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Research · my bookshelf
My bookshelf
What's actually open on the desk right now, what's next, and the wider shelf I read toward. Notes from these turn up in Writing — and the reading series below are the ones I'm writing through a chapter at a time.
Jump to: reading now · series · the wider shelf · how I study these →
Reading now · 28
Reading nowTaylor's Theorem: A Selection of Classic Mathematical Articles and Exercises · anthology (Algebra)Working the exercises by hand — scans in the Notebook. the series →
Reading nowNine Algorithms That Changed the Future · John MacCormickA chapter-a-day read-through — notes in Writing. the series →
Reading nowArtificial Intelligence: A Modern Approach · Russell & NorvigThe map of the whole field.
Reading nowModern Multivariate Statistical Techniques · IzenmanGoing through all 17 chapters — each tied to a demo, explore, or client use case. the series →
Reading nowAlgebraic Foundations for Applied Topology and Data Analysis · SchenckThe algebra under TDA.
Reading nowMathematical Principles of Topological and Geometric Data Analysis · Joharinad & JostGeometry-first TDA.
Reading nowIntroduction to Topological Manifolds · LeeGround floor for manifolds.
Reading nowApplied Linear Statistical Models · Kutner, Nachtsheim, Neter & LiRegression, done thoroughly (5th ed).
Reading nowComputational Topology · Edelsbrunner & HarerThe engine under persistent homology.
Reading nowInformation Theory · Polyanskiy & WuFrom coding to learning.
Reading nowThe Cauchy–Schwarz Master Class · J. M. SteeleA whole method of proof — its own series. the series →
Reading nowAn Introduction to Infinite Products · Little, Teo & van BruntLearn-and-teach — its own series. the series →
Reading nowNaive Lie Theory · John StillwellLie groups, gently.
Reading nowAbstract Algebra · JudsonOpen-source, 2020 edition.
Reading nowLinear Algebra Done Right · AxlerDeterminants last (4th ed).
Reading nowJohn E. Freund's Mathematical Statistics with Applications · Miller & MillerTheory with worked applications (8th ed).
Reading nowIntroduction to Mathematical Statistics · Hogg, McKean & CraigThe rigorous core (7th ed).
Reading nowThe Web of Modularity · Ken OnoModular forms & q-series.
Reading nowBasic Hypergeometric Series and Applications · Nathan FineThe hypergeometric backbone.
Reading nowProblems in the Theory of Modular Forms · Murty, Dewar & GravesModular forms by problem. the series →
Reading nowChallenging Mathematical Problems with Elementary Solutions, Vol. I & II · Yaglom & YaglomElementary but deep. the series →
Reading now(Almost) Impossible Integrals, Sums, and Series · VăleanThe hard ones, solved. the series →
Reading nowMore (Almost) Impossible Integrals, Sums, and Series · VăleanAnd harder still. the series →
Reading nowPhenomenology and QBism · Berghofer & WiltscheNew approaches to quantum mechanics — feeds P2.
Reading nowCounterexamples in Analysis · Gelbaum & OlmstedWhere intuition breaks. the series →
Reading nowCounterexamples in Topology · Steen & SeebachThe zoo of strange spaces. the series →
Reading nowCounterexamples in Probability · StoyanovWhen the obvious is false. the series →
Reading nowCounterexamples in Measure and Integration · Schilling & KühnThe measure-theoretic traps. the series →
Next up · 2
Next upThe Arithmetic of Elliptic Curves · SilvermanThe spine — slow and forever.
Next upA First Course in Modular Forms · Diamond & ShurmanAfter the spine.
On deck · 6
On deckFrom Classical L-Functions to Modern Reciprocity Laws · Claus SørensenThe Langlands reciprocity thread, up close.
On deckAn Interactive Introduction to Knot Theory · Johnson & HenrichKnots, hands-on.
On deckAn Introduction to Knot Theory · LickorishThe graduate-level treatment.
On deckBayes' Rule with R · James V. StoneProbability vs likelihood, priors, and Bayes from the ground up — the reference for a Bayesian deep dive.
On deckBayesian Analysis with Python · Osvaldo MartinPractical Bayes (PyMC) — pairs with the Pyodide compute lab.
On deckHecke's Theory of Modular Forms and Dirichlet Series · Berndt & KnoppHecke's correspondence — modular forms ↔ Dirichlet series by Mellin transform, and the converse theorem. The analytic spine under the Eigenbook.
Reading series
Books I'm reading and writing — a chapter at a time, my notes plus the broader context.
Nine Algorithms That Changed the Future →
in progressJohn MacCormick · A chapter-a-day read-through of MacCormick's tour of the algorithms running quietly under everyday computing — my notes on each chapter, plus the part a 2011 book can't: where each algorithm class came from, and where it has gone since.
Modern Multivariate Statistical Techniques →
plannedAlan Julian Izenman · The whole multivariate toolkit as one map. Izenman's 17 chapters, regrouped from the book's order into the strata a practitioner works in — foundations, regression, classification, ensembles, dimension reduction, latent structure — each lit to where the idea already lives here: a live demo, a research explore, a pillar, or a lab. A chapter at a time; the map fills in as I read.
The Cauchy–Schwarz Master Class →
plannedJ. M. Steele · Learning one inequality so deeply it becomes a method — Steele's master class on Cauchy–Schwarz and the craft of the mathematical inequality. A planned read-and-teach series.
An Introduction to Infinite Products →
plannedLittle, Teo & van Brunt · Products instead of sums — learning and teaching the theory of infinite products, from convergence to the product formulas behind the sine, the Gamma function, and the zeta function. A planned read-and-teach series.
Philosophy for math & decisions →
plannedvarious traditions · A slow series on the traditions I lean on — read both for living well and for thinking clearly under uncertainty, tying contemplative practice to how we actually decide. A planned read-and-teach series.
Problem books — solving for understanding →
plannedvarious · Working problems is how the ideas become mine. A running series of solved problems — the elegant, the brutal, and the ones that teach a whole method — drawn from the problem-book shelf.
Counterexamples — where intuition breaks →
plannedvarious · The fastest way to truly understand a theorem is to meet the object that almost satisfies it. A running series on the great counterexamples — one strange object at a time, and the plausible-but-false claim it kills. The shelves have dozens.
Taylor's Theorem — by hand →
plannedanthology (Algebra) · Working a classic anthology on Taylor's theorem the long way: from binomial coefficients and the metric/topology axioms up to the Taylor series of sin, cos, and exp, then out to q-series and Hensel's number-field/function-field analogy. The handwritten pages live in the Notebook; the polished derivations land on /derivations.
The wider shelf — by area
The reach beyond what I'm actively reading, by area. Some of it is years out; keeping it on one shelf is how the threads stay connected.
Elliptic curves & modular forms — the thread
Rational Points on Elliptic Curves
Silverman & Tate · the gentle door in
The Web of Modularity
Ken Ono · modular forms & q-series
From Classical L-Functions to Modern Reciprocity Laws
Claus Sørensen · the Langlands reciprocity thread
Modular forms & Ramanujan
The Eigenbook
Bellaïche · p-adic families of eigenforms
Non-vanishing of L-Functions and Applications
Murty & Murty · analytic L-function methods
Hecke's Theory of Modular Forms and Dirichlet Series
Berndt & Knopp · the Hecke correspondence
Development of Elliptic Functions According to Ramanujan
Venkatachaliengar · Ramanujan's elliptic functions
Harmonic Analysis on the Real Line
Fourier groundwork
q-series & hypergeometric
Topics and Methods in q-Series
McLaughlin · the q-series toolkit
The Power of q
Hirschhorn · q-series identities
Basic Hypergeometric Series and Applications
Nathan Fine · the hypergeometric backbone
p-adic analysis
p-adic Numbers, p-adic Analysis, and Zeta-Functions
Koblitz · the standard entry
Unreal Analysis
Pollack · a friendly first taste of the p-adics
p-adic Numbers
Gouvêa · a friendly introduction (3rd ed)
Formally p-adic Fields
Prestel & Roquette · the model-theoretic angle
p-adic Banach Space Representations
Ban · representation theory
The p-adic Simpson Correspondence
Abbes & Gros · toward the frontier
Harmonic Analysis on Reductive p-adic Groups
Harish-Chandra; Bushnell & Fröhlich · local representation theory
Riemann, complex & the zeta function
Riemann's Zeta Function
Edwards · the RH and its history
Complex Variables
Flanigan · a working introduction
Complex Analysis: A Self-Study Guide
Murphy · the self-study path
A Study of Riemann's 1859 Paper
Murphy · the source, read closely
A Study of Riemann's Zeta Function
Murphy · ζ, in depth
In Pursuit of Zeta-3
Nahin · the odd zeta values and their mysteries
Complex Integration: A Compendium of Smart and Little-Known Techniques
Gordon · evaluating integrals & sums
Inside Interesting Integrals
Nahin · integration as a sport
Prime Obsession
Derbyshire · the human story of the RH
Analysis
A Course of Modern Analysis
Whittaker & Watson · the classic on special functions
Theory of Functions
Knopp · complex function theory
Probability Theory
Laha & Rohatgi · measure-theoretic probability
Algebra & algebraic geometry
Abstract Algebra
Judson · an open first pass
Linear Algebra Done Right
Axler · determinants last
Algebraic Number Theory
Lang · the classical reference
Ideals, Varieties, and Algorithms
Cox, Little & O'Shea · computational algebraic geometry
Naive Lie Theory
Stillwell · Lie groups, gently
Algebraic Geometry I & II
Görtz & Wedhorn · schemes & cohomology
Algebraic Geometry
Hartshorne · the language of Langlands & BSD
Topology & geometry
Computational Topology
Edelsbrunner & Harer · the engine under TDA
Algebraic Topology
Hatcher · the canonical text
Introduction to Topology
Gamelin & Greene · point-set foundations
Introduction to Topological Manifolds
Lee · ground floor
Introduction to Smooth Manifolds
Lee · the language of modern geometry
Introduction to Riemannian Manifolds
Lee · curvature & geometry
Manifolds, Sheaves, and Cohomology
Wedhorn · the sheaf-theoretic bridge
Visual Complex Analysis
Needham · geometry you can see
Visual Differential Geometry and Forms
Needham · curvature, visually
Algebraic Foundations for Applied Topology and Data Analysis
Schenck · the applied angle
Mathematical Principles of Topological and Geometric Data Analysis
Joharinad & Jost · the applied angle
Category theory & foundations
Category Theory in Context
Riehl · the working view
Foundations of Geometry
Hilbert · the axiomatic turn
Proofs & method
How to Prove It
Velleman · the grammar of proof
Proofs: A Long-Form Mathematics Textbook
Cummings · proof as a way of thinking
Problem books
Problems in the Theory of Modular Forms
Murty, Dewar & Graves · modular forms by problem
Challenging Mathematical Problems with Elementary Solutions, Vol. I & II
Yaglom & Yaglom · elementary but deep
(Almost) Impossible Integrals, Sums, and Series
Vălean · the hard ones, solved
More (Almost) Impossible Integrals, Sums, and Series
Vălean · and harder still
Counterexamples
Counterexamples in Analysis
Gelbaum & Olmsted · where intuition breaks
Counterexamples in Topology
Steen & Seebach · the zoo of strange spaces
Counterexamples in Probability
Stoyanov · when the obvious is false
Counterexamples in Measure and Integration
Schilling & Kühn · the measure-theoretic traps
Artificial intelligence & computation
Artificial Intelligence: A Modern Approach
Russell & Norvig · the map of the field
Algorithms for Optimization
Kochenderfer & Wheeler (MIT) · methods I actually reach for
Concrete Mathematics
Graham, Knuth & Patashnik · the CS–math bridge
Information Theory
Polyanskiy & Wu · from coding to learning
Quantum & mathematical physics
Quantum Theory for Mathematicians
Hall · QM in the right language
Topological Quantum
Simon · anyons & topological phases
Statistics & inference
Modern Multivariate Statistical Techniques
Izenman · the multivariate toolkit
Applied Linear Statistical Models
Kutner, Nachtsheim, Neter & Li · regression, done thoroughly
Introduction to Mathematical Statistics
Hogg, McKean & Craig · the rigorous core
John E. Freund's Mathematical Statistics with Applications
Miller & Miller · theory with worked applications
Robust Estimation & Hypothesis Testing
for when the model is wrong
Numerical analysis
Chebyshev & Fourier Spectral Methods
Boyd · high-accuracy computation
Algorithms for Optimization
Kochenderfer & Wheeler (MIT) · iterative methods in Julia
History & how mathematicians think
The Gray trilogy — Real & Complex · Change & Variations · Abstract Algebra
Jeremy Gray · mathematics across three eras
How Mathematicians Think
Byers · ambiguity as a feature
How to Solve It
Pólya · the heuristics bible
A Brief History of Mathematical Thought
Heaton · the short tour