Final-year workbooks

For a final-year student aiming at a preparatory class, I wrote a collection of exercise workbooks in mathematics (specialty and expert options), physics-chemistry and Python. Each workbook takes up a chapter of the course. Each skill begins there with a reminder and a worked example, followed by a box of cautions, then exercises spread over four levels. Two summary reviews close the workbook.

A workbook is a single data file where each exercise carries its level, its statement, its hint and its solution. A program draws the LaTeX and the two editions from it, one for the student with the hints, the other complete with detailed corrections. The levels rise from applying a definition to chaining guided steps, then choosing and justifying a method, and finally proving, designing or discussing a model.

Every numerical result is recomputed by an independent checking program, separate from the workbook. Each workbook is then reread against the course chapter, and every error found is corrected. I recheck myself, I look at pages of both editions, and I merge.

The student had asked me for a gradual progression. So each skill opens with direct applications with simple values, and no level starts harder than the previous one ended. An essential path marks the exercises to do first, the rest serving as a reserve and an extension, in order to keep the workload manageable.