Mathematics
The mathematics section exists for foundations that help technical work survive contact with real problems: probability, optimization, graphs, stochastic processes, geometry and modelling.
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- Why Math and Statistics Foundations Matter in Data Science
- Fourier Analysis for Data Science
- Information Geometry for Data Science
- Discrete Mathematics for Data Science
Applied foundations
Information Geometry for Data Science: Curvature, Models, and Learning
Information geometry treats probability models as geometric objects, making it easier to reason about distance, curvature, uncertainty, and learning.
Discrete Mathematics for Data Science: States, Constraints, and Algorithms
Discrete mathematics is the part of mathematics that explains how data systems make decisions, count possibilities, represent relationships, and enforce constraints.
Bayesian Decision Theory for Data Science: From Uncertainty to Action
Bayesian decision theory connects statistical uncertainty to action by asking not only what is likely, but what decision is best under uncertainty.
Fourier Analysis for Data Science: From Signals to Features
Fourier analysis is more than a signal-processing trick. It is a way to ask which cycles, rhythms, and scales explain variation in data.
The Dangerous Push Toward Practical Mathematics: Why Pure Research Must Remain Protected
The pressure to justify mathematics by immediate usefulness misunderstands how mathematical progress works. Pure research needs protection precisely because its value is often invisible at the moment it is created.
Mathematics and Electronic Music: The Symphony of Numbers
Discover how mathematics influences electronic music creation through sound synthesis, rhythm, and algorithmic composition. Explore the role of numbers in shaping digital signal processing and generative music.
The Undervalued Power of Mathematics in Modern Society
Explore how mathematics shapes modern society across fields like technology, education, and problem-solving. This article delves into the often overlooked impact of mathematics on innovation and societal progress.
Central Limit Theorems: A Comprehensive Overview
The Central Limit Theorem (CLT) is one of the cornerstone results in probability theory and statistics. It provides a foundational understanding of how the distribution of sums of random variables behaves. At its core, the CLT asserts that under certain conditions, the sum of a large number of ra...
Pseudo-Supervised Outlier Detection
1. Introduction
Exploring Outliers in Data Analysis: Advanced Concepts and Techniques
Outliers are data points that significantly deviate from the rest of the observations in a dataset. They can arise from various sources such as measurement errors, data entry mistakes, or inherent variability in the data. While outliers can provide valuable insights, they can also distort statist...
The Sunrise Problem: A Bayesian vs Frequentist Perspective
Sunrise in Lisbon Harbour, December 2020
Mathematical modelling
Optimization, stochastic processes, graph theory and numerical methods.
Discrete Mathematics for Data Science: States, Constraints, and Algorithms
Discrete mathematics is the part of mathematics that explains how data systems make decisions, count possibilities, represent relationships, and enforce constraints.
Why Data Scientists Need Math and Statistics
Mastering mathematics and statistics is essential for understanding data science algorithms and avoiding common pitfalls when building models.
Exploring Kernel Density Estimation: A Powerful Tool for Data Analysis
Kernel Density Estimation (KDE) is a non-parametric technique offering flexibility in modeling complex data distributions, aiding in visualization, density estimation, and model selection.
The Rich Get Richer: The Physics of Wealth Distribution and Inequality
The rich are getting richer while the poor remain poor. This article dives into the physics-based models that explain the inherent inequality in wealth distribution.
Emmy Noether: Revolutionizing Abstract Algebra and Theoretical Physics
Emmy Noether’s work in algebra and physics established her as a pioneer, particularly through her groundbreaking theorem linking symmetries to conservation laws.
Mary Somerville: Pioneer in Astronomy and Mathematical Physics
Mary Somerville’s work in astronomy and mathematical physics earned her recognition as one of the first female scientists, making complex scientific concepts accessible.
Understanding the Connection Between Correlation, Covariance, and Standard Deviation
This article explores the deep connections between correlation, covariance, and standard deviation, three fundamental concepts in statistics and data science that quantify relationships and variability in data.
Mary Jackson: NASA’s First Black Female Engineer and Advocate for Diversity
Mary Jackson was NASA’s first Black female engineer and a trailblazer in aerospace engineering. Her dedication to diversity and inclusion made her an advocate for opportunities for women and minorities in STEM.
Understanding Outlier Detection: A Deep Dive into Distance Metric Learning
Explore the intricacies of outlier detection using distance metrics and metric learning techniques. This article delves into methods such as Random Forests and distance metric learning to improve outlier detection accuracy.
The Undervalued Power of Mathematics in Modern Society
Explore how mathematics shapes modern society across fields like technology, education, and problem-solving. This article delves into the often overlooked impact of mathematics on innovation and societal progress.