Sources and component terms

The lessons identify the human mathematical sources used, exact editions and proof locations, and the hypotheses carried into each argument. The references below are useful entry points; the lesson bibliographies give the complete source-specific account. Access to a source does not imply permission to redistribute its PDF.

• Lars Hörmander, On the theory of general partial differential operators (1955)
• Lars Hörmander, Fourier integral operators I (1971)
• Johannes Duistermaat and Lars Hörmander, Fourier integral operators II (1972)
• Lars Hörmander, The existence of wave operators in scattering theory (1976)
• Nicolas Lerner, Metrics on the Phase Space and Non-Selfadjoint Pseudodifferential Operators, author edition (2009)
• Gerald Teschl, Mathematical Methods in Quantum Mechanics, second edition (2014)
• Gerald Teschl, Ordinary Differential Equations and Dynamical Systems (2012)
• Erik Koelink, Scattering Theory (2006)

Included proof readings

• analytic foundations for preparation
• bounded strips
• classical scalar calculus
• compact fredholm families
• compact spectrum domains
• coordinate inverses and integration
• critical multiplication
• dirichlet domain and compactness
• euclidean approximation and convolution
• finite derivative l2
• finite trace ideals
• finite weighted calculus
• hilbert valued integration
• phase geometry and stationary phase
• quantitative polynomial growth
• scalar transport and phase action
• self adjoint spectral domains
• smooth dirichlet powers
• sobolev traces
• transverse composition and graph operators
• unitary spectral foundation
• wavefront qualified pullback
• weighted positivity

Authorship and rights

GPT-6.1 Sol (OpenAI), at Ultra, wrote the initial course exposition, original figures and proof adaptations. GPT-6 Astra (OpenAI) contributed additional proofs and explanations. Programme references retain their own stated AI and human credits.

Original course prose, guide, metadata, figures and original proof readings are dedicated under CC0 1.0 Universal, subject to the expressly excluded components below. Reproducible figure sources are in figures/; editable lessons are in src/.

The algebra component includes unchanged Stacks proof excerpts and readable adaptations from Unofficial Stacks Project AI Drafts, revision 565b10e987aba5969b21145a0833f42d69f96790. The Stacks Project authors wrote the inherited text; the fork and this adaptation include AI contributions. No Stacks review, approval or endorsement is claimed. These files retain GNU FDL 1.2 and are excluded from the CC0 grant. Read the complete component notice, preserved source notice and licence text.

The included Analytic foundations for preparation follows Jean-Pierre Demailly’s freely available author treatment, preserves his authorship and retains his custom OpenContent grant. That reading is excluded from the course’s CC0 dedication. Its exact source version and added explanations are identified in the reading.

The included Coordinate inverses, integration and surface measure is an expanded derivative reading of Jiří Lebl’s freely available Basic Analysis II, version 6.3, 15 May 2026, Sections 8.5 and 10.7. It retains CC BY-SA 4.0 and is excluded from the course’s CC0 dedication. The reading identifies its added arguments and source locations.

The static reader includes KaTeX code, styles and fonts under the MIT licence. Other human source works are linked and retain their own terms; their PDFs are not included in the download.