course
Honors Math B

May 2020

It's not an exaggeration to say Evan's class changed my life. He talks about linear algebra and multivariable calculus in a rigorous yet intuitive way. He lectures for the entire 75 minutes without stopping except for questions, providing definitions and proving theorems. The class goes fast. The material is hard. But with dedication, it's manageable even for someone like me who is mediocre at math. The class is filled with geniuses, but most of the time they're kind and willing to help their classmates. There is a strong sense of camaraderie. Get a few friends in the class to work together on homework. Taking this class with Warner will make you appreciate math in a new way if you haven't really been exposed to pure math and proofs before. This is not for an easy A. This is for a hard-earned introduction to higher mathematics through highly rigorous calculus and linear algebra.

May 2015

Having taken Gallagher for two semesters now in the Honors Math A-B sequence, my overall feelings for him are definitely very mixed. If you are looking for an easy time in an otherwise difficult class (Gallagher also teaches Modern Algebra and Modern Analysis), look no further. He prints out his own notes and doesn't need a textbook so everything you need to know is on those packets. You don't even need to go to lecture, since he just repeats everything he puts on the packets in lecture. As for grades, let's just say that last semester 75% of students got an A-range grade according to my transcript. He also gives out many A+'s. That said, if you are looking to really learn the presented material and get something out of the class, I would stay away. As a math major with a strong passion for the subject, I don't think I'll ever be taking a Gallagher class again. - He is not a good lecturer. He speaks very softly in at a volume that is probably softer than a normal person's talking voice so it's very hard to pay attention, especially when he's just repeating what's on the notes anyway. - He doesn't use a textbook. Some see this as a good thing, but as someone who learns best when given a very rigorous (albeit dense) presentation of the material, I found it hard to really learn the material through his notes. Gallagher's notation is his own which can be confusing, especially when his LaTeX skills are subpar and when his notes are not immune to typos. Besides from this, his class can also be a pain with problem sets and midterms. - Problem sets. The questions can be very tedious ("An exercise for the hands, not the mind" he calls them), very vague, or occasionally just plain wrong (which he doesn't acknowledge until a day before the set is due). Plus each problem set varies greatly in length - one week we had a four problem set which took less than an hour and the next week we had a twenty problem set. Not to mention, the TA's only end up grading a very small fraction of the questions, so it's possible that you get those questions wrong and get everything else right and get an atrocious grade on the problem set overall. Plus it just doesn't feel good to write out two pages of tedious computations if they're not going to be graded anyway. I just don't see the point. - He is very vague with midterms. He never makes the format explicitly clear, nor does he make the content. For our second midterm of this semester, we asked what would be tested on the midterm and he vaguely responded "everything, but only the short proofs." First of all, I don't see the merit in making us know every definition, theorem, and short proof to the point that we can recite them - it would be better to give us a list of the important ones he wants us to know and have us remember those (which my other professors do). Second of all, the proof he gave us ended up being Green's Theorem, which was one of the longest proofs of the semester (it was two pages long)! On the other hand, sometimes he surprises you with an easy midterm, which means that tiny mistakes have a huge impact. I forgot to state that an eigenvector must be non-zero and I lost 5/100 points on a test where we had to recite 25 total definitions/theorems verbatim. - The final is easy. 25 T/F questions. He tries to trick you, but if you know your stuff it's pretty easy to figure things out. All in all, Gallagher's class can be tedious and frustratingly vague, but definitely easier than other options for these theoretical math classes, and he gives out good grades VERY leniently. If you're looking to get something out of the class and really learn the material, I would choose another professor - they may be more difficult but it's worth it.

May 2015

If you are interested in mathematics as a field and have not yet finished the calculus sequence, take this course. It is much more interesting than the alternatives. It has some fun proofs and introduces topics like Fourier series and group theory that you would not see in a calc sequence. Grading is reasonable, workload on the lighter side. The midterms can be a little unpredictable, but usually fair. One warning: if you are only interested in calculus and linear algebra as a means to an end, do not take this course. You could certainly get the computational skills you need in the calc sequence instead; in fact, Honors Math is a little light on computations.

Mar 2015

This is not your grandfather's math class. Not your great-grandfather's either. In fact, Gallagher is the most brilliant mathematician I have ever seen. He loves the material and enjoys teaching a lot, and sometimes tell jokes about Prof. Goldfeld (who was his student!) or other mathematicians. Try talk to him after class, especially if you want to major in Math. He has notes for all the math classes taught here and knows every professor the extremely well. He is absolutely the best adviser you can have. (Also ask him about what he did on Goldbach conjecture, what his middle initial X stands for, how does he translate Vietnamese songs to English etc.) The con side of this course are that Gallagher go over the more advanced stuff pretty fast(maybe because they are not the main focus of tis class). It can be pretty hard to grasp when it comes to Analysis. Another problem is the way he teaches is based on theorems and definitions, which can be really hard to understand. But you are more than welcomed to go to his office hours to ask him for a geometrical explanation or questions on any problem for any math class. For the exams, midterms are straightforward, but final is something like 25 tricky true or false questions---they will be the most tricky true or false questions you will ever have unless you take another course with Prof. Gallagher.

Feb 2015

Very nice and funny professor. Not a really good lecturer. He just reads and writes down what's in the handouts and sometimes couldn't explain everything ( especially on the second part of the class) You could do fine on his class by just taking his handouts and learning the stuff. Midterms and Finals were pretty easy. They basically consisted of Definitions/Theorems and True/False questions. You can get an A or an A+ in the class by just learning the definitions and proofs word by word and paying attention to the True/False questions which can sometimes be tricky. Don't underestimate all the questions though, each one could cost you third of a letter grade.

May 2014

This is absolutely a worthwhile course to take if you have the necessary prerequisites and are thinking of becoming a math or sciences major. Don't be put off by NSOP's awkward avoidance of the Honors sequence -- if you're interested in proof-based math and up for a bit of a challenge, try it on for size. Like several students in Honors Math, I took both linear algebra and multivariable calculus in high school, so I very much appreciated a differently-motivated and more rigorous perspective. And this course will prepare you for upper-echelon math courses like no other. For example, Mu-Tao starts the first semester defining fields and finite-dimensional vector spaces, definitions traditionally seen first in abstract algebra, and often uses functional notation rather than matrix notation for linear transformations. In the second semester, Prof. Wang introduces you to analysis with the completeness of the real number system, and throws quite a few bones to topology along the way. As a previous reviewer noted, Mu-Tao is an excellent, excellent lecturer. He structures and organizes effortlessly, he tries to develop intuition (especially geometrically; as a analytic geometer he's also an accomplished sketch artist), he proves almost everything he states in a way that's easy to understand -- and he responds well to questions. He's also very friendly and helpful in office hours. Homework assignments are due every class (the assignments due after the weekend are generally longer, 2~4 hours instead of 1~3). In the first semester, most of the problems are Mu-Tao's own, but a couple of weeks into the second, all of them come from Apostol. With that shift comes a shift away from rigorous proofs and towards problem-solving. Additionally, the cramming of all of Calc III & IV into the second semester may at times feel a bit rushed. But all in all, this is not a difficult course to follow if you put your mind to it. Exams are all in-class and can be tough to complete at times, but Prof. Wang understands this and grades generously. As the previous reviewer noted, there's a good mix of problems, so you can play to your strengths, but there's not a lot of correlation between the material on problem sets and the material tested on the exams. That said, do the homework anyway because it'll enhance your understanding of the material from in class. Then when an exam comes around, do the practice exams, go to the review sessions (one before each exam in addtion to regular weekly recitation), and re-read your notes -- you'll be good.

May 2013

Overall, I walked away pretty happy with this course. Based on reviews of previous iterations of the course, it sounds like this one wasn't nearly difficult was the killer courses with Savin and Friedman. It follows the second volume of Apostol's textbook very closely, and served as coverage of linear algebra and multivariable calculus, and basic proofs. Since multivariable calculus is covered in two separate courses, calculus 3 and calculus 4, taking this class is a good idea if you want get the material out of the way in a single semester. Professor Wang was an excellent lecturer who covered material very thoroughly in class. He moved quickly, but he was very thorough and wrote down everything that was important on the blackboard. He did tend to focus on long proofs that were never to be seen again, but he also did a great job conveying the intuition behind the material. Homework was assigned twice a week every week, and the length of the homework varied a bit, but it usually didn't take too long. The assignments were almost always out of the book, and this was probably the biggest weakness of the course, because the problems in the book were generally not all that great. During the first semester, when we did linear algebra, they were generally decent. During the second semester, when we covered multivariable calculus, some of the problems required excessive tedious algebra without having much value or relating to what we were emphasizing in class. There were three times when the professor wrote his own assignments that were not from the book, and honestly these were the most interesting and relevant assignments that we had. It would've been nice to have more proofs assigned during the second semester, where the homework assignments were almost entirely computational. The exams were very fair. Usually 40% of the points came from true/false questions and the remaining 60% of the points came from longer problems. There was usually a good mix of computations, conceptual problems, and short proofs. Usually the average was between 70 and 80. He clearly didn't design the exams with the intention of them being brutal and the averages being very low, as he expressed disappointment when the average was in the low 70s. He is also very good at writing problems that simplify very neatly, and is not interested in making the students crank through a lot of tedious algebra on the exams. He also does not penalize students multiple times for the same mistake, and if a problem has multiple parts, missing one does not imply you won't be able to do the later parts. The most relevant preparation for the exams was the practice exams that he provided beforehand, for which solutions were provided, and he or the TA worked them out in a review session the night before the exam. Seriously, these were golden. The exams weren't copies of these, but some of the questions on exams did emphasize similar points (that might not be seen in the homework) and got you thinking in the right direction. Comparatively, the homework was not very helpful for exam preparation.

May 2012

Well, I just survived a year of Honors Math, and now that I've gone home and thought about it, here's my review of the course. To begin, Prof. Savin is a savant (look him up online and be amazed at all his accomplishments, which includes a perfect score at the IMO) who can effortlessly teach without notes and solve most challenging proof problems on the spot. Really, the greatest impediment to the teaching is his wonderful but sometimes incomprehensible accent, but his notes on the board and his office hours more than make up for this minor shortcoming. If you truly enjoy the intricacies of math, I highly recommend you take this class, which serves at the alternative to the laughable Calc III sequence. (The class started with 90 but eventually whittled down to about 30 by the end of second semester.) It's sufficiently challenging enough to get you well-acquainted with the higher-level math courses in the department, and despite the incredibly low test averages (see below), there is a very generous curve that will save your grade at the end of the semester. Plus, the second semester of the course is much easier than the first; perhaps at that point, Savin has successfully conditioned his students to expect the worst on his exams and they react accordingly. Lastly, the only way to study for Savin's tests are to make sure your definitions and ability to do computations are solid, because you're going to get destroyed on the proofs he gives out regardless.

May 2012

Savin is a brilliant guy, but brilliance doesn't necessarily come from other brilliant people. This is not his first time teaching a freshman course, but he clearly did have much higher expectations at the beginning than we were capable of fulfilling. Much of this was due to the lack of transition from computational math to proofs. His proof-based homeworks were very insightful, or at least they would have been if anyone knew how to do them, and those who claim they did can't really be sure since the TA was clearly not thorough. It takes a lot to teach this class, and Savin did a great job. However, there is a stern line between teaching how to get from point A to point B and just telling a class it should be at point B by next Monday. This was particularly true once multivariate integration came back and the class had absolutely no clue how to handle parametrization let alone surface integrals, divergence theorem, etc. Savin had little time, and that's probably the Achille's heel of this class, so he has to send his students to the book for practice. Unfortunately, Apostol (our textbook) sucks at establishing a basic understanding of the subjects it teaches. It teaches from a proof-oriented perspective and then throws a bunch of poorly worded and arbitrary calculation based problems in the exercises, but I do have to admit the grueling differentiation exercises were good. All and all, the nature of this course is much like reviewers for other professors have stated, so I can't really blame him for the content. The curve is alright but nothing to keep your hopes up for. I think Savin curved the mean to a B+, and if you screwed up any of the actually do-able problems you were thrown back far. If you did the impossible, you were thrown ahead. Studying helps to a point, but intuition is where its at. Savin's personality is very unique. I don't think I could do it much more justice than has been done below, especially the amazon one. He's an impersonal but warm fellow who is always looking to help when he's teaching (he really does scan peoples expressions to see if they understand what's up), but he won't go out of his way to help you or show you a drop of mercy. The TA was good for the most part, but he quit giving homework solutions after they were turned in, which would have helped a lot for some problem sets. Overall I'm glad I took this course. It was a good introduction to higher mathematics and whats along the future. Would honors linear algebra and Calc 3 and 4 have been better? GPA-wise probably. Proof learning-wise probably. Stress-wise probably. Experience-wise who knows... probably. Savin's great (not that he'll even be teaching it again), but the course is too vast to give more than a wishy-washy understanding of all it entails and the grade distribution promises to hurt at least half the class.

May 2011

Professor Friedman is awesome. Having had absolutely no background in higher math, and a lot less experience than some of the class, I still truly enjoyed both semesters. That said, I'm not one to be demoralized by seemingly impossible problem sets, or less than fantastic grades, and didn't ever find that either of those things interfered with my enjoyment of the class. For those who aren't this way, be wary, but if you are willing to put in the work, you will come out of Friedman's class with a tremendous improvement and a truly deep understanding of what you've learned. Though all of my classmates that I've talked to have varying opinions on the class itself, we all agreed on that. Often Friedman wont answer questions immediately because he carefully plans out the structure of his classes, and likes to stick to this. This never bothered me because his lesson plan is brilliant and incredibly well thought out. I also really liked his teaching style and thought he was very clear, but it may take some getting used to. He wrote our class notes, which totaled a few hundred pages, himself. The problem sets are difficult, and existential-crisis-inducing if you decide to start them 12 hours before they are due. However, they are meant to be done in groups, and they often took my friends and I even longer to finish because they inspired conversations that gave us a deeper understanding of the material. Ultimately, I loved this class and was so glad I took it. Friedman is fantastic, and though the class is incredibly challenging, it is completely worth it.