A first introduction to counting and graph theory in a freely readable web format. Useful for building discrete proof techniques before specialized combinatorics.
David Guichard · Textbook · Introductory · English (legacy metadata)
Online text
A first introduction to counting and graph theory in a freely readable web format. Useful for building discrete proof techniques before specialized combinatorics.
A course develops analytic functions, contour integration and residues before gamma and zeta functions, the prime number theorem and asymptotic analysis.
The complete 74-page PDF opened on the author's host.
A course develops analytic functions, contour integration and residues before gamma and zeta functions, the prime number theorem and asymptotic analysis.
Preparation: Undergraduate real analysis and familiarity with complex numbers.
Use: Connect the core complex-analysis toolkit with analytic-number-theory and asymptotic applications.
Chinese seminar notes on condensed mathematics and analytic rings, with corrections and comparisons to the cited versions of the original lecture notes.
Online lecture text; chapters can be read separately.在线讲义，可按章节阅读。
Original title: 凝聚态数学
Chinese seminar notes on condensed mathematics and analytic rings, with corrections and comparisons to the cited versions of the original lecture notes.关于凝聚态数学与解析环的中文讨论班讲义，也记录了对所引用原讲义版本的修正与比较。
Preparation: Sheaves, homological algebra and higher categories.层、同调代数和高阶范畴。
Use: Read after the basic sheaf and derived-category language; use the original references for version comparisons.熟悉层和导出范畴语言后再读，并与原始参考文献对照版本。
Version: Spring 2021 seminar2021年春季讨论班 · Checked 2026-11-03
Andrew Snowden · Online lecture course · Research · English
Online text
Official 23-lecture HTML index and full text of lectures 2 and 23 read through the web source reader; a separate automated GET encountered a challenge.
Develops elliptic curves, group schemes, modular curves and Hecke algebras toward rational torsion classification.
The complete available preliminary manuscript develops virtual smooth geometry. The author warns that later published definitions differ; it is not the final OUP book.
The complete available preliminary manuscript develops virtual smooth geometry. The author warns that later published definitions differ; it is not the final OUP book.
Brian Conrad · Expository research paper · Research · English
PDF
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 detailed exposition of Nagata compactification, explaining Deligne’s scheme-theoretic proof and related applications to rational maps and blow-ups.详细阐述Nagata紧化定理，整理Deligne的概形论证明，并讨论有理映射和爆破的相关应用。
Preparation: Schemes, proper morphisms and blow-ups.概形、固有态射与爆破。
Use: Use the introduction to fix the hypotheses before following the proof.先在引言中核对假设，再读证明。
An applied first course combines first-order equations, numerical methods, linear algebra, oscillations, Laplace transforms, phase planes, systems and series solutions.
Grant B. Gustafson · Textbook · Introductory · English
PDF
The author page permits personal and educational use and links the complete textbook PDF.
An applied first course combines first-order equations, numerical methods, linear algebra, oscillations, Laplace transforms, phase planes, systems and series solutions.
Preparation: Single-variable calculus; linear algebra is developed within the text.
Use: Build computational and modelling foundations for later differential-equations courses.
Version: Author's August 2022 release; copyright 1999–2022 · Checked 2026-10-13
Develops curves, surface curvature, geodesics and Gauss–Bonnet, with exercises and selected solutions. Later sections introduce hyperbolic geometry and variational problems.
Theodore Shifrin · Textbook · Intermediate · English
PDF
The complete PDF opens on the author’s or university’s public site.
Develops curves, surface curvature, geodesics and Gauss–Bonnet, with exercises and selected solutions. Later sections introduce hyperbolic geometry and variational problems.
Preparation: Multivariable calculus; linear algebra; elementary ODE.
Develops distributions and elliptic methods through applications including Hodge theory. These graduate notes are a specialized analytic path, not an elementary PDE survey.
Develops distributions and elliptic methods through applications including Hodge theory. These graduate notes are a specialized analytic path, not an elementary PDE survey.
Preparation: Real and functional analysis; Fourier analysis.