Additive Combinatorics
From Roth’s theorem and sumsets to entropy methods and Polynomial Freiman–Ruzsa.
Additive Combinatorics
From Roth’s theorem and sumsets to entropy methods and Polynomial Freiman–Ruzsa.
Mathematics Library
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Advanced Stochastic Analysis
Graduate notes on Gaussian analysis, Malliavin calculus and hypoellipticity.
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Advanced Stochastic Analysis
Graduate notes on Gaussian analysis, Malliavin calculus and hypoellipticity.
Algebra + Homotopy = Operad
Explains operads, operadic syzygies and the homotopy transfer theorem through algebraic examples.
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Algebra + Homotopy = Operad
Explains operads, operadic syzygies and the homotopy transfer theorem through algebraic examples.
Algebraic Combinatorics: Walks, Trees, Tableaux, and More
Connects enumerative questions with algebra through walks, trees and tableaux.
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Algebraic Combinatorics: Walks, Trees, Tableaux, and More
Connects enumerative questions with algebra through walks, trees and tableaux.
Algebraic Geometry
A first graduate course centered on abstract algebraic varieties, providing a bridge toward schemes.
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Algebraic Geometry
A first graduate course centered on abstract algebraic varieties, providing a bridge toward schemes.
Algebraic Geometry and Analytic Geometry (GAGA)
The original comparison of coherent algebraic and analytic sheaves on complex projective varieties, including cohomology.
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Algebraic Geometry and Analytic Geometry (GAGA)
The original comparison of coherent algebraic and analytic sheaves on complex projective varieties, including cohomology.比较复射影簇上的代数凝聚层与解析凝聚层及其上同调的原始论文。
Found via — References: Géométrie algébrique et géométrie analytique
Algebraic Geometry over C∞-Rings
Develops the algebraic language underlying smooth and derived differential geometry.
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Algebraic Geometry over C∞-Rings
Develops the algebraic language underlying smooth and derived differential geometry.
Algebraic Number Theory
A standard graduate course with proofs. A natural bridge from fields and Galois theory to arithmetic of number fields.
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Algebraic Number Theory
A standard graduate course with proofs. A natural bridge from fields and Galois theory to arithmetic of number fields.
Algebraic Number Theory
A long course on Dedekind domains, number fields, ramification and local/global arithmetic.
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Algebraic Number Theory
A long course on Dedekind domains, number fields, ramification and local/global arithmetic.
Algebraic Topology
Geometric examples accompany fundamental groups, homology and cohomology. A substantial first graduate text; 'introductory' refers to the field, not to university mathematics.
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Algebraic Topology
Geometric examples accompany fundamental groups, homology and cohomology. A substantial first graduate text; 'introductory' refers to the field, not to university mathematics.
Full-text source checked: 2026-11-03
Found via — References: Algebraic Topology
Almost Complex Structures on Spheres
Explains the obstruction to almost complex structures on spheres through characteristic classes and Bott periodicity.
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Almost Complex Structures on Spheres
Explains the obstruction to almost complex structures on spheres through characteristic classes and Bott periodicity.通过示性类与Bott周期性解释球面上殆复结构的障碍。
Found via — References: Almost Complex Structures on Spheres
An (Algebraic) Introduction to Number Theory
Moves from integer arithmetic to rings, quadratic and cyclotomic examples, factorization, congruences and sums of squares. Later chapters are drafts or outlines.
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An (Algebraic) Introduction to Number Theory
Moves from integer arithmetic to rings, quadratic and cyclotomic examples, factorization, congruences and sums of squares. Later chapters are drafts or outlines.
An Epsilon of Room, I: Real Analysis
Advanced measure theory is connected to Hilbert and Banach spaces, duality, interpolation, distributions, Fourier transforms and Hausdorff dimension.
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An Epsilon of Room, I: Real Analysis
Advanced measure theory is connected to Hilbert and Banach spaces, duality, interpolation, distributions, Fourier transforms and Hausdorff dimension.
An Infinitely Large Napkin
A broad bridge from undergraduate subjects toward first-year graduate ideas. Some planned chapters and exercises are unfinished; it is not a substitute for a full course in each field.
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An Infinitely Large Napkin
A broad bridge from undergraduate subjects toward first-year graduate ideas. Some planned chapters and exercises are unfinished; it is not a substitute for a full course in each field.
An Introduction to Analytic Prime Number Theory (UCLA 254A)
Connects multiplicative number theory and complex-analytic techniques with sieve theory, prime gaps and multiplicative-function methods. The archive includes supplements.
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An Introduction to Analytic Prime Number Theory (UCLA 254A)
Connects multiplicative number theory and complex-analytic techniques with sieve theory, prime gaps and multiplicative-function methods. The archive includes supplements.
An Introduction to Determinants 行列式入门
A book devoted to determinants, including their definitions, identities and methods of calculation. Use selected chapters alongside a linear-algebra course rather than replacing the whole course with determinant…
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An Introduction to Determinants
A book devoted to determinants, including their definitions, identities and methods of calculation. Use selected chapters alongside a linear-algebra course rather than replacing the whole course with determinant techniques.专门讨论行列式的定义、恒等式和计算方法。适合在线性代数课程中按需选读，不必将整门课程变成行列式技巧训练。
An Introduction to Formal Logic
An introduction to propositional and first-order logic with worked proof techniques.
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An Introduction to Formal Logic
An introduction to propositional and first-order logic with worked proof techniques.
An Introduction to Gödel’s Theorems
Explains computability, arithmetization and the incompleteness theorems.
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An Introduction to Gödel’s Theorems
Explains computability, arithmetization and the incompleteness theorems.
An Introduction to Mathematical Optimal Control Theory
Develops deterministic and stochastic control ideas alongside differential equations and variational methods.
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An Introduction to Mathematical Optimal Control Theory
Develops deterministic and stochastic control ideas alongside differential equations and variational methods.
An Introduction to Measure Theory
Develops Lebesgue measure, integration and related convergence theorems. Follow the author’s online-text link for the full manuscript.
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An Introduction to Measure Theory
Develops Lebesgue measure, integration and related convergence theorems. Follow the author’s online-text link for the full manuscript.
An Introduction to Proofs and the Mathematical Vernacular
Uses number systems, polynomials and determinants to practise reading and constructing longer mathematical arguments.
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An Introduction to Proofs and the Mathematical Vernacular
Uses number systems, polynomials and determinants to practise reading and constructing longer mathematical arguments.
An Introduction to Stochastic PDEs
Introduces Gaussian measures, semigroups and stochastic evolution equations.
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An Introduction to Stochastic PDEs
Introduces Gaussian measures, semigroups and stochastic evolution equations.
An Invitation to General Algebra and Universal Constructions
Studies universal constructions, free objects and algebraic structures with categorical language and exercises.
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An Invitation to General Algebra and Universal Constructions
Studies universal constructions, free objects and algebraic structures with categorical language and exercises.
An Untitled Book Project about Symmetric Spectra
Builds symmetric spectra, smash products and stable model structures. This is the complete available unfinished project, not a published edition.
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An Untitled Book Project about Symmetric Spectra
Builds symmetric spectra, smash products and stable model structures. This is the complete available unfinished project, not a published edition.
Analytic Combinatorics
Connects generating functions with complex-analytic asymptotic methods. Use after elementary enumeration and a first complex-analysis course.
Details and sources
Analytic Combinatorics
Connects generating functions with complex-analytic asymptotic methods. Use after elementary enumeration and a first complex-analysis course.