Mathematics

Core mathematical foundations for physics, cosmology, computer science, and machine learning

Available
Vector Calculus & Tensor Analysis
Essential for General Relativity
Comprehensive coverage of vector operations, tensor algebra, differential geometry, and their applications in physics. Includes covariant derivatives, curvature tensors, and metric tensor manipulations.
Vectors Tensors Differential Geometry General Relativity
In Progress
Linear Algebra for ML/DL
Matrix Operations & Eigenvalues
Matrix operations, eigenvalue decomposition, singular value decomposition (SVD), principal component analysis (PCA), and their applications in machine learning algorithms.
Matrices Eigenvalues SVD Machine Learning
Coming Soon
Complex Analysis
Functions of Complex Variables
Complex functions, contour integration, residue theorem, and conformal mapping. Essential for quantum mechanics and advanced physics applications.
Complex Numbers Contour Integration Residues Quantum Mechanics
Available
Fourier Analysis
Transform Methods
Fourier series, Fourier transforms, and their applications in signal processing, cosmological data analysis, and solving partial differential equations.
Fourier Series Transforms Signal Processing Data Analysis
Λ

Cosmology

Understanding the universe at the largest scales

Available
Λ
ΛCDM Model
Standard Model of Cosmology
Comprehensive overview of the Lambda-Cold Dark Matter model, including Friedmann equations, dark energy, dark matter, and cosmic microwave background physics.
Dark Matter Dark Energy Friedmann Equations CMB
In Progress
f
Modified Gravity Theories
f(R) Gravity & Beyond
Detailed study of modified gravity theories including f(R) gravity, Horndeski theories, and their observational signatures in cosmological surveys.
f(R) Gravity Horndeski Theory Modified Gravity Observational Tests
Available
P
Power Spectrum Analysis
Statistical Cosmology
Power spectrum fundamentals, correlation functions, galaxy clustering, CMB angular power spectra, and cross-correlation analysis methods.
Power Spectrum Correlation Functions Galaxy Clustering Statistical Methods
Coming Soon
Observational Cosmology
LSST, Euclid & Future Surveys
Overview of current and future cosmological surveys, data analysis techniques, systematic effects, and parameter estimation methods.
LSST Euclid Data Analysis Parameter Estimation

Physics

Fundamental physics concepts and advanced topics

Available
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General Relativity
Einstein's Theory of Gravity
Complete treatment of Einstein's field equations, spacetime geometry, black holes, gravitational waves, and cosmological applications. Includes problem-solving techniques and physical interpretations.
Einstein Field Equations Spacetime Black Holes Gravitational Waves
Available
ψ
Quantum Mechanics
Wave Functions & Operators
Schrödinger equation, quantum operators, uncertainty principle, quantum harmonic oscillator, and applications to atomic physics. Includes computational quantum mechanics methods.
Schrödinger Equation Operators Uncertainty Principle Atomic Physics
In Progress
S
Statistical Mechanics
Thermodynamics & Phase Transitions
Boltzmann distribution, partition functions, phase transitions, critical phenomena, and applications to condensed matter physics and cosmology.
Boltzmann Distribution Partition Functions Phase Transitions Critical Phenomena
Coming Soon
E
Electromagnetism
Maxwell's Equations & Applications
Maxwell's equations, electromagnetic waves, relativistic electrodynamics, and applications to particle accelerators and astrophysical phenomena.
Maxwell Equations EM Waves Relativistic ED Astrophysics

Miscellaneous

Computer science, machine learning, and interdisciplinary topics

Available
AI
Machine Learning Fundamentals
Algorithms & Implementation
Supervised and unsupervised learning algorithms, neural networks, deep learning architectures, and applications to scientific data analysis and cosmological surveys.
Neural Networks Deep Learning Supervised Learning Data Analysis
In Progress
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Scientific Computing
Python, NumPy & Scientific Libraries
Python programming for scientific applications, numerical methods, data visualization, and computational tools for physics and cosmology research.
Python NumPy SciPy Matplotlib
Available
χ²
Statistics & Data Analysis
Bayesian Methods & MCMC
Statistical inference, Bayesian analysis, Markov Chain Monte Carlo methods, and their applications to parameter estimation in cosmology and physics.
Bayesian Statistics MCMC Parameter Estimation Statistical Inference
Coming Soon
R
Research Methods
Academic Writing & Collaboration
Academic writing techniques, research methodology, collaboration tools, version control with Git, and best practices for scientific research and publication.
Academic Writing Research Methods Git Collaboration