Seriously, what is this supposed to be? "Teaching Math to Retards the Wrong Way"?
Again, the dumb bitch puts matrices in the middle of the bloody paragraph instead of using display mode. More over, this is supposed to be for mathematicians correct? Then you don't need a retarded example of 3I to each this. Just give the genera definition, i.e. a scalar matrix i a matrix of the for cI where I is the identity matrix. Even then, that's something you learn in Algebra II (high school not university) level math, so that whole paragraph is unnecessary. Even if it was, the only thing seemingly of substance, the determinant being lambda^d is not explained at all. If someone doesn't know what a scalar matrix is, how will they know the lambda^d thing? What she should've explained is the determinant in its full generality and then illustrated how, for a triangularized matrix, the determinant reduces to the product of the diagonal. That way the result is obvious. [Again, none of this should even be here though, especially if this is a thesis. Even if it's a book to teach math, it's a horrible approach, even for a "learn by example" approach].
She also says things in words which would be easier said with symbols (i.e. such that could be | or : to condense). It's just so atrocious. I honestly cannot stand it.
Also, the way she writes her cycles in the first image is disgusting. There should at least be a small space in between them, or, at minimum, between the ldots and the numbers. Also, maybe my understanding of the symbols is incorrect, but how does (11…1k) represent a k cycle? A n-cycle means that, effectively, only n elements are changing from their original position (in a cyclical pattern, i.e. to differentiate from two separate 2-cycles). But the above symbol doesn't convey that. You'd be better off saying (x_{1} … x_{n}) to convey an n-cycle. Also, she mathbbs NUMBERS? Honestly, why not just use N, Z, or, if "NUMBERS" is something special "A"? Lastly, 20 = card(Z)/card(20Z). Now, I'm no logician/set theorist, however, since the cardinalities are both infinite and division for cadinals >= omega_{0} are not well-defined, the result makes no sense. Actually, if anything, Z and 20Z have the same cardinality, hence the result would be "1" if someone wanted to actually attach some form of measure to this. (Really, the best you could do is a re-imagining of for cardinals, letting 0 denote less, 1 denote equal, and \infty denote less than).
Honestly, I want this shit spammed everywhere along with corrections to her work/pointing out how it should be done. Mathematicians may be passive aggressive but when forced to eat their words (at least when from what I've seen) they do. They might not side with you, but they'll shut the fuck up.
Also, I just noticed in image 1:
Well, I guess that explains why it sounds so fucking retarded. They really do read like someone's personal scratch notebook and not like a legit. text. (Even then, the point of a course is to go over general material and sufficient examples such that you understand the deeper meaning of the material. Consequently, by looking at the general definition one can recall and understand the entirety of the idea. Therefore, for her note-styled book to be riddled with examples [low-tier examples at that, for basic math] shows that she didn't truly grasp the material the first time).