Bibliographic record
Abstract
The following problem is one that many first year calculus students find quite difficult:Given a formula for a function f in a variable x, find a formula for its n th derivative. Example 1.1: [1, p. 229] If f ( x ) = x m , (1)then its n th derivative is f ( n ) ( x ) = m- n x m-n , (2)where m- n = m ( m - 1) ( m - 2) ⋅⋅⋅ ( m - n + 1).The difficulties for students include, first, the discovery of a formula valid for all integers n and, second, the proof (for example, by induction) that the formula is correct. Can computer algebra systems do better?It is certain that Macsyma could (we remember commands for infinite Taylor series expansion of elementary functions, and that necessarily involves discovering a correct formula for the n th derivative of the input). Currently, Maple cannot---at least, not without help, just with one command, now that the Formal Power Series package in the share library is no longer supported.
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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.013 | 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".