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. It is a dependency graph where (generally, albeit crudely) A -> B if A is needed to study B in a rigorous introductory level. The dependencies are purely from my own opinion and experience, and there may be other dependencies not included in this graph, since the fields of STEM are so interdependent. Each of the notes is a work in progress, with the ones labeled with an asterisk (*) representing notes I have not written and the ones labeled with a hat (^) indicating fields I am (or have) researched in or worked with extensively. I also color coded them so that math subjects are labeled in red, physics in green, statistics in blue, and computer science in yellow.

The first graph represents the fields of mathematics, physics, and statistics. This is where my academic focus is more on at the moment. The more pure math and physics concepts are towards the right side, while the applied math and statistics are on the left, though you can see that subjects like signal processing have heavy relevance in both fields and others like statistical learning theory require relatively advanced mathematics like functional analysis to derive theoretical implications of deep learning. There are many courses missing here, such as electromagnetism and otpics, but I just do not have enough knowledge to know where to put them. The second graph consists of the subjects in computer science, hardware, and software design. They are focused on general workflows one can use to deploy applications, accelerate hardware, and have better control over computers. 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.

- 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

- 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

- 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

- 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*

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