The Number

Mathematics

Study books with worked problems: calculus, algebra, probability, proof. Open the shelf →

Written by Rajesh Ranjan Mahapatra

• Analysis from First PrinciplesFrom the Real Numbers to the Calculus of Learning Machines
• Calculus from First PrinciplesLimits, Change, Accumulation and the Mathematics of Learning
• Chance, Data and InferenceProbability, Statistics and Random Processes from First Principles to the Frontier
• Counting, Structure and ChanceCombinatorics from first principles
• Fields and FlowsVector Calculus from First Principles
• Linear Algebra from First PrinciplesSpaces, Operators, Matrix Analysis and the Mathematics of Learning
• Mathematics for Machine LearningA visual study book
• Number Theory from First PrinciplesFrom divisibility and primes to the research frontier
• Probability from First PrinciplesIntuition, Computation, and the Frontier
• StructuresModern Algebra from First Principles
• The Logic of ChanceProbability with Intuition, Proof and Simulation
• The Mathematics of Artificial Intelligence from First PrinciplesFrom School Algebra to the Frontier of Machine Learning and Large Language Models
• The Shape of LinearityPython companion
• The Shape of ProofMathematical reasoning through objects, pictures and arguments
• Visual Linear AlgebraFirst principles and Python

Essays

4 essays, newest first where the site knows the date.

• Handoffs, Escalations and the Geometry of Shared Work | Rajesh MahapatraResearch essaysA practical guide to choosing transfers, typed relays, parallel work, reciprocal workspaces and consequence-led escalation for shared human
• Measuring Transformation Without Counting Deployments | Rajesh MahapatraResearch essaysA six-receipt transformation evidence spine that separates deployment activity from structural, behavioural, flow, outcome, capture and resi
• Orchestration Across Deterministic and Probabilistic Steps | Rajesh MahapatraResearch essays
• Service Levels for Probabilistic Systems | Rajesh MahapatraResearch essaysAn executive method for defining AI service levels across outcome quality, uncertainty, human capacity, tails, controls, recovery and change

Research papers

6 papers from the research programmes.

• Calculus, chain rules and credit assignment
• Choosing agent topology from task structureA practical method for compiling hierarchy, market, debate, swarm and pipeline agent topologies from task dependencies and authority boundar
• Counting and combinatorial explosionWhy small independent choices create search spaces that defeat enumeration, and how pruning, bounds, symmetry, state merging and approximati
• Embeddings and latent geometryA first-principles guide to when useful latent structure emerges, why probe accuracy can overstate mechanism, and how to test causal use wit
• Networks, topology and collective dynamicsWhy identical nodes can produce different collective behaviour when only their connections change, with an executable rewiring and synchroni
• Probability and Bayesian model comparisonA first-principles guide to Bayesian model comparison, Bayes factors, marginal likelihood, predictive checking and a rival-first evidence co

Insight Editions

16 study editions with covers, PDFs and EPUBs. All editions →

• The Drunkard's WalkLeonard Mlodinow
• Euclid's WindowLeonard Mlodinow
• The Lady Tasting TeaDavid Salsburg
• The Theory That Would Not DieSharon Bertsch McGrayne
• Hands-On Machine Learning with Scikit-Learn and PyTorchAurélien Géron
• The Cambridge Companion to Bertrand RussellNicholas Griffin (ed.)
• Solar LotteryPhilip K. Dick
• Metamagical ThemasDouglas R. Hofstadter
• Gödel, Escher, BachDouglas R. Hofstadter
• I Am a Strange LoopDouglas R. Hofstadter
• The Road to RealityRoger Penrose
• The Emperor's New MindRoger Penrose
• A World Without TimePalle Yourgrau
• Gödel Meets EinsteinPalle Yourgrau
• Kurt Gödel: Collected Works, Volume IKurt Gödel
• Kurt Gödel: Collected Works, Volume IIKurt Gödel