Is it conventional to point out harmless typos in mathematical derivations in lecture notes?

Question

I am on a physics course. Often I struggle with following mathematical derivations, so I aim to scrutinize them very carefully to make sure I understand them. Sometimes I find mistakes in the lecture notes, which are harmless from the overall point of view (ie we get the same result, it won't affect subsequent lines). Nevertheless, they are wrong. Ie instead of writing J(x) (J as a function of x), lecture notes contain Jx, ie function of J times x. We mean the former, and later use the former interpretation. Or: writing exp(0-), where 0- is the limit of x as x approaches 0 from below, while the right thing which follows from the previous lines would be exp(-0-). Of course these are equal so not much harm done, but it is still wrong. Or when on the lecture it is said that "do check this at home you will get X", and I go home and check it and the answer is not X, that seems to be problematic. Almost noone bothers to check though, so it doesn't seem to be a big issue.

My usual reaction to this is to write a kind email to the professor to point these out. I thought it is useful for both of us, he gets to correct a typo, or I get to learn something new in case it is not a typo & I am wrong. I noticed though that this is not something common to do. Once I checked this on a course, and more than half of the entries on the list of erratum in lecture notes are the things I have pointed out. Am I a weirdo and I should stop pointing these out, or this is normal behaviour?

Answer 1

I think it is a good idea. While the typos you find may be harmless in their respective contexts, they can be a hindrance to properly understanding the concepts, particularly for students who find the material challenging and are not immediately able to identify when something is just a typo. A harmless typo, such as an incorrect expression that just happens to match with the correct answer for a particular problem, can lead to errors if applied to other problems. Furthermore, "do check this at home you will get X" not giving X is not harmless — students would not be sure if they did not get X because they applied a method incorrectly or because it was just a typo, which would waste time and cause confusion, as you also mentioned.

Whether you should report the typos depends on the professor. If they explicitly encourage students to report them, then certainly you should. If there is no explicit guidance, then unless they react negatively to your corrections, it would be a good idea to inform them, and as you say, get a confirmation that your understanding is correct. If you are still in doubt, you can always ask what they would prefer.

In your specific case, the fact that they maintain an erratum suggests that they see it positively. Some professors create a collection of notes that they refine and keep using for future offerings of the course, so you are probably helping future students as well. In fact, some may encourage it to the extent of giving extra credit for finding errors.

I am not aware if it is "conventional" or "normal" behaviour in general, but I see no reason to not do this, as long as your corrections are accurate, useful, and you have the (even implicit) support of your professor.

Answer 2

Culturally, some physics people seem to take pride in using notation that's just sloppy - expecting the reader to figure out what was meant from the context if they understand the physics. For example, Lev Landau (Nobel 1962) sometimes wrote just T (temperature) when he meant kT (energy = constant * termperature). He also sometimes wrote "(something)/2mT" when he meant "(something)/(2mT)". He figured, if you understand the context, you can't possibly misinterpet this as "(something)/2 * m *T". My own grandfather was a physics professor and sometimes wrote like this too (they both studied under Abram Ioffe). I heard a plausible conjecture that some physicists who write like this, studied Hebrew as children and were taught to write just the consonants without the vowel signs, and expect the reader to figure the vowels from the context.

In my opinion, learning to decipher what the writer meant, from the context, as opposed to what they literally wrote, is still a useful skill for a physics major to learn. (Less so in other disciplines, such as economics or chemistiry, where most people aim to make their mathematical notation as readable as they possibly can.)

But there are way more than enough examples of this phenomenon in physics papers to master this skill. Helping make your class notes better for future generations is a noble goal. You also learn something in the process. Your instructors don't seem to mind (they maintain the errata). As long as they don't tell you that your corrections are over the top, you should keep going.