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    • Calculus
      • Single Variable Calculus
        • Real Numbers and Limits of Sequences
        • Continuity of Functions
        • Derivatives and Differentials of Functions
        • Indefinite Integrals
        • Definite Integral
        • Ordinary Differential Equations
      • Multivariable Calculus
        • Limits and Continuity of Multivariate Functions
        • Differential of Multivariable Functions
        • Implicit Function and Inverse Mapping Theorem
        • Integrals with Parameters and Improper Integrals
        • Multiple Integrals
        • Integration of Functions on Curves and Surfaces
        • Calculus of Vector Fields
        • Series
        • Series of Functions and Power Series
        • Fourier Series
    • Math for CS and AI
      • Discrete Probability
      • Sampling and Concentration
      • Generating Functions
      • Continuous Probability
      • Central Limit Theorem
      • Optimization
      • Continuous Approximations
    • General Physics
      • Mechanics and Thermal Physics
        • Kinematics
        • Newton’s Laws
        • Momentum
        • Energy and Work
        • Angular Momentum
        • Collision Theory
        • Rigid Body
        • Oscillation
        • Waves
        • Lagrangian and Hamiltonian Mechanics
        • Special Relativity
        • Temperature, Heat, and the First Law of Thermodynamics
        • Kinetic Theory of Gases
        • Second Law of Thermodynamics
        • Statistical Mechanics
      • Electricity and Magnetism
        • Scalar and Vector Fields
        • Electrostatics
        • Magnetostatics
        • Laws of Induction
        • Maxwell Equations and Solutions
        • AC Circuits
        • Resonators
        • Waveguides
        • Quantum Information Processing
    • Deep Learning
      • Supervised Learning
      • Energy-Based Model
      • Generative Adversarial Network
      • Normalizing Flow & Variational Autoencoder
      • Diffusion Models & Flow Matching
      • Sequence Modeling
    • Advanced Applied Probability
      • Measure Theory
    • Machine Learning
      • Optimization
    • Advanced Computer Graphics
      • Geometry
    • Artificial Intelligence

Notes

A collection of notes to reference.

import sys

print(sys.executable)
print("Hello from VS Code")
/opt/hostedtoolcache/Python/3.12.14/x64/bin/python3
Hello from VS Code

This is a simple mathematical equation:

\[ y = x^2 + 2x + 1 \]

import pandas as pd
import matplotlib.pyplot as plt

data = pd.DataFrame({
    "epoch": [1, 2, 3, 4, 5],
    "accuracy": [0.55, 0.68, 0.76, 0.82, 0.87]
})

data
epoch accuracy
0 1 0.55
1 2 0.68
2 3 0.76
3 4 0.82
4 5 0.87
plt.plot(data["epoch"], data["accuracy"], marker="o")
plt.xlabel("Epoch")
plt.ylabel("Accuracy")
plt.title("Training Accuracy")
plt.grid()
plt.show()

Calculus