Reader’s guide to the Articulated Course · episode 7 / 8 · 3 min 46 s
Three companion books: abridged course, compendium, formula handbook
Abridged course, compendium, formula handbook: three companions, three ways to work.
In this episode
For each of the first three volumes, the course has three companions: the abridged course (for learning, or learning again), the compendium (for revisiting a course already learned) and the formula handbook (for looking things up). Seventh episode of the reader’s guide: what each contains, what it leaves out, and how they share the work with the volume, which calls for sustained work.
In the book: “How to Use This Book” in the abridged course, compendium and formula handbook (volumes I to III).
Read the transcript
Reopen a whole volume?
A theorem, a formula, a notation: you know it is somewhere, and you have no wish to reopen a whole volume. Or, the other way round, you want to go through an entire course again in a few evenings. For each of the first three volumes, the course has companions: three books, three uses. Articulated Course in Mathematics. Reader’s guide, episode seven: three companion books.
Three companions per volume
An abridged course, a compendium, a formula handbook. For volumes one, two and three, in French and in English. All of them follow the plan of the volume, chapter by chapter, under the same numbers. Chapter twelve of the volume is chapter twelve of each of its companions. You don’t get lost.
The abridged course
The abridged course is the whole course, compressed. It can be read straight through, and studied without another book. Theorems appear with all their hypotheses. One example per concept. The idea of each proof, in one sentence. Methods and pitfalls run through the text, where they are needed. After each section title, a marker, article twelve, or articles twelve to fourteen, points to the full articles of the volume. And the closing reference says where to find the proofs, the practice exercises, the studies and the expeditions.
The compendium
The compendium is one sheet per chapter. It opens on the idea of the chapter, in a few lines. It gathers the working definitions, the identities, the tables. It states the chapter’s theorems in full. And it gives, in one line, the methods and the pitfalls. No proofs, no worked examples, no exercises. The compendium states what is true, and how to use it. The volume explains why it is true, and how it is discovered.
The formula handbook
The formula handbook is more austere still. One sheet per chapter: the working definitions, the identities, the tables, the theorems, stated in full, with their hypotheses. No result is quoted merely “under the usual assumptions”. It is a reference book: you use it to check a formula, a statement, a notation. You learn nothing in it.
Three books, three ways of working
Three companions, three ways of working. The formula handbook is for looking things up. The compendium is for revisiting a course already learned. The abridged course is for learning, or learning again. And the volume calls for sustained work: it explains why the results are true, and how they are discovered.
To remember
To remember. Three companions per volume, from volume one to volume three. Same plan, same numbers. The abridged course to learn, the compendium to revisit, the formula handbook to check. The companions are presented on the Éditions Clementinium website. The link is in the description. Next episode: the research cycle, volumes four and five.
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