Personal Notes: Quantitative & Analytical Studies
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: Linear Algebra, Multivariate Calculus, Real Analysis, Measure Theory, Abstract Algebra, Combinatorics
- Dynamics: Ordinary, Partial, Stochastic Differential Equations
- Stochasticity: Probability, Stochastic Processes, Concentration of Measure
- Analysis: Complex Analysis, Functional Analysis
- Algebra: Category Theory, Representation Theory, Number Theory
- Topology: Point-Set Topology, Algebraic Topology
- Geometry: Smooth Manifolds, Differential Geometry, Algebraic Geometry, Symplectic Geometry
Statistics
- Frequentist Statistics
- Bayesian Statistics
- Information Theory & Signal Processing
- Machine Learning: Learning Theory & Classical Algorithms
- Deep Learning: Algorithms
- Computer Vision
- Natural Language Processing
- Sampling, Optimization, Integration
Computer Science
- Classic Theory
- Hardware
- Compilers and Operating Systems
- Data Structures
- Algorithms
- Backend Development: Computer Networking, APIs, Databases, Webscraping
- Frontend Development: Web, App Development
- Cybersecurity
- Blockchain Development
- Quantum Computing
- Simultaneous Localization and Mapping
- Languages: Python, Julia, Javascript, Java, C/C++, Bash, SQL, Flutter, HTML, CSS, Solidity, Qsikit
Natural Sciences
- Classical Mechanics: Newtonian, Lagrangian, Hamiltonian
- Electromagnetism:
- Molecular Dynamics: Atomic Structures, Langevin Dynamics, Dissipative Particle Dynamics
- Theoretical: Quantum Mechanics, General Relativity, Quantum Field Theory, String Theory