A one-semester applied undergraduate course covering random variables, common distributions, limit theorems, estimation, testing and regression. It is not a substitute for a measure-theoretic probability course.
唐聿劼 (Yujie Tang) · Course notes · Introductory · Chinese
Online text
Online lecture text; chapters can be read separately.在线讲义，可按章节阅读。
Original title: 概率与数理统计
A one-semester applied undergraduate course covering random variables, common distributions, limit theorems, estimation, testing and regression. It is not a substitute for a measure-theoretic probability course.一学期本科应用课程，涵盖随机变量、常见分布、极限定理、估计、检验和回归。若要学习测度论概率，还需要另补测度与积分。
Preparation: Single-variable calculus and elementary linear algebra.一元微积分和初等线性代数。
Use: Start with the probability chapters; continue to statistical inference after expectations and limit laws.先读概率部分，掌握期望和极限定理后再读统计推断。
Version: Fall 2024–2025 undergraduate course2024—2025学年秋季本科课程 · Checked 2026-11-03
Graduate course notes for measure-theoretic probability. More concise than a first undergraduate textbook; readers should work through proofs rather than rely only on examples.
Amir Dembo · Course notes · Advanced · English (legacy metadata)
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Graduate course notes for measure-theoretic probability. More concise than a first undergraduate textbook; readers should work through proofs rather than rely only on examples.
Dieter Degrijse, Markus Hausmann, Wolfgang Lück, Irakli Patchkoria and Stefan Schwede
Research · PDF
Constructs equivariant spectra and cohomology theories for proper Lie-group actions, with compact isotropy and applications to infinite discrete groups.
Dieter Degrijse, Markus Hausmann, Wolfgang Lück, Irakli Patchkoria and Stefan Schwede · Research monograph · Research · English
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The complete author-deposited preprint opens in arXiv.
Constructs equivariant spectra and cohomology theories for proper Lie-group actions, with compact isotropy and applications to infinite discrete groups.
Preparation: Stable homotopy theory; equivariant topology; model categories.
Use: Continue from finite-group equivariant courses to proper actions and equivariant K-theory.
Version: arXiv v2, October 14, 2020 · Checked 2026-10-13
Grigory Andreychev · Research paper · Research · English
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Public full text; checked against the title and contents.已核对题名和目录，可公开阅读全文。
Uses condensed analytic rings to study descent for pseudocoherent and perfect complexes and vector bundles on analytic adic spaces.利用凝聚态解析环研究解析adic空间上伪凝聚复形、完美复形与向量丛的下降。
Public full text; checked against the title and contents.已核对题名和目录，可公开阅读全文。
A survey connecting hitting, commute and cover times with graph eigenvalues, electrical networks and algorithmic applications.将到达时间、往返时间和覆盖时间与图的特征值、电网络及算法应用联系起来的综述。
Preparation: Finite Markov chains; linear algebra; graphs.有限马尔可夫链、线性代数和图论。
Use: Read the basic parameters first, then the electrical-network and spectral interpretations.先理解基本时间参数，再读电网络与谱的解释。
Version: Yale technical-report version, 38 PDF pages耶鲁技术报告版本，PDF共38页 · Checked 2026-11-03
A research course explains the architecture of partial regularity proofs using rectifiable currents, multivalued functions, center manifolds, frequency estimates and blow-up arguments.
Emanuele Spadaro · Lecture notes · Research · English
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The complete 53-page author-submitted manuscript opened on arXiv.
A research course explains the architecture of partial regularity proofs using rectifiable currents, multivalued functions, center manifolds, frequency estimates and blow-up arguments.
Preparation: Geometric measure theory, Sobolev spaces and calculus of variations.
Use: Move from measure-theoretic surfaces to singularity and regularity research; several technical results are explained through proof outlines.
Explains the set-theoretic foundations of mathematics and the motivation for ZFC. Its emphasis is conceptual and philosophical, not graduate forcing theory.
Tim Button · Textbook · Introductory · English (legacy metadata)
Online text
Explains the set-theoretic foundations of mathematics and the motivation for ZFC. Its emphasis is conceptual and philosophical, not graduate forcing theory.
Preparation: Basic logic and high-school mathematics.
Develops completeness, compactness and undecidability after elementary formal logic. A structured bridge from proof systems to mathematical metatheory.
Richard Zach · Textbook · Intermediate · English (legacy metadata)
Online text
Develops completeness, compactness and undecidability after elementary formal logic. A structured bridge from proof systems to mathematical metatheory.