Bibliographic record
Abstract
These are the notes for five one hour lectures delivered at the 2016 CRM summer school in Spectral Theory at Laval University. They were intended to provide some general background on classical and quantum mechanics to advanced undergraduate and beginning graduate students in mathematics. The first four lectures contain an outline of these two theories from a mathematical point view and a comparison of the classical and quantum descriptions of some simple systems. The last lecture is about hidden variables and is meant to illustrate the essential strangeness of the quantum description of nature. I have tried to make these notes more accessible by including an outline of some basic ideas in measure theory and operator theory. A similar outline of the basics of manifolds, tangent and cotangent spaces and differential forms would have been useful for understanding the sections on Lagrangian submanifolds and Hamilton-Jacobi equations. Unfortunately I did not have time to include this. I am grateful to Cyrus Bhiladvala and the referee for making suggestions for improvement.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.063 | 0.007 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".