Math, applied to things
people already care about

No fabricated data

Every dataset links to a public source you can check yourself. When data is missing, we say so rather than filling the gap with something invented.

Documented methodology

Every investigation includes the method, the data dictionary, and enough detail that someone with the source data could redo the analysis from scratch.

Explicit limitations

Every investigation has a limitations section. Good analysis is honest about what the data does not show, and null results get published here too.

Applied Mathematics

Differential equations, linear algebra, real analysis, and discrete mathematics as the underlying language of quantitative reasoning.

• Ordinary & partial differential equations
• Linear algebra & matrix methods
• Optimization theory
• Real analysis

Data Science

Statistical methods for extracting knowledge from structured and unstructured data at scale, with rigorous attention to uncertainty quantification.

• Statistical estimation & inference
• Machine learning methodology
• Regression & classification
• Cross-validation & model selection

Signal Processing

The mathematics of transforming, analyzing, and extracting information from signals, from audio waveforms to financial time series.

• Fourier & wavelet transforms
• Spectral analysis
• Filter design
• Time-frequency representations

Optimization

Finding the best solution from a set of feasible alternatives, subject to constraints: the core mathematical framework for decision making.

• Linear & quadratic programming
• Convex optimization
• Stochastic optimization
• Game theory

Statistical Modeling

Building probabilistic descriptions of data-generating processes, quantifying uncertainty, and testing hypotheses rigorously.

• Bayesian & frequentist inference
• Generalized linear models
• Time series modeling
• Causal inference

Machine Learning

Algorithmic methods that allow systems to learn from data, applied at Pattern with attention to interpretability and validation.

• Supervised & unsupervised learning
• Neural networks
• Ensemble methods
• Feature engineering