Bibliographic record
Abstract
This book is a rigorous introduction to real analysis, suitable for a onesemester course at the second-year undergraduate level, based on my experience of teaching this material many times in Australia and Canada. My aim is to give a treatment that is brisk and concise, but also reasonably complete and as rigorous as is practicable, starting from the axioms for a complete ordered field and a little set theory. Along with epsilons and deltas, I emphasise the alternative language of neighbourhoods, which is geometric and intuitive and provides an introduction to topological ideas. I have included a proper treatment of the trigonometric functions. They are sophisticated objects, not to be taken for granted. This topic is an instructive application of the theory of power series and other earlier parts of the book. Also, it involves the concept of a group, which most students won't have seen in the context of analysis before. There may be some novelty in the gentle, example-based introduction to metric spaces at the end of the book, emphasising how straightforward the generalisation of many fundamental notions from the real line to metric spaces really is. The goal is to develop just enough metric space theory to be able to prove Picard's theorem, showing how a detour through some abstract territory can contribute back to analysis on the real line. Needless to say, I claim no originality whatsoever for the material in this book.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.473 | 0.336 |
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".