Mathematics
Notes on mathematical concepts — from calculus to graph theory.
Figure: Leonhard Euler's notation and results appear across analysis, graph theory, and number theory. Image: Wikimedia Commons, Jakob Emanuel Handmann, public domain.
Figure: Carl Friedrich Gauss is central to number theory, linear algebra, statistics, and numerical methods. Image: Wikimedia Commons, Gottlieb Biermann after Christian Albrecht Jensen, public domain.
Figure: The Mandelbrot set turns iteration of a simple complex quadratic map into intricate geometry. Image: Wikimedia Commons, Einottaja, attribution required.
Topics
- Calculus — limits, derivatives, integrals, series
- Linear Algebra — vectors, matrices, eigenvalues
- Engineering Mathematics — ODEs, PDEs, transforms, complex analysis
- Statistics — distributions, hypothesis testing, regression
- Probability — Lane-derived introduction; sample spaces, distributions
- Probability and Random Variables — rigorous theory from MIT 18.440 (Sheffield)
- Discrete Mathematics — logic, combinatorics, graphs, recurrences
- Numerical Analysis — interpolation, integration, ODE solvers, stability
- Graph Theory — connectivity, trees, planarity, coloring
How these notes are organized
Each section starts with an intro page that gives the big picture and lists subtopics. Subtopic pages have:
- Definitions stated formally
- Intuition in plain English
- Worked examples with derivations
- Code samples where computation matters