Letter and improvement on Algebra recovery

[Dens]

I am going to separate the thread into two topics. I don't think it's necessary to make two threads

I am a math major in 3rd year doing an honors degree. My college's honors program doesn't require a thesis, but I am going to do it anyways to challenge the messed up system we have here

Letter

I am wondering if it is okay to ask professors to include the following things in their letter.

1. I go to a fairly small college, undergrad research is there, but limited (not to mention fairly competitive). I unfortunately needed to take summer classes pretty much every year (and next year too), so I will not have any time to do research and this could hurt my application.

Does it sound like an "excuse" (it technically isn't) to ask one of my prof to write this? What happens if more than one prof includes this? Two of my profs are gladly to take me on, but after I informed them about my situation, they understood. I am not sure if they'll both write it and it would be rude to pry.

2. About some terrible performance in 1st year. Is it unnecessary to include things about first years or some courses that were horrendously impossible? One of my writers was a prof who's known to give out dumb down hard exams and I've aced most of hers, so I am darn sure she's going to write something about it,

Algebra

So I recently took a course called "Abstract Algebra" (aka Modern Algebra, but I will refer to it as "Algebra" throughout) and this was single-handedly the worst math class I've taken in my life. It may have something to do with the fact that I was also taking Real Analysis at the same time, but this course was just ridiculous. Let me explain how I am mathematically damaged in this class.

The professor is a nice funny guy (crazily funny, to the point where he acts more like a clown sometimes), but he just absolutely cannot teach. He gives us wrong intuition and methods for doing things. For instance, you know how we are supposed to evaluate compositions of functions from right to left? He does it the other way around and tells us left to right is stupid and the book is wrong. Most lectures consist of him writing a proof, messing it up, rewriting it, messes it up again, and finishes the proof and the class.

Asking questions in class was pretty much hopeless because none of us knew what the prof was doing and sometimes he even doesn't know what he is doing. Getting ahead is even more impossible because we aren't going very linearly. To give you an idea, we somehow did subgroups before did groups and then we did direct products before isomorphisms

The evaluation is the worst. To the point where people are getting undeserving grades. On one midterm he asked us to write out the $D_4$ (dihedral group) table in an hour long exam, yes that was actually a question. In another question, he put a question on a chapter where he specifically said we should skip. The other questions were okay and fair, but the marking was crazy. He pretty much gave you 100% if you attempted something. The guy who sits nexts to me does not even know what the symmetry group (take $S_3$) is and he got over 90% because he told me his strategy was "take the opposite of what he says in class and write whatever definitions that's relevant to the question". While, I on the other hand did the proofs correctly and not write random things and got the same mark as the guy who regurgitated a bunch of definitions and got the same grade I did.

On another midterm, I was bedridden and the health center was closed (conveniently) and I had to write these crazy exams while running out of the exam room to the bathroom a couple of times. Naturally I did horrible.

We had our finals last week and he told us he would give us a practice final and 80% of the practice final would be the same as the real one. The real one came and it was the opposite, 80% was different.

Self-studying was difficult since we didn't use a textbook, but an out of print book the prof used when he was an undergrad.

Reading many forums, it would appear that this is not normal, that is, as someone who is taking Analysis and Algebra together, it would make sense that one would do much better in Algebra than in Analysis and boy is that not for me.


So thanks to this, I am discouraged from Algebra and don't know how to recover. Algebra is an important class for grad school and being fed with wrong concepts and ideas from the get go is damaging my future. Any algebraist could give some advice? I plan to start over and doing everything linearly and get a real textbook. I've stocked up Fraleigh's and Dummit's look decent.

 

[Vargo]

So you didn't like how the professor taught the Algebra course. My number one piece of advice is to keep it to yourself. Plain and simple: professors distrust students that complain about other professors. Try to stay "professional" and avoid dramatic words like "damaged". Also, avoid saying anything disparaging about the school you are coming from. If you are doing a thesis for your own edification, that is great, but never refer to your school's "messed up system" because you will be seen as a product of that system whether you like it or not.

A question for other people. Does undergraduate research matter that much? I suppose at the very least, it is an avenue to get a better recommendation letter.

I wouldn't ask your recommenders to include any particular thing in their letter. If there is something you want to say to the graduate program, you can say it in your own letter. On the other hand, you can bring up this issue with them as a concern. See what they say. Do you think they would agree with your assessment that undergraduate research is impossible in your situation? Ultimately, they probably agreed to write a letter for you because they think they can write something helpful. You should defer to their judgment and experience on what a graduate program (in mathematics??) would like to know about you.

Back to algebra. I am not an algebraist but I did pass my grad school's exam on algebra. I used Hungerford to prepare. As an undergrad I had Dummit and Foote. D&F never really suited me. Too wordy maybe. Why do you think you need to revisit algebra before grad school? At the minimum you could probably get by just knowing what is a group, a ring, a field, and a module. Learn linear algebra really well. Graduate level algebra usually starts at the beginning.

 

[Robert1986]

As a side note, the composition thing really isn't that crazy and some people prefer to write things that way; I don't see how this could give you wrong intuition.

What book is it that your prof is using, BTW?

I'm not an algebraist (well, I'm not an anything at this point) but I really like Dummit and Foote, and it seems that most people either really like it, or really don't like it. I think that if you have a fairly good understanding of groups, rings, fields, modules, vector spaces and the like, D&F is a good book. As Vargo said, it pretty much starts from the beginning, but it goes faster and covers much much more than an normal undergrad algebra book. For example, neither of Herstein's two books even mentions things like group actions, yet this is an extremely important algebraic concept. I also think D&F explain things like isomorphisms better than lots of other books.