Bibliographic record
Abstract
This book is intended as an introductory text for senior undergraduate and beginning graduate students wishing to learn the fundamentals of algebraic number theory. It is based upon a course in algebraic number theory given by the second author at Carleton University for more than thirty years. Keeping in mind that this is an introductory text, the authors have strived to present the material in as straightforward, clear, and elementary fashion as possible. Throughout the text many numerical examples are given to illustrate the theory. Each chapter closes with a set of exercises on the material covered in the chapter, as well as some suggested further reading. References cited in each chapter are listed under suggested reading. Biographical references for some of the mathematicians mentioned in the text are also given at the end of each chapter. For the convenience of the reader, the book concludes with page references for the definitions, theorems, and lemmas in the text. In addition an extensive bibliography of books on algebraic number theory is provided. The main aim of the book is to present to the reader a detailed self-contained development of the classical theory of algebraic numbers. This theory is one of the crowning achievements of nineteenth-century mathematics. It came into being through the attempts of mathematicians of that century to prove Fermat's last theorem, namely, that the equation x n + y n = z n has no solutions in nonzero integers x, y, z, where n is an integer ≥ 3.
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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.378 | 0.263 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".