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Personal reflections, practical guides for aspiring researchers, and explainer posts. Below, you will also find some of my study notes covering the mathematical and physical foundations of these fields.

[Most posts are placeholders for now. This page will be updated soon with all materials.]

Posts & Guides

Personal Reflections

Coming Soon

Why Cosmology?

On the questions that first pulled me toward studying the universe, and why I keep returning to them. A note for anyone wondering whether to chase the big questions.

PersonalMotivationCosmology
Coming Soon

Lessons from My First Research Project

What worked, what completely failed, and the things I wish someone had told me before I sent my first email to a professor. Plenty of honest mistakes.

ReflectionResearch LifeBeginnings
Coming Soon

On Failure and Slow Progress

Most days in research don't feel like a discovery. A short essay on staying motivated when results take months — or years — to appear.

MindsetResilienceProcess
Coming Soon

Balancing Curiosity and Output

How I think about chasing the topics that genuinely fascinate me versus the very real pressure to publish, ship code, and graduate.

CareerCuriosityProductivity

For Aspiring Researchers

Coming Soon

Applying to Graduate School

A timeline, reading list, and breakdown of what each part of a PhD application is actually testing — SOP, recommendation letters, GRE/PGRE, and fit.

Grad SchoolPhDApplicationsSOP
Coming Soon

Finding Research Internships

Where to look for undergraduate research opportunities (REUs, DAAD-RISE, IUSSTF, summer schools), how to time applications, and what makes a strong one.

InternshipsREUSummer Schools
Coming Soon

Cold-Emailing Professors

How to write the first email to a researcher whose work excites you — what to say, what to never say, and how to follow up without being a nuisance.

OutreachNetworkingEmail
Coming Soon

Building Research Collaborations

On finding co-authors, navigating long-distance collaborations, joining open-source astronomy projects, and being someone people want to work with again.

CollaborationNetworkingCommunity
Coming Soon

Writing Your First Paper

How to turn a tangle of code, plots, and half-formed ideas into a paper your collaborators will sign off on. Tools, structure, and submission tips.

WritingPapersLaTeX
Coming Soon

Choosing a Research Topic

Heuristics for spotting topics that are tractable, interesting, and aligned with where you want to be in five years — without getting stuck in someone else's agenda.

StrategyTopicsCareer

Skill Building

Coming Soon

Python for Astrophysics

A learning path through the Python ecosystem every working astronomer relies on: numpy, scipy, astropy, healpy, scikit-learn, and JAX. With small projects to practice each.

PythonAstropyProgramming
Coming Soon

Mastering LaTeX & arXiv

How to set up LaTeX painlessly, write equations that read well, manage references with BibTeX, and submit your first preprint to arXiv without panic.

LaTeXWritingarXivTools
Coming Soon

Reading Research Papers Effectively

A three-pass method for cutting through dense astrophysics papers, taking notes that stick, and knowing when to read deeply versus skim and move on.

ReadingPapersStudy Skills
Coming Soon

Building a Research Portfolio

How to set up a personal site (yes, like this one), structure GitHub repos so people actually want to read them, and prepare clean talks that get remembered.

PortfolioGitHubPersonal Brand
Coming Soon

Machine Learning Foundations

The bare minimum ML you need to do credible work at the intersection of astrophysics and machine learning: linear algebra, optimization, neural nets, and best practices.

MLFoundationsDeep Learning
Coming Soon

Open-Source Astronomy Tools

A curated tour of the software stack working astronomers use day to day: TOPCAT, ds9, CASA, JupyterLab, Snakemake, and how to learn each one fast.

ToolsOpen SourceWorkflow

Study Notes

Mathematics

In Progress
Vector Calculus & Tensor Analysis
Comprehensive coverage of vector operations, tensor algebra, differential geometry, and their applications in physics. Includes covariant derivatives, curvature tensors, and metric tensor manipulations.
VectorsTensorsDifferential GeometryGeneral Relativity
In Progress
Linear Algebra for ML/DL
Matrix operations, eigenvalue decomposition, singular value decomposition (SVD), principal component analysis (PCA), and their applications in machine learning algorithms.
MatricesEigenvaluesSVDMachine Learning
In Progress
Complex Analysis
Complex functions, contour integration, residue theorem, and conformal mapping. Essential for quantum mechanics and advanced physics applications.
Complex NumbersContour IntegrationResiduesQuantum Mechanics
In Progress
Fourier Analysis
Fourier series, Fourier transforms, and their applications in signal processing, cosmological data analysis, and solving partial differential equations.
Fourier SeriesTransformsSignal ProcessingData Analysis

Cosmology

In Progress
ΛCDM Model
Comprehensive overview of the Lambda-Cold Dark Matter model, including Friedmann equations, dark energy, dark matter, and cosmic microwave background physics.
Dark MatterDark EnergyFriedmann EquationsCMB
In Progress
Modified Gravity Theories
Detailed study of modified gravity theories including f(R) gravity, Horndeski theories, and their observational signatures in cosmological surveys.
f(R) GravityHorndeski TheoryModified GravityObservational Tests
In Progress
Power Spectrum Analysis
Power spectrum fundamentals, correlation functions, galaxy clustering, CMB angular power spectra, and cross-correlation analysis methods.
Power SpectrumCorrelation FunctionsGalaxy ClusteringStatistical Methods
In Progress
Observational Cosmology
Overview of current and future cosmological surveys, data analysis techniques, systematic effects, and parameter estimation methods.
LSSTEuclidData AnalysisParameter Estimation

Physics

In Progress
General Relativity
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 EquationsSpacetimeBlack HolesGravitational Waves
In Progress
Quantum Mechanics
Schrödinger equation, quantum operators, uncertainty principle, quantum harmonic oscillator, and applications to atomic physics. Includes computational quantum mechanics methods.
Schrödinger EquationOperatorsUncertainty PrincipleAtomic Physics
In Progress
Statistical Mechanics
Boltzmann distribution, partition functions, phase transitions, critical phenomena, and applications to condensed matter physics and cosmology.
Boltzmann DistributionPartition FunctionsPhase TransitionsCritical Phenomena
In Progress
Electromagnetism
Maxwell's equations, electromagnetic waves, relativistic electrodynamics, and applications to particle accelerators and astrophysical phenomena.
Maxwell EquationsEM WavesRelativistic EDAstrophysics

Miscellaneous

In Progress
Machine Learning Fundamentals
Supervised and unsupervised learning algorithms, neural networks, deep learning architectures, and applications to scientific data analysis and cosmological surveys.
Neural NetworksDeep LearningSupervised LearningData Analysis
In Progress
Scientific Computing
Python programming for scientific applications, numerical methods, data visualization, and computational tools for physics and cosmology research.
PythonNumPySciPyMatplotlib
In Progress
Statistics & Data Analysis
Statistical inference, Bayesian analysis, Markov Chain Monte Carlo methods, and their applications to parameter estimation in cosmology and physics.
Bayesian StatisticsMCMCParameter EstimationStatistical Inference
In Progress
Research Methods
Academic writing techniques, research methodology, collaboration tools, version control with Git, and best practices for scientific research and publication.
Academic WritingResearch MethodsGitCollaboration
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