Study Notes
Welcome to my collection of study notes! Here you'll find comprehensive materials covering the mathematical foundations essential for physics, cosmology, computer science, and machine learning, along with detailed notes on cosmology, physics, and various other topics. These notes are designed to serve as both learning resources and quick references for advanced concepts.
[This page will be updated soon with all materials]
Mathematics
Core mathematical foundations for physics, cosmology, computer science, and machine learning
In Progress
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.
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.
In Progress
Complex Analysis
Functions of Complex Variables
Complex functions, contour integration, residue theorem, and conformal mapping. Essential for quantum mechanics and advanced physics applications.
In Progress
Fourier Analysis
Transform Methods
Fourier series, Fourier transforms, and their applications in signal processing, cosmological data analysis, and solving partial differential equations.
Cosmology
Understanding the universe at the largest scales
In Progress
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.
In Progress
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.
In Progress
Power Spectrum Analysis
Statistical Cosmology
Power spectrum fundamentals, correlation functions, galaxy clustering, CMB angular power spectra, and cross-correlation analysis methods.
In Progress
Observational Cosmology
LSST, Euclid & Future Surveys
Overview of current and future cosmological surveys, data analysis techniques, systematic effects, and parameter estimation methods.
Physics
Fundamental physics concepts and advanced topics
In Progress
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.
In Progress
Quantum Mechanics
Wave Functions & Operators
Schrödinger equation, quantum operators, uncertainty principle, quantum harmonic oscillator, and applications to atomic physics. Includes computational quantum mechanics methods.
In Progress
Statistical Mechanics
Thermodynamics & Phase Transitions
Boltzmann distribution, partition functions, phase transitions, critical phenomena, and applications to condensed matter physics and cosmology.
In Progress
Electromagnetism
Maxwell's Equations & Applications
Maxwell's equations, electromagnetic waves, relativistic electrodynamics, and applications to particle accelerators and astrophysical phenomena.
Miscellaneous
Computer science, machine learning, and interdisciplinary topics
In Progress
Machine Learning Fundamentals
Algorithms & Implementation
Supervised and unsupervised learning algorithms, neural networks, deep learning architectures, and applications to scientific data analysis and cosmological surveys.
In Progress
Scientific Computing
Python, NumPy & Scientific Libraries
Python programming for scientific applications, numerical methods, data visualization, and computational tools for physics and cosmology research.
In Progress
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.
In Progress
Research Methods
Academic Writing & Collaboration
Academic writing techniques, research methodology, collaboration tools, version control with Git, and best practices for scientific research and publication.