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Sources & Textbooks

Books and video series used across the visualization library

Video Series

Essence of Linear Algebra
3Blue1Brown (Grant Sanderson)
YouTube — 16 videos
Dot Product Cross Product Determinant Inverse Eigenvectors Change of Basis
Primary source for the linear algebra section. Builds geometric intuition first — transformations, area scaling, eigendirections — before algebraic formalism. Pairs with Singh for rigour.
Differential Equations
3Blue1Brown (Grant Sanderson)
YouTube — 8 videos
Heat Equation Fourier Series
Source for the heat equation lesson. The series covers ODEs, Fourier analysis, and the connection between eigenfunctions and boundary-value problems.

Textbooks — Engineering & Physics

Introduction to Space Dynamics
William T. Thomson
Dover Publications
Kinematics Circular Motion Euler Angles Particle Dynamics Orbital Mechanics Hohmann Transfer Gyrodynamics
Primary source for kinematics, particle dynamics, orbital mechanics, and gyrodynamics. Sections 4.7 (satellite orbits, Binet's substitution) and 4.9 (orbit from initial conditions, χ parameter, Fig 4.9-2) map directly to lessons.

Online Resources

Probability — Course Notes
Richard Weber
University of Cambridge, Statistical Laboratory · 2015
Probability Random Variables Distributions
Part IA course notes for first-year mathematicians at Cambridge. Self-contained lecture units covering classical probability, distributions, random walks, and generating functions. Includes examples sheets and a table of distributions.

statslab.cam.ac.uk/~rrw1/prob
Probability — Example Sheets
Cambridge DPMMS
Part IA, 2025–2026
Probability Problem Sets
Official Part IA Probability example sheets from the Department of Pure Mathematics and Mathematical Statistics. Four sheets per year; archive goes back to 2007.

dpmms.cam.ac.uk/study/IA/Probability

Textbooks — Mathematics

Linear Algebra: Step by Step
Kuldeep Singh
Oxford University Press, 2013
Vectors Dot Product Cross Product Linear Algebra
Supplementary reference for the linear algebra section alongside 3Blue1Brown. Provides formal algebraic treatment alongside 3B1B's geometric approach.
Ordinary Differential Equations
V.I. Arnold, trans. Silverman
MIT Press, 1978
ODE Overview Slope Fields Pendulum Phase Portraits
Source for the ODE overview and pendulum lessons. Arnold's geometric/qualitative approach — phase portraits, slope fields, separatrices — shapes how the visualizations are framed.
PHASE 4
Understanding Analysis
Stephen Abbott
Springer, Undergraduate Texts in Mathematics · 2nd ed.
Real Analysis Sequences Continuity Riemann Integral
Real analysis foundation before Armstrong's topology. Abbott's §3 (topology of ℝ — open sets, compactness, connectedness) directly prepares for Armstrong's general treatment. Oct–Dec 2026.
PHASE 5
Basic Topology
M.A. Armstrong
Springer, Undergraduate Texts in Mathematics
Topology Homeomorphisms Fundamental Group Surfaces
Planned source for the topology section. Covers point-set topology through to algebraic topology — connectedness, compactness, classification of surfaces, simplicial homology. Jan–Apr 2027.
PHASE 6
Introduction to Probability
Joseph K. Blitzstein & Jessica Hwang
CRC Press / Chapman & Hall, 2014
Probability Random Variables Distributions Markov Chains
Primary probability source. Developed from Harvard Stat 110 lectures (free on YouTube). Covers counting, Bayes, distributions, expectation, limit theorems, and Markov chains. Apr 2027+.

PDF →

Textbooks — Signal Processing & Navigation

PHASE 7
Discrete-Time Signal Processing
Alan V. Oppenheim & Ronald W. Schafer
Prentice Hall · 3rd ed.
Sampling Convolution Z-Transform FFT
Standard reference for discrete-time signals and systems. Covers LTI systems, Z-transform, DFT, FFT, and filter design — the mathematical machinery underlying all digital signal processing.
PHASE 7
Statistical Signal Processing (2 vols.)
Steven M. Kay
Prentice Hall
Estimation Theory Detection Theory Kalman Filter MVUE
The definitive reference for statistical signal processing. Vol. 1 covers estimation (MVUE, MLE, Cramér–Rao, Kalman filtering). Vol. 2 covers detection theory. Central to SSA and PNT work.
PHASE 7
Understanding GPS/GNSS: Principles and Applications
Elliott Kaplan & Christopher Hegarty
Artech House · 3rd ed.
GNSS PNT Spoofing Jamming Navigation
Applied reference for GPS and GNSS systems. Covers signal structure, receiver architecture, error sources, and resilience to spoofing and jamming — directly relevant to the PNT resilience problem space.

Textbooks — Machine Learning & AI

PHASE 8
Understanding Deep Learning
Simon J. D. Prince
MIT Press, 2024 · free PDF at udlbook.github.io
Neural Networks Backpropagation Transformers Diffusion Models VAEs GANs Reinforcement Learning
Primary source for the deep learning phase. Builds from shallow networks through to modern generative models and RLHF. Assumes the linear algebra, probability, and calculus developed in earlier phases. Pairs with the visualizations planned for Phase 8.