Analysis of Ideas Changing in the History of Mathematical Analysis
Bibliographic record
Abstract
Analysis is a branch of mathematics that deals with continuous change and with certain general types of processes that have emerged from the study of continuous change, such as limits, differentiation, and integration. In the history of mathematics, analysis is the first subject became epidemic, the development of analysis originated from the British mathematician and physicist, the Sir Isaac Newton, and the German mathematician, Gottfried Wilhelm Leibniz, who developed the theory of Calculus, with hundred-years developing, the modern analysis is now very ample and has widely applications, it has grown into an enormous and central field of mathematical research, with applications throughout the sciences and in areas such as finance, economics, and sociology. In this paper, we investigated in some detail with the changing of the ideas in mathematical analysis. By numerating historical facts and the mathematical ideas, we concluded the result that the ideas changing is because of the changing of the studying objects, the conclusion are studied detailly in the paper.
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 | 0.006 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.003 | 0.015 |
| Scholarly communication | 0.006 | 0.016 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".