Tutorial's MATLAB codes to vectorized implementations in numpy from scratch, together with their scikit-learn's counterparts.