Commutative
Algebra1969
Introduction to Commutative Algebra
From tensor products and localization to primary decomposition, integrality, and Artinian structure. Selected exercises anchor the return.
A reading shelf
Books I return to, ideas I work through, and references that lead to the next question. Reading is recorded by its actual scope.
Targeted second pass
Basic
Category
Theory2014
Basic Category Theory
Naturality, adjunctions, units and counits, comma categories; returning to representability.
Reading scope
Recent saved discussions cover §§2.2–2.3. Chapter 4 is the next entry.Monomial
IdealsLecture notes
Eight Lectures on Monomial Ideals
Multigrading, Stanley–Reisner rings, syzygies, and torus-fixed ideals.
Reading scope
Lecture II §2.1. Koszul and the general Hochster proof remain study targets.Algebraic
Topology2002
Algebraic Topology
From van Kampen and the fundamental group to Δ-complexes, torus homology, and singular chains.
Reading scope
Saved material reaches early Chapter 2; no claim of a complete book reading.Algebraic
Geometry2021–22 notes
Algebraic Geometry
Affine and projective geometry, regular functions, dimension, sheaves, and stalks alongside a lecture course.
Reading scope
Used selectively to locate proofs and geometric examples.Fermat’s
DreamNumber Theory I
Number Theory 1: Fermat’s Dream
Pell equations, quadratic rings, p-adic ideas, Hilbert symbols, and the arithmetic motivation for new structures.
Reading scope
Chapter 2 surveyed; Chapter 3 read selectively; an entry into Chapter 4 is saved.Introductory
CombinatoricsFifth edition
Introductory Combinatorics
Counting constructions, permutations, orders, generating functions, and proof mechanisms.
Reading scope
Möbius inversion is saved for later study; a saved explanation is not a completion claim.Category Theory
in Context2016
Category Theory in Context
A companion for the connections between representability, limits, and adjunctions.
Reading scope
Part of a reading plan, not recorded as a completed text.Read original PDF
Author’s current revision; pagination may differ from the reading copy.
Local
Algebra2000
Local Algebra
Noetherian polynomial and formal power series rings, read alongside the Hilbert basis theorem in Atiyah–Macdonald.
Reading scope
Saved reading includes Chapter I §4 and its connection to A–M Theorem 7.5. It does not establish a complete reading of Local Algebra.Categories for
the Working
MathematicianGTM 5
Categories for the Working Mathematician
A reference for standard definitions, theorem formulations, and the classical organization of category theory alongside Leinster and Riehl.
Reading scope
Recorded as a reference route, not a completed or cover-to-cover reading. The original-book link opens the publisher record.Combinatorial
Commutative
AlgebraGTM 227
Combinatorial Commutative Algebra
The systematic companion to monomial ideals, multigrading, simplicial complexes, and resolutions; a separate book from Miller–Perkinson’s Eight Lectures.
Reading scope
The local material is the preface, contents and errata. The saved active reading is Eight Lectures; this is not a full-text completion claim.Courses & lecture materials
Course materials are recorded separately from books, with their actual reading scope.
Algebraic geometry lecture course
Saved progress reaches Episode 018: regular functions, sheaves and stalks, with Gathmann as a companion. The lecturer and exact public URL remain to be identified.
Public source link to be addedDI31011 · Analysis
Metrics, norms, closure, Cauchy sequences, completeness, and contractions; course notes and Labs 1–2.
Public source link to be addedDI22008 · Linear algebra
Vector spaces, row reduction, inner products, eigenvalues, and diagonalisation.
Public source link to be addedMathematics 2B · Multivariable calculus
Partial derivatives, the chain rule, constrained extrema, double integrals, and change of variables.
Public source link to be addedDI22013 · Statistics and probability
Sampling distributions, statistical inference, estimation, and single- and two-sample tests.
Public source link to be addedThe covers are original typographic illustrations. Labels distinguish active reading, selected chapters, revisiting, and references; a book on this shelf does not imply that every chapter or exercise is complete.