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My professor gave me a module on history that contains several spelling and grammatical errors. Should I tell him about this or just ignore these mistakes?

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8  
First check whether there is an errata web site for the book, and if so check whether your corrections have already been found. – Patricia Shanahan Mar 12 at 15:42
32  
What do you mean, if? – JeffE Mar 12 at 16:04
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I recall professors who offered a bottle of champagne for the student who caught the most errata during the term. It helps them if they plan to turn their lecture notes into a book ... – o.m. Mar 12 at 17:25
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@o.m. Well, the most famous of all the rewarders is certainly D. E. Knuth, who used to send a $2.56 check to all those who found a typo in his celebrated book series The art of computer programming. – Massimo Ortolano Mar 12 at 19:18
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@Mas No he doesn't, he stopped a while ago because no one deposited them, but posted pictures of them with his account info on it. Now you get money deposited to the "Bank of San Serrife" Check his website – Azor-Ahai Mar 13 at 0:57

For the textbook I've written, I appreciate any feedback, including typos, misformed sentences, vague formulations and of course errors. Some points to consider (partly contained in the other answers):

  • Wait until you have a reasonable list or, e. g., until a chapter is over, the whole book, or the course.
  • Check if there is some errata available somewhere. Some authors maintain an errata on their webpage, sometimes the publisher hosts this, for some lecture notes I have a blog post. Only send the points that are not already in the errata.
  • There is no need to ask if such a list would be welcome. I guess it is safe to assume that this is the case (but others seem to disagree - see the comment below).
  • For other feedback than errors and typos (e. g. feedback for formulations or the organization of the book) be prepared that your comments may not be taken into account for various reasons.

Oh, and for the lecture notes I reward bonus points for every mistake spotted and submitted by a student.

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9  
There is no need to ask if such a list would be welcome. Well, I would probably ask first, because it's not worth the time to compile the list if they're not. I know one author who seemed to have little interest in this, and have heard of another who disliked getting errata. – Kimball Mar 12 at 23:57

Many professors are interested in receiving feedback about possible errors in their lecture notes or, more generally, in their course material, albeit they might not be able to amend it immediately.

Since your professor might already know about those errors, ask them politely, e.g. (maybe it's not the best possible phrase, but it's just to get the idea):

Dear Prof. X,

Since I'm currently reading your history module, would it be useful for you if I compile a list of errata?

Sincerely,

user50284

In this way you should not have any issue, even if they do not care.

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Collect all the mistakes/comments you find throughout the semester. Wait until the semester ends, and your grade is assigned. Send email to the professor with all your comments. You can also mention that you enjoyed taking the class, if you did indeed. Professors usually enjoy feedback, when it is made on clear professional grounds.

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9  
There is rarely a need to wait until the semester ends (unless you are actively trying to prevent the errors from being corrected -- indeed, authors are most active on their notes when they are teaching from them!). – darij grinberg Mar 12 at 19:19
    
Well, I've encountered people who would punish you if you embarrassed them in any way. So I agree with waiting until the grade is no longer a potential punishment. – WGroleau Mar 13 at 4:51
    
On the other hand, I've seen professors who reward good erratas. For example, in my country, the gradable activities in a module sum up to 100 points from which the grades are derived, but professors are allowed to provide a number of "bonus" points as well, so pointing out a mistake in the lecture notes can sometimes result in getting a bonus point or two. – AndrejaKo Mar 13 at 17:51

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