[MATH V2010] Linear Algebra

Bayer is very interesting as a person and very intelligent, but I think that doesn't necessarily equate to being able to teach. He's incredibly unorganized and assumes that everyone in the class knows what matrices are and how to work with them. One class, he breezed over a new topic but then spent about ten minutes talking to us about how to factor a second degree polynomial.

He posts tons of practice exams on his site, which are the key to studying. However, I feel that, by doing his previous test problems, I'm learning a method for how to solve his specific questions, I'm not learning linear algebra. If I took another linear algebra course elsewhere I'd have to start essentially from scratch.

So sure, if you're naturally really good at math and have never had to study it, you probably will get an A. For me, I had to work really hard to do decently, and I still don't feel as though I'm learning anything. I really don't recommend this class.

Let me start of by saying this: only around 50% of the students showed up to class. Maybe it was the time that this class was offered (6:10-7:25 pm), or his monotonous voice that seemed to put half of what was left in class to sleep, but it made it very appealing to most to just simply skip class and read out of the textbook (which he followed very closely).

If you do show up to class though and listen closely, you can get a lot out of the class. Although many students got by skipping classes and handing in tedious problem sets, Professor Stein is very knowledgeable about both Linear Algebra and what exists beyond it. He goes into many proofs in class (albeit terse) that are not necessary for exams but may be of interest to some math majors. The last class he gave us a very brief preview of analysis and modern algebra, which was very interesting to say the least.

Professor Stein is extremely helpful when it comes to office hours. He is exceptional proficient at fielding questions both from the homework and those outside of class and is always available for assistance. Professor Stein is unique in that he insists on solving problems his own way, and learning about the logic behind his methods is very helpful in understanding the underlying concepts behind the course. Although theory is not emphasized nearly as much as problem solving especially in the textbook, going to office hours is a huge help in this regard.

Lastly, the exams. Around 6 problems each of the two midterms, and around 10-11 for the final. Both midterms have around 5 problems modeled after homework problems, while the last problem is usually a more tricky question that involves some of theory and understanding the concepts behind the problem solving. The final is also straightforward except for some tricky questions. Going through past problem sets over again is easily the best preparation for all of his exams. Be sure to be extra careful with arithmetic calculations; you can lose a lot of points from simple miscalculations.

Many that take this class find repetitive weekly problem sets and exams. But for those willing to show up to class and willing to go to office hours because they want to learn more about the problem solving and understand why linear algebra is important, there is a lot to be found with Professor Stein. The amount of interest you put into this class is directly proportional to how much you get out of it.

Catherine Williams is probably the best math professor I've had at Columbia. If you're in SEAS like myself and you have the choice of taking the math department linear algebra with her I would take that opportunity. I can't speak to which course is more difficult, but I've heard bad things about other linear algebra sections in both the math and applied math departments, which some of my classmates found to be painful, and certainly far from enjoyable experiences. Not so with Catherine Williams. I mean the fact that she speaks English clearly and fluently already makes her a cut above the rest for a science/math professor, but moreover the clarity in her proofs and explanations is second to none. Tests aren't easy, but generously curved, she's helpful in office hours and she'll bother to remember your name if you show up, which is a nice touch for a large lecture. I also agree with the other reviewer who mentioned that she's not exactly an eyesore either.

Bayer is not only a phenomenal teacher, he's also an all around incredible guy. Spend time talking to the man, he always has fascinating stories. He also is a great teacher, being in class is not necessary but very fun and helpful. You don't need the textbook since he'll make sure he teaches a ton of different approaches in class, including some really great short cuts. This class was easy, but only because he gave us the tools to make it easy. Take this class with Bayer, you'll get a good grade, learn something, and have fun while you're at it.

I loved Catherine's class!

I've been into math through high school and college, but this was my first time taking linear algebra. Catherine was by far the best teacher I've had at Columbia so far. Her lessons were clear, and she was very helpful during office hours. Compared to other sections, I felt like her class was indeed harder, but put in the effort, and it'll be worth it. The exams were challenging, but she grades generously at the end.

Warning!
This class is extremely easy.
You have to be really dumb to not do well in this class. To elucidate my point, I'd like to point out that more than half the class got 100% on the first midterm, and the trend was more or less maintained through the second midterm and the final.
I went to the class only for midterms and the final, and I got an A+. The secret to doing that is to solve all the previous exam questions he has on his website before the test. And you'll learn it by doing it. The questions are always asked in the same fashion as he has been for the last 10 years, so no surprises there.

For all the people heading to the bookstore to buy/rent the textbook for this course, I'd say please don't. It will be completely useless with Bayer because you don't have any homework.

Linear Algebra is a requirement for many majors, so there were people from many different backgrounds, which was interesting. It is supposed to be very different from Calculus III - and it is. Though matrices might seem confusing at first, by the end of the course I realize how useful they can be in so many problems, especially if you are interested in economics.

Bayer is an amazing instructor and focuses on intuitive approaches to math, rather than old textbook formula-learning. He writes on the black board extensively, so it is one of those classes where keeping up with lectures is a must. He has a sense of humor and also recalls many funny stories. He is also eager to push students into more advanced math classes and to explain complex topics which are not really in the scope of Linear Algebra, but fascinating nonetheless. I really enjoyed his approach and would recommend Bayer to anyone actually interested in Math.

I thought Catherine was an awesome prof! After being turned off math from a bad experience first semester of Freshmen year, I now wish I had majored in it. Partly I think this is because the material was pretty cool, and Catherine will never fail to point out how neat some of the theorems and proofs are (I agree!). But it sure helped that she was genuinely enthusiastic about linear algebra and tried to get us excited as well. She always stayed behind to entertain whatever questions, scheduling problems or vague mathematical ruminations we had. I thought it was incredibly nice of her to try and remember all our names.

Catherine is really good at explaining abstract concepts and won't shy away from attempting an intuitive explanation or non-intuitive ideas. I'm a senior this year, and this is my first CULPA review. I just felt compelled to write one because I really think she's a star instructor.

Catherine was by far the best math teacher I've had at Columbia. Her lectures were extremely easy to follow, she made a fairly drab class pretty lively with her ebullient personality, and since I'm a non-math major guy, most importantly, she's quite good looking.

Catherine really cared about her students and made herself available often for office hours, and one thing that really stuck in my mind was that she made an effort to memorize all of the students' names, even though it was a 100 person lecture.

I don't know if she's tenured and will be teaching again, but she should be- her linear algebra class was my favorite class of the semester, mostly because of her teaching style.

ZOMG Catherine is amazing! Her lectures are really well structured and easy to follow. She does cover a lot of ground in a short time though, so its easy to miss major things.
She also brings a level of enthusiasm to her lectures that is rare for a math class, and it helped keep my attention from wandering during class.

I got the feeling Prof. Williams wanted us to have a really solid conceptual appreciation of the math. Homeworks and exam problems tended to be 1. tough 2. reliant on knowledge of the theory. You won't get very far by just knowing how to do the cookbook algorithms for problems.

She's also very helpful discussing concepts or tough hw problems (lots of these) in office hours, which meant they tended to be overrun, but that's not her fault.

She's also really nice, will remember you by name for the entire semester, and when her phone accidentally went off on the first day of class, the ringtone was the Star Wars cantina song! *heart*

Odd but brilliant and a fairly good teacher. This was a tough subject matter to teach in 6weeks, but Irena manged to get most points across. Proof intensive, so make sure you have time to absorb such ideas (unless such things are not an issue for you). Irena was always there after class to go over the points of the class. However sometimes her points were not so helpful as "look at it harder" doesn't always help. Nevertheless I found her willingness to go over the problems and each step of a proof to be helpful.

To Monty Python fans:
Lectures play out as the lost Linear Algebra segment of Life or Death Struggles.
http://www.youtube.com/watch?v=0p-cY1XWN_Q

It does become a life or death struggle to stay awake during lectures, but the achievement is worth more than the accompanying bragging rights: Ovi knows his stuff and consistently explains things clearly, not to mention the in-class examples are very useful when it comes time to do the problem sets, as the textbook is scrimps on the details in places.

The midterms are fairly straight-forward -- similar to homework problem sets and most certainly the practice exams in difficulty and material. But the final was another beast entirely, as it was much trickier, more time-consuming, and generally harder than the midterms (no helpful multiparted questions to walk you through to the major point - he goes straight for the jugular on the final). The general consensus was that the class average was too high going into the final, and Ovi decided this had to change. Read: a very manageable class up until the final 2 weeks or so, when you tie your brain in knots trying to remember every minute detail about linear in/dependence etc. and then try to think critically. It's not necessarily catastrophic, but there will be an explosion of some degree.

Ovi is just as awkward one-on-one as he is in class, but he is quite reasonable, even nice (apologetic may be pushing it) if you've been unfairly graded.
Bonding with the TA's isn't necessary, but it wouldn't hurt your cause if you were unjustly docked points, which is a more common occurance in this class than others because of the extensive room for error in dealing with high-volume matrices.

Overall, it's not a difficult class, but do expect to put in some effort. Actually sleeping at night is essential, because with all the numbers running around in the matrices, it is very, very easy to lose a lot of points on careless errors (speaking from a friend's experience). Not an earth-shatteringly enlightening class, but recommended considering it opens the door to the fancier cryptography class on making and breaking codes (MATH V3025). And hey, Ovi's goofy mannerisms are kind of endearing (be on the lookout for his understated but abrupt expressions of personal opinion -- even if you don't appreciate the perhaps unintentional comedy, it'll at least make you pay attention).

I had Linear Algebra with Dvora during the summer semester of 2009. I found her explanations to be very clear, in spite of the difficulty of the subject matter. I truly believe that any mature student who has a solid background in Calculus and Differential Equations will be ok in this course. Dvora seemed very approachable and had no problems answering questions. I don't know how accessible she was because I work full time but she did offer opportunities to meet before the class to go over the homework. I found this to be very helpful. I would take her again.

Elliott Stein does not deserve a silver nugget. True he may be fluent in English, but he teaches with so little enthusiasm, I (an applied math major) could not pay attention for any length of time. Also, he teaches straight out of the textbook, which in most cases is not a bad thing, except the textbook chosen for Linear Algebra was deplorable. It only teaches equations/applications, so there are no underlying concepts motivating the subject. Again, this seems like a minor issue, but when you're doing hours of repetitive homework every week, it begins to weigh heavily on the class.

Now, about the homework. From the beginning, it took hours to get through. He assigns two of every type of problem, which is unnecessary for introductory ideas and time-consuming for later ones. In short, the work was tedious.

Perhaps the saving grace of the class was its exams. They were very straightforward: out of six questions on each of the two midterms, five followed straight from the homework and the last one was only slightly different. But beware, the grading is tough. My friend made one addition error and got less than half credit for the question. The final was basically two midterms.

Honestly, I took this class because it is required and I wanted a decent grade. That is all I got out of it, too, since I learned next to nothing in terms of linear algebra. As to whether I would recommend it, well, if you are simply looking for a good grade and don't mind setting aside a few painful hours a week, this is the class for you. But still, keep your eyes peeled for a professor that can make the class less frustrating.

I had the unfortunate experience of having her for Linear Algebra over the summer. Dvora is someone you want to avoid at all costs, even if it means taking the class a different semester. She has no problem ridiculing a student in front of the entire class, and is unavailable to help when asked. She will ensure that all students in the class know which students are doing poorly. Her explanations are unclear and disorganized, and if you ask for clarification she will tell you how simple it is and that you should have understood it the first time. I cannot stress enough how much you want to avoid her.

As the first reviewer said, Thibaut is hands down one of the best instructors you could ever hope to have. He's a great communicator, and a great lecturer who really does care about whether or not his students learn. Outside of call, he's incredibly generous with his time (e.g. holding office hours every day for an hour during the summer term, when most summer instructors will only give an hour a week in the summer). He'll ask a lot of you, and work you incredibly hard, but you'll be rewarded with a very solid grasp of the underlying mathematical theory that should prove immensely helpful in future courses that use linear algebra. Highly recommended.

Professor Pugin was hands-down the best professor I've had for any math course. He's extremely demanding, but he's great at explaining and he works very hard to help the students, so you walk away learning an incredible amount. He's also French, which means that you learn a lot of theory and proofs in his class, and less applications. For me, that was great, I'm going on to pure math. For people who want to do applied stuff, well, it's still great. Because you'll understand the math you'll apply later.

One problem was that it was a summer class and he didn't like the textbook. I agree the textbook sucked, but in a summer class you really have to do a lot of work at home, so you need to have a text that you can refer to. Not having that made the class very difficult.

Also, his tests are rather difficult even if you understand the class material, and I've heard that this is true for other classes he has taught.

There is no doubt that Professor Zheng is a talented mathematician, but he clearly lacks basic teaching skills. You can barely hear him in class, and he faces the board most of the time, even when he is explaining things, which made it almost impossible to know what he is talking about. Also, his class was incredibly boring, so most students simply skipped his lectures and only attended class to take the exams. I went to class for the first month or so, but then I realized that I actually learned more from reading the textbook by myself and stopping by the Math Help Room when needed. The material from this class was not particularly difficult, so if you are willing to spend time reading the textbook and understanding the assigned homework problems, you should do fine. Now, that is not to say the class was easy. So do consider taking it with another professor if you can.

Professor Hou is a great math teacher. After having taken classes with him over the course of 3 years, he is one teacher that I can rely on. His lecturing style may be quick but each lecture is very clear. He breaks things down and explains concepts thoroughly, plus he draws really awesome pictures/graphs to go with almost everything. He seems very conscious of his English skills, but he speaks clearly albeit with a slight accent. On the board he is not only legible (which, in the math department is hard to find) but he writes nice and big and always steps away for you to copy down the notes. Although he may make a few mistakes during class, he doesn't make many (always double check with the textbook). His courses are the few math classes where I studied more often from my notes than from the textbook.

For all of the courses, he has a different strategy for grade breakdown, but it never strays too far from a standard h/w-midterm-massive final mold. His course website always is up-to-date with assignments, assignment solutions, and dates of tests/exams. He usually posts practice midterm(s) and final with solutions and gives a little review of topics before each.

He may seem kinda awkward, that is because he is. Thus, he may seem unapproachable, but do not fear, you can usually find him napping/wearing awesome slippers in his office during office hours because nobody goes. He has office hours twice a week (for A+O an additional problem session on fridays) and he is always happy to explain things if you just ask!

The bottom line: he covers material in a timely fashion, and he is organized. If you want to actually learn some math and not just stumble through a course, Hou is the man. It is totally possible to get a good grade in the course if you put the necessary effort in, and I would say the grading in the courses is consistently fair (curved to a B/B+ avg). If you have the opportunity, take Hou. (his vast collection of sweater-vests is also a plus)

I highly disagree with the previous comment. Matt was a dedicated teacher, put into a difficult situation because of the range of student-ability in the class and the fast paced summer schedule. Nevertheless, he had office hours every day and was always willing to meet at other times and discuss problems. The tests were fair in the sense that many of the problems were similar to the homeworks assigned with one or so problem more challenging. All in all I felt I walked away appreciating linear algebra and would recommend taking a course from Matt.

By-the-book (literally), fair, and utterly unremarkable professor. Mind you I'm writing this review more than a year after the course, but it was really quite ordinary, about what you'd expect from a large lecture where you do the problem sets, take the tests, and you're done. I got the tools I needed for more advanced classes and I have no complaints.

Problem sets were weekly with one dropped, entirely fair. Lectures were boring when I went and followed the textbook almost to the letter. Professor Hou's English was fine, and he's nice enough.

As I recall, the midterms were much easier than the final, which incorporated some not-in-the-textbook material introduced in the last lecture, which I didn't attend. Oops.

Worse teacher in the Math Department by far.

I am a math major and I've seen a bunch of professors in the Math Department. This lady is the worse by far. Use itunes U; look up the MIT lectures if you really want to learn the material (at least that's what my friends and I did) since her lectures are a waste of time. There were 42 kids in the class. Less than 10 showed up to the lectures.

Mirela will waste all of class on a single proof that she will not even finish. She does not draw any maps of subspaces nor any proper graphs in 3-D space of the vectors she discusses.

It is crucial to have an answer manual to the textbook. This will teach you how to do the homework problems. There was never an occasion when she did any problems remotely similar to the homework in class.

Mirela is neither a good teacher nor a particularly nice teacher. She refuses to move a midterm if you have a family emergency-- instead, she is "willing" to shift your grade to another midterm. That doesnt reall help. Teaches too long on the easy stuff and is forced to go really fast through all the easy things, often not teaching the stuff in class that is on the homework. The book is absolutely terrible so good luck learning anything from that either. While the first midterm may be easy, dont be fooled. The class gets hard and she just gets worse and worse. She is very hard grader and refuses to curve until the end of the class. I would suggest finding a different professor if you can.

Dvora is amazing! She is really clear and genuinely cares about students learning the material. She goes over the proofs and examples in such a way that teaches the students the methods rather than simply encouraging memorization. Her enthusiasm for teaching the material is contagious-I looked forward to going to class! The only thing is that she definitely likes a bell-curve distribution set around B-, so she does not usually curve since this is generally where the exam grades fall. But go to class and do the work and you are fine!

First the good part: it's an easy A/A-. Now the bad part: There is nothing you can learn from this class. The prof is condescending, and he never teaches the basics: he simply assumes you know them and then goes on to illustrate extensively his own methods (which by the way are useless) of solving his own problems. This class itself is completely useless: if you are a math major, it will leave you unprepared for higher level classes, and if you are taking it for personal enrichment, it will be a total waste of your time. The only use you can draw from this class is getting an A-, but it will cost you 3 hours of your life, every week, for 4-5 months, for which you will get nothing else but the grade in return.

So, initially the class looked really good because Spiegelman is a nice guy (VERY BUSY though outside of class) and easy to talk to and ask questions.
However, I ended up not going to class for pretty much half of the semester mostly because I got a lot more out of Strang's book than I did from lecture. It was also the added complication of the Smart Board and premade slides which made it very difficult to take notes because he moved so fast.
Also, watching some of Strang's lectures was pretty useful.
All in all, a relatively straightforward math class. Read the book and PRACTICE problems and you'll do fine.

This man speaks English fluently and without an accent. Hallelujah. Professor Stein may not be a dazzling speaker, but he presents the material clearly and concisely. Occasionally he works through short proofs, but this is always enlightening and rarely confusing. The book was a nice complement to his lectures. The class is based less around proofs than the other LA sections, which is a relief. Stein's exams were fair and usually left a lot of time to go back and check answers (not just for me, for most people in the class). Bottom line: good professor, certainly a good catch for a math class.

I've taken two other semesters with Prof. Hou (Calc III and IV) and I expected no less from him this semester. I've reviewed him before and again I must say he is as straightforward as you could possibly want from the Math department. He follows the text, but will extend to more challenging material even though it won't be on the exams. He emphasizes what will be on the exams, which are primarily drawn from the homework. He is very nice and extremely approachable, and is also very knowledgeable. Even though many people say to take Linear Algebra through the Applied Math dept. for various reasons, if you still want the theory and a good instructor, go with Hou.

Truly horrendous experience. He is not interested at all in teaching. He copies his own notes on the board quickly, mostly in theorem-proof-theorem-proof-theorem-proof mode (obscurely, and he often screws up on the board too), and then gives you quizzes and exams that have nothing to do with what he talked about, or even with the contents of the textbook!!!. He marks no transitions, and he makes no emphasis on important points or essential contents. And he doesn't allow formula sheets on exams either.
As a result, the grading of homework, quizzes and exams is absolutely unfair, so not only will you learn nothing from his class, but your GPA will suffer unduly.
Any resemblance between teaching (even bad teaching) and what he does in a classroom is entirely coincidental. I am truly amazed that he is allowed to teach independently at Columbia.
The worst is I actually was very interested and excited to learn linear algebra. I guess I'll have to buy the Schaum's Outline...

Dave is probably the most brilliant math teacher that you will come across. You finally get to see the practical applications of math rather than running around in endless proofs which seem of no consequence. The curve is mighty mighty generous. If you studied only the night before the exam, but studied well, you can easily get an A. Yeah, you probably didn't understand linear algebra really well, cause the way he teaches it is unconventional without the proofs. But you can see the way he thinks through analogies, and you start to think like that, and then math surprisingly becomes a hell lot of fun. Oh, and don't touch the text book. Its useless. Do only the practice exams.

Prof. Ciperiani doesn't know how to teach. People won't show up to class just because it's so useless. If you spend 3 hours a week studying on your own and teaching yourself, it would be better than attending a class that would put you to sleep.
The tests are easy. Just do the Homework problems and you will be fine.
As for the problem sets, take them serious and attend the TA sessions, you won't be able to do well otherwise.

Thaddeus is a nice guy who genuinely loves the subject and shows it in class. His lectures, while difficult are actually quite clear so as long as you copy down the board and pay somewhat attention as he explains it you should understand the material. The only problem is his grading setup: no homework or midterm which is really cool but since there is no graded homework it's hard to motivate yourself to do it. But you definitely should do the homework because they are a big help for his 8 30-minute pop quizzes given during class. These are really annoying because they can be unexpected and detailed. He is very proof-oriented rather than focusing on just problem solving which I found annoying. All that said I struggled with around a 50% quiz average but I studied for the final and after the curve I ended with a B in the class. Good professor if he just changes his pop quiz system.

Mirela is obsessed with cheating. She thought people were stealing homeworks from her box, so she made them due a day earlier. People got points taken off their homeworks for plagiarizing. She made up two different versions of the tests and handed a different one to every other person. And she even warned people during the final that she saw someone looking at another person's paper.
The class itself was good at the beginning and bad by the end. I never really got a good complete picture of what we were trying to do. I still don't understand what an orthogonal projection is and what inner products have to do with linear algebra. And I went to class and did well in the course.
Note: this course becomes proof based after the first midterm. Between one third and a half of the second midterm and final consisted of proofs. So if you don't know how to write a proof, you are screwed. But you won't know it until it's too late to drop the class.

Honestly, if you spend the time in class to study on your own, you will be better off. You could do very well in this class since the midterms are easy and straight forward. The material is interesting. But I bet that you would NEVER use your class notes, so just study on your own and you'll be more than fine!

When I was first trying to decided if I wanted to take LA with Bayer, I was thoroughly confused by the conflicting reviews on CULPA. Having just finished his class, I decided to write this definitive review, the only one YOU need to read to know all about Bayer. Let none question, or argue afterwards.

First of all, my final score of 85, was in the 33rd percentile, and I got an A. I'm pretty happy with that. The text book is indeed useless. Even though he posts chapters that he supposedly is covering, reading those chapters won't help you at all for the tests. The best way to get high grades is to have one friend go to all the classes, take all the notes (especially on the day before the test when he tells you EXACTLY what's going to be on the test). Then have said friend, teach everyone else taking the class how to do the problems the night before the test. Presto, instant high scores.
Although you do have to be careful, he isn't so clear in his explainations of how to do the problems sometimes and your friend can be wrong some times. Also, he will throw curve balls when everyone's getting high scores. To be on the safe side, you'd better better go to office hours and ask him for help so that you are sure you know how to do the problems that he told you will be on the test.

Yes, as a lecturer, Bayer goes on a lot of tangents. They are mildly entertaining, but nothing really endearing. These tangents really aren't so bad considerring your mind can take a break and day dream a little. And yes, when you go to office hours, he can be a little condescending, but unless you're the type who expects profs to kiss ass all the time, it's really not that bad. He's perfectly willing to answer your questions and help you. And yeah, if you're really into math, you'll have fun with him during office hours.

Once you're armed with knowing exactly what's on the test, with Bayer's own solutions to the problems, and with your friend's notes, you're pretty much set. I mean, 30% of the class gets A's. Com'on.

So Bayer is very laid back and very approachable. He's friendly and class is relatively interesting, especially considering the pretty boring nature of most topics covered. He grades fairly and generously, his curve is usually centered almost around an A- is the impression I got and he himself admits to grading too generously at times.
I'd recommend him to anyone with one warning; he kind of likes to use methods that he "creates" for some simple problems (like finding the inverse of certain matrices) and expects to see you use his strategy on exams.

Dave is the best math teacher ever. I never thought Linear Algebra could be presented as easily as he did. Have trouble with math? Dave breaks down Linear Algebra so a 3rd grader could understand it. Dave teaches you his own methods for doing complex tasks that other professors wouldn't be able to test on.

The guy is a damn genius. He does all of the lecture with no script (like many professors) doesn't screw up, and everything always comes out as whole numbers.

People can say his class is easy all they want, but there were a lot people with hurt feelings when they saw that they were at the bottom of the curve.

If you're looking to have your hand held like a 16 year old, you're in the wrong place. You're whole grade is based off of 4 tests, so you have to have the dicipline to keep up on your own. This also rules out the possibility that you can just cram for 2 test and ace the class.

the worst teacher ever, in my opinion. he tries to make the class interesting but he always fails. midterms and final exam questions are very analogous to the exam questions from the last few years.

Mirela Ciperiani is not a good professor. She is generally a nice woman, except when you dare to breathe too loudly in her class (in which case you will get an evil glare and/or be asked if you have a question).

Her biggest downside is that she focuses on easy topics for far too long and is then forced to breeze through the tougher/more useful topics. For example, she spent an entire class on matrix addition and simple multiplication...

On the other hand, her tests are very, very easy. In fact, they are so easy that she has to curve the class down. BEWARE, Ciperiani considers a straight (no curve) 90-95 an A-.

Take this course if you don't want to work for a good grade and could care less if you've learned the material. Dave comes up with his own ways for solving problems and totally ignores the book, which I've heard is very good but is useless since he teaches different crap. He expects you to come up with generic formulas after doing a problem on an exam. A nearly impossible task. Good thing is, his curve is amazing so your likely to do fine if you don't get good grades on the exams.

She is unbelievably nice and sweet. She is also the easiest teacher in the math department. I suck at math, but got an A+ in her class. Barely any work, and her tests come straight out of the homework/book. You will not only learn Linear Algebra in her class, but will have an easy and very unstressful time.

I totally second the opinion of the first reviewer. Robert Lipshitz is a pleasure to learn from. It is clear that he really cares whether the students learn the material. He is extremely nice and very approachable. The students who transferred out of his class in the early going should regret having done so. His first couple of problem sets were way, way too long, prompting mass defection of students, but, after the remaining students complained, he paired the problem sets down to a reasonable length. He wasn't the easiest professor I've ever had, nor the hardest, but struck a good balance so that you were challenged but not overwhelmed and discouraged. If you did your homework and attended class you would be prepared for his exams, which were fair, and I would say of about average difficulty compared to other math professors' exams.

If you have a chance, take this guy!

Lipshitz LOVES linear algebra. Like the poster next to me, I found Lipshitz to be the best Math teacher I took at Columbia. It was his first semester, straight from Stanford. He's a man of small proportions but his passion for linear algebra is anything but small. Now LinAl as I like to call it isn't really a class anyone looks forward to taking. But Lipshitz does the best job to make this sometimes boring material interesting. He does encourage his students to participate and does answer ALL questions from the suck up questions regarding future material and to the slacker questions that you should have known 2 classes ago. He just wants you to learn the material.

Saying he's organized is an understatement. The guy loves using courseworks which is great because I'm one of those people who check courseworks every time I'm on a computer. He posts lecture notes (very helpful supplement to the book when doing the HW), grades a week after their due, and a simple syllabus. But the best thing is that whenever he updates CW he writes what he updated under the Intro section. How many times have your profs updated CW w/o telling exactly what changed, leaving you to stumble through the Lecture or Syllabus or Grades changing wondering what was changed?

Now, as the other reviewer did, I'll say something about the negatives of this class. With Lipshitz's ability to make the class pretty interesting and his outstanding organizational skills comes hard HW. Notice the other reviewer liked to start the HW's early. I would've liked to start early, too.. but I can't ever do that. I'm one of those people. I started the Monday before it was due and it would take me from 7pm to 4am to finish them sometimes (working slower as I got more tired and sleepy). It could take anywhere from 5 to 12 hours and on average 8 or 9.

Why was the HW so hard? Lipshitz loves proofs which aren't too easy. And the "simple" computation problems are cooked (he loves this word) so that they're not so easy after all. The book that we use (LEON) is terrible and I found myself using MIT's online lectures (recommended) and Google (good luck) often to find solutions to the problems.

I'm not a math major and LinAl is never going to be more than a tool for me but I stuck through the class. Half the people from the first day dropped - I'm not kidding. So the class became self-selective and the curve put me in the middle or even slightly above.

If you're tired of not learning anything and you want to remember something a week after the final, take this class. Linear Algebra has TONS of applications and we talk about some (Google Pagerank). Lipshitz is the best Math/Sci teacher I've had here. Start the HW early if you can (some people really can't). I'm sure you'll do fine . It's not as much of a terror as I made it out to be. It's just a class called Linear Algebra made me automatically think it was going to be one of the least priority classes that semester when I should have made it a higher priority.

Despite being a grown-up Jeff Spicoli, Professor Bayer's lectures made sense of the potential madness known as linear algebra. I sat in for two graduate student-taught linear classes during the summer and they consisted either of intense, non-stop writing or class discussions that left the class with more questions than answers. Prof B understands the flaws behind these methods and has developed his own innovative style. He genuinely cares about his teaching and adapts to accomodate. Always entertaining, he often goes off on tangents in his own lectures but his classes never left me confused nor bored. He explains just about everything clearly and the material he discusses ambigulously can easily be researched on the web (i.e. casting out nines on wikipedia). Plus he's very receptive to questions about linear algebra, rock climbing and swimming. With the Fall 2006 class, he decided to have three exams and a final, with the final being the remaining material not covered. Prior to Fall 2006, he had only two exams and a final. The exams and final consist of five problems with the first four being straight forward while the fifth was a bit more tricky. As written by another reviewer, Prof B recommends solving problems from the text but doesn't collect homework so homework doesn't figure into the class grades. In fact, Prof B's lectures diverge so much from the required text that a student could earn a good grade without purchasing it. He suggested this in class and his class website recommends ways to save money for those interested in purchasing the textbook. Prof B grades on a fair curve. However, those who didn't attend class regularly tended to score poorly. I highly recommend Professor Bayer for students willing to attend every class and solve problems without the incentive to do so.