Data science is one of the most growing scientific disciplines today. This course will introduce various mathematics related to modern data science. The subjects that will be covered for the semester include Introduction to data science and big data, Preprocessing of data, Interpolating data, Classification of data, Generating scheme of data, Text, sound, and image data, Stochastic and chaotic characteristics of data, data-driven computing, Topological and geometrical understanding of data, Manifold representation of data, Artificial intelligence and data, Data analysis with Python and visualization, etc. Students will also implement the learned materials into Python programming.

It is recommended, but not required, to take linear algebra, differential equations.

Class attendance: 10%
Homework: 30%
Midterm exam: 30%
Final research project: 30%

Introduction to Mathematical Data Science - by example (Instructor's lecture note), 2021.

1. Basic Python programming
A. Basic grammar
B. SC library
C. Data analysis with Pandas
2. Introduction to data science
A. What is data science?
B. History of data science
C. What do we do with data science
3. Epidemics - modeling from data
A. Covid-19 data
B. Modeling with differential equations
C. Particle simulation (dynamical system)
D. Cellular automata (discrete system)
4. Random versus chaotic data
A. Paramecium Aurelia data
B. Population data
C. Logistic map
D. Chaotic behavior of data - Butterfly effect
E. Random versus chaotic data
5. Population prediction with data
A. 한국통계청 홈페이지
B. Data interpolation/extrapolation - interpolation theory
C. Regularization (overfitting, L1 regularization)
D. Least squares approximation (regression)
6. Prediction with regression
A. Prediction with data
B. Linear regression & polynomial regression
C. Overfitting & regularization
D. Bias & variance
7. Classification with data
A. Data Source: Titanic data (from Kaggle)
B. Regression (Logistic regression, optimization)
C. Linear regression, Logistic regression, SVM
D. Deep learning - multiple layers
8. Image classification via convolutional neural network
A. Data source: cat vs. dog (from Kaggle)
B. Intro - Edge detection (image data)Jump function, differential map
C. Introduction of CNN
9. Text data
A. Python nltk
B. Text analysis (word frequency, Zipf law)
C. Corpus analysis
10. Unsupervised learning
A. Supervised versus unsupervised learning
B. Clustering
C. Dimensional reduction (PCA, TSNE)
11. Sampling of data
A. Sampling from simulation data
B. Monte Carlo versus polynomial chaos
12. Topological data analysis
A. Data analysis using homology and mapper (MNIST hand-writing data)
B. persistent homology
C. Mapper

The class is composed of lecture and tutorial sessions. Each class will provide both the theoretical and practical (computational) aspects of data science with hands-on tutorials. Weekly homework will be assigned. Students are required to attend the class regularly and submit their homework on time.