Online lecture text; chapters can be read separately.在线讲义，可按章节阅读。
Original title: 集合论基础
An introduction to logic and set theory, developing the language of sets and basic constructions used throughout undergraduate mathematics.逻辑与集合论入门，讲解集合语言及本科数学常用的基本构造。
Preparation: School mathematics; no previous axiomatic set theory assumed.中学数学，无须先学公理集合论。
Use: Read the logical language and basic constructions before the more advanced axiomatic-set-theory sequel.先读逻辑语言和基本构造，再进入公理集合论的进阶讲义。
A developing sequence on formal set-theoretic theories and construction principles. Read the existing chapters selectively; a listed language-extension section is still unfinished.
Online lecture text; chapters can be read separately.在线讲义，可按章节阅读。
Original title: 集合论进阶 A：公理集合论基础
A developing sequence on formal set-theoretic theories and construction principles. Read the existing chapters selectively; a listed language-extension section is still unfinished.讨论形式集合论理论及构造原则的进阶讲义，仍在编写中。可选读已有章节，目录中的语言扩展部分尚未完成。
Preparation: First-course set theory and first-order logic.集合论基础与一阶逻辑。
Use: Compare the axioms and the resulting theories after a first course in sets.学过集合论基础后，用来比较不同公理及其形成的理论。
A focused treatment of generating functions and counting. Read after elementary combinatorics; the authorized free edition is the second, not the commercial third.
Herbert S. Wilf · Textbook · Intermediate · English (legacy metadata)
Online text
A focused treatment of generating functions and counting. Read after elementary combinatorics; the authorized free edition is the second, not the commercial third.
Preparation: Combinatorics; power series and calculus.
Connects Dehn functions and nonpositive curvature to recognition and isomorphism problems. The complete lecture manuscript is informal rather than a polished journal treatment.
Martin R. Bridson · Lecture notes · Research · English
PDF
The complete PDF opens on the author’s or university’s public site.
Connects Dehn functions and nonpositive curvature to recognition and isomorphism problems. The complete lecture manuscript is informal rather than a polished journal treatment.
Preparation: Group presentations; fundamental groups; geometric group theory.
Use: Use after a first geometric group theory course to explore algorithmic questions.
Version: Lectures June 12–14, 2003 · Checked 2026-10-13
The author offers free online viewing of the main text. Downloadable complete ebooks and exercise hints are separate paid editions; use the official page.
Covers core graph theory and routes toward structural results. Free browser viewing is not the same as a freely downloadable full PDF.
Preparation: Proof-writing; discrete mathematics.
Use: Bridge undergraduate graphs and graduate combinatorics.
Connects extremal graph theory, pseudorandomness and additive combinatorics. The full author manuscript differs slightly from the published edition; exercises and companion lectures support study.
Connects extremal graph theory, pseudorandomness and additive combinatorics. The full author manuscript differs slightly from the published edition; exercises and companion lectures support study.
Preparation: Undergraduate algebra, analysis and linear algebra.
A foundational French treatment of motivic operations and nearby-cycle constructions. The archive supplies the full first volume; the companion volume is Astérisque 315.
Joseph Ayoub · Research monograph · Research · French
Online text
Original title: Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique (I–II)
A foundational French treatment of motivic operations and nearby-cycle constructions. The archive supplies the full first volume; the companion volume is Astérisque 315.
A first graduate course from holomorphic functions to conformal mapping and analytic continuation. Appendices review analysis prerequisites; exercises remain important for understanding.
Jiří Lebl · Textbook · Intermediate · English (legacy metadata)
PDF
A first graduate course from holomorphic functions to conformal mapping and analytic continuation. Appendices review analysis prerequisites; exercises remain important for understanding.
Preparation: Real analysis; metric spaces; multivariable calculus.
Fourier series and integrals are treated through maximal functions, Hilbert and Riesz transforms, Calderón–Zygmund decomposition and interpolation, followed by sampling and uncertainty.
Richard S. Laugesen · Lecture notes · Graduate · English
PDF
The complete 176-page author-submitted manuscript opened on arXiv.
Fourier series and integrals are treated through maximal functions, Hilbert and Riesz transforms, Calderón–Zygmund decomposition and interpolation, followed by sampling and uncertainty.
Preparation: Lebesgue integration, Lp spaces and elementary Hilbert-space theory.
Use: Take a first theoretical harmonic-analysis course with a dedicated problem section.
Version: arXiv v2, May 17, 2017; manuscript dated May 18, 2017 · Checked 2026-10-13