Aaron Landesman (notes from Kannan Soundararajan's course)
Graduate · PDF
A sustained course transcription developing analytic techniques for arithmetic functions and primes; authorship distinguishes lecturer from note-taker.
Aaron Landesman (notes from Kannan Soundararajan's course) · Lecture-course transcription · Graduate · English
PDF
Full PDF opened publicly on the author or university host.
A sustained course transcription developing analytic techniques for arithmetic functions and primes; authorship distinguishes lecturer from note-taker.
Preparation: Complex analysis; elementary number theory.
Use: Work through an analytic number theory course.
Version: Stanford Math 249A, Fall 2017 · Checked 2026-10-13
Connects wavefront sets and Fourier integral operators with tomography and boundary measurements; introductory microlocal discussion is partly nontechnical.
Mikko Salo · Minicourse notes · Research · English
PDF
The complete 31-page manuscript opened at users.jyu.fi.
Connects wavefront sets and Fourier integral operators with tomography and boundary measurements; introductory microlocal discussion is partly nontechnical.
Combines enumeration, graphs, posets and optimization. The breadth supports several course choices; the linked full HTML is the established 2016 edition.
Mitchel T. Keller and William T. Trotter · Textbook · Intermediate · English (legacy metadata)
Online text
Combines enumeration, graphs, posets and optimization. The breadth supports several course choices; the linked full HTML is the established 2016 edition.
An informal introduction focused on representation theory over non-Archimedean local fields, with finite-group examples and smooth representations. It does not supply the planned full global theory.
Kevin Buzzard · Long lecture notes · Graduate · English
PDF
Full PDF opened publicly on the author or university host.
An informal introduction focused on representation theory over non-Archimedean local fields, with finite-group examples and smooth representations. It does not supply the planned full global theory.
Preparation: Representation theory, local fields and graduate algebra.
Use: A local-representation bridge toward automorphic forms and the local Langlands correspondence.
Version: Cover dated 26 April 2012; informal course May–July 2003; text notes last modification 1 June 2004 · Checked 2026-10-13
Builds real-line analysis before metric spaces, with many exercises. Reviewers describe it as adaptable to undergraduate courses; self-study requires actively writing proofs.
Jiří Lebl · Textbook · Introductory · English (legacy metadata)
PDF
Builds real-line analysis before metric spaces, with many exercises. Reviewers describe it as adaptable to undergraduate courses; self-study requires actively writing proofs.
Preparation: Calculus; an introductory proof course.
Continues to multivariable analysis, inverse and implicit function theorems, approximation and Fourier series. A natural sequel, not a replacement for measure theory.
Jiří Lebl · Textbook · Intermediate · English (legacy metadata)
PDF
Continues to multivariable analysis, inverse and implicit function theorems, approximation and Fourier series. A natural sequel, not a replacement for measure theory.
A course on variational solitary waves, concentration compactness, orbital stability and dispersive estimates, with spectral and numerical discussions.
Jeremy L. Marzuola · Lecture notes · Research · English
PDF
The complete 256-page text opened at marzuola.web.unc.edu.
A course on variational solitary waves, concentration compactness, orbital stability and dispersive estimates, with spectral and numerical discussions.
Preparation: Graduate PDE, functional analysis and Fourier analysis.
Use: Move from nonlinear-wave well-posedness to stability and spectral research techniques.
Version: Courses given in summer 2012 and summer 2013; PDF revision date not stated · Checked 2026-10-13
A transition from calculation to proofs, with sets, induction and cardinality. Selected solutions help self-study; it is preparation rather than an advanced subject text.
Richard Hammack · Textbook · Introductory · English (legacy metadata)
PDF
A transition from calculation to proofs, with sets, induction and cardinality. Selected solutions help self-study; it is preparation rather than an advanced subject text.
An illustrated first course with examples and applications. Useful for computational foundations; a proof-based real analysis text is needed for a mathematics-major transition.
Gilbert Strang and Edwin 'Jed' Herman · Textbook · Introductory · English (legacy metadata)
PDF
An illustrated first course with examples and applications. Useful for computational foundations; a proof-based real analysis text is needed for a mathematics-major transition.
Develops homotopy-theoretic constructions in a categorical setting. A continuation after basic topology and category theory rather than a first topology course.
Emily Riehl · Monograph · Advanced · English (legacy metadata)
PDF
Develops homotopy-theoretic constructions in a categorical setting. A continuation after basic topology and category theory rather than a first topology course.
Online lecture text; chapters can be read separately.在线讲义，可按章节阅读。
Original title: 示性类
Seminar chapters on vector bundles and their characteristic classes, connecting topological definitions with geometric constructions.讨论向量丛及示性类的讨论班讲义，将拓扑定义与几何构造联系起来。
An undergraduate research exposition constructing characteristic classes from curvature and comparing them with topological Chern classes; appendices review bundles and connections.
Adel Rahman · Student exposition · Graduate · 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。
An undergraduate research exposition constructing characteristic classes from curvature and comparing them with topological Chern classes; appendices review bundles and connections.本科科研项目讲义，从曲率构造示性类，并与拓扑的陈类比较；附录复习向量丛与联络。
A detailed advanced continuation of algebraic number theory. Read after local and global number-field foundations, not immediately after elementary congruences.
J. S. Milne · Course notes · Advanced · English (legacy metadata)
PDF
A detailed advanced continuation of algebraic number theory. Read after local and global number-field foundations, not immediately after elementary congruences.
Online lecture text; chapters can be read separately.在线讲义，可按章节阅读。
Original title: 有限群的经典表示理论
A short course approaching finite-group representations through the structure of algebras, rather than starting only with character computations.从代数结构的观点进入有限群表示论的短篇讲义，不仅围绕特征标计算展开。
Preparation: Linear algebra; finite groups; rings and modules.线性代数、有限群、环与模。
Use: Use it to connect a first representation-theory course with semisimple algebra.用来连接初等表示论与半单代数。