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Develops locally trivial fibrations, vector and principal bundles, classifying spaces and characteristic classes, with connections and curvature.
Develops locally trivial fibrations, vector and principal bundles, classifying spaces and characteristic classes, with connections and curvature.从局部平凡纤维化、向量丛和主丛讲到分类空间与示性类，也讨论联络和曲率。
Found via — References: The Topology of Fiber Bundles
Gowers discusses theory-building and problem-solving, using combinatorics to examine mathematical value and communication.
Gowers discusses theory-building and problem-solving, using combinatorics to examine mathematical value and communication.
Develops the theory of weights in étale cohomology, extending the framework of the Weil conjectures.
Develops the theory of weights in étale cohomology, extending the framework of the Weil conjectures.发展平展上同调中的权理论，扩展Weil猜想所涉及的理论框架。
Found via — References: La conjecture de Weil. II
Analytic Lp spaces on the disc are developed through growth estimates, reproducing kernels, density and bounded Bergman projections.
Analytic Lp spaces on the disc are developed through growth estimates, reproducing kernels, density and bounded Bergman projections.
An interconnected tour of mathematical physics, categories, topology, geometry and algebra.
An interconnected tour of mathematical physics, categories, topology, geometry and algebra.
Probability tools and spectral methods leading to semicircle and circular laws, free probability and Gaussian ensembles.
Probability tools and spectral methods leading to semicircle and circular laws, free probability and Gaussian ensembles.
Connects topological Hochschild and cyclic homology to integral p-adic comparison theory.
Connects topological Hochschild and cyclic homology to integral p-adic comparison theory.
English title: Topology. A course in sets, general topological spaces, compactness and separation, followed by an introduction to homotopy.
English title: Topology. A course in sets, general topological spaces, compactness and separation, followed by an introduction to homotopy.
Develops elementary number theory through Farey diagrams, continued fractions and quadratic forms. Offers a geometric route toward class groups.
Develops elementary number theory through Farey diagrams, continued fractions and quadratic forms. Offers a geometric route toward class groups.
A first course emphasizing topological definitions and proof practice. Useful before algebraic topology; elementary prerequisites do not mean the abstractions require little effort.
A first course emphasizing topological definitions and proof practice. Useful before algebraic topology; elementary prerequisites do not mean the abstractions require little effort.
A course connecting point-set topology with fundamental groups and covering spaces. The introduction states that this 2021 lecture series is no longer being updated.
A course connecting point-set topology with fundamental groups and covering spaces. The introduction states that this 2021 lecture series is no longer being updated.从点集拓扑进入基本群与覆盖空间的课程讲义。前言注明这是2021年的课程材料，已经停止更新。
Develops categorical foundations, toposes, monads and algebraic theories, with structural theorems connecting them.
Develops categorical foundations, toposes, monads and algebraic theories, with structural theorems connecting them.
Moves from classical transcendence proofs to rational approximation and bounds for algebraic numbers.
Moves from classical transcendence proofs to rational approximation and bounds for algebraic numbers.
Builds motivic categories and the six-operation formalism in a systematic treatment.
Builds motivic categories and the six-operation formalism in a systematic treatment.
Two courses develop FBI transforms, holomorphic weighted spaces and analytic microlocal techniques, including analytic WKB constructions.
Two courses develop FBI transforms, holomorphic weighted spaces and analytic microlocal techniques, including analytic WKB constructions.
Available portions cover vector bundles, characteristic classes and complex Bott periodicity. The author says only about half the planned book is posted.
Available portions cover vector bundles, characteristic classes and complex Bott periodicity. The author says only about half the planned book is posted.
Full-text source checked: 2026-11-03
Found via — References: Vector Bundles and K-Theory
A visual, problem-centered approach to classical curves and surfaces. Emphasizes essential techniques; the authors describe its presentation as elementary and 'virtually rigorous'.
A visual, problem-centered approach to classical curves and surfaces. Emphasizes essential techniques; the authors describe its presentation as elementary and 'virtually rigorous'.
Examines multiple sources of mathematical value and the connections that can develop between them.
Examines multiple sources of mathematical value and the connections that can develop between them.
A compact treatment of differential and integral calculus that uses infinitesimals to explain derivatives and accumulation.
A compact treatment of differential and integral calculus that uses infinitesimals to explain derivatives and accumulation.