Notes: Quantitative Sciences
Below is a map of all the materials that I have studied or would like to study during my time in the Korean military and at Duke. As these notes are primarily for my personal use, I did not spend as much time writing them in a manner that is clear for all readers. But since it would be a waste not to share them, I uploaded them on this website.
All of my personal notes are free to download, use, and distrbute under the Creative Commons "Attribution- NonCommercial-ShareAlike 4.0 International" license. Please contact me if you find any errors in my notes or have any further questions. I have used the LaTeX editing program Overleaf to create my notes; diagrams are often drawn using the tikz package or iPad Notes.
Mathematics
- Fundamentals: Logic, Set Theory
- Structures: Point-Set Topology, Abstract Algebra, Linear Algebra, Algebraic Topology
- Analysis: Real/Complex Analysis, Measure Theory, Functional Analysis
- Algebra: Number Theory, Representation Theory
- Probability: Probability, Stochastic Processes/Calculus, Concentration of Measure
- Dynamics: Ordinary, Partial, Stochastic Differential Equations
- Geometry: Smooth Manifolds, Differential Geometry, Algebraic Geometry
Statistics
- ECE: Information Theory, Signal Processing
- Statistics: Frequentist Inference, Bayesian Inference, Optimization, Sampling
- Learning Theory: Statistical Learning Theory, Decision Theory
- Machine Learning: Regression, Classification, Time Series, Kernels/Smoothers, Trees, Ensembles, Factors/Components, Clustering, Graphical Models, Reinforcement Learning
- Deep Learning: MLP, CNN, RNN, Energy Models, Encoder-Decoder, VAE, GAN, Flows, Graph Nets, Memory Nets, Diffusion, Attention, Semisupervision, Meta-Learning, Adversarial Attacks, Bayesian Nets
- Applications: Computer Vision, Natural Language Processing
Computer Science
- Classic Theory: Data Structures, Algorithms, Computability, Complexity, DFA
- Quantum Theory: Quantum Computing, Quantum Information Theory
- Architecture: Hardware, Assembly (x86, ARMv7)
- Foundational Software: Compilers, Operating Systems (Unix), C, C++
- Applications: Networks, Distributed Systems, Databases, SLAM, Blockchain, Python, Javascript
- Tools: Git, Continuous Integration/Development, LaTeX, Vim, Linux Desktop, Package Management, SSH
- Miscellaneous: Blockchain, Simultaneous Localization and Mapping