110A is a sort of weird class because there is a lot of math that you learn in high school and college that keeps building on itself and this class just doesn't use any of it. Theorems in this class require no calculus, no vectors knowledge, or anything like that, and so it would really not be hard for a 7th grader to understand the theorems.

That being said, the homework forces you to get really good at guessing. The theorems are easy to understand, but it takes a lot of homework problems to learn how to apply them. It is really hard to find a consistent way to learn how to tackle the problems but I think the book sets them up in a fairly good way, so regardless of what the homework problems actually assigned are, you should do the problems in the textbook in order.

Roughly speaking, the class spends the first 2 weeks talking about integers, modular arithmetic, and congruence classes in Zn. This was the material covered up to the first midterm.

The third and fourth weeks are spent mostly discussing rings, integral domains, fields, and their properties, such as units, zero divisors, field implies integral domain, and so on.

The fifth week through seventh week or so are spent covering polynomial rings and discussing the similarities they have with the integers. About half the material from polynomials appeared on the second midterm.

The eight and half of ninth week were spent on congruence classes of polynomials with material covering when such congruence classes were made modular irreducible polynomials.

The rest of the time was spent covering ideals and quotient rings (though one lecture was missed due to the fire). The material on the final focused not just on the later material, but also ways in which the later material could be combined with the earlier material. For example, prove Z28 x Z5 is congruent to Z35 x Z4.

The tests were fair, though like the homework, they require a spark of creativity to understand how to prove the problem.
First Midterm Average: 76%
Second Midterm Average: 73%
Third Midterm Average: 80%

Basically, don't screw up on a test because the averages are high and they don't get dropped. Also, I get the feeling he doesn't give out a lot of As. Got an 89 on the first midterm and 95s on both the second midterm and final and ended up with an A- in the class.

Lectures are really clear and also he pretty much just follows the book, doing the same examples and ideas, and really only skipping one or two sections. The class did not feel rushed and yet we covered pretty much all of the course material.

Overall, professor with great understanding about material, accent pretty much unnoticeable, nice course about number systems with a lot of practice and examples, just little to no idea of how to apply it outside of computer science and somewhat hard grading.

Ascenbrenner is a really nice guy. The first day of the class, he tells you that the class is curved, and that scares the hell out of you because you know only a certain number of people will be getting A's and some people will definitely fail. But as you move along, it's not all that bad. He does a lot of proofs to try and get you to understand the math so you don't have to memorize any formulas. His tests were not really all that bad. I remember getting a question on the second midterm completely wrong because I flipped a minus sign to a plus sign, and I still got 9/10 points. Overall in the class, I had a test average of about 87% or 88%, and about 90% on the homework, and I ended up getting an A-. You'll end up learning a lot from him, and he's not really a tough professor at all. I do recommend him, even though I heard Park was easier. (P.S., the curve ALWAYS helps you)

Professor Aschenbrenner is not really the best professor I've ever had. He's always showing up to class disheveled and it's very easy to get distracted by a variety of his colloquialisms. This having been said, his lectures themselves are straight-forward, and his homework is not particularly difficult. It is strange, then, that his midterms and final were so difficult to perform well in. The grading is very strict and there are almost always some sly tricks which make it very easy for students to mess up. He's very strict with partial credit as well so make sure you check your work many times over. My quarter there were two very different curves for the same class, so I would make sure you try your best to get the best TA in your lecture.
He's a pretty good professor though.

Professor Aschenbrenner is a great person but not so much a great professor. His lectures are very straightforward and follow the textbook almost word-for-word, which is not the greatest motivation for you to attend lectures. After all, you can just read the textbook. However, his lectures are not too bad. He is a genuinely nice guy, and he seems to care very much about his students doing well in his class, and I guess that makes going to lectures just a tad bit more attractive. His tests (two midterms and a final) were all very straightforward. He taught us everything we needed to know to do well on his tests. He even gave us hints one day as to what would be on the final. Both of the lectures he taught had very high averages, which in a sense is good but will destroy your grade if you don't score close to or higher than the average.

I had Professor Aschenbrenner for Math 31A. I had already taken Calculus AB in high school, and gotten a 4 on the AP exam (like most students in this class). Many kids never showed up, except to turn in their homework on Friday. I, personally, am the type who would rather spend the allotted time in class learning the material, rather then teach myself on my own time, but since everyone pretty much knew it already, it wasn't a huge deal. The homework was easy and short, but graded pretty harshly, so make sure you do them all right (although it is not a huge portion of your grade). The two midterms and final were pretty difficult and there was a spread of 11%-100% on all of them. I got a 76 and a 63 on the midterms, and an 85 on the final. My final grade was a B+ in the class. The curve definitely helps. Know your absolute value, he makes every easy problem harder by making it an absolute value problem. The discussions were not that helpful, as most of the students already knew the material, but they were used to get answers to more difficult homework problems. All in all, it was a pretty fair math class, and by taking it again, I understand it in much greater depth than I did in high school.

Aschenbrenner explains concepts very well; rather than throwing formulas up on the board, he guides students through the math by presenting a problem and then walking through how to solve it. His proofs were extremely helpful.

His tests are pretty difficult, but also generously curved, so I never really had a problem with them.

I highly recommend him. Great teacher and fair tests.

Funny professor but the material he covers are merely examples from the book. Going to his office hours are useless because he looks frightened when students ask him a question (he does not know how to correctly phrase his answers). In order to do well in this class 1. be really good at algebra 2. do the homework well in advanced before your discussion (and try to pick a Thursday discussion since 2 lectures are already covered) and 3. PRACTICE. The good thing about this professor is that he offers a vast amount of practice exams on his website. However, his teaching method should, no MUST, be improved. Also I noticed that his teaching style correlates strongly to that of the Calculus videos from MIT...

HE COMPLETELY SUX !! HE IS ALSO MEAN ! DONT TAKE HIM!!!

I had him for both 31A and 31B. It's pointless to complain that he just reads off the book, cuz he explain the stuff so well along the way so you don't need to read the textbook on your own. Lots of sample problems in the lectures are highly related to the tests but are not in the textbook. Other than that, he's a funny & approachable person, giving out around 30% A's (Brown gives out 13%, Radko 23%, Biskup's is unknown but good luck with him). Get a great TA is also important (Matthew for 31A, Jaclyn for 31B). Got 2 A's with almost minimal work, so I would highly recommend him.