Talk:Exercise (mathematics)

Exercise discussion

Readers that find issue with Exercise (mathematics) are invited to make comments on this Talk page.Rgdboer (talk) 23:39, 2 June 2012 (UTC)

This article seems to give a somewhat narrow definition of exercise, as most exercises at the upper undergraduate level and graduate level go (to varying extents) beyond routine application of theorems to questions such as asking for proofs of minor claims made in the main text, asking for proofs of variants or generalizations of theorems proved in the text, or asking for proofs of new statements requiring insightful applications of several discussed theorems. Some exercises also ask for either proof or a counterexample for a plausible statement or the construction of an object satisfying certain properties, with proof. A general definition should really be any set of difficulty-calibrated problems given by teachers to students with the goal of improving and sharpening their mathematical understanding and skills. Alsosaid1987 (talk) 05:03, 19 November 2025 (UTC)

Some folks would stop considering those to be "exercises"; terms here are not very strictly or consistently defined though. –jacobolus (t) 07:54, 19 November 2025 (UTC)

This article considers exercise in the context of mathematics education, the math context of the general reader. As for college or university mathematics, there is the article on mathematical problems which corresponds to the notion of exercise expressed by User:Alsosaid1987. — Rgdboer (talk) 01:37, 20 November 2025 (UTC)

I would have to disagree with the distinction, as many advanced undergraduate or graduate textbooks explicitly mark problems of this type as exercises (e.g., Rudin's "Principles of Mathematical Analysis" and Atiyah and Macdonald's "Introduction to Commutative Algebra", both of which are famous textbooks (see their respective Wikipedia articles) with well noted collections of exercises (and are called "exercises" and not "problems" in both texts)).

It's all in the eye of the beholder: A professional mathematician would find these to be quite routine or even trivial, while most new students to these areas would find the exercises in the books to be challenging.

I'll just leave this comment here, without attempting to edit the article. I am not well versed in pedagogy in general. Alsosaid1987 (talk) 19:52, 27 November 2025 (UTC)

Add examples?

Mostly to see how a typical math exercise could look like per grade. Plus, it would illustrate the article quite well, so that it isn't all theory.

An example could look like this:

"A new weather forecaster is tasked with listing the temperatures of the day's forecast. She knows that to convert Fahrenheit into Celsius, she must subtract 32 from the initial Fahrenheit value, then multiply by 5 and divide by 9. The temperature she is tasked with listing is 25°C. What is its equivalent in Fahrenheit?" NikoPalad67140 (talk) 12:56, 14 February 2026 (UTC)