Homotopical Algebraic Geometry I: Topos Theory
Constructs homotopical sites, stacks and topoi using model categories.
Homotopical Algebraic Geometry I: Topos Theory
Constructs homotopical sites, stacks and topoi using model categories.
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Homotopical Algebraic Geometry II: Geometric Stacks and Applications
Develops geometric derived stacks and applications to moduli. Distinct from the foundational first volume.
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Homotopical Algebraic Geometry II: Geometric Stacks and Applications
Develops geometric derived stacks and applications to moduli. Distinct from the foundational first volume.
Homotopical and Homological Algebra 同伦代数与同调代数
Seminar notes motivated by similarities between algebraic topology and homological algebra, leading toward infinity-categorical language and localization.
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Homotopical and Homological Algebra
Seminar notes motivated by similarities between algebraic topology and homological algebra, leading toward infinity-categorical language and localization.从代数拓扑与同调代数中的相似现象出发，引入局部化及无穷范畴语言的讨论班讲义。
Homotopy Type Theory: Univalent Foundations of Mathematics
Develops univalent foundations through dependent type theory and homotopical ideas.
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Homotopy Type Theory: Univalent Foundations of Mathematics
Develops univalent foundations through dependent type theory and homotopical ideas.
Incompleteness and Computability
Covers recursive functions, arithmetization and Gödel's theorems. Best read after a first metalogic course, not as an introduction to proofs.
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Incompleteness and Computability
Covers recursive functions, arithmetization and Gödel's theorems. Best read after a first metalogic course, not as an introduction to proofs.
Integral p-adic Hodge Theory
Develops integral comparison constructions using perfectoid methods.
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Integral p-adic Hodge Theory
Develops integral comparison constructions using perfectoid methods.
Introduction to A-infinity Algebras and Modules
Introduces A-infinity structures, modules and their derived categories through a compact exposition.
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Introduction to A-infinity Algebras and Modules
Introduces A-infinity structures, modules and their derived categories through a compact exposition.
Introduction to Abstract Mathematics
English title: Introduction to Abstract Mathematics. Builds a foundation in propositional and predicate logic, sets, functions, orders and induction, with exercises and challenges.
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Introduction to Abstract Mathematics
English title: Introduction to Abstract Mathematics. Builds a foundation in propositional and predicate logic, sets, functions, orders and induction, with exercises and challenges.
Introduction to Analysis in One Variable
Constructs the number systems and develops metric-space reasoning, continuity, rigorous calculus and approximation.
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Introduction to Analysis in One Variable
Constructs the number systems and develops metric-space reasoning, continuity, rigorous calculus and approximation.
Introduction to Analysis in Several Variables (Advanced Calculus)
Develops rigorous multivariable differentiation and integration, differential forms, Stokes' theorem and Fourier analysis.
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Introduction to Analysis in Several Variables (Advanced Calculus)
Develops rigorous multivariable differentiation and integration, differential forms, Stokes' theorem and Fourier analysis.
Introduction to Bernoulli Percolation
An exercise-based introduction to phase transitions, correlation inequalities and critical planar percolation.
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Introduction to Bernoulli Percolation
An exercise-based introduction to phase transitions, correlation inequalities and critical planar percolation.
Introduction to Complex Analysis
A full complex-analysis course extending from holomorphic functions and residues to conformal geometry, elliptic functions and complex differential equations.
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Introduction to Complex Analysis
A full complex-analysis course extending from holomorphic functions and residues to conformal geometry, elliptic functions and complex differential equations.
Introduction to Functional Analysis (18.102)
A course-length development of Banach spaces, Lebesgue integration, Hilbert spaces and applications. The author notes ongoing revisions; useful before more specialized graduate functional analysis.
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Introduction to Functional Analysis (18.102)
A course-length development of Banach spaces, Lebesgue integration, Hilbert spaces and applications. The author notes ongoing revisions; useful before more specialized graduate functional analysis.
Introduction to Homotopy Type Theory
Builds dependent type theory and univalent foundations from basic rules, with exercises and mathematical constructions.
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Introduction to Homotopy Type Theory
Builds dependent type theory and univalent foundations from basic rules, with exercises and mathematical constructions.
Introduction to Microlocal Analysis
Develops pseudodifferential calculi, microlocalization and boundary/scattering methods. This is the available developing manuscript, not a finished textbook.
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Introduction to Microlocal Analysis
Develops pseudodifferential calculi, microlocalization and boundary/scattering methods. This is the available developing manuscript, not a finished textbook.
Introduction to Microlocal Analysis
Fourier and Sobolev tools lead to Littlewood–Paley theory, pseudodifferential calculus, propagation and paradifferential operators.
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Introduction to Microlocal Analysis
Fourier and Sobolev tools lead to Littlewood–Paley theory, pseudodifferential calculus, propagation and paradifferential operators.
Introduction to Probability
A calculus-level introduction to probability using conditioning, distributions and simulation. This is distinct from the existing Grinstead–Snell book with a similar title.
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Introduction to Probability
A calculus-level introduction to probability using conditioning, distributions and simulation. This is distinct from the existing Grinstead–Snell book with a similar title.
Introduction to Probability, 2nd edition
Examples and exercises develop discrete and continuous probability, with Markov chains and generating functions. Reviewers note broad coverage; graduate measure theory lies beyond its starting point.
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Introduction to Probability, 2nd edition
Examples and exercises develop discrete and continuous probability, with Markov chains and generating functions. Reviewers note broad coverage; graduate measure theory lies beyond its starting point.
Introduction to Random Graphs
A book-length treatment of random graph models, thresholds, components, connectivity and extremal properties.
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Introduction to Random Graphs
A book-length treatment of random graph models, thresholds, components, connectivity and extremal properties.
Introduction to Real Analysis
A proof-based route through sequences, continuity, differentiation and integration.
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Introduction to Real Analysis
A proof-based route through sequences, continuity, differentiation and integration.
Introduction to Representation Theory
Introduces representations using algebra and many exercises. Appropriate for strong undergraduates with linear algebra; the pace assumes comfort with abstract structures.
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Introduction to Representation Theory
Introduces representations using algebra and many exercises. Appropriate for strong undergraduates with linear algebra; the pace assumes comfort with abstract structures.
Introduction to Symplectic and Hamiltonian Geometry
A shorter course on symplectic structures and Hamiltonian geometry, distinct from the longer Lectures on Symplectic Geometry. Useful for orientation and selective review.
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Introduction to Symplectic and Hamiltonian Geometry
A shorter course on symplectic structures and Hamiltonian geometry, distinct from the longer Lectures on Symplectic Geometry. Useful for orientation and selective review.
Introduction to Teichmüller Theory and its Applications to Dynamics of Interval Exchange Transformations, Flows on Surfaces and Billiards
Translation surfaces, Teichmüller flow and the Kontsevich–Zorich cocycle, with interval-exchange and billiard applications.
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Introduction to Teichmüller Theory and its Applications to Dynamics of Interval Exchange Transformations, Flows on Surfaces and Billiards
Translation surfaces, Teichmüller flow and the Kontsevich–Zorich cocycle, with interval-exchange and billiard applications.
Introduction to the Transfer Operator Method
Introduces transfer operators as an analytic tool for studying statistical behavior of dynamical systems.
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Introduction to the Transfer Operator Method
Introduces transfer operators as an analytic tool for studying statistical behavior of dynamical systems.
Introductory Lectures on Contact Geometry
Introduces contact structures and their local models, characteristic foliations, tightness and Legendrian knots.
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Introductory Lectures on Contact Geometry
Introduces contact structures and their local models, characteristic foliations, tightness and Legendrian knots.